ISSN 1451 - 9372(Print)
ISSN 2217 - 7434(Online)
JULY-SEPTEMBER 2013
Vol.19, Number 3, 321-460
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Faculty of Technology, University of Niš, Leskovac, Serbia
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Srđan Pejanović
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Faculty of Technology, University of Novi
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ICEHT/FORTH, University of Patras,
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Dimitrios P. Tassios
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ENITIAA,
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Hui Liu
China University of Geosciences, Wuhan, China
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Vol. 19
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No. 3
CONTENTS
Hassan Golmohammadi, Abbas Rashidi, Seyed Jaber Safdari, Prediction of ferric iron precipitation in bioleaching
process using partial least squares and artificial neural
network ............................................................................... 321
A.C. Arvadiya, P.P. Dahivelker, Development and validation
of novel RP-UPLC method for estimation of atropine
sulphate in pharmaceutical dosage form ........................... 333
Arkan Jasim Hadi. Ghassan Jasim Hadi, Ghazi F. Najmuldeen, Iqbal Ahmed, Syed F. Hasany, Gas–liquid equilibrium prediction of system CO2-aqueous ethanol at
moderate pressure and different temperatures using
PR-EOS .............................................................................. 339
S.E. Moradi, J. Khodaveisy, R. Dashti, Removal of anionic
surfactants by sorption onto aminated mesoporous
carbon................................................................................. 347
Xiao-Qin Xiong, Ke-Jing Huang, Chun-Xuan Xu, Chun-Xue
Jin, Qiu-Ge Zhai, Glassy carbon electrode modified
with poly(taurine)/TiO2-graphene composite film for
determination of acetaminophen and caffeine ................... 359
Jelena Đ. Marković, Nataša Lj. Lukić, Aleksandar I. Jokić,
Bojana B. Ikonić, Jelena D. Ilić, Branislava G. Nikolovski, 2D simulation and analysis of fluid flow between
two sinusoidal parallel plates using lattice Boltzmann
method................................................................................ 369
S. Ramesh, R. Muthuvelayudham, R. Rajesh Kannan, T.
Viruthagiri, Response surface optimization of medium
composition for xylitol production by Debaryomyces
hansenii var. hansenii using corncob hemicellulose
hydrolysate ......................................................................... 377
Saša Ž. Drmanić, Jasmina B. Nikolić, Aleksandar D. Marinković, Gavrilo M. Šekularac, Bratislav Ž. Jovanović,
The effects of solvents and structure on the electronic
absorption spectra of the isomeric pyridine carboxylic
acid N-oxides ...................................................................... 385
Hadi Baseri, Ali Haghighi-Asl, Mohammad Nader Lotfollahi,
thermodynamic modeling of solid solubility in supercritical carbon dioxide: comparison between mixing
rules .................................................................................... 389
S. Nadeem, Arshad Riaz, R. Ellahi, Peristaltic flow of a Jeffrey
fluid in a rectangular duct having compliant walls ................ 399
Mohammad Ramezani, Navid Mostoufi, Mohammad Reza
Mehrnia, Effect of hydrodynamics on kinetics of
gluconic acid enzymatic production in bubble column
reactor ................................................................................. 411
Contents continued
Wei Li, Jinhui Peng, Shenghui Guo, Libo Zhang, Guo Chen,
Hongying Xia, Carbothermic reduction kinetics of
ilmenite concentrates catalyzed by sodium silicate and
microwave-absorbing characteristics of reductive
products .............................................................................. 423
Yu Sun, Shuangshuang Xu, Yanling Geng, Xiao Wang,
Tianyou Zhang, Isolation and purification of lignans
from Schisandra chinensis by combination of silica gel
column and high-speed counter-current chromatography ................................................................................. 435
Husein Dibaei Asl, Majid Abdouss, Mahmoud Torabi Angaji,
Aminoddin Haji, Surface and mechanical properties of
polypropylene/clay nanocomposite ..................................... 441
A. Abdallah El Hadj, C. Si-Moussa, S. Hanini, M. Laidi, Application of PC-SAFT and cubic equations of state for the
correlation of solubility of some pharmaceutical and
statin drugs in sc-CO2......................................................... 449
Available on line at
Association of the Chemical Engineers of Serbia AChE
www.ache.org.rs/CICEQ
Chemical Industry & Chemical Engineering Quarterly 19 (3) 321−331 (2013)
HASSAN GOLMOHAMMADI1
ABBAS RASHIDI2
SEYED JABER SAFDARI1
1
Nuclear Science and Technology
Research Institute, AEOI, Tehran,
Iran
2
Department of Chemical
Engineering, Faculty of
Engineering, University of
Mazandaran, Babolsar, Iran
SCIENTIFIC PAPER
UDC 66:004.8
DOI 10.2298/CICEQ120403066G
CI&CEQ
PREDICTION OF FERRIC IRON
PRECIPITATION IN BIOLEACHING PROCESS
USING PARTIAL LEAST SQUARES AND
ARTIFICIAL NEURAL NETWORK
A quantitative structure-property relationship (QSPR) study based on partial
least squares (PLS) and artificial neural network (ANN) was developed for the
prediction of ferric iron precipitation in bioleaching process. The leaching temperature, initial pH, oxidation/reduction potential (ORP), ferrous concentration
and particle size of ore were used as inputs to the network. The output of the
model was ferric iron precipitation. The optimal condition of the neural network
was obtained by adjusting various parameters by trial-and-error. After optimization and training of the network according to back-propagation algorithm, a
5-5-1 neural network was generated for prediction of ferric iron precipitation.
The root mean square error for the neural network calculated ferric iron precipitation for training, prediction and validation set were 32.860, 40.739 and
35.890, respectively, which were smaller than those obtained by the PLS
model (180.972, 165.047 and 149.950, respectively). The obtained results
reveal the reliability and good predictivity of the neural network model for the
prediction of ferric iron precipitation in bioleaching process.
Keywords: quantitative structure-property relationship; ferric iron precipitation; bioleaching process; partial least squares; artificial neural network.
Bioleaching employs the oxidation ability of
bacteria to dissolve metal sulphides and help the
extraction and recovery of valuable and base metals
from main ores and concentrates [1,2]. Metal-winning
processes derived from the activity of microorganisms
propose a possibility to attain metal ions from mineral
resources not available by traditional techniques. Microbes such as bacteria and fungi change metal compounds into their water-soluble types and are biocatalysts of this process called microbial leaching or
bioleaching [3,4]. Recently, Acidithiobacillus ferrooxidans were believed to be the common significant microorganisms in the bioleaching of metal ions from
ores [5].
Acidithiobacillus ferrooxidans is an acidophilic
chemolithoautotrophic proteobacterium that achieves
Correspondence: H. Golmohammadi, Nuclear Science and
Technology Research Institute, AEOI, P.O. Box 11365-3486,
Tehran, Iran.
E-mail: Hassan.gol@gmail.com
Paper received: 3 April, 2012
Paper revised: 20 June, 2012
Paper accepted: 20 June, 2012
its energy from the oxidation of ferrous iron, elemental
sulfur, or partially oxidized sulfur compounds [6].
Owing to its capacity of oxidation, Acidithiobacillus
ferrooxidans has abundant industrial appliances in
biohydrometallurgy. The most important applications
can be established in the field of mining [7] where the
oxidative effects are utilized for the bioleaching of different metals such as copper from minerals like pyrite
or chalcopyrite [8,9] or even uranium [10].
The mechanism of uranium extraction assisted
by the indirect oxidation purpose of this microbe is
probably as follows:
UO2 + Fe2(SO4)3 → UO2SO4 + 2FeSO4
4+
3+
6+
U + 2Fe → U + 2Fe
2+
(1)
(2)
Uranium is barely soluble in an aqueous environment when it is in the +4 oxidation state; however, in
an acidic medium the ferric iron oxidizes U4+ to U6+,
which is easily dissolved. As a conjugate reaction to
the oxidation of U4+, the ferric iron reduces to ferrous
iron and through the oxidation function of Acidithiobacillus ferrooxidans it is re-oxidized back to the ferric
state which is then able to continue oxidizing U4+ to U6+.
321
H. GOLMOHAMMADI, A. RASHIDI, S.J. SAFDARI: PREDICTION OF FERRIC IRON…
Temperature and pH of leaching solution can
vary widely in the completeness of time. In addition,
as the values of this parameter increase, ferric iron
precipitation increases and consequently the leaching
efficiency reduce. Therefore, it is very important to
predict ferric iron concentration recycled by a comprehensive model for the design, monitoring and
organization of bioleaching operations.
As an alternative to physical models, artificial
neural networks (ANNs) are a valuable estimate tool.
Up to now, numerous applications of ANN models in
the engineering area were reported. For example,
Laberge et al. applied ANN to predict the metal (Cu,
Zn and Cd) solubilization percentages in municipal
sludge treated with a continuous bioleaching process
[11]. Jorjani et al. used ANN to estimate the effects of
operational parameters on the organic and inorganic
sulfur removal from coal by sodium butoxide [12].
Acharya and co-workers developed a neural network
to model the extent of sulphur removal from three
types of coal using native cultures of Acidithiobacillus
ferrooxidans [13]. Diamond et al. utilized ANN for the
Study of pH on the fungal treatment of red mud [14].
Nikhil et al. employed ANN for prediction of H2 production rates in a sucrose-based bioreactor system
[15]. They also modeled the performance of a biological Fe2+ oxidizing fluidized bed reactor (FBR) by a
popular neural network-back-propagation algorithm
under different operational conditions [16]. Yetilmezsoy and Demirel used a three-layer artificial neural
network (ANN) model to predict the efficiency of Pb(II)
ions removal from aqueous solution by Antep pistachio (Pistacia vera L.) shells based on 66 experimental sets obtained in a laboratory batch study [17].
Daneshvar et al. employed an artificial neural network
(ANN) to model decolorization of textile dye solution
containing C.I. Basic Yellow 28 by electrocoagulation
process [18]. Sahinkaya and co-workers developed
an artificial neural network model for estimation of the
performance of a fluidized-bed reactor (FBR) based
sulfate reducing bioprocess and control the operational conditions for improved process performance
[19]. Sahinkaya also modeled the biotreatment of
zinc-containing wastewater in a sulfidogenic CSTR by
using artificial neural network [20].
Thus, to successfully extract the costly metals
from the minerals, the suitable process and control of
bioleaching purposes have become very essential. In
relation to recent considerations, the dissolution of
metals happens only chemically with the assist of ferric ions, which operate as oxidizing agents. Superior
control of bioleaching may be acquired by using a
strong model to predict convinced key factors derived
322
CI&CEQ 19 (3) 321−331 (2013)
from past surveillances [21]. Models rooted in ANNs
may be efficiently employed in bioleaching applications and very helpful at arresting the nonlinear correlations existing between variables in complex systems
like bioleaching. The main aim of this investigation is
using this aptitude of artificial neural network for prediction of ferric iron precipitation in bioleaching process. In this study, an artificial neural network method
using the back-propagation algorithm was proposed
for the prediction of ferric iron precipitation in uranium
bioleaching process under different operational
conditions.
MATERIAL AND METHODS
Uranium ores
The uranium ores used in the experiments was
supplied by the Nuclear Science and Technology
Research Institute, AEOI. The ore was ground using
mortar and then sieved. The particle size of the
sieved material ranged from 70 to 500 µm, with an
average particle size of 100±10 µm.
Microorganism and culture
The medium for Acidithiobacillus ferrooxidans
growth was 9K medium which is a mixture of mineral
salts ((NH4)2SO4, 3.0 g/l, K2HPO4, 0.5 g/l, MgSO4⋅7H2O,
0.5 g/l, KCl, 0.1 g/l and Ca(NO3)2, 0.01g/l). FeSO4⋅7H2O
was added as energy source. The pH of the medium
was adjusted to 2.0 using 2.0 M H2SO4. The culture
was cultivated at 35 °C for 2-3 days before centrifugation. The yield cells of Acidithiobacillus ferrooxidans were suspended in a fresh solution of the mineral salt medium for the preparation of the bacterial
concentrate [22].
Bioleaching experiments
The experiments were performed in 250 ml
Erlenmeyer flasks containing 5 g of ore and 100 ml of
9K medium. Erlenmeyer flasks covered with hydrophobic cotton to admit oxygen but reduce water loss
through evaporation. Control experiments were carried out without bacteria and with 2% bactericide
agent (formaldehyde). The concentrations of Fe were
2 and 4 g/l using FeSO4⋅7H2O. Each experiment was
accomplished twice under same standard conditions
at 30-40 °C, 180 rpm shaking speed and pH 2.0 [23].
A known amount of sample was drawn at 6 days
interval for analysis of Iron. The pH of the leach solution was maintained daily with 2 M sulfuric acid. The
oxidation/reduction potential (ORP) was measured
against saturated calomel electrode (SCE).
H. GOLMOHAMMADI, A. RASHIDI, S.J. SAFDARI: PREDICTION OF FERRIC IRON…
Analytical procedures
Total iron was analyzed using the PG T80+
UV/Vis spectrometer according to Karamanev method
[24]. The ferrous iron concentration was determined
using PG T80+ UV/Vis spectrometer by the modified
colorimetric orthophenantroline method [25]. A Metrohm pH meter (model 827) with a combined glass
electrode was used for pH measurements. The
changes in oxidation/reduction potential (ORP) were
monitored using an ORP meter (Metrohm model 827).
Partial least squares model for the prediction of ferric
iron precipitation
PLS is a familiar multivariate method [26-28],
which provides a stepwise solution for a regression
model. It extracts principal component-like latent variables from original independent variables (predictor
variables) and dependent variables (response variables), respectively. Assume that X characterizes
independent variables (X is a matrix) and Y represents dependent variables (Y is a vector). Then a
brief description of computations is given as follows:
X = TPT + E
T
Y = QS + F
(3)
(4)
The matrices E and F include residual for X and Y,
respectively. T and P are score and loading matrices
associated with the X, Q and S are the score and
loading of Y and superscript T indicates the transposed matrix. The relationship between scores and
dependent variable is obtained from:
Y = TBQT + F
(5)
where B is the matrix of the regression coefficient
achieved by a least squares procedure. The PLS
algorithm used in this study was the singular value
decomposition (SVD)-based PLS. This algorithm was
proposed by Lobert et al. in 1987 [29]. A concise
discussion of the SVD-based PLS algorithm can be
found in the literature [30-32]. The program of PLS
modeling based on SVD was written with MATLAB 7
in our laboratory [33].
Artificial neural network model for the prediction of
ferric iron precipitation
An artificial neural network is a kind of artificial
intelligence that emulates some purpose of the
human brain. Neural networks are general-purpose
computing techniques that can solve complex nonlinear problems. The network comprises abundance
of simple processing elements linked to each other by
weighted connections along with a specified architecture. These networks learn from the training data by
CI&CEQ 19 (3) 321−331 (2013)
altering the connection weights [34]. A detailed explanation of the theory behind a neural network has been
sufficiently described elsewhere [35-37]. Therefore,
only the points related to this work are illustrated
here. An essential procession element of an ANN is a
node. Each node has a series of weighted inputs, Wij,
and performs as a summing point of weighted input
signals. The summed signals pass through a transfer
function that may be in sigmoidal form. The output of
node j, Oj , is given by Eq.(6):
Oj = 1/(1 + exp(-X))
(6)
where X is defined by the following equation:
X = W ij Oi + B j

(7)
In Eq. (7), Bj is a bias term, Oi is the output of the
node of the previous layer and Wji represents the
weight between the nodes of i and j.
A feed-forward neural network consists of three
layers. The first layer (input layer) consists of nodes
and operates as an input buffer for the data. Signals
introduced to the network, with one node per element
in the sample data vector, pass through the input
layer to the layer called the hidden layer. Each node
in this layer sums the inputs and forwards them
through a transfer function to the output layer. These
signals are weighted and then pass to the output
layer. In the output layer the processes of summing
and transferring are repeated. The output of this layer
now signifies the calculated value for the node k of
the network.
As well as the network topology, a significant
constituent of nearly all neural networks is a learning
rule. A learning rule permits the network to alter its
connection weights so as to correlate given inputs
with corresponding outputs. The training of the network has been performed by using a back-propagation algorithm, in which the network reads inputs and
outputs from an appropriate data set (training set) and
iteratively calculates weights and biases to facilitate
decrease the sum of squared dissimilarities between
predicted and target values. The training is stopped
when the error in prediction achieves a preferred level
of accuracy. However, if the network is gone to train
too long, it will overtrain and misplace the aptitude to
prediction. In order to avoid overtraining, the predictive recital of the trained ANN is controlled by running
the back-propagation algorithm on a data set not
used in training.
Neural networks are rooted in the principle that
an extremely unified system of effortless processing
elements can learn intricate interrelationships between
independent and dependent variables. The perfor-
323
H. GOLMOHAMMADI, A. RASHIDI, S.J. SAFDARI: PREDICTION OF FERRIC IRON…
mance and properties of such a network is reliant on
the computational elements, especially the weights
and the transfer function, in addition to the net topology. Usually the network topology and the transfer
function are particular in advance and are kept fixed,
so just the weights of the synaptic connections and
the number of neurons in the hidden layer need to be
evaluated. The error function should be minimized so
that the neural network accomplishes the finest performance. Dissimilar algorithms have been grown to
minimize the error function. The most traditional is the
so-called back-propagation (BP) algorithm, which
belongs to the group of supervised learning methods.
The error at the output layer in a BP neural network
propagates rearward to the input layer during the hidden layer in the network to acquire the final beloved
output. The gradient descent technique is employed
to compute the weights of the network and regulate
the weights of interconnections to minimize the output
error. In this work, multi layered feed forward neural
networks were used, which utilized the algorithm of
back-propagation of errors and a gradient-descent
technique, known as the “delta rule” [38,39] for the
adjustment of the connection weights (further called
BP networks). BP networks include one input layer,
one (or possibly several) hidden layer(s) and an output layer. The number of nodes in the input and output layers are described by the difficulty of the problem being solved. The input layer collects the experimental information and the output layer encloses the
response sought. The hidden layer codes the information attained from the input layer, and transports it
to the output layer. The number of nodes in the hidden layer may be considered as an adjustable factor.
In the present work, an ANN program was written with MATLAB 7. This network was feed-forward
fully connected and had three layers with tangent
sigmoid transfer function (tansig) at the hidden layer
and linear transfer function (purelin) at the output
layer. The operational conditions of the bioleaching
process were used as inputs of the network and its
output signal represents the ferric iron precipitation.
Therefore, this network has five nodes in input layer
and one node in output layer. The value of each input
was divided into its mean value to bring them into the
dynamic range of the sigmoidal transfer function of
the network. The initial values of weights were
randomly selected from a uniform allocation that
ranged between -0.3 to +0.3 and the initial values of
biases were set to be 1. These values were optimized
during the network training. The back-propagation
algorithm was used for the training of the network.
Before training, the network parameters would be
324
CI&CEQ 19 (3) 321−331 (2013)
optimized. These parameters are: number of nodes in
the hidden layer, weights and biases learning rates
and the momentum. Procedures for the optimization
of these descriptors were reported elsewhere [38,39].
Then the optimized network was trained using a training set for adjustment of weights and biases values.
To maintain the predictive authority of the network at
an enviable level, training was stopped when the
value of error for the prediction set started to
increase. Since the prediction error is not a good
evaluation of the generalization error, the prediction
potential of the model was assessed on a third set of
data, named validation set. Experiments in the validation set were not used during the training process
and were reserved to evaluate the predictive power of
the generated ANN.
Evaluation of the predictive ability of a QSPR model
For the optimized QSPR model, numerous parameters were chosen to test the prediction capability of
the model. A real QSPR model may have a high
predictive aptitude, if it is close to ideal one. This may
involve that the correlation coefficient R between the
experimental (actual) y and predicted y properties
must be close to 1 and regression of y against y or
y against y through the origin, i.e., y r 0 = ky and
y r 0 = k ' y , respectively, should be illustrated by at
least either k or k ' close to 1 [40]. Slopes k and k ' are
calculated as follows:
k =

y i yi
yi2
(8)
y i yi
y i2
(9)

k'=


The criteria formulated above may not be adequate for a QSPR model to be really predictive.
Regression lines through the origin defined by
y r 0 = ky and y r 0 = k ' y (with the intercept set to
one) should be close to optimum regression lines
y r = ay + b and y r = a ' y + b ' (b and b ' are intercepts). Correlation coefficients for these lines R 02 and
R '02 are calculated as follows:
R02 = 1 −

( yi − y ir 0 )2
( yi − y )2
(10)

R '02 = 1 −

( y i − yir 0 )2

( y i − y )2
(11)
where y and y are the average values of the
observed and predicted properties, respectively, and
the summations are over all n compounds in the
validation set.
H. GOLMOHAMMADI, A. RASHIDI, S.J. SAFDARI: PREDICTION OF FERRIC IRON…
A difference between R2 and R 02 values ( Rm2 )
desires to be studied to examine the prediction potential of a model [41]. This term was defined in the
following manner:
Rm2 = R 2 (1− R 2 − R02 )
(12)
Finally, the following criteria for evaluation of the
predictive ability of QSPR models should be considered:
1. High value of cross-validated R2 (q2 > 0.5).
2. Correlation coefficient R between the predicted and actual properties from an external test set
close to 1. R 02 or R '02 should be close to R2.
3. At least one slope of regression lines (k or k')
through the origin should be close to 1.
4. Rm2 should be greater than 0.5.
Diversity validation
The essential investigated theme in chemical
database analysis is the diversity of sampling [42].
The diversity problem involves defining a different
division of representative compounds. In this study,
diversity analysis was done on the data set to make
sure that the structures of the training, prediction or
validation sets can characterize those of the whole
ones. We consider a database of n experiments
m
generated from m highly correlated variable {Χ J } .
j =1
Each experiment, Xi, is represented as following
vector:
Χ i = ( x i 1, x i 2 , x i 3 ,...x im ) for i = 1,2,..., n
n
d
j =1 ij
CI&CEQ 19 (3) 321−331 (2013)

di =
n −1
, i = 1,2,..., n
(16)
Then the mean distances were normalized
within the interval of zero to one. In order to calculate
the values of mean distances in accordance with Eqs.
(15) and (16), a MATLAB program was written that
combines maximum dissimilarity search algorithms
and general multi-dimensional measurements of chemical similarity rooted in different experiments. The
closer to one the distance is, the more diverse to each
other the compound is. The mean distance of experiments were plotted against ferrous iron precipitation
(EXP) (Figure 1), which shows the diversity of the
experiments in the training, prediction and validation
sets. As can be seen from this figure, the experiments
are diverse in all sets and the training set with a broad
representation of the chemistry space was adequate
to ensure the model’s stability and the diversity of prediction and validation sets can prove the predictive
capability of the model.
(13)
where xij indicates the value of variable j of experiN
ment Xi. The collective database Χ = {Χ i } is
i =1
represented a n×m matrix of X as follows:
 x11 x 12

x x
 21 22
T
X = (X 1, X 2 ,..., X N ) = 



x n1 x n 2

... x 1m 

... x 2m 

  

... x nm 

(14)
Figure 1. Scatter plot of experiments for training, prediction and
validation sets.
where the superscript T represents the vector/matrix
transpose. A distance score, dij, for two different
experiments, Xi and Xj, can be measured by the
Euclidean distance norm:
d ij = Χ i − Χ j =
m
(x
k =1 ik

− x jk )2
(15)
The mean distances of one experiment to the
remaining ones were computed as:
RESULTS AND DISCUSSION
PLS Modeling
The descriptive statistics of corresponding
observed PLS and ANN predicted values of ferric iron
precipitation of all experiments studied in this work
are shown in Table 1. The independent variables of
leaching temperature, initial pH, oxidation/reduction
potential (ORP), ferrous iron concentration and particle size of uranium ore were used in the develop-
325
H. GOLMOHAMMADI, A. RASHIDI, S.J. SAFDARI: PREDICTION OF FERRIC IRON…
CI&CEQ 19 (3) 321−331 (2013)
Table 1. Descriptive statistics of observed and predicted values of ferric iron precipitation (mg/l); EXP refers to experimental; PLS refers
to partial least squares; ANN refers to artificial neural network
Set
n
Minimum
Maximum
Mean
Standard deviation
Training (EXP)
40
317
2514
1282
572
Training (PLS)
40
304
2489
1308
556
Training (ANN)
40
314
2498
1279
568
Prediction (EXP)
20
506
2327
1298
586
Prediction (PLS)
20
381
2271
1306
565
Prediction (ANN)
20
512
2310
1296
582
Validation (EXP)
20
486
2421
1207
607
Validation (PLS)
20
392
2377
1213
558
Validation (ANN)
20
492
2415
1206
600
ment of PLS method. By interpreting the variables in
the models, it is possible to gain some insight into factors that are probable related to ferric iron precipitation. For assessment of the relative importance and
donation of each variable in the model, the value of
mean effect (ME) was calculated for each variable by
the following equation:
β j n d ij
ME j = m i =n1
β
d
j j i =1 ij


(17)

where MEj is the mean effect for considered variable
j, βj is the coefficient of variable j, dij is the value of
interested variables for each experiment, and m is the
number of variables in the model. The calculated
values of MEs are represented in the last column of
Table 2 and are also plotted in Figure 2. Table 3
represents the correlation matrix for these variables.
The value and sign of mean effect demonstrates the
relative contribution and direction of influence of each
variable on the ferric iron precipitation. As shown in
Table 2, the most relevant variables based on their
mean effects are pH and leaching temperature. The
positive coefficient of these variables mean as the
value of this variables increase, the values of ferric
iron precipitation increase. These results are in accordance with those we have obtained in bioleaching
experiments.
Figure 2. Plot of descriptor's mean effects.
Neural network modeling
The next step was the production of ANN and
training of it. Input and output data normalization is a
significant feature of training the network and performed to avoid problems with saturation of the neuron transfer function. Input and output data are typically normalized in the range (0,1) or (-1,+1). The type
of normalization is problem dependent and may have
Table 2. The partial least squares regression coefficients
Variable
Leaching temperature
Notation
Coefficient
Mean effect
1345.67
t
38.75
pH
732.43
1432.27
Oxidation/reduction potential
ORP
-2.28
-1173.20
Ferrous iron concentration
Fe (II)
-1.16
945.13
PS
-8.50
-765.00
–
13666.56
–
Initial pH
Particle size
Constant
326
H. GOLMOHAMMADI, A. RASHIDI, S.J. SAFDARI: PREDICTION OF FERRIC IRON…
CI&CEQ 19 (3) 321−331 (2013)
Table 3. Correlation matrix between selected variables
t
pH
t
pH
ORP
Fe (II)
PS
1
-0.029
0.213
-0.124
0.144
1
-0.668
0.750
0.196
1
-0.642
0.251
1
-0.097
ORP
Fe (II)
PS
1
some effects on how well the ANN trains. Here we
use Scaled normalization to bring the data into dynamic range of the tangent sigmoid transfer function of
the network. Before training the ANNs, the parameters of network including the number of nodes in the
hidden layer, weights and biases learning rates and
momentum values were optimized. In order to determine the optimum number of nodes in hidden layer
several training sessions were conducted with different number of hidden nodes. The values of standard
error of training (SET) and standard error of prediction
(SEP) were calculated after each 1000 iterations and
calculation was stopped when overtraining began,
then SET and SEP values were recorded. The
recorded values of SET and SEP were plotted against
the number of nodes in hidden layer, and the number
of hidden nodes with minimum values of SET and
SEP was chosen as the optimum one (Figure 3). It
can be seen from this figure that 6 nodes in the hidden layer were sufficient for a good performance of
the network. Learning rates of weights and biases
and also momentum values were optimized in a similar way and the results are shown in Figures 4-6, res-
pectively. As can be seen, the optimum values of the
weights and biases learning rates and momentum
were 0.2, 0.2 and 0.3, respectively. The generated
ANN was then trained by using the training set for the
optimization of weights and biases. However, training
was stopped when overtraining began. For the evaluation of the prediction power of network, trained
ANN was used to simulate the ferric iron precipitation
included in the prediction set.
Table 4 shows the architecture and specification
of the optimized network. After optimization of the network parameters, the network was trained by using
training set for adjustment of the weights and biases
values by back-propagation algorithm. It is recognized
that the neural network can become overtrained. An
overtrained network has usually learned completely
the motivation pattern it has seen but cannot give
precise forecasting for unobserved stimuli, and it
would no longer be capable to generalize. There are
various methods for overcoming this problem. One
method is to utilize a prediction set to assess the prediction power of the network during its training. In this
method, after each 1000 training iterations, the
Figure 3. The values of SET and SEP versus number of nodes
in hidden layer.
Figure 4. The values of SET and SEP versus weight
learning rate.
327
H. GOLMOHAMMADI, A. RASHIDI, S.J. SAFDARI: PREDICTION OF FERRIC IRON…
q 2 = 1− 
network was used to calculate ferric iron precipitation
included in the prediction set. To preserve the
predictive power of the network at an enviable level,
training was stopped when the value of errors for the
prediction set started to increase.
CI&CEQ 19 (3) 321−331 (2013)
( y i − yˆ i )2
(18)
 (y i − y )
2
where y i and yˆ i , respectively are the measured and
predicted values of the dependent variable (ferric iron
precipitation), y is the averaged value of dependent
variable of the training set and the summations cover
all the compounds. The calculated value of q 2 was
0.996.
Table 4. Architecture and specifications of optimized ANN model
Parameter
Value
Number of nodes in the input layer
5
Number of nodes in the hidden layer
6
Number of nodes in the output layer
1
Weights learning rate
0.2
Biases learning rate
0.2
Momentum
0.3
Transfer function (hidden layer)
Tangent sigmoid
Transfer function (output layer)
Linear
Table 1 shows the descriptive statistics of
observed and predicted values of ferric iron precipitation for the training, prediction and validation sets.
The statistical parameters obtained by ANN and PLS
models for these sets are shown in Table 5. The standard errors of training, prediction and validation sets
for the PLS model are 180.972, 165.047 and 149.950,
respectively, which would be compared with the
values of 32.860, 40.739 and 35.890, respectively, for
the ANN model. Comparison between these values
and other statistical parameters in Table 5 discloses
the superiority of the ANN model over PLS ones. The
key power of neural networks, unlike regression analysis, is their aptitude to supple mapping of the
selected features by manipulating their functional
dependence implicitly.
The statistical values of validation set for the
ANN model was characterized by q2 = 0.996, R2 =
= 0.996 (R = 0.998), R 02 = 0.996 , Rm2 = 0.988 and k =
= 1.002. These values and other statistical parameters (Table 5) reveal the high predictive ability of the
model. Figure 7 shows the plot of the ANN predicted
versus experimental values for ferric iron precipitation
of all of the experiments in data set. The residuals of
the ANN calculated values of the ferric iron precipi-
Figure 5. The values of SET and SEP versus biases learning
rate.
Figure 6. The values of SET and SEP versus momentum.
The predictive power of the ANN models developed on the selected training sets are estimated on
the predictions of validation set chemicals, by calculating the q2 that is defined as follow:
Table 5. Statistical parameters obtained using the ANN and PLS models; R is the correlation coefficient, SE is standard error and F is
the statistical F value
Model
SET
SEP
SEV
RT
RP
RV
FT
FP
FV
ANN
32.860
40.739
35.890
0.998
0.997
0.998
10400
3517
4727
PLS
180.972
165.047
149.950
0.943
0.957
0.966
306
197
254
328
H. GOLMOHAMMADI, A. RASHIDI, S.J. SAFDARI: PREDICTION OF FERRIC IRON…
tation are plotted against the experimental values in
Figure 8. The propagation of the residuals on both
sides of the zero line signifies that no systematic error
exists in the constructed QSPR model.
CI&CEQ 19 (3) 321−331 (2013)
oxidation/reduction potential, ferrous concentration
and particle size of uranium ore provide some information related to different experiments which can
affect the ferric iron precipitation. The good agreement between experimental results and predicted
values verifies the validity of obtained models. The
calculated statistical parameters of these models
reveal the superiority of ANN over PLS model. The
results show that the ANN model can accurately describe the relationship between the operational conditions of bioleaching process and ferric iron precipitation.
Nomenclature
QSPR
ANN
PLS
ORP
PS
Figure 7. Plot of calculated ferric iron precipitation against
experimental values.
CONCLUSIONS
Results of this study disclose that ANN can be
used successfully in development of a QSPR model
to predict the ferric iron precipitation in uranium
bioleaching process. Variables appearing in this
QSPR model such as leaching temperature, initial pH,
R
ME
t
SE
F
FBR
W
O
B
k
EXP
q
SCE
X
Y
T
Quantitative structure-property relationship
Artificial neural network
Partial least squares
Oxidation/reduction potential
Particle size
Correlation coefficient
Mean effect
Leaching temperature
Standard error
Statistical F value
Fluidized bed reactor
Weight signal
Output of the node
Bias term
Slope of regression line
Experimental
Cross validated coefficient
Saturated calomel electrode
Predictor (independent) variable
Response (dependent )variable
Score of X
Figure 8. Plot of residual versus experimental values of ferric iron precipitation.
329
H. GOLMOHAMMADI, A. RASHIDI, S.J. SAFDARI: PREDICTION OF FERRIC IRON…
P
Q
S
E
F
BP
d
SET
SEP
SEV
Loading of X
Score of Y
Loading of Y
Residual for X
Residual for Y
Back-propagation
Distance score
Standard error of training
Standard error of prediction
Standard error of validation
CI&CEQ 19 (3) 321−331 (2013)
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H. GOLMOHAMMADI, A. RASHIDI, S.J. SAFDARI: PREDICTION OF FERRIC IRON…
HASSAN GOLMOHAMMADI
ABBAS RASHIDI
SEYED JABER SAFDARI
Nuclear Science and Technology
Research Institute, AEOI, Tehran, Iran
NAUČNI RAD
CI&CEQ 19 (3) 321−331 (2013)
PREDVIĐANJE PRECIPITACIJE FERI JONA U
PROCESU BIOLUŽENJA PRIMENOM PARCIJALNIH
NAJMANJIH KVADRATA I VEŠTAČKE
NEURONSKE MREŽE
Razvijena je kvanitativna zavisnost između strukture i svojstava zasnovana na parcijalnim najmanjim kvadratima i veštačkoj neuronskoj mreži u cilju predviđanja precipitacije
gvožđe(III) jona u procesu bioluženja. Ulazne promenljive bile su: temperatura luženja,
početni pH, oksido-redukcioni potencijal, koncentracija gvožđe(II) i veličina čestica rude.
Izlaz iz modela je bila precipitacija gvožđe(III) jona. Optimalni uslov veštačke neuronske
mreže je dobijen podešavanjem različitih parametara metodom probe i greške. Posle
optimizovanja i učenja mreže pomoću algoritma sa povratnom propagacijom, generisana je neuronska mreža 5-5-1 radi predviđanja precipitacije gvožđe(III) jona. Vrednosti
korena srednje kvadratne greške za učenje, predviđanje i validaciju neuronske mreže
bile su 32,860; 40,739 i 35,890, redom, koje su manje od onih dobijenih modelom parcijalnih najmanjih kvadrata (180,972; 165,047 i 149,950, redom). Dobijeni rezultati pokazuju pouzdanost i dobru prediktivnost neuronske mreže za predviđanja precipitacije
gvožđe(III) jona u procesu bioluženja.
Ključne reči: kvanitativna zavisnost struktura-svojstvo, precipitacija gvožđe(III)
jona, proces bioluženja, parcijalni najmanji kvadrati, veštačka neuronska mreža.
331
Available on line at
Association of the Chemical Engineers of Serbia AChE
www.ache.org.rs/CICEQ
Chemical Industry & Chemical Engineering Quarterly 19 (3) 333−337 (2013)
A.C. ARVADIYA
P.P. DAHIVELKER
R.C. Patel Institute of
Pharmaceutical Education and
Research, Shirpur, Dist. Dhule
(M.S.), India
SCIENTIFIC PAPER
UDC 543.2/.9:615
DOI 10.2298/CICEQ120319068A
CI&CEQ
DEVELOPMENT AND VALIDATION OF NOVEL
RP-UPLC METHOD FOR ESTIMATION OF
ATROPINE SULPHATE IN PHARMACEUTICAL
DOSAGE FORM
A simple, precise, accurate, sensitive and repeatable RP-UPLC method was
developed for quantitative determination of atropine sulphate in pharmaceutical dosage form. The method was developed by using a C18 column Hiber HR
Purospher Star (100 mm×2.1 mm id, 2 µm particle size) as stationary phase
with phosphate buffer:acetonitrile (87:13, v/v) as a mobile phase; pH was
adjusted to 3.5 by orthophosphoric acid at a flow rate of 0.5 mL/min and the
column temperature was maintained at 30 °C. Quantification of the eluted compound was achieved with a PDA detector at 210 nm. Atropine sulphate followed linearity in concentration range of 2.5-17.5 µg/mL with r2 = 0.9998 (n = 6).
Limit of detection (LOD) and limit of quantification (LOQ) values were 0.0033
and 0.0102 µg/mL for atropine sulphate. The validation study was carried out
as per International Conference on Harmonization (ICH) guidelines. This
method was successfully applied for the estimation of atropine sulphate in
pharmaceutical formulation.
Keywords: atropine sulphate, method validation, reversed phase ultra
pressure liquid chromatography.
Tropane alkaloid (atropine) is extracted from
deadly nightshade (Atropa belladonna), jimsonweed
(Datura stramonium), mandrake (Mandragora officinarum) and other plants of the family Solanaceaeare
widely used as parasympatolytic, anticholinergic and
antiemetic drugs [1]. Atropine sulphate is (RS)(1R,3r,5S)-3-tropoyloxytropanium sulphate monohydrate (Figure 1).
Figure 1. Structure of atropine sulphate.
Atropine sulphate injection is official in Indian
pharmacopeia, British Pharmacopeia and United States Pharmacopeia. Some methods for the determination of tropane alkaloids appearing in the literature
are based on TLC [2-3], gas chromatography [4], LC-MS [5,6], high performance liquid chromatography [7–
-12], capillary zone electrophoresis [13,14], chiral
separation [15], with fluorescence detection [16], with
conductometric detection [17], cation exchange [18],
ion-pair high performance chromatography [19]. To
the best of our knowledge, there is no RP-UPLC
method reported in literature for determination of atropine suphate. Therefore, the aim of the present work
is to develop a simple, rapid, accurate and precise
RP-UPLC method for determination of atropine sulphate in pharmaceutical formulation.
EXPERIMENTAL
Apparatus
Correspondence: P.P. Dahivelker, R.C. Patel Institute of Pharmaceutical Education and Research, Shirpur, Dist: Dhule (M.S.)
India 425 405.
E-mail: raj17579@rediffmail.com
Paper received: 19 March, 2012
Paper revised: 25 June, 2012
Paper accepted: 26 June, 2012
The chromatography was performed on a Water
(Acquity) RP-UPLC instrument equipped with a PDA
detector and Em-power 2 software. The column
“Hiber HR Purospher Star C18” (100 mm×2.1 mm id, 2
µm particle size, Merck, Germany) was used. An
333
A.C. ARVADIYA, P.P. DAHIVELKER: DEVELOPMENT AND VALIDATION OF NOVEL RP-UPLC…
analytical balance (Mettler Toledo, Germany) and
ultrasonic cleaner (Frontline FS 4, India) were used in
the preparation process.
Reagents and materials
The active pharmaceutical ingredient standard
and sample were supplied by Nirlife, Healthcare division of Nirma, Ahmedabad, India. The commercial
product was procured from the local market. The
HPLC grade Acetonitrile and KH2PO4 were purchased
from Finar Reagent (Ahemedabad, India). The filter
paper was Whatmann filter paper No. 41 (Whatmann
International Ltd., England).
Preparation of mobile phase
To prepare the buffer solution, 6.8 gm potassium dihydrogen orthophosphate was weighed and
dissolved in 1000 mL HPLC grade water. The buffer
solution and HPLC grade actonitrile were mixed in a
1000 mL volumetric flask to make a mobile phase
ratio buffer:acetonitrile (87:13, v/v), and the pH was
adjusted to 3.5 by using orthophosphoric acid. The
mobile phase was filtered and degassed in an ultrasonic bath.
Chromatographic condition
The flow rate of mobile phase was adjusted to
0.5 mL/min and the injection volume was 2 µl. The
column temperature was maintained at 30 °C, while
the detection wavelength was 210 nm (Figure 2).
CI&CEQ 19 (3) 333−337 (2013)
by dissolving 50 mg of atropine sulphate and then
diluted to volume with mobile phase as a diluent.
Preparation of standard atropine sulphate injection
solution (500 µg/mL)
An atropine sulphate injection standard solution
at concentration of 500 µg/mL was prepared in a 1000
mL volumetric flask by dissolving 1 mL of atropine
sulphate injection from marketed formulation (Brand
Name: atronir, label: atropine sulphate - 500 mg/mL)
and diluted to volume with mobile phase.
Preparation of calibration curve
A calibration curve was plotted over concentration range of 2.5-17.5 µg/mL. Aliquots (0.5, 1, 1.5, 2,
2.5, 3, and 3.5 mL) of standard stock solution were
transferred in a series of 100 mL volumetric flasks
and diluted with mobile phase. Each solution was injected under the operating chromatographic condition as
described above and areas were recorded. A regression equation was obtained for the calibration curve
by plotting the peak area versus the concentration.
Analysis of atropine sulphate Injection (500 mg/mL)
Atropine sulphate injection sample solution of
concentration 10 µg/mL was prepared in a 100 mL
volumetric flask by diluting 2 mL of standard atropine
sulphate injection solution with mobile phase. The
solution was sonicated for 5 min and filtered through
Whatmann filter paper No. 41. Sample solution (2 μL)
was injected six times under the operating chromatographic condition as described above and areas were
recorded.
RESULTS AND DISCUSSION
Optimization of chromatographic conditions
Figure 2. UV Spectra of atropine sulphate.
Preparation of standard stock Solution of atropine
sulphate (500 µg/mL)
Atropine sulphate standard solution containing
500 µg/mL was prepared in a 100 mL volumetric flask
334
The main objective of the chromatographic
method was to quantify atropine sulphate. Atropine
sulphate was eluted using different stationary phases
such as C18, C8, phenyl, amino and cyano as well as
different mobile phases containing buffers like phosphate, sulphate, and acetate with different pH (2–5)
and using organic modifiers like acetonitrile, methanol
and ethanol in the mobile phase. The peak shape of
the atropine sulphate was found to be symmetrical at
210 nm wavelength. In optimized chromatographic
conditions, atropine sulphate was separated with typical retention time of 2.76 min.
Validation of method
The method was validated with respect to linearity, limit of detection (LOD), limit of quantitation
A.C. ARVADIYA, P.P. DAHIVELKER: DEVELOPMENT AND VALIDATION OF NOVEL RP-UPLC…
(LOQ), accuracy, precision, ruggedness in compliance with ICH guidelines (Q2B) [20].
System suitability parameters
The system suitability test of the proposed chromatographic method was performed before each validation run. Six replicate injections of standard solution
containing 10 µg/mL atropine sulphate were injected
to confirm column efficiency (theoretical plate) and
tailing factor. System suitability parameters are summarized in Table 1.
Table 1. System suitability data obtained from optimum condition
Value±SD (n = 6)
Parameter
Retention time
2.76±0.006
Theoretical plates
11802±93.27
Tailing
1.49±0.01
Linearity
A seven point calibration curve was obtained in
the concentration range of 2.5-17.5 µg/mL for atropine sulphate. The response of the drug was found to
be linear in the investigated range and the regression
equation was found to be y = 10027x + 269 (n = 6)
(Figure 3), with the correlation coefficient 0.9998 (n = 6),
as listed in Table 2.
CI&CEQ 19 (3) 333−337 (2013)
three concentration levels of 80, 100 and 120% of the
specified limit. The percentage recoveries of atropine
sulphate were calculated with RSD range of 0.07-0.11% and the results are shown in Table 3.
Table 3. Recovery data of atropine sulphate for the proposed
method; initial amount: 5 µg/mL
Amount added, %
Recovery, %
RSD / % (n = 3)
80
99.67
0.11
100
99.69
0.07
120
99.89
0.07
Precision
The precision of the method was evaluated in
terms of inter-day and intra-day by carrying out independent assays of three concentrations chosen from
the high, medium and low range of the standard
curves (5, 10 and 15 µg/mL) and the RSD of assay
(inter-day and intra-day) was calculated. The results
are shown in Table 4. The developed method was
found to be precise as the RSD values for intra-day
ranged from 0.06-0.44% and inter-day ranged from
0.13-0.61%.
Table 4. Results of intraday and interday precision (amount
found in µg/mL)
c / µg mL-1
Intra-day
Inter-day
Mean RSD / % (n = 3)
Mean RSD / % (n = 3)
5
4.98
0.08
4.97
0.13
10
10.03
0.44
10.03
0.61
15
14.99
0.06
15
0.34
Limit of detection and limit of quantification
Figure 3. Linearity of atropine sulphate.
Table 2. Linearity of atropine sulphate for proposed method
Value (n = 6)
Parameter
Linearity
2.5-17.5 µg/mL
Slope
10027
Intercept
269
2
Correlation coefficient (r )
0.9998
Accuracy
The accuracy of the method was determined by
spiking of atropine sulphate to prequantified sample
solutions of atropine sulphate (5 µg/mL) in triplicate at
The limit of detection (LOD) and limit of quantitation (LOQ) of the method were evaluated by standard deviation of response and slope method. LOQ
and LOD were calculated by the equations LOD =
= 3.3N/B and LOQ = 10N/B, where N is the standard
deviation of the peak areas of the drugs (n = 6), taken
as a measure of noise, and B is the slope of the
corresponding calibration curve. The limit of detection
(LOD) and limit of quantitation (LOQ) were found to
be 0.0033 and 0.0102 μg/mL, respectively.
Ruggedness
The ruggedness of the method was ascertained
by repeatedly injecting (n = 6) standard solutions of
atropine sulphate (10 μg/mL) without changing the
chromatographic parameters with two analysts, on
two different days and by using two equipment in
same laboratory and calculated RSD. The result of
ruggedness study is shown in Table 5. The developed
335
A.C. ARVADIYA, P.P. DAHIVELKER: DEVELOPMENT AND VALIDATION OF NOVEL RP-UPLC…
CI&CEQ 19 (3) 333−337 (2013)
method was rugged as the RSD was less than 2 for
all condition.
Validation parameters for the assay method are
summarized in Table 5.
to be 100.61% and RSD value was 0.55% by RPUPLC (Figure 4).
Table 5. Summary of validation parameters for the proposed
RP-UPLC method
A new, reversed-phase UPLC method has been
developed for estimation of atropine sulphate in pharmaceutical dosage forms. The method was validated
by employment of ICH guidelines. The validation data
is indicative of good precision and accuracy, and
proves the reliability of the method. The developed
method has been used to monitor the atropine sulphate content in production batches.
Method parameter
Result
Linearity (correlation coefficient)
0.9998
Ruggedness, RSD / % (n = 6)
Analyst-I
0.43
Analyst-II
0.21
Day 1
0.33
Day 2
0.53
Equipment 1
0.50
Equipment 2
0.47
Sensitivity
Limit of detection, µg/mL
0.0033
Limit of quantitation, µg/mL
0.0102
Precision, RSD / %
Intraday (n = 3)
0.06-0.44
Interday (n = 3)
0.13-0.61
Repeatability (n = 6)
0.52
Robustness
Robust
CONCLUSION
Acknowledgement
The authors are thankful to Nirlife HealthCare,
Ahmedabad, India, for providing a sample and facilities for research. The authors are thankful to Dr. S.J.
Surana, Principle, and Dr. H.S. Mahajan, Head of
Quality Assurance Department, R.C. Patel Institute of
Pharmaceutical Education & Research, Shirpur,
Maharashtra, India, for them valuable remarks in carrying out the experimental.
REFERENCES
F.S.K Barar., Essentials of Pharmacotherapeutics, 4
ed., S. Chand and Xo. Ltd., New Delhi, 2007, pp. 246-247
[2]
The British Pharmacopoeia, Vol. 3, the Pharmaceutical
Press, London, 2009, pp. 8019-8020
[3]
S. El-Masry, S.A.H. Khalil, J. Pharm. Sci. 62 (1973) 1332-1334
[4]
P. Majlat, J. Chromatogr. 241 (1982) 399-403
Analysis of atropine sulphate injection
The validity of the proposed assay method for
pharmaceutical formulation was studied by assaying
atropine sulphate injection (label claim 500 mg/mL
atropine sulphate). The percentage purity was found
th
[1]
Figure 4. Chromatogram of assay for atropine sulphate solution by RP-UPLC method.
336
A.C. ARVADIYA, P.P. DAHIVELKER: DEVELOPMENT AND VALIDATION OF NOVEL RP-UPLC…
[5]
C. Abbara, I. Bardot, A. Cailleux, G. Lallement, A. Le
Bouil, A. Turcant, P. Clair, B. Diquet, J. Chromatogr., B
874 (2008) 42-50
[6]
H.X. Chen, Y. Chen, P. Due, F.M. Han, Chromatographia
65 (7-8) (2007) 423-429
[7]
I.L. Honigberg, J.T. Stewart, A.P. Smith, R.D. Plunkett,
E.L. Justice, J. Pharm. Sci. 64 (1975) 1389–1393
[8]
L.J. Pennington, W.F. Schmidt, J. Pharm. Sci. 71 (1982)
951–953
[9]
U.S. Pharmacopeia, XXIII Review, U.S. Pharmacopeial
Convetion, Rockville, MD, 1995, pp. 145–148
[10]
R. Verpoorte., A.B. Svendsen, J. Chromatogr. 120 (1976)
203–205
[11]
U. Lund, S.H. Hansen, J. Chromatogr. 161 (1978) 371-378
[12]
S. Paphassarang, J. Raynaud, R.P. Godeau, A.M. Binsard, J. Chromatogr. 319 (1985) 412–418
A.C. ARVADIYA
P.P. DAHIVELKER
R.C. Patel Institute of Pharmaceutical
Education and Research, Shirpur, Dist.
Dhule (M.S.), India
NAUČNI RAD
CI&CEQ 19 (3) 333−337 (2013)
[13]
M. Eava, J.P. Salo, K.M.O. Caldenty, J. Pharm. Biomed.
Anal. 16 (1998) 717-722
[14]
L. Mateus, S. Cherkaoui, P. Christen, J.L. Veuthey, J.
Chromatogr. A. 868 (2000) 285–294
[15]
D. Breton, D. Buret, P. Clair, M. Lafosse, J. Chromatogr.
A. 1088 (2005) 104-109
[16]
M.Takahashi, M. Nagashima, S. Shigeoka, M. Nishijima,
K.Kamata, J.Chromatogr.A. 775 (1997) 137-141
[17]
O. W. Lau, C. S. Mok, J. Chromatogr., A. 766 (1997) 270–276
[18]
T. Mroczek, K. Glowniak, J. Kowalska, J. Chromatogr., A
1107 (2006) 9-18
[19]
N.B. Brown, H.K. Sleeman, J. Chromatogr. 150 (1978)
225–228
[20]
ICH, Validation of Analytical Procedures: Methodology
(Q2R1), International Conference on Harmonization,
Food and Drug Administration, USA, 1996.
RAZVOJ I VALIDACIJA NOVE RP-UPLC METODE
ZA ODREĐIVANJE ATROPIN-SULFATA U
FARMACEUTSKIM PREPARATIMA
U radu je razvijena jednostavna, precizna, tačna, osetljiva i reproduktivna RP-UPLC
metoda za kvantitativno određivanje atropin-sulfata u farmaceutskim preparatima. Uzorci su analizirani na C18 koloni Hiber HR Purospher Star (100 mm×2.1 mm, veličina čestica 2 µm). Kao mobilna faza korišćena je smeša fosfatni pufer:acetonitril (87:13, v/v).
pH pufera je podešen na 3,5 dodatkom ortofosforne kiseline. Brzina protoka mobilne
faze je 0,5 mL/min, a temperatura kolone je 30 °C. Komponente su detektovane PDA
detektorom na 210 nm. Nađeno je da metoda ima zadovoljavajuću linearnost u opsegu
koncentracija od 2,5-17,5 µg/mL sa r2 = 0,9998 (n = 6). Limit detekcije za ovu metodu
određivanja atropin-sulfata je 0,0033 μg/ml, a limit kvantifikacije 0,0102 μg/ml. Metoda je
validirana u skladu sa ICH uputstvima. Metoda je uspešno primenjena za određivanje
atropin-sulfata u farmaceutskim preparatima.
Ključne reči: atropin-sulfat, metoda validacije, RP-UPLC hromatografija.
337
Available on line at
Association of the Chemical Engineers of Serbia AChE
www.ache.org.rs/CICEQ
Chemical Industry & Chemical Engineering Quarterly 19 (3) 339−346 (2013)
ARKAN JASIM HADI1
GHASSAN JASIM HADI2
GHAZI F. NAJMULDEEN1
IQBAL AHMED1
SYED F. HASANY1
1
Faculty of Chemical engineering
and Natural Resource, University
Malaysia Pahang, Kuantan,
Malaysia
2
Al Dour Technical Institution,
Technical Education Organization,
Tikrit, Iraq
SCIENTIFIC PAPER
UDC 544.344.2-14-13:546.264-31:66
DOI 10.2298/CICEQ120324067H
CI&CEQ
GAS–LIQUID EQUILIBRIUM PREDICTION OF
SYSTEM CO2-AQUEOUS ETHANOL AT
MODERATE PRESSURE AND DIFFERENT
TEMPERATURES USING PR-EOS
One of the most important design considerations that should not be ignored
during industrial purpose equipment designing is vapour-liquid equilibrium
(VLE). Thus, in chemical engineering, the first step is the computation of VLE
properties of materials by employing equations of state (EOS). In this study,
we have used a thermodynamic model established for a binary system of carbon dioxide (1)–aqueous ethanol (2), which was employed to estimate the gas–liquid equilibrium at moderate pressures (up to 6 bar) and varying temperatures (288–323 K). The Peng-Robinson EOS was employed to determine the
VLE properties. Mixing rules such as van der Waals and quadratic mixing rules
were also used for the determination of ethanol-water mixture critical parameters, which entails the pseudo-critical method as one component, and the
results obtained from this study were similar to the ones reported in recent
literature for empirical phase equilibrium studies.
Keywords: gas-liquid equilibrium, carbon dioxide, mixture, moderate
pressure, PR-EOS.
Several attempts have been made during the
last five decades to compute the VLE properties of
different materials by employing a mathematical
model, but unfortunately due to lack of theoretical
basis, all attempts resulted in no significant outcome.
The advent of computer technology and programs
has made it possible to interpolate, extrapolate and
predict thermodynamic information, which is crucial in
designing of equipment sand modeling of process
operations [1].
Intensive research has been conducted on gas
solubility in liquids during the last three decades. This
is significant from an industrial application point of
view where gas solubility in pure and mixed liquids
are of considerable importance, e.g. carbonation processes employed for wastewater treatment, stripping
columns, gas absorption, soft drinks and alcoholic
beverages, etc. [2].
Correspondence: A.J. Hadi, Faculty of Chemical engineering
and Natural Resource, University Malaysia Pahang, Kuantan,
26300, Malaysia.
E-mail: arkanaldoury72@gmail.com
Paper received: 24 March, 2012
Paper revised: 26 April, 2012
Paper accepted: 26 June, 2012
However, gas solubility in diluted liquids is also
of considerable importance from a theoretical point of
view. Molecular theories are being tested by employing empirical solubility data and it is also utilized to
illustrate the intermolecular interactions and microscopic structure of materials. Wilhem et al. [3]
reported the dependence of benefits of low-pressure
gas solubility over high-pressure equilibrium data and
it was based on the observation that inaccuracies
brought by semi-empirical relation is insignificant and
it has no effect on the final observations, e.g. the
impact of the solute’s partial molar volume on indefinite diluted solvent and besides this some definite
assumptions make possible the thermodynamic treatment of the system [2].
Other different thermodynamic information, such
as volumetric characteristics and phase equilibrium of
mixture and pure compounds (carbon dioxide either
with alkane or alkanol), has great interest in the
domains of chemical engineering, oil and biotechnology areas. It is also used for the establishment and
validation of some models of thermodynamics. Identification of global phase behavior of different systems
in a specified range of temperature and pressure is
also crucial in this context [4].
339
A.J. HADI et al.: GAS–LIQUID EQUILIBRIUM PREDICTION OF SYSTEM CO2-AQUEOUS ETHANOL…
Empirical observations for gas solubility in common systems that are employed for the establishment
of models for studying different parameters, especially at high pressures, can be found in the existing
literature. The carbon dioxide and water binary system was also studied by Alain et al. [5], who reported
new empirical observations for VLE data at a wide
range of temperature (278.2–318.2 K) and pressure
around 80 bar. These observations were consistent
with the ones already present in the literature. Gas
solubility and Henry’s data was also extensively
researched by Dalmoelin et al. [2], who employed
carbon dioxide gas to check its solubility in pure water
and ethanol and a mixture of both and for this they
chose temperature in range of (288–323K) whereas
pressure was maintained up to 6 atm for pure solvents as well as their mixture with varying amounts of
both solvents. The CO2 and alkanol system was
studied by Elizalde-Solis et al. [4], who measured
their VLE values. The temperature range for carbon
dioxide and 1-propanol system was around 344 to
426 K and its equilibrium values were determined.
However, for CO2 + 2-propanol, temperature in range
of 334 to 443 K was used. 1-Butanol with CO2 system
was studied at temperature 354 to 430 K. Polyethylene glycol 200 as a solvent was also studied using
carbon dioxide as gas model by Minqiang Hou et al.
[6]. They used the following solvents and their mixtures in his study; PEG200, PEG with an average
molecular weight of 200 g/mol), 1-pentanol and
1-octanol. PEG200 + 1-pentanol, and PEG200 +
1-octanol and the reported temperature range was
303.15, 313.15 and 323.15 K up to 8.0 MPa, respectively. With increase in the pressure, increase in
the gas solubility was reported by [6]; also, increased
alcohol concentration was found to also have significant impact on mixed solvents. However, at increasing temperature, the solubility decreases and it was
found to be different for different solvents. Carbon
dioxide had high solubility in PEG200 + 1-pentanol.
Thiophene as a solvent for carbon dioxide was investigated by Elizalde and Galicia-Luna [7] and CO2 +
1-propanol was also studied. The Peng-Robinson
equation of state along with the classical mixing rule
was employed for the computation of VLE data of
binary mixtures. Comparative analysis of empirical
and theoretical observations was made in the end.
Secuianu et al. [8] studied the phase behavior of the
carbon dioxide in methanol; they measured the VLE
of this system and reported data at 293.15, 303.15,
313.15, 333.15 and 353.15 K and pressures between
5.2 and 110.8 bar. They modeled the measured VLE
data and literature data by using a general cubic
340
CI&CEQ 19 (3) 339−346 (2013)
equation of state combined with a classical van der
Waals two parameter conventional mixing rule. They
used one set of interaction parameters to predict the
critical and subcritical VLE in binary mixture CO2 and
ethanol in a varied temperature. They also concluded
from the comparison between the predicted results,
experimental data and the literature data, the phase
behavior was suitable reproduced.
Results obtained from this research for PR-EOS
in CO2 (1)–aqueous ethanol (2) at optimum pressure
and temperature was analyzed and compared with
empirical data obtained from [2].
THERMODYNAMIC MODEL
For the computation of phase equilibrium
behaviour, the thermodynamic model employed for
this purpose must meet the requirements mentioned
in the expression mentioned below. This expression
is for two-phase equilibrium in which one phase is
represented by prime (') and the other by double
prime (").
fi′ = fi″, i = 1,2,3,…,m
(1)
In the above expression f indicates the fugacity
of component (i) in a multi-component mixture [9].
EOS
A component’s fugacity in a phase is computed
by employing a thermodynamic equilibrium model utilizing EOS. Interaction energies and size factors have
been observed to have an impact on the results of the
models used for fugacity computation. This creates
the requirement of mixing rules development for the
estimation of highest energy and size parameters as
needed by EOS.
For modeling phase behaviour, cubic EOS are
generally employed, which are quite simple and extensively employed for empirical data analysis [10,11].
The following modified equation was proposed
by Peng and Robinson:
P =
RT
a (T )
−
(v − b ) v (v + b ) + b (v − b )
(2)
At the critical point:
a (Tc ) = 0.45724
b (Tc ) = 0.0778
R 2Tc2
Pc
RTc
Pc
(3)
(4)
At other temperatures, the parameter T is
changed as:
A.J. HADI et al.: GAS–LIQUID EQUILIBRIUM PREDICTION OF SYSTEM CO2-AQUEOUS ETHANOL…
a (T ) = a (Tc )α (Tr ,ω )
(5)
The efficiency of this term was improved by Graboski and Daubert [13] to explain the correlation
terms of the vapour pressure curve up to the critical
point as follows:
α 0.5 = 1 + (1 −Tr 0.5 )(0.37464 + 1.5422ω − 0.26992ω 2 ) (6)
Replacement of v in the general representation
of Eq. (2) in terms of ZRT/P will give the expression
for compressibility factor of PR-EOS as follows:
Z 3 − (1 − B )Z 2 + ( A − 2B − 3B 2 )Z −
A=
aαP
αP
= 0.45724 2r
R 2T 2
Tr
(8)
B=
bP
P
= 0.0778 r
RT
Tr
(9)
Determination of compressibility factor can be
made through the cubic EOS by simplifying it with an
iterative procedure via the Newton–Raphson method.
As pressure-explicit EOS are the more general
types of equations, the significant relation for determination of fugacity coefficients can be made by
using the following equation:
ln ϕˆi =
1
RT 
v
 ∂P 
RT 

dV − ln Z
−

 ∂ni T ,v ,nj V 
(10)
b
2
× i −
 bm am


j
am =
n
n
i
j
 x x a
i
 bm
1− v

am

  + 2.828RTb ×

m
bm

  1 + 2.414
v
x i aij  ln 
bm
 
  1 − 0.414
v






bm =
j
(12)
ij
(11)
Fugacity computation of components present in
the gas phase was performed by employing equation
11 in which yi and entire PR-EOS a and b values
were substituted by their corresponding terms. EOS
was first formulated for pure components and later it
was modified for mixed components by using mixing
rules which combine pure component parameters [16].
n
n
i
j
 x x b
i
j
(13)
ij
The following mixing rule equations were
employed in this study:
Modified van der Waal’s mixing rules (MR1):
n
am =
i
n
n

x i x j a ij and bm =
x b
i
i
i
j
with
a ij = (1 − k ij )(a i a j )
Quadratic mixing rules (MR2):
n
am =
n

i
where V indicates the total system volume whereas n1
and n2 represent the mole numbers of components 1
and 2, respectively. Substituting PR-EOS into Eq.
(10) will yield the following closed-form expression for
fugacity coefficient, which it acquires in the liquid
phase:

b
ln ϕˆi = i (Z − 1) − ln  Z
bm

Van der Waal’s mixing rule has been used for
the derivation of simple EOS expressions and later
modifications may have been introduced in it. Onefluid mixing rules can be employed for the computation of the mixture parameters am and bm for the
EOS as shown in Eqs. (12) and (13). Combining rule
is the exception between the two and it helps in the
calculation of cross coefficients aij and bij.
and
A and B are defined as:
∞
Mixing rules
(7)
−( AB − B 2 − B 3 ) = 0
CI&CEQ 19 (3) 339−346 (2013)
j
x i x j a ij and bm =
n
n
i
j
 x x b
i
j
ij
with
a ij = (1 − k ij )(a i a j ) and bij = (bi + b j 2)(1 − l ij ) .
RESULTS AND DISCUSSION
Prediction of VLE by employing cubic EOS
expressions along with physical characteristics of
pure components and adjustable parameters of binary
system of CO2 (1)–aqueous ethanol (2) was the major
objective of this research. van der Waal’s equation
was altered by PR-EOS and mixing rule. The quadratic rule is generally employed for finding the correlations of empirical observations for VLE. Comparison
of calculations with empirical observations was made
after the computation of CO2 mole fraction in the
liquid phase (x). For comparative analysis, empirical
data was obtained from [2].
Critical parameters of water-ethanol mixture at
different compositions, such as critical temperature
341
A.J. HADI et al.: GAS–LIQUID EQUILIBRIUM PREDICTION OF SYSTEM CO2-AQUEOUS ETHANOL…
(Tcm), critical pressure (Pcm) and acentric factor ωm
were approximated by the following expressions [18]:
T x
= p x
= ω x
Tcm =
Pcm
ωm
ci
ci
i
(14)
i
(15)
i
(16)
i
In the above expression the symbols Tcm, Pcm
and ωm represent the critical temperature, pressure
and acentric factor, respectively, for a given mixture,
whereas Tci, Pci and ωi are the critical parameters of
ethanol and water. The expression xi shows the mole
fraction of components (water and ethanol). The critical properties of the carbon dioxide, ethanol and
water are shown in Table 1.
Table 1. Critical properties (Tc and Pc) and acentric factor (ω) of
CO2, ethanol and water [8,14]
Component
Tc / K
Pc / bar
ω
CO2
304.7
73.8
0.225
Ethanol
513.9
61.47
0.6447
Water
647.9
221
0.344
The mentioned Eqs. (14)–(16) were employed
for the transformation of the multicomponent mixture
(ethanol-water) to a single component and it was
CI&CEQ 19 (3) 339−346 (2013)
aimed to convert the ternary system (carbon dioxide–ethanol-water) system into a binary system (carbon
dioxide and aqueous ethanol). Mixing rules entail
some adjustable parameters such as k12 and L12 and
the latter one can be calculated by using two different
approaches and it need the empirical observations
and later it is fitted into EOS expression. A trial and
error method was adapted for the identification of
MR2. Computation of mole fraction solubility was performed by using each isotherm pressure. The minimum mean absolute deviation (MAD) obtained by
acceptable values of k12 and L12 was calculated as:
MAD =
100
N
x
exp.
− x calc.
(17)
where N represents the number of considered data
points.
Computational and programming details have
been described previously [19]. For all the given compositions, acceptable values of k12 and L12 were used
and the MAD values taken at different temperatures
and varying compositions utilizing PR-EOS in CO2–
–aqueous ethanol system are shown in Table 2. The
comparative observations for computed and empirical
data sets that took place at the temperature in the
range of 288 to 323 K for all the given mixture compositions are shown in Table 2. MAD for MR2 was
found to be lower than MR1 and this difference in the
Table 2. Values of adjustable parameters k12 and L12, obtained from fitting with PR-EOS. Mean absolute deviation (MAD) percentage
between the experimental and pedicted mole fraction solubility of CO2 in aqueous ethanol with different mixing rules using PR-EOS
Composition of mixtures (ethanol + water)
0.1 Ethanol + 0.9 water
0.25 Ethanol + 0.75 water
0.5 Ethanol + 0.5 water
0.75 Ethanol + 0.25 water
0.9 Ethanol + 0.1 water
342
T/K
MR1
MAD / %
MR2
k12
k12
L12
MR1
MR2
288
-0.1119
-0.1119
-0.117
2.285
2.069
298
-0.1038
-0.1038
2.198
1.828
308
-0.0946
-0.0946
-0.181
-0.004
0.926
323
-0.0817
-0.0817
-0.087
0.691
0.918
0.625
288
-0.0843
-0.0843
-0.025
2.337
2.272
298
-0.0796
-0.0796
-0.046
3.397
3.306
308
-0.0747
-0.0747
-0.228
3.023
2.733
323
-0.06966
-0.06966
-0.003
1.281
1.279
288
-0.0375
-0.0375
-0.088
2.358
2.160
298
-0.03768
-0.03768
-0.091
2.063
1.872
308
-0.03232
-0.03232
-0.048
3.113
2.990
323
-0.02806
-0.02806
-0.017
0.957
0.930
288
0.03148
0.03148
-0.134
3.971
3.740
298
0.03541
0.03541
-0.074
5.334
5.177
308
0.03722
0.03722
-0.163
2.535
2.530
323
0.04064
0.04064
-0.321
3.086
2.706
288
0.07616
0.07616
-0.035
0.747
2.661
298
0.08107
0.08107
-0.116
2.093
1.948
308
0.08797
0.08797
-0.154
1.827
1.610
323
0.09538
0.09538
-0.158
2.055
1.928
A.J. HADI et al.: GAS–LIQUID EQUILIBRIUM PREDICTION OF SYSTEM CO2-AQUEOUS ETHANOL…
values is negligible. We have found that thermodynamic model using PR-EOS along with MR1 and MR2 is
best suited to run this system smoothly. Figures 1-8
show the comparative analysis of theoretical and
empirical data values.
Figure 1. Phase composition diagram of CO2–mixture system at
288 K using PR with MR1.
Figure 2. Phase composition diagram of CO2–mixture system at
288 K using PR with MR2.
A decrease in k12 has been observed with
increase in temperature. This data is valid for the mixtures of composition starting with 0.1 ethanol + 0.9
water and goes to 0.5 ethanol + 0.5 water. An
increase in k12 values was noticed in mixtures with the
following compositions; 0.75 ethanol + 0.25 water and
0.9 ethanol + 0.1 water. However, it should be noted
that alteration in the values of k12 is insignificant when
CI&CEQ 19 (3) 339−346 (2013)
compared to temperature values which are larger. L12
values are also referred as vacillation values. The
binary interaction parameter k12 decreases with the
increase in ethanol concentration in the mixture.
Figure 3. Phase composition diagram of CO2–mixture system at
298 K using PR with MR1.
Figure 4. Phase composition diagram of CO2–mixture system at
298 K using PR with MR2.
It is obvious that there is good agreement
between the calculated data using PR-EOS and the
previous work Ghazi et al. [20] using the Soave-Redlich-Kwong equation of state (SRK) and experimental
data. However, it is noticeable that there is small deviation between the results of the two equations where
the MAD of the SRK that is less than the MAD for the
PR-EOS for the two mixing rules.
343
A.J. HADI et al.: GAS–LIQUID EQUILIBRIUM PREDICTION OF SYSTEM CO2-AQUEOUS ETHANOL…
CI&CEQ 19 (3) 339−346 (2013)
conditions in CO2 mixtures. In the studied system,
variation in the L12 values was observed.
Figure 5. Phase composition diagram of CO2–mixture system at
308 K using PR with MR1.
Figure 7. Phase composition diagram of CO2–mixture system at
323 K using PR with MR1.
Figure 6. Phase composition diagram of CO2–mixture system at
308 K using PR with MR2.
CONCLUSION
We used PR-EOS along with MR1 and MR2 for
studying VLE and the obtained observations were
consistent with empirical data provided in [2]. We
used this model for the computation of VLE for CO2
(1)–mixture (2) (ethanol and water) at varying temperatures and moderate pressures. In the mixing rule
MR2, two adjustable parameters named k12 and L12
are used, which yielded reduced MAD compared to
the one obtained by MR1. The latter one was used to
determine the equilibrium data for CO2 (1)–mixture (2).
Besides this, MAD variation between MR1 and MR2
was insignificant. This results in the preferable use of
MR1 with k12 parameter to study gas equilibrium
344
Figure 8. Phase composition diagram of CO2–mixture system at
323 K using PR with MR2.
Acknowledgment
The authors express special gratitude to University Malaysia, Pahang, who provided the lab facility
for the successful completion of this research and
financial support through the Doctoral Scholarship
scheme (No. GRS100357).
Nomenclature
a, b
A, B
parameters in the equation of state
dimensionless parameters
A.J. HADI et al.: GAS–LIQUID EQUILIBRIUM PREDICTION OF SYSTEM CO2-AQUEOUS ETHANOL…
f
kij, Lij
n
ni
N
P
R
T
x, y
Z
V
ν
fugacity, bar
adjustable parameters
number of components
number of moles of component i, mol
number of data points
pressure, bar
universal gas constant, 0.08314 L bar/(mol K)
temperature , K
liquid and gas mole fractions, respectively
compressibility factor
total system volume, L
total system molar volume , L/mol
[5]
A. Valtz, A. Chapoy, C. Coquelet, P. Paricaud, D. Richon,
Fluid Phase Equilib. 226 (2004) 333-344
[6]
M. Hou, S. Liang, Z. Zhang, J. Song, T. Jiang, B. Han,
Fluid Phase Equilib. 258 (2007) 108-114
[7]
O. Elizalde-Solis, Fluid Phase Equilib. 230 (2005) 51-57
[8]
Secuianu, Catinca, Feroiu, Viorel Geană, Dan, Fluids 47
(2008) 109-116
[9]
J. Smith, H. van Ness, M. Abbott, Introduction to chemical
engineering thermodynamics, McGraw-Hill, New York,
2001
[10]
E. Bender, U. Klein, W.P. Schmitt, J.M. Prausnitz, Fluid
Phase Equilib. 15 (1984) 241-255
[11]
R.D. Deshmukh, A.E. Mather, Fluid Phase Equilib. 35
(1987) 313-314
[12]
D.Y. Peng, D.B. Robinson, Ind. Eng. Chem. Fund. 15
(1976) 59-64
[13]
M.S. Graboski, T.E. Daubert, Ind. Eng. Chem. Process
Des. Dev. 18 (1979) 300-306
[14]
T. McCalla, Introduction to numerical methods and
Fortran programming, Wiley, New York, 1967
[15]
S.M. Walas, Phase equilibria in chemical engineering,
Butterworth, Boston, MA, 1985
[16]
K.A.A. Mnam, Phase Equilibrium study for the separation
of solid and liquid components using supercritical carbon
dioxide, PhD Thesis, University of Technology-Iraq,
Baghdad, 1998
[17]
Y. Adachi, H. Sugie Fluid Phase Equilib. 28 (1986) 103-118
[18]
H.C. Smith, Van Ness, Introduction to Chemical Engineering Thermodynamics, 4 ed., McGraw-Hill, New York
1987
[19]
A.J. Hadi, Thermodynamic Model for High Pressure Phase
Behavior of Carbon Dioxide in Several Physical Solvents
at Different Temperatures, Tikrit J. Eng. Sci. 15 (2008)
32-50
[20]
G.F. Najmuldeen, G.J. Hadi, A.J. Hadi, I. Ahmed, Phys.
Chem. 2(1) (2012) 1-5.
Greek symbols

ϕ
ω
fugacity coefficient in mixture
acentric factor
Subscripts and Superscripts
c
exp.
calc.
g
i,j
m
r
critical condition
experimental value
calculated value
gas phase
component
mixture
reduced property
REFERENCES
[1]
R. Sytryjeck, J.H. Vera, Can. J. Chem. Eng. 64 (1986)
323–333
[2]
I. Dalmolin, E. Skovroinski, A. Biasi, M. Corazza, Fluid
Phase Equilib. 245 (2006) 193-200
[3]
E. Wilhelm, R. Battino, R.J. Wilcock, Chem. Rev. (Washington, DC, U. S.) 77 (1977) 219-262
[4]
O. Elizalde-Solis, L.A. Galicia-Luna, L.E. CamachoCamacho, Fluid Phase Equilib. 259 (2007) 23-32
CI&CEQ 19 (3) 339−346 (2013)
345
A.J. HADI et al.: GAS–LIQUID EQUILIBRIUM PREDICTION OF SYSTEM CO2-AQUEOUS ETHANOL…
ARKAN JASIM HADI1
GHASSAN JASIM HADI2
GHAZI F. NAJMULDEEN1
IQBAL AHMED1
SYED F. HASANY1
1
Faculty of Chemical engineering and
Natural Resource, University Malaysia
Pahang, Kuantan, Malaysia
2
Al Dour Technical Institution,
Technical Education Organization,
Tikrit, Iraq
NAUČNI RAD
CI&CEQ 19 (3) 339−346 (2013)
PREDVIĐANJE RAVNOTEŽE GAS-TEČNOST
SISTEMA CO2-VODENI RASTVOR ETANOLA NA
UMERENOM PRITISKU I RAZLIČITIM
TEMPERATURAMA PRIMENOM
PENG-ROBINSON-OVE JEDNAČINE STANJA
Jedan od navažnijih aspekata projektovanja, koji ne sme biti zanemaren pri projektovanju opreme za industrijsku primenu, jeste ravnoteža para-tečnost (VLE). Zbog toga je
u hemijskom inženjerstvu prvi korak izračunavanje ravotežnih podataka primenom jednačine stanja. U ovom radu je korišćen termidinamički model koji je utvrđen za binarni
system CO2-vodeni rastvor etanola. Ovaj model je korišćen za izračunavanje ravnoteže
gas-tečnost na umerenim pritiscima (do 6 bar) i različitim temperaturama (280-323 K).
Peng-Robinson-ova jednačina stanja je korišćena za određivanje ravnotežnih svojstava.
Pravila mešanja, kao što su van der Waals-ovo i kvadratno pravilo, su takođe korišćeni
za određivanje kritičnih parametara smeše etanol-voda koji zahteva pseudo-kritičnu
metodu kao jednu komponentu. Dobijeni rezultati su slični sa nedavno objavljenim empirijskim istraživanjima fazne ravnoteže.
Ključne reči: ravnoteža gas-tečnost, CO2, smeša, umereni pritisak, Peng-Robinson-ova jednačina stanja.
346
Available on line at
Association of the Chemical Engineers of Serbia AChE
www.ache.org.rs/CICEQ
Chemical Industry & Chemical Engineering Quarterly 19 (3) 347−357 (2013)
S.E. MORADI1
J. KHODAVEISY2
R.DASHTI2
1
Young Researchers Club, Islamic
Azad University - Sari Branch, Iran
2
Young Researchers Club, Islamic
Azad University-Booshehr Branch,
Iran
SCIENTIFIC PAPER
UDC 504.5:544.723.2:661.183:66.061.3
DOI 10.2298/CICEQ120204069M
CI&CEQ
REMOVAL OF ANIONIC SURFACTANTS BY
SORPTION ONTO AMINATED MESOPOROUS
CARBON
Direct and indirect releases of large quantities of surfactants to the environment may result in serious health and environmental problems. Therefore,
surfactants should be removed from water before release to the environment
or delivery for public use. In the present work, the removal of anionic surfactants, benzene sulfonate (BS), p-toluene sulfonate (TS) and 4-octylbenzene
sulfonate (OBS) from water by adsorption onto amino modified mesoporous
carbon (AMC) were studied. The AMC surface chemistry and textural properties were characterized by nitrogen adsorption, XRD and FT-IR analyses.
Experiments were conducted in batch mode with variables such as amount of
contact time, solution pH, dose of adsorbent and temperature. Finally, the
adsorption isotherms of anionic surfactants on mesoporous carbon adsorbents
were in agreement with a Langmuir model. AMC has shown higher anionic
surfactants adsorption capacity than the untreated mesoporous carbon, which
can be explained by the strong interaction between the anionic surfactant and
the cationic surface of the adsorbent.
Keywords: aminating; mesoporous carbon; anionic surfactant; Langmuir model.
Surfactants are widely used compounds, as
their dual hydrophobic/hydrophilic nature makes them
invaluable for flocculation, detergency and stabilization processes in industrial and domestic applications. There has been an exponential increase in the
production and use of these substances over the past
century. Despite the high biodegradability required by
law for these products, the enormous amount of
waste they produce has a severe impact on waters
and soils [1-4]. A rough estimate of the worldwide
surfactant production is 10 million tons per year, of
which anionic surfactants account for about 60%.
Anionic surfactants are popular detergent ingredients,
because of their straightforward synthesis and consequently low production costs [5].
Surfactants in wastewaters can partly be biodegraded especially under aerobic conditions. However, under anaerobic conditions they are not biodegradable and show adverse effects on aquatic life.
Correspondence: S.E. Moradi, Young Researchers Club, Islamic
Azad University - Sari Branch 48164-194, Iran.
E-mail: er_moradi@hotmail.com
Paper received: 14 February, 2012
Paper revised: 14 June, 2012
Paper accepted: 2 July, 2012
Furthermore, they can act synergistically with some
other toxic chemicals which may be present in wastewaters increasing their negative effects on the environment [6-8]. Moreover, the discharge of this compound into waters has produced numerous problems
of environmental contamination and therefore a
marked reduction in the quality of sources of drinking
water. Therefore, the amount of surfactants present in
wastewaters of many industries, especially detergent
and textile, must be reduced at least to acceptable
levels before discharging to the environment. The
conventional methods for surfactant removal from
water involve processes such as chemical and electrochemical oxidation, membrane technology, chemical precipitation, photo-catalytic degradation, adsorption and various biological methods [5,8]. Many of
these processes are not cost effective and/or not suitable for application on a household scale. Adsorption
technology can be of low cost and can be applied in
small devices. It therefore offers potential for use on
household scale, also in low-income households. At
this stage of the project, re-use of the spent adsorbent
is not considered. We propose to use an environmentally harmless absorbent that can be discarded or
burnt as low-volume domestic waste. The preparation
347
S.E. MORADI, J. KHODAVEISY, R.DASHTI: REMOVAL OF ANIONIC SURFACTANTS…
of low-cost adsorbents from waste materials has
several advantages, mainly of economic and environmental nature. A wide variety of novel adsorbents
have been recently prepared from different waste
materials utilizing agricultural as well industrial and
municipal wastes. Although many articles have been
published [9-19] so far discussing the importance of
low-cost adsorbents in water pollution control, many
of them are generally either adsorbate-specific or
adsorbent-specific.
Recently, Ryoo et al. prepared ordered mesoporous carbons (CMK-x) from mesoporous silica templates such as MCM-48, SBA-1 and SBA-15 using
sucrose as the carbon source [20–23]. Adsorption
plays an important role in these processes. Therefore,
the interactions of such compounds with the mesoporous carbon surface must be studied in detail. The
mesoporous carbon materials adsorption capacity
depends on quite different factors. Obviously, it
depends on the mesoporous carbon’s characteristics:
texture (surface area, pore size distributions), surface
chemistry (surface functional groups) [24–26]. Mesoporous carbon materials with ordered pore structure,
high pore volume, high specific surface area, and
tunable pore diameters can be used as an effective
adsorbent in industry. Due to its open pore structure
and mesoporous properties, mesoporous carbon provides marked advantages over typical activated carbon in the adsorption and diffusion process [27].
Ordered mesoporous carbon materials have some
superiority in contrast with microporous carbon adsorbents. The most important superiorities are given as
higher specific surface area and specific pore volume
that increases the contact area between adsorbent
and adsorbate to reach to maximum of organic and
inorganic molecules adsorption. Moreover, highly
ordered structure and mesopore size of this novel
ordered nanoporous carbon that affect on equilibrium
time decrease for removal of pollutant. However, the
hydrophobic and inert nature of mesoporous carbons
can be unfavorable for several applications. Surface
modification or functionalization of porous carbon
materials is crucial not only for the development and
application of hybrid mesoporous materials but also to
change the hydrophobicity and hydrophilicity character of the surface of the materials in order to make
them available as good adsorbents or catalysts for the
selective removal of some organic contaminants [28].
The objective of this study is to investigate the
adsorption characteristics of some anionic surfactants
onto amino modified and unmodified mesoporous
carbon adsorbents in relation to wastewater purifycation. The influence of the surface modification of
348
CI&CEQ 19 (3) 347−357 (2013)
mesoporous carbon adsorbent was analyzed in terms
of adsorption rate (adsorption kinetic) and capacity
(adsorption isotherm) for anionic surfactants. Interestingly, it was found that the adsorption capability of
different types of amino modified ordered mesoporous carbon for anionic surfactants is much higher
compared to that of pristine mesoporous carbon.
MATERIALS AND METHODS
Materials
The reactants used in this study were tetraethyl
orthosilicate (TEOS) as a silica source, cetyltrimethylammonium bromide (CTAB) as a surfactant, sodium
hydroxide (NaOH), sodium fluoride (NaF), deionized
water for synthesis of mesoporous silica (MCM-48),
sucrose as a carbon source, sulfuric acid as a catalyst
for synthesis of mesoporous carbon, aqueous ammonia, sodium hydrosulfite, acetic anhydride, fuming
nitric acid, and sulfuric acid as fictionalization agents,
benzene sulfonate (BS), p-toluene sulfonate (TS) and
4-octylbenzene sulfonate (OBS). All chemicals were
of analytical grade from Merck (Darmstadt, Germany).
Working standard solutions were prepared by appropriate dilution of the stock standard solution. The following buffers were used to control the pH of water
samples: hydrochloric acid–glycine (pH 1–3), sodium
acetate–acetic acid (pH 3–6), disodium hydrogen
phosphate–sodium dihydrogen phosphate (pH 6–8),
and ammonium chloride–ammonia (pH 8–10).
Synthesis of silica template and MC
MCM-48 was prepared using CTAB as a surfactant and TEOS as a silica source, according to
Shao et al. [29]. Briefly, 10 mL of TEOS was mixed
with 50 mL of deionized water, and the mixture was
vigorously stirred for 40 min at 35 °C, then 0.9 g of
NaOH was added into mixture, and at the same time,
0.19 g of NaF was added into the mixture. After the
NaF was added completely, the required content of
sources, respectively, were added. After another 60
min of vigorous stirring, 10.61 g of CTAB was added
to the mixture, and stirring continued for 60 min. The
mixture was heated for 24 h at 393 K in an autoclave
under static conditions, and the resulting product was
filtered, washed with distilled water, and dried at 373
K. The sample was calcined at 823 K for 4 h in air to
remove the surfactant completely. The product thus
obtained was referred to as MCM-48. Then 1.25 g
sucrose and 0.14 g H2SO4 were dissolved in 5.0 g
H2O, and this solution was added to 1 g MCM-48. The
sucrose solution corresponded approximately to the
maximum amount of sucrose and sulfuric acid that
S.E. MORADI, J. KHODAVEISY, R.DASHTI: REMOVAL OF ANIONIC SURFACTANTS…
could be contained in the pores of 1 g MCM-48. The
resultant mixture was dried in an oven at 373 K, and
subsequently, the oven temperature was increased to
433 K. After 6 h at 433 K, the MCM-48 silica containing the partially carbonizing organic masses was
added with an aqueous solution consisting of 0.75 g
sucrose, 0.08 g H2SO4 and 5.0 g H2O. The resultant
mixture was dried again at 373 K, and subsequently
the oven temperature was increased to 433 K. The
color of the sample turned very dark brown or nearly
black. This powder sample was heated to 1173 K
under vacuum using a fused quartz reactor equipped
with a fritted disk. The carbon-silica composite thus
obtained was washed with 1 M NaOH solution of 50%
ethanol – 50% H2O twice at 363 K, in order to dissolve
the silica template completely. The carbon samples
obtained after the silica removal were filtered, washed
with ethanol.
Treatment before modification on MC
The prepared MC was vacuum-dried at 110 °C
for 24 h after being washed with deionized water until
the electroconductivity of the filtrate became nearly
the same as that of the water. It was then treated with
hydrogen at 100 °C according to the previous report
[30]. Surface modification was done by nitrating the
carbon surface through electrophilic substitution and
then aminating it through reduction. Reagent grade
acetic anhydride, fuming nitric acid, and sulfuric acid
were used as supplied in nitration. Distilled water for
injection as the solvent, 28% aqueous ammonia, and
reagent grade sodium hydrosulfite were employed as
purchased in amination.
Surface modification of mesoporous carbon
AMC was prepared using MC, according to Abe
et al. [31]. Briefly, nitration was allowed to proceed in
a 1000 mL three-neck flask containing MC, acetic
anhydride, and concentrated sulfuric acid with dropwise addition of fuming nitric acid in 5 h while keeping
the temperature below 5 °C. The reaction was completed after 19 h of stirring at room temperature.
Modified MC thus obtained was thoroughly washed
with deionized water until the electroconductivity of
filtrate attained a value nearly the same as that of the
water and vacuum-dried for 24 h at 110 °C. Reduction
of the nitrated mesoporous carbon was permitted to
proceed in a 1000 mL flask containing deionized
water, 28% aqueous ammonia, sodium hydrosulfite,
and the carbon with stirring for 24 h in nitrogen atmosphere at room temperature. The aminated mesoporous carbon thus obtained was vacuum-dried at 110
°C after being washed with deionized water until the
electroconductivity of filtrate became nearly the same
CI&CEQ 19 (3) 347−357 (2013)
as that of the water. This carbon sample is hereafter
abbreviated to AMC.
Characterization
X-ray powder diffraction patterns were recorded
on a Philips 1830 diffractometer using CuKα radiation
(XRD, Philips Electronic Instruments, PW 1710). The
diffractograms were recorded in the 2θ range of 0.8–
10 with a 2θ step size of 0.01° and a step time of 1 s.
Adsorption-desorption isotherms of the synthesized
samples were measured at 77 K on micromeritics
model ASAP 2010 sorptometer (Norcross, GA, USA)
to determine an average pore diameter. Pore-size
distributions were calculated by the Barrett-JoynerHalenda (BJH) method, while surface area of the
sample was measured by Brunaure-Emmet-Teller
(BET) method. Elemental analysis was carried out to
determine the amount of nitrogen-containing groups
introduced onto mesoporous carbon surface with an
elemental analyzer (CHN-O-RAPID type, Heraeous
Co., Ltd.).
Adsorption studies
Each of the synthesized adsorbents was transferred to a 50 mL flask with a stopper, containing 50
mL of anionic surfactant dissolved in Mili-Q water.
The initial concentrations of anionic surfactants in
adsorption experiments were less than 2.1 mmol/L.
After stirring for different times at 25 °C, the mixture
was filtered through a Dismic filter (pore size 0.2 mm).
The first 10 mL of filtrate was discarded and the rest
was harvested for analysis by a UV–Vis spectrophotometer (Hitachi U2000 with 1 cm quartz cell) at 212,
222 or 224 nm for benzene sulfonate (BS), p-toluene
sulfonate (TS) or 4-octylbenzene sulfonate (OBS),
respectively. Samples with higher anionic surfactant
concentration than CMC (critical micelle concentration) were analyzed after diluting to less than 2.1
mmol/L. The adsorption capacities were calculated
based on the differences of the concentrations of
solutes before and after the experiment according to
Eq. (1) [32]:
qe =
(c 0 − c e )V
W
(1)
where qe is the concentration of the adsorbed solute
(mmol/g), c0 and ce are the initial and final (equilibrium) concentrations of the solute in solution
(mmol/L), V (mL) is the volume of the solution and W
(g) is the mass of the adsorbent.
Adsorption kinetics of anionic surfactants
For the measurement of the time resolved
uptake of anionic surfactant onto adsorbents, 15 ml of
349
S.E. MORADI, J. KHODAVEISY, R.DASHTI: REMOVAL OF ANIONIC SURFACTANTS…
distilled water was mixed with 60 mg of adsorbent in a
500 ml flask for about 10 min. 285 ml of anionic
surfactant solution was quickly introduced into the
flask (keeping the initial concentrations of the resulting solutions at 2.1 mmol/L) and stirred continuously
at 20 °C. Samplings were done by fast filtration at
different time intervals. The concentration of residual
anionic surfactant in the solution was determined and
the adsorption amount qt was calculated according to
Eq. (2) [33]:
qt =
(c 0 − ct )V
W
where qt is the adsorption amount at time t, c0 is the
initial concentration of anionic surfactant solution, ct is
the concentration of anionic surfactant solution at time
t, and V is the volume of anionic surfactants solution
and m is the mass of MC and AMC.
pH point of zero charge
The suspension test of the carbonaceous adsorbent, to provide a quick and reliable way of determining the pH point of zero charge (pHPZC), was carried out using the pH drift method used by Yang et al.
[34], with the modification that sodium chloride was
used as an inert electrolyte. Prior to measurement of
pH drift, the carbonaceous adsorbent was thoroughly
washed with water followed by dilute sodium hydroxide (pH ∼10) to neutralize any free sulfuric acid
that may have remained and finally soaked in HCl for
24 h. After filtration, it was washed with distilled water
till the filtrate was free of chloride and sulfate ions as
detected by AgNO3 and barium sulfate tests. The
“enriched” carbon adsorbent was then air-dried. This
was done to ensure the removal of any potential
effects on pH drift due to dissolution of salts in carbon
adsorbent. The pH of test solutions was adjusted in
0.005 M NaCl in the range between 1.92 and 10.90
using 0.5 M HCl or 0.5 M NaOH. Then, 0.06 g of
carbonaceous adsorbent was added into 20 mL of the
pH adjusted solution in a plastic capped vial and equilibrated for 24 h. The final pH was measured and plotted against the initial pH. The pH at which the curve
crosses the pHinitial = pHfinal line was taken as pHPZC.
RESULT AND DISCUSSION
Characterization
Nitrogen physisorption is the method of choice
for gaining knowledge about mesoporous materials.
This method gives information on the specific surface
area and the pore diameter. Calculating pore diameters of mesoporous materials using the BJH
350
CI&CEQ 19 (3) 347−357 (2013)
method is common. Former studies show that the
application of the BJH theory gives appropriate qualitative results which allow a direct comparison of relative changes between different mesoporous materials.
The nitrogen sorption isotherms of the MC and
AMC have a typical type IV shape. Interestingly, the
pore size distributions are essentially the same as
before amine functionalization. The adsorption uptakes
at relative pressure close to p/p0 = 0 are identical.
However, the total uptakes are slightly different,
(2) shown in
decreasing with the surface modification. As
Table 1, the decreases in the specific surface areas
and pore volumes are 4.2 and 8.6%, respectively.
From the nitrogen sorption isotherms (Figure 1) of
mesoporous carbon type carbons before and after
amine functionalization, it can be seen that after
amine functionalization the obtained carbons still
have type IV isotherms, indicating that mesoporousity
is still preserved. However, the amine functionalization leads to a decrease in the total uptake of the
amine functionalized carbons, which reflects the
decrease of the total pore volume resulting from
amine functionalization. Interestingly, the amine functionalized carbons essentially keep the bimodal pore
size distribution, which is characteristic of the parent
MC. The textural parameters listed in Table 1 clearly
confirm the structural changes of amine functionalized
MC. The variations of the surface area and pore
volume are especially significant with the increase in
the acid concentration.
Table 1. Textural parameters of the MC and AMC employed in
this study
Adsorbent
d Spacing, nm
ABET / m2 g-1 Vp / cm3 g-1
MC
3.4
1010.5
0.69
AMC
3.1
967.4
0.63
In order to check the structural degradation,
XRD data of AMC and MC were obtained on a Philips
1830 diffractometer using CuKα radiation of wavelength 0.154 nm. Figure 2 shows the XRD peaks of
the samples. The XRD patterns of AMC showed three
diffraction peaks that can be indexed to (110), (210),
and (220) in the 2θ range from 0.8 to 10°, representing well-ordered cubic pores [20]. The XRD patterns of MC carbon and AMC (Figure 2) show wellresolved reflections indicating that MC carbon nicely
maintains it original structure even after amine functionalization. For AMC sample, the cubic structure of
MC was maintained well; but, the XRD reflections
become less pronounced that might be due to the
partial damage of the mesoporous (cubic) structure or
S.E. MORADI, J. KHODAVEISY, R.DASHTI: REMOVAL OF ANIONIC SURFACTANTS…
CI&CEQ 19 (3) 347−357 (2013)
600
MC
Volume Adsorbed (cm3/g) STP
500
AMC
400
Pore Volume, (cm3/g)
300
200
100
0.4
0.3
0.2
0.1
0
0
5
10
Pore Diameter, (nm)
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Relative Pressure (P/Po)
Fig. 1. Adsorption-desorption isotherms of nitrogen at 77 K on MC and AMC. The insert shows the BJH pore size distribution calculated
from the desorption branch of the isotherm.
6
5
MC
AMC
Intensity
4
3
2
1
0
0
1
2
3
4
2θ
5
6
7
8
9
Fig. 2. XRD Pattern of AMC and MC.
due to the decreased contrast between walls and
pores because of the cleavage of the carbon species
from the pore walls.
The FT-IR technique was used to monitor
changes on the surface of the ordered mesoporous
carbon and the content of the introduced nitrogen-containing functional surface group. Figure 3 shows the
FT-IR spectra of MC and as treated AMC samples.
A broad band at around 3450 cm −1 was
observed in the MC sample. It was mainly caused by
the O–H stretching vibration of the adsorbed water
molecules, which also had a bending vibration mode
corresponding to the band recorded at 1600 cm−1.
Bands at 1600–1745 cm−1 denoted the absorption of
stretching and bending vibration modes of –COOH on
the surface of mesoporous carbon materials. In addition, the broad band that appeared at 1150 cm−1 was
caused by the stretching vibration of C–O bonds. The
AMC sample FT-IR showed that the surface amino
group was produced after chemical modification, IR
absorption bands for C-N bond stretching were
detected at 1170-1240 cm-1, broad NH2 stretching at
3250–3450 cm-1, and an N-H deformation peak at
1640–1560 cm-1.
Table 2 shows the results of elemental analysis
performed to check if amino groups have really been
introduced to the mesoporous carbon adsorbents.
Since 2.1% of nitrogen was detected for AMC though
no nitrogen was detected for MC, the results in the
351
S.E. MORADI, J. KHODAVEISY, R.DASHTI: REMOVAL OF ANIONIC SURFACTANTS…
CI&CEQ 19 (3) 347−357 (2013)
Fig. 3. FT-IR Spectra of MC and AMC samples.
table demonstrate the presence of nitrogen-containing functional groups.
Table 2. Elemental analyses of mesoporous carbons
Sample
%C
%H
%N
MC
93.5
0.49
0
AMC
89.8
1.48
2.1
pH of point of zero charge for AMC and MC
The pHPZC of any adsorbent is a very important
characteristic that determines the pH at which the
surface has net electrical neutrality. In this work the
pH drift method was employed to determine this
parameter. It was noted that despite extensive washing of the amino modified mesoporous carbon, the
final pH after equilibration decreased rapidly as shown
in Figure 4. The curve obtained cuts the pHinitial =
12
AMC
MC
10
pHzpc(MC) =
5.34
pHzpc(AMC) = 4.05
Final pH
8
6
4
2
0
0
2
4
6
Initial pH
8
10
12
Fig. 4. Suspension test for determining the pH of point of zero charge of mesoporous carbon adsorbents by pH drift method.
352
S.E. MORADI, J. KHODAVEISY, R.DASHTI: REMOVAL OF ANIONIC SURFACTANTS…
= pHfinal line at 4.05 (and 5.34 for MC). The importance of this value is that one can readily expect that
removal of anionic surfactants is not feasible below
this pH because the net positively charged surface is
unlikely to attract the cations. This intrinsic acidity of
the carbonaceous material is due to the treatment
with concentrated sulfuric acid and could not be
removed upon thorough washing with distilled water.
CI&CEQ 19 (3) 347−357 (2013)
process, the adsorption of benzene sulfonate on carbonaceous adsorbent was studied as a function of
contact time and the results are shown in Figure 5. It
is seen that the rate of uptake of the surfactant is
rapid in the beginning and 50% adsorption is completed within 100 min. Figure 5 also indicates that the
time required for equilibrium adsorption is 200 min. In
order to be confident about equilibrium, the equilibration period was kept 300 min [35]. The effect of
concentration on the equilibration time was also
investigated as a function of initial surfactant concentration and the results are shown in Figure 6 (on
Effect of contact time and concentration
In order to establish equilibration time for maximum uptake and to know the kinetics of adsorption
2
Amount adsorbed (mmol.gr-1)
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0
100
200
300
400
500
600
700
Contact time(min)
Fig. 5. Effect of contact time on removal of anionic surfactant (benzene sulfonate = 2.1 mmol/L, agitation speed = 150 rpm, adsorbent
dosage = 0.2 g/l, room temperature = 25 °C).
2
200 ppm
100 ppm
50 ppm
25 ppm
Amount adsorbed (mmol gr-1)
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0
100
200
300
400
500
600
700
Contact time (min)
Fig. 6. Effect of initial concentration on removal of benzene sulfonate (agitation speed = 150 rpm,
adsorbent dosage = 0.2 g/l, room temperature = 25 °C).
353
S.E. MORADI, J. KHODAVEISY, R.DASHTI: REMOVAL OF ANIONIC SURFACTANTS…
zene sulfonate adsorbed (mmol g−1) at equilibrium
and at any time. The equilibrium adsorption capacity
(qe), and the second order constants (k2) can be
determined experimentally from the slope and intercept of plot t/q versus t. The calculated qe, k2 and the
corresponding linear regression correlation coefficient
values are summarized in Table 3. R2 value is greater
than 0.99. As seen from Table 3, the values of qe
calculated from pseudo-second order kinetics almost
agreed well with the experimental values of qe. These
results indicate that the adsorption of benzene sulfonate on the amino modified mesoporous carbon follows pseudo-second order kinetics.
AMC). At lower initial surfactant concentrations, sufficient adsorption sites are available for the sorption of
benzene sulfonate. Conversely, the numbers of benzene sulfonate at higher initial concentrations are
relatively more as compared to the available adsorption sites. Hence, the percentage of benzene sulfonate removal correlates inversely with the initial surfactant concentration.
Kinetics of adsorption
The study of adsorption kinetics is significant as
it provides valuable insights into the reaction pathways and the mechanism of the reactions. Any
adsorption process is normally controlled by the three
diffusion steps: i) transport of the solute from bulk
solution to the film surrounding the adsorbent, ii) from
the film to the adsorbent surface and iii) from the
surface to the internal sites followed by binding of the
surfactants to the active sites. The slowest steps
determine the overall rate of the adsorption process
and usually it is thought that the step (ii) leads to
surface adsorption and the step (iii) leads to intraparticle adsorption [36]. Several kinetic models are
used to explain the mechanism of the adsorption
processes. A simple pseudo-first order equation is
given by the Lagergren equation [36]:
log(q e − q ) = log q e −
kit
Effect of temperature on adsorption of anionic
surfactants on MC
The amount of benzene sulfonate adsorbed on
mesoporous carbon depends on temperature and the
chemical structure. The activation energy is the amount
of energy required to ensure that a reaction happens.
According to the Arrhenius equation:
log k = -Ea/(2.303RT)+const.
where qe and q are the amounts of benzene sulfonate
adsorbed (mmol/g) at equilibrium time and any time t,
respectively, and k1 is the rate constant of adsorption
(min−1). A plot of log (qe−q) versus t gives a straight
line for first order adsorption kinetics, which allows
computation of the rate constant k1. The calculated qe,
k1 and the corresponding linear regression correlation
coefficient values are summarized in Table 3. As seen
from Table 3, the calculated linear regression correlation coefficient was relatively small (R2 = 0.984) and
the experimental qe values did not agree with the
calculated values obtained from the linear plots.
The pseudo-second order equation based on
equilibrium adsorption is expressed as [36]:
t
1
t
=
+
2
q k 2q e q e
(5)
where k is the rate coefficient, Ea is the activation
energy, R (8.314 J mol−1 K−1) is the universal gas
constant, and T is the temperature (K), we found the
activated energy for benzene sulfonate.
After linearization of the Arrhenius equation, we
achieved the values of the activated energy for benzene sulfonate 15.03 J mol-1. According to the results,
the amount of benzene sulfonate adsorbed on the
mesoporous carbon increased with an increase in
temperature. As it is widely agreed, the adsorption is
a spontaneous exothermic process but according to
the results, anionic surfactant adsorption increases
with the increase in temperature. It has been suggested that in aqueous solution the anionic surfactant
forms a hydrated complex containing up to six water
molecules attached to each unit and therefore a
decrease in surfactant–water hydrogen bonding with
increase in temperature can explain the higher
adsorption capacity.
(3)
2.303
CI&CEQ 19 (3) 347−357 (2013)
Effect of surface modification
In order to evaluate the efficacy of the prepared
adsorbents, the equilibrium adsorption of the anionic
surfactants was studied as a function of equilibrium
concentration. The adsorption isotherms of benzene
(4)
where k2 is the pseudo-second order rate constant (g
mmol−1 min−1), qe and q represent the amount of ben-
Table 3. Pseudo-first order and pseudo-second order constants for the removal of benzene sulfonate by AMC
Pseudo-first order constants
qe,exp / mmol g
1.48
354
–1
qe,cal / mmol g
1.01
–1
Pseudo-second order constants
–1
k1 / g mmol min
0.024
–1
2
R
qe,cal / mmol g–1
k2 / g mmol–1 min–1
R2
0.984
1.45
0.026
0.996
S.E. MORADI, J. KHODAVEISY, R.DASHTI: REMOVAL OF ANIONIC SURFACTANTS…
sulfonate (BS), p-toluene sulfonate (TS) and 4-octylbenzene sulfonate (OBS) on AMC and MC are shown
in Figures 7 and 8. It is seen that order of adsorption
in terms of amount adsorbed (mmol/g) on different
adsorbents is: AMC > MC.
It is interesting that the amount of anionic surfactants adsorbed increases with increasing solution
pH for both samples. Further, AMC registers higher
anionic surfactants adsorption capacity (2.1, 1.7 and
1.4 mmol/g for benzene sulfonate (BS), p-toluene sulfonate (TS) and 4-octylbenzene sulfonate (OBS))
than the untreated mesoporous carbon (1.1, 0.87 and
0.71 mmol/g for benzene sulfonate (BS), p-toluene
CI&CEQ 19 (3) 347−357 (2013)
sulfonate (TS) and 4-octylbenzene sulfonate (OBS)).
The higher adsorption capacity of AMC can be
explained by the undoubtedly increasing interaction
as a result of the amino functional group in AMC. It
means that a new and strong interaction between the
anionic surfactant and cationic surface of the adsorbent is introduced [37].
Langmuir and Freundlich isotherms
In order to indicate the sorption behavior and to
estimate the adsorption capacity, adsorption isotherms were studied. The adsorption processes of
benzene sulfonate were tested with Langmuir and
1.2
1
Amount adsorbed, (mmol/gr)
OBS
TS
BS
0.8
0.6
0.4
0.2
0
0
0.2
0.4
0.6
0.8
1
Equilibrium concentration, (mmol/lit)
1.2
1.4
1.6
Fig. 7. Adsorption isotherm for benzene sulfonate (BS), p-toluene sulfonate (TS) and 4-octylbenzene sulfonate (OBS) on MC (contact
time = 300 min, agitation speed = 150 rpm, adsorbent dosage = 0.2 g/l, room temperature = 25 °C).
Amount adsorbed, (mmol/gr)
2.5
OBS
TS
BS
2
1.5
1
0.5
0
0
0.2
0.4
0.6
0.8
1
Equilibrium concentration, (mmol/lit)
1.2
1.4
1.6
Fig. 8. Adsorption isotherm for benzene sulfonate (BS), p-toluene sulfonate (TS) and 4-octylbenzene sulfonate (OBS) on AMC (contact
time = 300 min, agitation speed = 150 rpm, adsorbent dosage = 0.2 g/l, room temperature = 25 °C).
355
S.E. MORADI, J. KHODAVEISY, R.DASHTI: REMOVAL OF ANIONIC SURFACTANTS…
Freundlich isotherm models. Two commonly used
empirical adsorption models, Freundlich and Langmuir, which correspond to heterogeneous and homogeneous adsorbent surfaces, respectively, were employed in this study. The Freundlich model is given by:
ln q e = ln K f +
1
n
ln c e
(6)
where Kf and n are the Freundlich constants related
to adsorption capacity and intensity, respectively. In
the second model, the Langmuir equation assumes
maximum adsorption occurs when the surface is
covered by the adsorbate, because the number of
identical sites on the surface is finite. The Langmuir
equation is given as:
ce
1
1
=
+
c
q e q mb q m
(7)
where qe (mmol/g) is the amount adsorbed at equilibrium concentration ce (mmol/L), qm (mmom/g) is the
Langmuir constant representing maximum monolayer
capacity and b is the Langmuir constant related to
energy of adsorption.
The isotherm data was linearized using the
Langmuir equation. The regression constants are
shown in Table 4. The high value of correlation coefficient indicated good agreement between the parameters. The same data was also fitted by the Freundlich equation (Table 4). The value of correlation coefficients showed that the data conform well to the
Langmuir equation.
CI&CEQ 19 (3) 347−357 (2013)
The kinetic data was best fitted to the pseudo-second
order model and adsorption isotherm was fitted well
by the Langmuir model. Isotherm data at 25 °C were
fitted by the Langmuir model better than the Freundlich model.
Acknowledgements
The authors thank The Research Council at the
Azad University for financial support.
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Adsorbent
Langmuir
Freundlich
qm / mmol g–1
b / L mmol–1
R2
KF / mmol g–1
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MC
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S.E. MORADI1
J. KHODAVEISY2
R.DASHTI2
UKLANJANJE ANJONSKIH SURFAKTANATA
SORPCIJOM NA AMINOVANOM MEZOPOROZNOM
UGLJENIKU
1
Young Researchers Club, Islamic
Azad University - Sari Branch, Iran
2
Young Researchers Club, Islamic
Azad University-Booshehr Branch, Iran
NAUČNI RAD
Direktno i indirektno oslobađanje velikih količina surfaktanata u životnu sredinu može
dovesti do ozbiljnih zdravstvenih i ekoloških problema. Stoga je neophodno ukloniti surfaktante iz vode pre ispuštanja u životnu sredinu ili upotrebu. U ovom radu je proučavano
uklanjanje anjonskih surfaktanta, benzen-sulfonata (BS), p-toluensulfonata (TS) i 4-oktilbenzen-sulfonata (OBS), iz vode adsorpcijom na amino modifikovanom mezoporoznom
ugljeniku (AMC). Hemija AMC površine i osobine same teksture su proučavane adsorpcijom azota, XRD i FTIR analizom. Eksperimenti su izvođeni u šaržnom režimu pri različitim operativnim uslovima, kao što su kontaktno vreme, pH rastvora, količina adsorbenta i temperatura. Na kraju, adsorpcione izoterme anjonskih surfaktanata na mezoporoznom ugljeniku opisane su Langmuir-ovim modelom. AMC je pokazao veći adsorpcioni kapacitet anjonskog surfaktanta od netretiranog mezoporoznog ugljenika, što se
može objasniti jakim interakcijama između anjonskog surfaktanta i katjonske površine
adsorbensa.
Ključne reči: aminacija; mezoporozni ugljenik; anjonski surfaktant; Langmuir-ov
model.
357
Available on line at
Association of the Chemical Engineers of Serbia AChE
www.ache.org.rs/CICEQ
Chemical Industry & Chemical Engineering Quarterly 19 (3) 359−368 (2013)
XIAO-QIN XIONG
KE-JING HUANG
CHUN-XUAN XU
CHUN-XUE JIN
QIU-GE ZHAI
College of Chemistry and Chemical
Engineering, Xinyang Normal
University, Henan, Xinyang, China
SCIENTIFIC PAPER
UDC 544.6:547.436:66.012.1
DOI 10.2298/CICEQ120325070X
CI&CEQ
GLASSY CARBON ELECTRODE MODIFIED
WITH POLY(TAURINE)/TIO2-GRAPHENE
COMPOSITE FILM FOR DETERMINATION OF
ACETAMINOPHEN AND CAFFEINE
A novel electrochemical sensor poly(taurine)/TiO2-graphene nanocomposite
modified glassy carbon electrode (PT/TiO2-Gr/GCE) was fabricated. This sensor was based on an electrochemically polymerized taurine layer on a TiO2-graphene modified glassy carbon electrode. The electrochemical behavior of acetaminophen and caffeine at the modified electrode was studied by cyclic voltammetry and differential pulse voltammetry. The results showed that the oxidation peak currents of acetaminophen and caffeine were linear with their concentrations in the range of 1×10-7-9×10-5 M and 2.5×10-5-2×10-4 M, respectively. The detection limits of acetaminophen and caffeine were 3.4×10-8 M and
5.0×10-7 M, respectively (S/N = 3). This modified electrode showed good sensitivity and stability, which has promising potential applications in electrochemical sensors and biosensors design.
Keywords: taurine; TiO2-graphene nanocomposite; acetaminophen; caffeine; electropolymerization.
Acetaminophen (N-acetyl-p-aminophenol or
paracetamol), an antipyretic and analgesic drug, is
widely used in the world. It is used mainly as an
effective medicine for the relief pain and reduction of
fever and a suitable alternative for patients who are
sensitive to aspirin [1-5]. Caffeine (3,7-dihydro-1,3,7-trimethyl-1H-purine-2,6-dione) is a natural alkaloid
N-methyl derivative of xanthine, and is extensively
present in foods such as coffee, tea, cola nuts, yerbamate, guarana berries and cacao bean. Caffeine
ingestion exerts many physiological effects, such as
stimulation of the central nervous system, diuresis
and gastric acid secretion [2]. The unique properties
of caffeine are also applied in analgesic preparations.
Therefore, acetaminophen and caffeine often occur
together in analgesic pharmaceutical formulations.
Generally, limited use of acetaminophen and
caffeine does not exhibit any harmful side effects.
However, overdosed ingestions of acetaminophen
lead to the accumulation of toxic metabolites, which
Correspondence: K-J. Huang, College of Chemistry and Chemical Engineering, Xinyang Normal University, Henan, Xinyang
464000, China.
E-mail: kejinghuang@163.com
Paper received: 25 March, 2012
Paper revised: 3 July, 2012
Paper accepted: 3 July, 2012
may cause severe and sometimes fatal heptatotoxicity and nephrotoxicity, which in some cases
associate with renal failure [4-7]. Caffeine is considered to be a risk factor for cardiovascular diseases
and may have behavior effects such as depression
and hyperactivity. Therefore, in analgesic preparation
ca. 200 mg per day of dosage is generally recommended [8]. It is vital to establish a simple, sensitive,
accurate methodology for simultaneous determination
of acetaminophen and caffeine. Some methods including titrimetry [9], spectrophotometry [10-12], liquid
chromatography [13-15] and electrochemistry [3,4,6,
16-22] have been developed for the individual estimation of two molecules. Only a few methods have
been reported for the determination of acetaminophen
and caffeine. Lau et al. used perchloric acid-methanol
(1:1) as the solvent and electrolyte to improve the
sensitivity and peak separation of acetaminophen and
caffeine. Obviously, it is difficult to make quantitative
determination due to the addition of easily evaporating methanol [23]. Zen and Ting used a nafion/ruthenium oxide pyrochlore chemically modified electrode
for the simultaneous determination of acetaminophen
and caffeine in drug formulation by square-wave voltammetry. The experiments were completed in 0.05 M
perchloric acid, high cost reagent with controlled sale
[8]. Fatibello-Filho et al. used a boron-doped diamond
359
X.-Q. XIONG et al.: GLASSY CARBON ELECTRODE MODIFIED WITH POLY(TAURINE)/TIO2-…
(BDD) electrode for acetaminophen and caffeine
simultaneous determination. However, prior to the
experiments, this electrode was cathodically pretreated in a 0.5 mol L-1 H2SO4 solution [2]. Sanghavi
et al. used an in situ surfactant-modified multi-walled
carbon nanotube paste electrode for simultaneous
determination of acetaminophen and caffeine. An
accumulation potential of -0.7 V and an accumulation
duration time of 300 s were used for stripping voltammetric analysis [24].
Recently, graphene (Gr) was found to be an
ideal two-dimensional (2D) catalyst support to anchor
metal and semiconductor catalyst nanoparticles
because of its unique two-dimensional geometric
structure, large surface area, and high mobility of
charge carriers [25]. Being a famous semiconductor,
TiO2 has received much attention due to its nontoxicity, long-term stability, low cost and mutifunctions
[26]. Most recently, we reported the TiO2-Gr nanocomposite prepared by hydrothermal method using
graphene as templates to immobilized TiO2 nanoparticles. The as-prepared TiO2-Gr exhibited remarkable
electrocatalytic activity toward dopamine oxidation
[23]. Taurine is a well-known dissociated amino acid,
which exhibits important physiological functions and
pharmacological characteristics. It has been widely
used as a food nutrition enhancer and common drug.
Taurine possesses electron-rich N atoms and high
electron density of sulfonic groups. Hence, the poly(taurine) (PT) film is negatively charged and is propitious to adsorb acetaminophen and caffeine from the
solution. PT modified electrodes have been reported
and have shown good electrochemical performance
[27, 28]. In this work, we report about the fabrication
of PT modified electrode by electrochemical polymerization of taurine on the TiO2-Gr-modified glassy carbon electrode (PT/TiO2-Gr/GCE) and the application
of the modified electrodes for simultaneous detection
of acetaminophen and caffeine.
EXPERIMENTAL
Chemicals and materials
Graphite powder (320 mesh, spectrum pure)
was purchased from Sinopharm Chemical Reagent
Co., Ltd., China. Titanium isopropoxide (Ti(OiPr)4)
was obtained from Aladdin Chemistry Co., Ltd.,
China. Acetaminophen and caffeine were purchased
from Alfa Aesar and used without further purification.
Taurine was purchased from Shanghai No. 1 Chemical Company (Shanghai, China). The phosphate
buffer solution (PBS) was prepared using Na2HPO4
360
CI&CEQ 19 (3) 359−368 (2013)
and NaH2PO4. Double distilled water was used to prepare all solutions used in the present work.
Apparatus
All electrochemical experiments were carried
out with a CHI660D electrochemical workstation (CH
Instruments, Shanghai). A conventional three-electrode system was used for all electrochemical experiments, which consisted of a platinum wire as counter
electrode, an Ag/AgCl/3M KCl as reference electrode,
and a bare or modified glassy carbon electrode (3mm
diameter) as working electrode. All pH measurements
were measured with a PHS-3C digital pH meter
(Shanghai Rex Instrument Factory, Shanghai, China).
A Hitachi S-4800 scanning electron microscope
(SEM) was used.
Preparation of TiO2-graphene nanocomposite
Graphene oxide was synthesized from graphite
powder according to the modified Hummers method
[29,30]. Gr was obtained by the chemical reduction of
a colloidal suspension of exfoliated graphene oxide
sheets in water with hydrazine hydrate [31]. To prepare TiO2-Gr nanocomposite, Gr (50 mg), titanium
isopropoxide (0.2 mL) and H2SO4 (1 M, 2 mL) was
firstly added into a 25-mL Teflon-sealed autoclave.
This resultant mixture was ultrasonicated for 10 min,
and then the autoclave was kept in oven for 24 h at
the temperature of 170 °C. Finally, black powder of
TiO2-Gr nanocomposite was obtained by filtration,
rinsed thoroughly with deionized water and methanol,
and dried in vacuum [25].
Preparation of the modified electrodes
The as-prepared TiO2-Gr nanocomposite (1.5
mg) was dispersed in DMF (4.0 mL) to form a homogenous suspension. Before modification, glass carbon electrode (GCE) was polished to a mirror-like
with 0.3 and 0.05 µM of alumina slurry, and then
washed successively with ultrapure water, anhydrous
alcohol and ultrapure water in an ultrasonic bath and
dried in N2 flow. The TiO2-Gr film-modified GCE
(TiO2-Gr/GCE) was prepared by dropping 6 µL of the
resultant suspension on the cleaned GCE, and dried
at room temperature.
The PT/GCE and PT/TiO2-Gr/GCE were prepared as follows. Cyclic voltammetry (CV) was used
to form polymerization film on the bare GCE and
TiO2-Gr/GCE, respectively. The polymeric film was
deposited by cyclic sweeping from -1.5 to 2.0 V at 100
mVs-1 for 10 cycles in PBS (pH 7.0) containing
2.0×10-3 M taurine. The obtained electrodes were
individually noted as PT/GCE and PT/TiO2-Gr/GCE.
X.-Q. XIONG et al.: GLASSY CARBON ELECTRODE MODIFIED WITH POLY(TAURINE)/TIO2-…
Serum sample preparation
Human blood serum samples were obtained
from healthy volunteers. The samples were centrifuged at 4000 rpm for 30 min at room temperature.
Then 1.2 mL of acetonitrile was added to remove
serum protein, followed by fortification with acetaminophen and caffeine. After vortexing for 1 min, the
mixture was centrifuged for 10 min at 10000 rpm to
remove the serum protein residues. The supernatant
was taken carefully and appropriate volumes of this
supernatant were transferred into the electrochemical
glass cell and diluted up to the volume with the PBS.
RESULTS AND DISCUSSION
Surface morphology of TiO2-graphene and
poly(taurine)/TiO2-graphene composite
The surface morphologies of TiO2-Gr and
PT/TiO2-Gr composite were examined by SEM observation (Figure 1). In Figure 1A, it can be seen that
TiO2 was formed in a highly faceted morphology on
the substrates of Gr with ca. 20-30 nm diameter for
the clusters. As shown in the SEM images, the asprepared TiO2-Gr nanocomposite exhibited considerable edge plane defect structures. These edge plane
defects have shown to be essentially responsible for
the high electron transfer kinetics and the electrocatalytic activity of Gr, which contributed significantly to
the electrochemical property of the present TiO2-Gr
nanocomposite as well. Figure 1B depicts the SEM
image of the PT/TiO2-Gr composite, showing that a
layer of PT was formed on the TiO2-Gr surface.
The electropolymerization of taurine
at the TiO2-graphene/GCE
In the previous reports, repeated cyclic voltammetry was used for the electrochemical formation of
PT film. The potential scan range was the most
CI&CEQ 19 (3) 359−368 (2013)
important factor. If the positive value for polymerization was below 1.6 V or if the negative one was above
-0.8 V, no polymer reaction occurred [26]. Therefore,
we selected the potential range of -1.5 and 2.0 V as
the electropolymerization potential window in this work.
Figure 2 shows CVs of electrochemical polymerization of taurine on the TiO2-Gr/GCE. One obvious
reduction peak was observed at -0.7 V. An increase in
cycle number results in the enhancement of the peak
currents and a slight shift of potential peak, which was
reflecting the continuous growth of the film. It could be
observed that the film growth was faster for the first
four cycles than for the other cycles. After modification, a shiny and light green color was found on the
electrode surface. These facts indicated taurine was
deposited on the surface of TiO2-Gr film modified
GCE by electropolymerization. The inset of Figure 2
shows CVs of electrochemical polymerization of taurine on the GCE, and a similar phenomenon was
obtained.
Effect of different electrodes
In the present study, the electrochemical
behavior of the mixture containing acetaminophen
and caffeine on the aforementioned electrodes (bare
GCE, TiO2-Gr/GCE, PT/GCE, PT/TiO2-Gr/GCE) was
investigated using the CV. Figure 3 depicts CVs
curves of the acetaminophen and caffeine (0.1 mM) in
PBS (0.1 M, pH 7.0) at a scan rate of 100 mVs-1. A
well shaped oxidation peak and a poorly defined
reduction peak on the bare GCE was observed (curve
a). The height of the reduction peak was lower than
that of the oxidation peak. For caffeine, the oxidation
peak was characterized by an extraordinarily asymmetric shape and no obvious reduction peak was
observed on the reverse scan, indicating that the oxidation was irreversible. The oxidation peak potentials
of acetaminophen and caffeine at bare GCE are 461
(A)
(B)
Figure 1. SEM of TiO2-Gr (A) and PT/TiO2-Gr (B).
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100
CI&CEQ 19 (3) 359−368 (2013)
10
0
100
I / µA
I / µA
1
-100
0
-100
-200
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
E/V
-200
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
E/V
Figure 2. Cyclic voltammograms for the polymerization of taurine on the TiO2-Gr/GCE. Inset: cyclic voltammograms for the
polymerization of taurine on bare GCE. Scan rate of 100 mV s-1. The supporting electrolyte: 0.1 M phosphate buffer (pH 7.0).
40
20
I / μA
0
-20
-40
c b
-60
a
d
-80
-100
0.0
0.3
0.6
0.9
1.2
1.5
E/V
Figure 3. Cyclic voltammetric curves of 110 µM acetaminophen and 320 µM caffeine in PBS (pH 7.0) on the different electrode: a) bare
GCE, b) TiO2-Gr/GCE, c) PT/GCE and d) PT/TiO2-Gr/GCE.
and 1433 mV, respectively. Compared to bare GCE,
the oxidation peak potential of acetaminophen at the
PT/GCE (curve c) shifted 23 mV negatively, and the
peak current decreased slightly. However, caffeine
showed the oxidation peak current increased slightly
without the change of peak potential. To TiO2-Gr/
/GCE, acetaminophen and caffeine demonstrated
broad oxidation peaks at 539 and 1476 mV, respectively. The charging current was obviously larger than
that at both the above electrodes (curve b). Also, the
peak current of acetaminophen enhanced slightly.
The highest improvement of the oxidation peak currents of acetaminophen and caffeine was obtained at
the PT/TiO2-Gr/GCE (curve d). These phenomena
indicated that the enhancement effect may be due to
the synergetic effect of PT and TiO2-Gr. The PT film
362
might facilitate the adsorption of acetaminophen and
caffeine from the solution to the modified electrode
surface through physical adsorption by the improvement of area of the modified electrode. Moreover, the
coarseness of the modified electrode surface also
contributed to this.
Effect of scan rate
The effect of scan rate was also studied at the
PT/TiO2-Gr/GCE. Figure 4 showed that the oxidation
peak shifted to a more positive value for both compounds, and the reduction peak of acetaminophen
shifted to more negative values with increasing scan
rates that had concurrent increases in current. For
acetaminophen, the plot of the anodic peak current
(ip) vs. the square root of scan rate showed excellent
X.-Q. XIONG et al.: GLASSY CARBON ELECTRODE MODIFIED WITH POLY(TAURINE)/TIO2-…
CI&CEQ 19 (3) 359−368 (2013)
30
I / µA
0
a
-30
-30
I / µA
-40
-60
i
ACOP
-50
-60
-70
-90
CF
-80
9
10
11
12
13
14
15
16
-1 1/2
(Scan rate / mV )
0.0
0.3
0.6
0.9
E/V
1.2
1.5
Figure 4. Cyclic voltammetric response of the PT/TiO2-Gr/GCE to 70 µM acetaminophen and 210 µM caffeine in 0.1 M BPS (pH 7.0) at
various scan rates (a-r): 90, 110, 130, 150, 170, 190, 210, 230 and 250 mV s-1. Inset: peak current vs. v1/2.
linearity over the range of 90-250 mV s-1, the corresponding equation was: ip (μA) = -3.38(v / mV s–1)1/2 +
+ 5.927 (R = 0.999) (inset a of Figure 4). Similarly, as
shown in inset to Figure 4, the oxidation peaks currents of caffeine increased linearly with the increase of
square root of scan rate, the corresponding equation
was: ip (μA) = -4.658(v / mV s–1)1/2 - 4.637 (R =
= 0.999). This revealed that the oxidation processes
of acetaminophen and caffeine on the surface of PT/
/TiO2-Gr/GCE were under diffusion control.
Effects of supporting electrolyte
The electrode reaction can be affected by the
buffer solution. The effect of different electrolyte on
the current responses was investigated. Some electrolytes including KHP-NaOH, NH4Cl, NaH2PO4Na2HPO4, BR, NaNO3, KCl and NH3-NH4Cl (each 0.1
M) were studied. The results showed that high current
peaks and good peak shape were obtained in phosphate buffer. Therefore, this solution was applied in
the subsequent studies.
Effect of pH
The effect of varying pH of buffer solution on the
electrochemical behavior of acetaminophen and caffeine at PT/TiO2-Gr/GCE was performed using CV in
0.1 M PBS. Figure 5 depicts the response of peak
current and potential of acetaminophen and caffeine
to pH. The anodic and cathodic peak potentials were
shifted negatively when the solution pH was increased
(Figure 5D). The anodic peak current of acetaminophen increased from pH 3.0 to 7.0 and reached the
maximum at pH 7.0, and then decreased again with
higher pH value (Figures 5A and 5C). The anodic
peak current of caffeine increased from pH 3.0 to 7.0
and kept almost unchanged in the pH range of 7.0-9.0
(Figure 5B). To obtain the high response signal for
acetaminophen and caffeine, the solution of pH 7.0
was used for the optimal supporting electrolyte.
Effect of TiO2-graphene amount
The effect of TiO2-Gr amount was investigated.
When the amount of TiO2-Gr suspension (0.375 mg
mL-1) increased from 0 to 6 µL, the oxidation peak
current of acetaminophen and caffeine increased
notably. However, when it exceeded 6 µL, the oxidation peak currents conversely showed gradual decline. Therefore, 6 µL of TiO2-Gr suspension was
selected for the fabrication of the electrochemical
sensor in this work.
Simultaneous determination of acetaminophen and
caffeine
Under the optimal experiment conditions, the
simultaneous determination of acetaminophen and
caffeine was carried out at PT/TiO2-Gr/GCE. The
experiment was performed by changing the equal
concentrations of acetaminophen and caffeine over
the range from 5×10-7 to 1×10-4 M. The differential
pulse voltammetric results (Figure 6) showed two
well-distinguished anodic peaks at potentials of 396
and 1372 mV, corresponding to the oxidation for acetaminophen and caffeine, respectively. The peak current values were proportional to the concentrations of
acetaminophen and caffeine in the mixture. The insert
of Figure 6 showed the relationship between the
anodic currents and the concentrations of acetaminophen (curve a) and caffeine (curve b). The oxidation
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40
10
A
20
-20
I / µA
0
I / µA
CI&CEQ 19 (3) 359−368 (2013)
-20
-40
B
-50
-80
-60
a
f
g
a
-110
-80
-100
0.0
-40
0.3
0.6
0.9
1.2
0.9
1.5
1.0
1.1
E/V
1.2
1.3
1.4
1.5
E/V
1.8
C
D
1.5
-50
ACOP
E/V
I / µA
1.6
-60
CF
1.2
0.9
0.6
-70
CF
ACOP
0.3
-80
0.0
3
4
5
6
pH
7
8
9
10
3
4
5
6
pH
7
8
9
10
Figure 5. A) Cyclic voltammograms of 160 µM of acetaminophen at PT/TiO2-Gr/GCE with different pH values of PBS (0.1 M) (a-f): pH 3,
4, 5, 7, 8 and 9; B) cyclic voltammograms of 390 µM caffeine at PT/TiO2-Gr/GCE with different solution pH values (a-f): pH 3, 4, 5, 6, 7,
8 and 9; C) peak current vs. pH value; D) peak potential vs. pH value.
peak current of acetaminophen was proportional to its
concentration over the range from 0.5 to 100 µM,
obeying the following equation: I (µA) = -0.302(C /
/ µM) - 6.143 (R = 0.991). The oxidation peak current
of caffeine was proportional to its concentration over
the range from 0.5 to 100 µM, obeying the following
equation: I (µA) = -0.186(C / µM) + 0.255 (R = 0.994).
The detection limits of acetaminophen and caffeine
were 3.4×10-8 and 5.0×10-7 M, respectively. A comparison of the detection methods are shown in Table 1,
which includes the limit of detection and the linear
range. Table 1 indicates that the proposed sensor
exhibited low detection limit and wide measurement
range. The reason might be as follows: firstly, the
excellent electrical conductivity of Gr enhanced the
charge transport; secondly, the formation of the PT
film increased the adsorb amount of analytes.
Individual determination of acetaminophen and
caffeine
For further investigation of electrochemical response when both substances are present in the solu-
364
tion, the DPV experiments were performed in solutions containing variable concentration of one species
and constant concentration of the other one. The
separate determination of acetaminophen in the concentration range of 1.0×10-7-9.0×10-5 M was accomplished in solutions containing caffeine at the fixed
concentration of 3.0×10-5 M. As shown in Figure 7A,
the peak current of acetaminophen clearly increased
gradually while that of caffeine remained fairly constant, suggesting that the change of acetaminophen
did not have significant influence on the peak currents
and peak potentials of the caffeine. On the other
hand, the separate determination of caffeine in the
concentration range of 2.5×10-5-2.0×10-4 M was
accomplished in solutions containing acetaminophen
at the fixed concentration of 1.0×10-6 M. As shown in
Figure 7B, the peak current of caffeine increased
gradually while that of acetaminophen remained fairly
constant. Furthermore, the peak currents of acetaminophen or caffeine increased linearly with the increase
of concentration in the presence of a constant concentration of the other compound (insert in Figure 7A
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CI&CEQ 19 (3) 359−368 (2013)
0
h
-10
I / μΑ
-40
I / µA
-30
CF
-20
-30
a
ACOP
-40
0
-20
20
40
60
80
100
C / μΜ
-10
0
0.0
0.3
0.6
0.9
1.2
1.5
E/V
Figure 6. Differential pulse voltammograms of PT/TiO2-Gr/GCE in 0.1 M PBS (pH 7.0) containing equal concentrations of
acetaminophen and caffeine: a) 0.5, b) 5, c) 7.5, d) 10, e) 25, f) 50, g) 75 and h) 100 µM. Inset: calibration plots of the oxidation peak
current versus different concentration of acetaminophen and caffeine.
and 7B). The calibration equations were ipa (µA) =
= -0.543(C / µM) - 2.432 (R = 0.990) and ipa(µA) =
= -0.179(C / µM) - 0.654 (R = 0.993) for acetaminophen or caffeine, respectively. The detection limits
were 3.4×10-8 and 5.0×10-7 M, respectively. Hence, it
was confirmed that for the oxidation of acetaminophen and caffeine at PT/TiO2-Gr/GCE, the other component did not give interference to the electrochemical signal.
Interference study
Under the optimized conditions, the influence of
various foreign species on the simultaneous determination of acetaminophen and caffeine (50 µM) was
investigated in PBS (pH 7.0). It was found that the
common ions such as Na+, K+, Fe3+, Cu2+, Al3+, Cl-,
NO3-, H2PO4-, HPO42-, CO32-, and SO42- had almost no
interference with acetaminophen and caffeine detection. As for the common interferences in pharmaceutical samples for the determination of acetaminophen
and caffeine, 10-fold sodium carbonate, saccharin,
citric acid, ascorbic acid, glucose, uric acid had no
obvious interference with the current response of acetaminophen and caffeine (signal change below 5%).
Stability, reproducibility and repeatability
In order to investigate the stability of PT/TiO2Gr/GCE, the reproducibility was tested. Repetitive CV
Table 1. Comparison of electrochemical sensors for acetaminophen (ACOP) and caffeine (CF)
Modified electrode
Linear range, μM
LOD / μM
Reference
Screen-printed carbon electrode
ACOP: 2.5-1000
ACOP : 0.1
[1]
Carbon-doped diamond electrode
ACOP: 0.5-83; CF: 0.5-83
ACOP: 0.49; CF: 0.035
[2]
Palladium nanoclusterspolyfuran/platinum electrode
ACOP: 0.5-100
ACOP: 0.0764
[3]
ZrO2 nanoparticles/carbon paste electrode
ACOP: 1.0-2500
ACOP: 0.912
[4]
ACOP: 0.1-20
ACOP: 0.032
[6]
ACOP: 5-250; CF: 10-250
ACOP: 2.2; CF: 1.2
[8]
ACOP: 1.0-100
ACOP: 0.5
[17]
CF: 5-200
CF: 2.0
[19]
CF: 0.995-10.6
CF: 0.798
[20]
Graphene/GCE
Nafion/ruthenium oxide pyrochlore/GCE
Poly(taurine)/multiwalled carbon nanotube/GCE
Nafion-ruthenium oxide pyrochlore/GCE
Nafion/GCE
Carbon nanotubes/carbon-ceramic electrode
Dowex50wx2 and gold nanoparticles/glassy carbon
paste electrode
In situ surfactant-modified multi-walled carbon nanotube
paste electrode
PT/TiO2-GR/GCE
ACOP: 0.2-100.0
ACOP: 0.12
[21]
ACOP: 0.0334-42.2
ACOP: 0.0047
[22]
ACOP, CF: 0.291-62.7
ACOP: 0.0258; CF: 0.0883
[24]
ACOP, CF: 0.05-100
ACOP: 0.034; CF: 0.5
This work
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-50
0
A
I / µA
-10
-40
j
f
0
-30
-10
-30
0
20
40
60
C / µM
80
100
-40
-20
a
-30
-20
a
I / μΑ
-40
-50
-20
B
-60
-20
I / µA
I / µA
CI&CEQ 19 (3) 359−368 (2013)
-40
30
60
90
120
150
180
210
C / μΜ
-10
0
0
0.0
0.3
0.6
0.9
1.2
1.5
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
E/V
E/V
Figure 7. A) Differential pulse voltammograms of PT/TiO2-Gr/GCE in 0.1M BPS (pH 7.0) containing 30 µM caffeine and different
concentrations of acetaminophen: a) 0.1, b) 1, c) 3, d) 5, e) 7, f) 10, g) 30, h) 50, i) 70 and j) 90 µM. Inset: plot of oxidation peak current
as a function of acetaminophen concentration. B) Differential pulse voltammograms of PT/TiO2-Gr/GCE in 0.1 M BPS (pH 7.0)
containing 1 µM acetaminophen and different concentrations of caffeine: a) 25, b) 50, c) 70, d) 90, e) 100 and f) 200 µM. Inset: plot of
oxidation peak current as a function of caffeine concentrations.
measurements were performed 20 times in 0.1 M
PBS (pH 7.0). The relative standard deviations (RSD)
were 1.81 and 3.17% for acetaminophen (100 µM)
and caffeine (100 µM), respectively. This result suggested that this sensor had a good reproducibility and
did not undergo surface fouling during the voltammetric measurements. The stability of PT/TiO2-Gr/GCE
towards the catalytic oxidation of acetaminophen (100
µM) and caffeine (100 µM) was examined as well.
The CVs of this binary solution were recorded after
this electrochemical sensor has been dipped into PBS
(pH 7.0) for 2 weeks. The anodic current responses of
acetaminophen and caffeine individually decreased
4.25 and 4.83%, indicating that the good stability of
developed sensor. Furthermore, the repeatability
between multiple PT/TiO2-Gr modified glassy carbon
electrodes was carried out by parallel determining of
100 µM acetaminophen and caffeine mixture. The
RSD was 3.29% for 6 independent glassy carbon
electrodes modified with PT/TiO2-Gr.
Analytic application
In order to testify the performance of this modified electrode in real sample analysis, four serum
samples from the hospital affiliated to our university
were examined by the developed electrochemical
sensor and the high-performance liquid chromatography (HPLC) method, respectively. The concentrations of acetaminophen and caffeine were measured
by the standard addition method, and the results
showed that no acetaminophen and caffeine were
found in the four serum samples. To test the reliability
of the measurements, a known amount of acetaminophen and caffeine standard was spiked in the
serum samples, and then analyzed with a standard
addition method. The obtained results were shown in
Table 2. The recoveries were in the range of 95.6% to
103.5%. It was in accordance with the result obtained
by using HPLC, which indicated the developed was
reliable and feasible.
Table 2. Determination of acetaminophen and caffeine in human serum samples
Serum sample
Detected by PT/TiO2-GR/GCE
Detected by HPLC
Added, µM
Found, µM
RSD / %
Recovery,%
Found, µM
RSD / %
ACOP
5
4.86
2.6
97.2
5.11
1.5
CF
10
9.56
2.4
95.6
9.82
1.8
2
ACOP
30
30.72
3.1
102.4
29.1
2.1
CF
50
49.05
2.4
98.1
49.2
1.6
3
ACOP
80
77.36
3.6
96.7
78.6
2.2
CF
120
124.2
1.9
103.5
125.1
2.7
4
ACOP
150
152.4
2.2
101.6
147.3
1.8
CF
200
195.6
1.8
97.8
197.5
2.0
1
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CONCLUSION
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Niaz, S. Mahesar, Spectrochim Acta, A 68 (2007) 747-751
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used for the simultaneous determination of acetaminophen and caffeine. The modified electrode exhibited many desirable properties including excellent
stability, reproducibility, high sensitivity, low detection
limit and satisfactory linear range. Furthermore, its
ease to construct, low cost and no treatment before
use make it feasible to be applied in routine determination.
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H. Filik, I. Sener, S.D. Cekic, E. Kilic, R. Apak, Chem.
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A. Goyal, S. Jain, Acta Pharm. Sci. 49 (2007) 147-151
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P.S. Selvan, R. Gopinath, V.S. Saravanan, N. Gopal, S.
A. Kumar, K. Periyasamy, Asian J. Chem. 19 (2007)
1004-1010
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J.C. Song, J. Yang, J.F. Zeng, J. Tan, L. Zhang, Sens.
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Acknowledgments
This work was supported by the National Natural
Science Foundation of China (20805040), Program
for Science and Technology Innovation Talents in
Universities of Henan Province (2010HASTIT025),
Excellent Youth Foundation of He’nan Scientific Committee (104100510020), and the Foundation of He’nan
Education Committee (2009A150023).
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367
X.-Q. XIONG et al.: GLASSY CARBON ELECTRODE MODIFIED WITH POLY(TAURINE)/TIO2-…
XIAO-QIN XIONG
KE-JING HUANG
CHUN-XUAN XU
CHUN-XUE JIN
QIU-GE ZHAI
College of Chemistry and Chemical
Engineering, Xinyang Normal
University, Henan, Xinyang, China
NAUČNI RAD
CI&CEQ 19 (3) 359−368 (2013)
ELEKTRODA OD STAKLASTOG UGLJENIKA
MODIFIKOVANA POLI(TAURIN)/TIO2-GRAFEN
KOMPOZITNIM FILMOM ZA ODREĐIVANJE
ACETAMINOFENA I KOFEINA
Napravljena je nova elektroda od staklastog ugljenika modifikovana poli(taurin)/TiO2-grafen nanokompozitnim filmom (PT/TiO2-Gr/GCE). Ovaj senzor je zasnovan na elektrohemijskoj polimerizaciji taurinskog sloja na TiO2 grafen modifikovanoj elektrodi od staklastog ugljenika. Elektrohemijsko ponašanje acetaminofena i kafeina na modofikovanim
elektrodama je proučavano cikličnom volatmetrijom i diferencijalnom pulsnom voltametrijom. Rezultati pokazuju da oksidacioni pik struje ima zadovoljavajuću linearnost u opsegu koncentracija od 1×10-7-9×10-5 M za acetaminofen i 2.5×10-5-2×10-4 M za kafein.
Limit detekcije za acetaminofen je 3.4×10-8 M, a za kofein 5.0×10-7 M. Ova modifikovana
elektroda je pokazala dobru osetljivost i stabilnost, pa ima obećavajuću potencijalnu primenu kao dobar elektrohemijski senzor i biosenzor.
Ključne reči: taurin; TiO2-grafen nanokomposit; acetaminofen; Kofein; elektropolimerizacija.
368
Available on line at
Association of the Chemical Engineers of Serbia AChE
www.ache.org.rs/CICEQ
Chemical Industry & Chemical Engineering Quarterly 19 (3) 369−375 (2013)
JELENA Đ. MARKOVIĆ
NATAŠA LJ. LUKIĆ
ALEKSANDAR I. JOKIĆ
BOJANA B. IKONIĆ
JELENA D. ILIĆ
BRANISLAVA G. NIKOLOVSKI
University of Novi Sad, Faculty of
Technology, Novi Sad, Serbia
SCIENTIFIC PAPER
UDC 66.045.1:66.06:5/.6
DOI 10.2298/CICEQ120309071M
CI&CEQ
2D SIMULATION AND ANALYSIS OF FLUID
FLOW BETWEEN TWO SINUSOIDAL
PARALLEL PLATES USING LATTICE
BOLTZMANN METHOD
In order to obtain better heat transfer, it is important to enhance fluid mixing in
heat exchangers. Since there are negative effects when heat exchangers are
operating in the turbulent regime (such as significant pressure drop and
increased size of the pump), it is necessary to apply techniques that would
provide better fluid mixing when heat exchangers are operating in the laminar
regime. Investigations have shown that the use of sinusoidal instead of flat
plates results in this effect. This study is a result of two-dimensional simulation
of fluid flow between two parallel sinusoidal plates. Simulation was done with
the use of modified OpenLB code, based on the lattice Boltzmann method. The
Reynolds number was varied from 200 to 1000, and the space between the
plates was varied from 3 to 5 cm. The results showed that sinusoidal plates
enhance fluid mixing, especially with greater values of Re and smaller space
between the plates, which is in agreement with previous investigations.
Keywords: lattice Boltzmann, fluid flow, sinusoidal plates, plate heat
exchanger, simulation.
In heat exchanger design it is very important to
obtain good fluid mixing, reduce heat transfer resistance, and minimize pressure drop. Good fluid mixing
can be obtained in heat exchangers working in the
turbulent regime, which, on the other hand, has a significant pressure drop as a negative effect. When
operating in the turbulent regime, the pumping cost
increases as the size of the pump increases, which is
often a limiting factor, especially in compact heat
exchangers or in heat exchangers with very viscous
fluids. Enhancement of fluid mixing in laminar regime,
which leads to better heat transfer, is possible to
obtain when chaotic fluid flow is established. Chaotic
advection occurs when pathlines that do not conform
to laminar regime are present in the fluid, and can be
generated in ducts with periodically perturbed geometry in downstream direction.
In order to obtain better heat transfer in plate
heat exchangers, several techniques have been used
so far. One of the most often applied techniques was
Correspondence: J.Đ. Marković, University of Novi Sad, Faculty
of Technology, Bulevar cara Lazara 1, 21000 Novi Sad, Serbia.
E-mail: jmarkovic@tf.uns.ac.rs
Paper received: 9 March, 2012
Paper revised: 27 June, 2012
Paper accepted: 4 July, 2012
the use of wavy plates instead of flat plates [1], and
many investigations showed that use of sinusoidal
instead of flat plates enhances heat transfer without
significant pressure drop [2-7].
The aim of this study was to simulate and
analyze the fluid flow between two parallel sinusoidal
plates with the use of the lattice Boltzmann method
(LBM). In recent years, LBM has developed into an
alternative and promising numerical scheme for simulating fluid flows and modeling physics in fluids. Unlike
conventional numerical schemes based on discretizations of macroscopic continuum equations, the
LBM is based on microscopic and mesoscopic kinetic
equations.
THEORETICAL PART
Lattice Boltzmann Method
The fundamental idea of the LBM is to construct
simplified kinetic models that incorporate the essential physics of microscopic or mesoscopic processes
so that the macroscopic averaged properties obey the
desired macroscopic equations. Even though it is
based on a particle picture, its principal focus is the
averaged macroscopic behavior. The kinetic equation
369
J.Đ. MARKOVIĆ et al.: 2D SIMULATION AND ANALYSIS OF FLUID FLOW…
provides many of the advantages of molecular dynamics, including clear physical pictures, easy implementation of boundary conditions, and fully parallel
algorithms. Because of the availability of very fast and
massively parallel machines, there is a current trend
to use the code that can exploit the intrinsic features
of parallelism. The LBM fulfills these requirements in
a straightforward manner.
The kinetic nature of the LBM introduces three
important features that distinguish it from other numerical methods. First, the convection operator (or
streaming process) of the LBM in phase space (velocity space) is linear. The feature is borrowed from
kinetic theory, and contrasts with the nonlinear convection terms in other approaches that use a macroscopic representations. Simple convection combined
with a relaxation process (or collision operator) allows
the recovery of the nonlinear macroscopic advection
trough multi-scale expansions. Second, the incompressible Navier-Stokes (NS) equations can be
obtained in the nearly incompressible limit of the
LBM. The pressure of the LBM is calculated using n
equations of state. In contrast, in the direct numerical
simulation of the incompressible NS equations, the
pressure satisfies a Poisson equation with velocity
strains acting as sources. Solving this equation for the
pressure often produces numerical difficulties requiring special treatment, such as iteration or relaxation.
Third, the LBM utilizes a minimal set of velocities in
phase space. In the traditional kinetic theory with the
Maxwell-Boltzmann equilibrium distribution, the phase
space is a complete functional space. The averaging
process involves information from the whole velocity
phase space. Because only two speeds and only a
few moving directions are used in LBM, the transformation relating the microscopic distribution function
and macroscopic quantities is greatly simplified.
The LBM originated from lattice gas (LG) automata, a discrete particle kinetics utilizing a discrete
lattice and discrete time, which consists of a regular
lattice with particles residing on the nodes. A set of
Boolean variables ni(x,t) (i = 0,…,M) describing the
particle occupation is defined, where M is the number
of directions of the particle velocities at each node.
The evolution equation of the LG automata is as follows:
ni ( x + e i ,t + 1) = ni ( x ,t ) + Ω(n ( x ,t )), i = 0,1…, M
(1)
where ei are local particle velocities starting from an
initial state. The configuration of particles at each time
step evolves in two sequential sub-steps: a) streaming, in which each particle moves to the nearest node
in the direction of its velocity and b) collision, which
370
CI&CEQ 19 (3) 369−375 (2013)
occurs when particles arriving at a node interact and
change their velocity directions according to scattering rules. For simplicity, the exclusion principle (no
more than one particle being allowed at a given time
and node with a given velocity) is imposed for memory efficiency and leads to a Fermi-Dirac local equilibrium distribution.
The main feature of the LBM is to replace the
particle occupation variables, ni (Boolean variables),
in Eq. (1) by single-particle distribution functions (real
variables), f i ni  , and neglect individual particle
motion and particle-particle correlations in the kinetic
equations, where  denotes an ensemble average.
An important simplification of the LBM was made by
linearization of the collision operator by assuming that
the distribution is close to the local equilibrium state.
An enhanced collision operator approach which is
linearly stable was proposed [10]. A particular linearized version of the collision operator makes use of
relaxation time towards the local equilibrium using a
single time relaxation. The relaxation term is known
as the Bhathnagar-Gross-Krook (BGK) collision operator and has been independently suggested by several authors [11,12]. In this lattice BGK model (LBGK),
the local equilibrium distribution is chosen to recover
the Navier-Stokes macroscopic equations. Use of
LBGK model makes the computations more efficient
and allows flexibility of the transport coefficients [13] .
Lattice Botlzmann equations
The lattice Boltzmann equation (LBE) is an
explicit time-marching finite-difference representation
of the continuous Boltzmann equation in phase space
and time. The LBE incorporating the single relaxation
BGK approximation has the form [11]:
f i ( x + c i Δt ,t + Δt ) − f i ( x ,t ) = ω [f i eq ( x ,t ) − f i ( x ,t )]
(2)
where ω ≡ Δt / τ denotes the relaxation factor with
limits 0 < ω < 2, c s = c / 3 is the speed of sound, and
c = Δx / Δt. The kinematic viscosity is given by the
relaxation factor:
ν = (2 / ω − 1)Δxc / 6
(3)
The local equilibrium distribution is an analog
version of the Maxwellian distribution function for
incompressible flows, and is expressed as:
f i eq ( x ,t ) = w i ρ [1 +
c iAu A u Au B c iAc iB
+
(
− δ AB )]
2c s2 c s2
c s2
(4)
In these expressions, the flow properties are
defined as:
Flow density: ρ =  f i
i
(5)
J.Đ. MARKOVIĆ et al.: 2D SIMULATION AND ANALYSIS OF FLUID FLOW…
Momentum: ρu A =  f i c iA
(6)
iA
In the equations above, sub-indices A and B
denote the components of the Cartesian coordinates
with implied summation for repeated indices. Furthermore, wi is the weighting which can be determined to
achieve isotropy of the fourth-order tensor of velocities and Galilean invariance [11]. Applying the
Chapman-Enskog expansion, the continuity equation
and the Navier-Stokes equations can be recovered
exactly at the second order approximation from the
LBE if the density variation is sufficiently small [14].
For the D2Q9 (two-dimensional nine velocities)
models, the weightings in Eq. (4) are assigned as
follows:
w i = 4 / 9 for c i = 0 (i.e., static particle),
w i = 1/ 9 for c i = 1 , and w i = 1/ 36 for c i = 2 . The
lattice Boltzmann method applies two essential steps,
namely collision and propagation, to reveal the flow
phenomena at the mesoscopic scale. Hence, the corresponding computations of LBM are performed as:
Collision step:
fi ( x ,t ) = f i ( x ,t ) + ω [f i eq ( x ,t ) − f ( x ,t )]
(7)
Propagation step:
f i ( x + c i Δt ,t + Δt ) = fi ( x ,t )
(8)
where fi denotes the post-collision state of the distribution function. From Eqs. (7) and (8), it is clear that
the collision process is fully local and the propagation
of the distribution functions is uniform. As a result, the
lattice BGK scheme is very simple when applied with
the unity lattice size (i.e., Δx = Δy = 1 ), and a relative
time step of Δt = 1 such that c = Δx / Δt = 1 [15].
Boundary conditions
The simulation was done with modified OpenLB
LBM code with the use of bounce back boundary
conditions.
To generate the solid boundary of an obstacle,
links between neighbouring nodes are selected to
best confirm to the shape of the obstacle. The nodes
CI&CEQ 19 (3) 369−375 (2013)
just outside the boundary no longer communicate with
their neighbours inside the obstacle. Instead, a particle striking this boundary bounces back in the direction from which it arrived. The bounce-back boundary
condition is known to model, to first order, a boundary
which lies halfway between these boundary nodes
and the neighbouring fluid nodes. It is apparent that
the boundary condition cannot directly model a general curvilinear surface but instead uses a stair-step
approximation of the surface.
The bounce-back condition is implemented in
the lattice Boltzmann scheme after the particle distribution is updated. After the particle distribution is
computed, the boundary condition reverses the direction of each component of particle distribution just
inside the boundary. These components leave the
boundary during the following time step.
In irregular geometries, even with the use of a
staircase approximation of domain boundaries, it is
quite difficult attributing the right boundary type to
each cell. In this approach, particle populations that
are opposite to each other are swapped at each iteration step, and no additional collision is executed. The
advantage of this procedure is that it is independent
of the orientation of the domain.
For the D2 Q9 scheme, the boundary conditions
at the wall are given as f2 = f4, f5 = f7 and f6 = f8. f7 is
bouncing back from left hand side lattice in the solid
wall and f8 is bouncing back from the right hand lattice
in the solid wall in reference to the main lattice
location. f4, f7 and f8 are known from the streaming
process. To ensure no-slip conditions velocity at the
wall is set to zero.
For low values of Re number calculations were
numerically stable, but for Re > 1000, depending on
the separation of the channel, in most cases it
became numerically unstable [16].
Geometry of the model
The geometry of plates used in the simulation is
given in Figure 1, while Eq. (9) defines the sine function used for plate geometry description.
Figure.1. Geometry model of parallel plates.
371
J.Đ. MARKOVIĆ et al.: 2D SIMULATION AND ANALYSIS OF FLUID FLOW…
h = Ax sin(
2π x
λx
)
(9)
where h is the height of the plate at a given coordinate x, Ax wave amplitude in the x direction, and λx is
a wavelength in the x direction. Dimensions used in
the calculations are: Ax = 0.45 cm, λx = 8.334 cm and
Havg = 4 cm. The dimensionless geometric parameters that describe the corrugated plate model are
given as λx = λx / H avg and β x = Ax / H avg , where Havg
is the separation between corrugated plates that form
the channel, which was varied from 3 to 5 cm
throughout the investigation.
The Reynolds number was defined as:
Re =
V inH avg
ν
CI&CEQ 19 (3) 369−375 (2013)
number and the wavelength from the channel inlet
increase, the recirculation regions increase in size
and begin to cover a larger region of the channel. At
the large Reynolds number, a weak recirculation
region appears in wave 1 as well as other types of
instabilities. These instabilities are rolling vortices that
appear in the limits between the principal flow and the
upper part of the recirculation.
(10)
where Vin is the average velocity at the inlet of the
corrugated plates and υ is the kinematic viscosity [1].
RESULTS AND DISCUSSION
The criterion used to determine if one wave has
macroscopic mixing is the presence of crossing paths
in the central flow, broken recirculation regions or too
big vortices compared to wave amplitude. Flow mixing occurs when the core flow undergoes large oscillations, resulting in large changes in the position of
the reattachment point of the free shear layer. When
the reattachment point moves far enough upstream,
the core flow impinging on the wall “injects” freestream fluid into the separation bubble; this injection
is accompanied by “ejection” of fluid from the separation bubble into the core flow. This dynamically driven
exchange of fluid results in macroscopic mixing [6].
Low Reynolds number was set at 200, while the
upper limit was 1000.
The flow pattern is very much like the one
reported in previous investigations [6,17]. At small
Reynolds numbers there are steady recirculation
regions along the sinusoidal channel. At very low
velocities (Re ≈ 200) there were no recirculation
regions throughout the channel. In general, the flow
moves and tries to follow the channel shape. This
case is a typical Stokes flow since the viscous forces
dominate the flow pattern. Steady recirculation regions
could be observed in the first wave for Reynolds
larger than 200. More recirculation regions are observed
along the channel as the Reynolds number increases.
Eventually, recirculation regions and rolling vortices
appear throughout the entire channel.
Figures 2 and 3 show the flow pattern that
appears in this type of channel. Recirculation regions
do not cover the entire wave. As the Reynolds
372
Figure 2. Pathlines; Havg = 4 cm, Re = 800.
When the Reynolds number is increased the
separation point moves closer to the beginning of the
wave, and the reattachment point is closer to the end
of the wave. In this case there are not symmetric
recirculation regions, which can also be observed in
Figures 2 and 3.
As the Reynolds number increases, instabilities
appear in waves closer to the channel inlet. At the
large Reynolds number (Re ≈ 800), some waves
present random particle paths that promote macroscopic mixing over all the separation between the
plates. It was observed that the wave number from
inlet where macroscopic mixing first occurs, decreases
as the Reynolds number increases. Macroscopic mixing was rarely observed in wave 1, even at large
Reynolds numbers. For large Havg, it becomes difficult
J.Đ. MARKOVIĆ et al.: 2D SIMULATION AND ANALYSIS OF FLUID FLOW…
appear. The vortices appear at the beginning of the
wave and move downstream to the end of the wave,
where they join the main core flow. When there are
waves in the channel with macroscopic mixing, there
are always waves with rolling vortices upstream from
this wave. However, it is not necessarily true that
macroscopic mixing exists when rolling vortices exist.
It is believed that instabilities in the central flow are
created by rolling vortices and flow asymmetry.
Finally, it is important to mention that rolling vortices
and macroscopic mixing move closer to the channel
inlet as the Reynolds number increases.
In addition to the appearance of macroscopic
mixing, which is also always followed by rolling vortices in downstream direction, it can be inferred that
rolling vortices instabilities appear at lower Reynolds
numbers than macroscopic mixing instabilities. This
behavior is independent of Havg (Figure 4; Tables 1
and 2).
Table 1 shows, for a range of the Re number,
the closest wave number from the inlet, in which rolling vortices appear compared to experimental data
found in literature [1].
The data in Table 1 shows that the increase of
the average separation between plates promotes
rolling vortices to appear at larger Reynolds numbers.
For example, with Havg = 5 cm and Re = 800 there is
already a rolling vortex in wave 4, but there is a rolling
vortex in wave 2 for Havg = 4 cm and Re = 800. This
indicates that increasing the average separation
between plates makes the flow pattern in the channel
steadier. Decreasing the average separation between
plates promotes macroscopic mixing to appear at
for macroscopic mixing to appear even in waves relatively far from the inlet.
Figure 3. Pathlines; Havg = 4 cm, Re = 400.
In the limits between the principal flow and the
upper part of the recirculation region, rolling vortices
Wave number
CI&CEQ 19 (3) 369−375 (2013)
10
9
8
7
6
5
4
3
2
1
0
0
200
400
600
800
1000
1200
Re
Wave with rolling vortices
Wave with macroscopic mixing
Figure 4. Comparison of the position of the first wave that presents the position of the rolling vortices and the position of the first wave
that represents macroscopic mixing, Havg = 5 cm.
373
J.Đ. MARKOVIĆ et al.: 2D SIMULATION AND ANALYSIS OF FLUID FLOW…
lower Reynolds numbers; this behavior is similar to
those of rolling vortices.
Table 1. Number of wave with rolling vortices counted from the
inlet - comparison of the experimental data from the literature [1]
and simulation data
Wave number, Havg / cm
Re
3
4
5
3
Experimental data
4
5
Simulation data
200
6
8
-
6
7
8
300
5
7
8
4
6
7
400
3
6
7
3
4
6
500
2
4
6
3
4
5
600
2
3
4
2
3
4
700
2
3
4
2
3
4
800
2
3
4
2
3
3
900
2
2
3
2
2
3
1000
2
2
3
2
2
3
Table 2. Number of wave with macroscopic mixing counted from
the inlet - comparison of the experimental data from the literature [1] and simulation data
Wave number, Havg / cm
Re
3
4
5
3
Experimental data
4
For Re values from 500 to 1000 wave numbers are
identical.
The closest wave number from the inlet that
presents macroscopic mixing can be observed in
Table 2, as a function of Re number for simulation
data and experimental data found in literature [1].
The data in Table 2 shows that wave 6 presents
macroscopic mixing up to Re = 800 and Havg = 5 cm,
while wave 4 at Havg = 4 cm already has macroscopic
mixing at Re = 800. This proves that increase of Havg
makes it more difficult for the macroscopic mixing to
appear.
Simulations results compared are in a very good
agreement with experimental data from the literature.
For lower Re values in some cases there are differences, like for Havg = 3 cm and Re = 200, the first
wave with macroscopic mixing according to experimental data is wave number 8, while simulations
results show that it is wave number 7. For Re values
from 600 to 1000 results are almost identical. There is
difference for Havg = 4 cm and Re values 700 and 800,
where simulation shows that the first wave is wave
number 4, but experimental results show that the first
wave with macroscopic mixing is wave number 3 [18].
5
CONCLUSIONS
Simulation data
200
8
8
8
7
7
8
300
7
7
7
7
7
7
400
6
5
7
7
6
7
500
5
5
7
5
6
6
600
5
4
6
5
5
6
700
4
3
6
4
4
6
800
3
3
6
4
4
6
900
3
3
6
3
3
6
1000
3
3
6
3
3
6
It can be seen that not only the visualized flow
pattern, but also the number of wave where the rolling
vortices first appear at given Re number is in a good
agreement with previous investigations. For Havg= 3
cm first wave in which rolling vortices appear differs
for Re 300 and 500. For Re 300 in simulation data
rolling vortices appear in wave number 4, while experimental data shows that they appear in wave number
5. When Re is 500 there is an opposite behavior,
experimental data shows appearance of rolling vortices in wave number 2, while simulation results show
that it appears in the next wave, number 3. Situation
is quite similar for Havg = 4 cm and Havg = 5 cm. For Re
values up to 500 there are slight variations of first
appearance of rolling vortices. Simulations results
compared to experimental data in some cases show
that they appear one wave before or one wave after.
374
CI&CEQ 19 (3) 369−375 (2013)
The visualized flow pattern for given geometry of
the heat exchanger agrees well with previous numerical and experimental investigations, which showed
that the application of lattice Boltzmann method is
successful in range of low Re values.
It is known that macroscopic mixing is an effective way to enhance the heat transfer and mixing in
sinusoidal plates because of its random particle trajectories and although it is in some ways an interesting phenomenon - capable of improving the heat
transfer and the stirring in sinusoidal plates, it does
not appear in waves very near the channel inlet at the
small Reynolds number range.
Previous investigations showed that enhancement of fluid mixing and formation of recirculation
regions improves heat transfer. However, additional
investigation on the heat transfer should be performed in order to obtain more information about the
influence of recirculation regions, vortex formation,
and chaotic mixing on the heat transfer enhancement.
Acknowledgement
This research was financially supported by the
Ministry of Education, Science and Technological
Development of the Republic of Serbia (Project No.
46010).
J.Đ. MARKOVIĆ et al.: 2D SIMULATION AND ANALYSIS OF FLUID FLOW…
CI&CEQ 19 (3) 369−375 (2013)
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JELENA Đ. MARKOVIĆ
NATAŠA LJ. LUKIĆ
ALEKSANDAR I. JOKIĆ
BOJANA B. IKONIĆ
JELENA D. ILIĆ
BRANISLAVA G. NIKOLOVSKI
Univerzitet u Novom Sadu, Tehnološki
fakultet, Novi Sad, Srbija
NAUČNI RAD
2D SIMULACIJA I ANALIZA STRUJANJA FLUIDA
IZMEĐU DVE PARALELNE SINUSOIDALNE PLOČE
PRIMENOM LATTICE BOLTZMANN METODE
U cilju postizanja boljeg prenosa toplote, neophodno je poboljšati mešanje fluida u razmenjivačima toplote. S obzirom na to da postoje negativni efekti pri radu razmenjivača
toplote u turbulentnom režimu (kao što su značajni pad pritiska i potreba za većom
pumpom) moraju se primeniti tehnike koje će obezbediti bolje mešanje fluida pri radu
razmenjivača toplote u laminarnom režimu. Istraživanja su pokazala da upotreba sinusodialnih umesto ravnih ploča daje upravo ovakav rezultat. U radu su predstavljeni rezultati
dvodimenzione simulacije strujanja fluida između dve paralelne sinusoidalne ploče. Simulacija je rađena modifikacijom OpenlB koda, na bazi lattice Boltzmann metode. Rejnoldsov broj prilikom simulacije je variran od 200 do 1000, a razmak između ploča od 3 do 5
cm. Rezultati pokazuju poboljšano mešanje fluida, naoročito pri većim vrednostima Rejnodsovog broja, što je u skladu sa prethodnim istraživanjima.
Ključne reči: lattice Boltzmann metod, strujanje fluida, sinusoidalne ploče, pločasti razmenjivači, simulacija.
375
Available on line at
Association of the Chemical Engineers of Serbia AChE
www.ache.org.rs/CICEQ
Chemical Industry & Chemical Engineering Quarterly 19 (3) 377−384 (2013)
S. RAMESH
R. MUTHUVELAYUDHAM
R. RAJESH KANNAN
T. VIRUTHAGIRI
Department of Chemical
Engineering, Annamalai University,
Annamalainagar, Tamilnadu, India
SCIENTIFIC PAPER
UDC 547.455.526:543:547.458.87(540)
DOI 10.2298/CICEQ120315072R
CI&CEQ
RESPONSE SURFACE OPTIMIZATION OF
MEDIUM COMPOSITION FOR XYLITOL
PRODUCTION BY Debaryomyces hansenii var.
hansenii USING CORNCOB HEMICELLULOSE
HYDROLYSATE
Optimization of the culture medium for xylitol production using Debrayomyces
hansenii var. hansenii was carried out. The optimization of xylitol production
using corncob hemicelluloses hydrolysate as substrate was performed with
statistical methodology based on experimental designs. The screening of nine
nutrients for their influence on xylitol production was achieved using a PlackettBurman design. MgSO4⋅7H2O, KH2PO4, (NH4)2SO4 and yeast extract were
selected for based on their positive influence on xylitol production. The selected
components were optimized using Response Surface Methodology (RSM).
The optimum conditions were: MgSO4⋅7H2O - 1.02 g/l, (NH4)2SO4 – 3.94 g/l,
KH2PO4 – 2.74 g/l and yeast extract – 3.45 g/l. These conditions were validated
experimentally, which revealed an enhanced xylitol yield of 0.76 g/g.
Keywords: xylitol; corncob; Debaryomyces hansenii var. Hanseni; optimization; RSM.
Xylitol is one of the most expensive polyol
sweeteners and considerable attention in the food
and pharmaceutical industries. They have medicinal
applications such as tooth decay, ear infection for
children, substitute for sugar to diabetic patients and
parenteral application to trauma patients [1-3]. Xylitol
is increasingly being used in chewing gum, candy,
soft drinks, ice creams and hygiene products.
Currently, xylitol is produced by chemical hydrogenation using nickel as a catalyst [4]; however, this
process is expensive. There are several steps involved in the purification of xylose before the chemical
reaction [5-7]. The microbial conversion of xylose to
xylitol is particularly attractive in that the process is
relatively easy and does not need toxic catalyst [8].
Xylitol production through bioconversion has been
proposed to alternative process utilizing microorganism such as yeast, bacteria and fungi [9,10]. Among
those, yeast has some desirable properties and was
proven to be a potential xylitol producer [11,12]. In the
Correspondence: S. Ramesh, Department of Chemical Engineering, Annamalai University, Annamalainagar-608002, Tamilnadu, India.
E-mail: Ramesh_lecturer@yahoo.co.in
Paper received: 15 March, 2012
Paper revised: 14 May, 2012
Paper accepted: 9 July, 2012
present study, yeast strain of species Dabaryomyces
hansenii var. hansenii were selected for xylitol production. Furthermore studies have showed that nutritional factors including sources of carbon and nitrogen influence xylitol production [13].
Corncob is a large volume solid waste that
results from the sweet corn processing industry in
India. They are currently used as animal feed and
returned to the harvested field for land application
[14]. Corncob contains approximately over 40% of dry
matter in corn residues [15] and value of raw material
for production of xylose, xylitol, arabinose, xylobiose
and xylooligosaccharides. The hemicelluloses fraction
in corncob can be easily hydrolysed to constituent
carbohydrates. These carbohydrates mainly consist
of xylose and other minor pentose [16-18]. In various
agricultural wastes, corncob is regarded as promising
agricultural resources for microbial xylitol production
because corn is widely cultivated, and corncobs are
rich in hemicellulose but are not effectively utilized.
Bioconversion of xylitol is influenced by factors
of the various concentrations of ingredients in culture
medium, so their optimization study is very important.
Response surface methodology (RSM) is a mathematical and statistical analysis that is useful for
modeling and analysis problems [19]. RSM has been
377
S. RAMESH et al.: RESPONSE SURFACE OPTIMIZATION OF MEDIUM COMPOSITION…
utilized extensively for optimizing different biotechnological processes [20,21].
In the present study, the screening and optimization of medium composition for xylitol production by
D. hansenii using Plackett-Burman and RSM were
carried out. The Plackett-Burman screening design
was applied for identifying the significant variables
that enhance xylitol production. The central composite
design (CCD) was further applied to determine the
optimum level of each significant variable.
MATERIALS AND METHODS
Microorganisms and maintenance
The yeast strain Dabaryomyces hansenii var.
hansenii (MTCC 3034) was collected from the Microbial Type Culture Collection and Gene bank, Chandigarh. The lyophilized stock cultures were maintained
at 4 °C in culture medium supplemented with 20 g
agar. The medium composition (g/l) is given as: malt
extract - 3.0; yeast extract - 3.0; peptone - 5.0; glucose - 10.0, with pH 7. It was sub-cultured every thirty
days to maintain viability.
Size reduction
Corncob was collected from agricultural farms at
perambalur, Tamilnadu, India. The collected raw
material were dried in sunlight for 2 days, crushed
and sieved for different mesh size ranging from 0.45
mm to 0.9 mm (20–40 mesh) and used for further
studies. The composition of corncob used for xylitol
production is given in Table 1.
Table 1. Composition (g/l) of the corncob hemicellulose hydrolysate
Component
Amount
Xylose
28.7
Glucose
5.4
Arabinose
3.7
CI&CEQ 19 (3) 377−384 (2013)
and unhydrolysed solid residue was washed with
warm water at 60 °C. The filtrate and wash liquid were
pooled together.
Detoxification
Hemicellulose acid hydrolysate was heated at
100 °C, and maintained for 15 min to reduce the
volatile components. The hydrolysate were overlimed
with solid Ca(OH)2 up to pH 10, in combination with
0.1% sodium sulfite and filtered to remove the insoluble materials. The filtrate was adjusted to pH 7 with
H2SO4. The water phase was treated with activated
charcoal and used for xylitol production.
Fermentation conditions
Fermentation was carried out in 250 ml Erlenmeyer flasks with 100 ml of pretreated corncob hemicelluloses hydrolysate at pH 7. This is supplemented
with different nutrient concentration for tests according to the selected factorial design and sterilized at
120 °C for 20 min. After cooling the flasks at room
temperature, the flasks were inoculated with 1 ml of
grown culture broth. The flasks were maintained at 30
°C under agitation at 200 rpm for 48 h.
During the preliminary screening process, the
experiments were carried out for 5 days and it was
found that the maximum production was obtained in
48 h. Hence, experiments were carried out for 48 h.
Analytical methods
Sugar and sugar alcohols in the culture broth
were measured by high performance liquid chromatography (HPLC), model LC-10-AD (Shimadzu, Tokyo,
Japan) equipped with a refractive index (RI) detector.
The chromatography column used was an Aminex
HPX-87H (300 mm×7.8 mm) column at 80 °C with 5
mM H2SO4 as mobile phase at a flow rate of 0.4
ml/min, and the injected sample volume was 20 µL.
Optimization of xylitol production
Cellobiose
0.5
Plackett–Burman experimental design
Galactose
0.7
Mannose
0.4
Plackett–Burman experimental design assumes
that there are no interactions between the different
variables in the range under consideration. A linear
approach is considered to be sufficient for screening.
Plackett–Burman experimental design is a fractional
factorial design and the main effects of such a design
may be simply calculated as the difference between
the average of measurements made at the high level
(+1) of the factor and the average of measurements
at the low level (–1).
To determine the variables significantly affect
xylitol production, the Plackett–Burman design was
used. Nine variables (Table 2) were screened in 12
Acetic acid
2
Furfural
0.8
Hydroxymethylfurfural
0.2
Acid hydrolysis
The pretreatment were carried out in 500 ml
glass flasks. 2 g corncob in solid loading of 10 mass%
mixed with 1 mass% dilute sulfuric acid and pretreated in an autoclave at 120 °C with residence time
of 1 h. The liquid fraction was separated by filtration
378
S. RAMESH et al.: RESPONSE SURFACE OPTIMIZATION OF MEDIUM COMPOSITION…
experimental runs (Table 3) and insignificant ones
were eliminated in order to obtain a smaller, manageable set of factors. The low level (-1) and high level
(+1) of each factor are listed in Table 2. The statistical
software package Minitab 15 was used to analyze the
experimental data. Once the critical factors were identified through the screening, the central composite
design (CCD) was used to obtain a quadratic model.
model parameter estimates are desired [19].
The coded values of the process parameters are
determined by the following equation:
xi =
1
Nutrient
-1
+1
Min. value, g/l
Max. value, g/l
7
A
K2HPO4
6.6
2
B
Yeast extract
1.5
5
3
C
Peptone
2
5
4
D
KH2PO4
1.2
3.6
5
E
Xylose
9.8
10.2
6
F
(NH4)2SO4
1
4
7
G
MgSO4⋅7H2O
0.7
1.3
8
H
Malt
2.8
3.2
9
I
Glucose
9.8
10.2
Xi − X0
Δx
(1)
where xi – coded value of the ith variable, Xi – uncoded
value of the ith test variable and X0 – uncoded value of
the ith test variable at center point. The regression
analysis is performed to estimate the response function as a second order polynomial:
Table 2. Nutrients screening using Plackett-Burman design
Ser. Nutrient
No. code
CI&CEQ 19 (3) 377−384 (2013)
Y = β0 +
k

i =1
βi X i +
k

i =1
βii X i2 +
k −1

k

i =1,i < j j = 2
βij X i X j
(2)
where Y is the predicted response, β0 constant, βi, βj
and βij are coefficients estimated from regression.
They represent the linear, quadratic and cross products of Xi and Xj on response.
Model fitting and statistical analysis
The regression and graphical analysis with statistical significance were carried out using Minitab 15.
In order to visualize the relationship between the
experimental variables and responses, the response
surface and contour plots were generated from the
models. The optimum values of the process variables
were obtained from the regression equation.
The adequacy of the models was further justified
through analysis of variance (ANOVA). Lack-of-fit is a
special diagnostic test for adequacy of a model and
compares the pure error, based on the replicate measurements to the other lack of fit, based on the model
performance [22]. F-value, calculated ratio between
the lack-of-fit mean square and the pure error mean
square are statistic parameters used to determine
whether the lack-of-fit is significant or not, at a significance level.
Central composite design
The central composite design is used to study
the effects of variables on their responses and subsequently in the optimization studies. This method is
suitable for fitting a quadratic surface and it helps to
optimize the effective parameters with minimum number of experiments, as well as to analyze the interaction between the parameters. In order to determine
the existence of a relationship between the factors
and response variables, the collected data were analyzed in a statistical manner, using regression. A regression design is normally employed to model a response as a mathematical function (either known or
empirical) of a few continuous factors and good
Table 3. Plackett–Burman experimental design for nine variables
Run Order
A
B
C
D
E
F
G
H
I
Xylitol yield, g/g
1.
1
1
-1
-1
-1
1
1
1
-1
0.21
2.
1
-1
1
-1
-1
-1
1
1
1
0.30
3.
-1
-1
-1
1
1
1
-1
1
1
0.40
4.
-1
1
1
1
-1
1
1
-1
1
0.45
5.
1
-1
-1
-1
1
1
1
-1
1
0.22
6.
-1
-1
-1
-1
-1
-1
-1
-1
-1
0.40
7.
1
-1
1
1
-1
1
-1
-1
-1
0.55
8.
1
1
1
-1
1
1
-1
1
-1
0.44
9.
1
1
-1
1
1
-1
1
-1
-1
0.55
10.
-1
1
1
-1
1
-1
-1
-1
1
0.64
11.
-1
-1
1
1
1
-1
1
1
-1
0.45
12.
1
1
-1
1
-1
-1
-1
1
1
0.61
379
S. RAMESH et al.: RESPONSE SURFACE OPTIMIZATION OF MEDIUM COMPOSITION…
Validation of the experimental model
The statistical models were validated with respect to xylitol production under the conditions predicted by the model in shake-flasks level. Samples
were drawn at the desired intervals and xylitol production was determined as described above.
RESULTS AND DISCUSSION
Plackett-Burman experiments (Table 3) showed
a wide variation in xylitol production. This variation
reflected the importance of optimization to attain
higher productivity. From the pareto chart (Figure 1)
the variables, viz., KH2PO4, yeast extract, MgSO4⋅7H2O
and (NH4)2SO4 were selected for further optimization
to attain a maximum response.
The level of factors KH2PO4, yeast extract,
MgSO4⋅7H2O and (NH4)2SO4) and the effect of their
interactions on xylitol production were determined by
central composite design of RSM. Thirty experiments
were preferred at different combinations of the factors
shown in (Table 4) and the central point was repeated
six times (1, 4, 16, 17, 22, 24). The predicted and
observed responses along with design matrix are
presented in Table 5. The results were analyzed
using ANOVA. The second order regression equation
provided the levels of xylitol production as a function
of KH2PO4, yeast extract, MgSO4⋅7H2O and (NH4)2SO4,
which can be presented in terms of coded factors as
in the following equation:
CI&CEQ 19 (3) 377−384 (2013)
Y = 0.748 + 0.006 − 0.01A − 0.0107B − 0.039C −
−0.0193D − 0.021A × A − 0.0244B × B −
−0.0356C × C − −0.0381D × D − 0.0048 A × B −
−0.00025 A × C − 0.014 A × D − 0.0125B × C +
+0.0163B × D + 0.0288C × D
(3)
where Y is the xylitol yield (g/g), A, B, C and D are
(NH4)2SO4, KH2PO4, MgSO4⋅7H2O and yeast extract,
respectively. ANOVA used for the response surface is
shown in Table 6. The p-value of the model was
0.04533, which was used as a tool to check the significance of each co-efficient, and indicated that the
model was suitable for using in this experiment. The
p-value less than 0.05 indicate model terms are significant. Values greater than 0.05 indicates model terms
are not significant. In the present work, linear terms of
B, C, D and all the square effects of A, B, C, D and
the combination of A×D, B×C, B×D and C×D were
significant for xylitol production. The co-efficient of
determination (R2) for xylitol production was calculated as 0.9488, and it is very close to 1 and can
explain up to 94.88% variability of the response. The
predicted R2 value of 0.7815 was in reasonable
agreement with the adjusted R2 value of 0.8938.
Table 4. Ranges of variables used in RSM
Ser. No.
1
Variable
Code
(NH4)2SO4
A
Levels, g/l
-2
-1
0
1
2
2
3
4
5
6
2
KH2PO4
B
1
2
3
4
5
3
MgSO4⋅7H2O
C
0.6
0.9
1.2
1.5
1.8
4
Yeast extract
D
2
3
4
5
6
Pareto Chart of the Standardized Effects
(response is C14, Alpha = .05)
4.303
G
D
F
Term
B
C
H
E
A
I
0
1
2
3
4
5
Standardized Effect
6
7
8
Figure 1. Pareto chart showing the effect of media components on xylitol production (G - MgSO4⋅7H2O, D - KH2PO4, F - (NH4)2SO4,
B - yeast extract).
380
S. RAMESH et al.: RESPONSE SURFACE OPTIMIZATION OF MEDIUM COMPOSITION…
Table 5. Central Composite Design (CCD) in coded levels with
xylitol yield as response
Xylitol yield, g/g
Run
A
B
C
D
Experimental
Predicted
1
0
0
0
0
0.75
0.742
2
-1
1
1
-1
0.55
0.543
3
-1
-1
1
1
0.60
0.627
4
0
0
0
0
0.75
0.742
5
1
1
-1
-1
0.70
0.688
6
1
1
-1
1
0.61
0.596
7
1
1
1
-1
0.54
0.541
8
1
-1
-1
-1
0.73
0.726
9
-1
1
-1
1
0.64
0.653
10
-1
-1
-1
-1
0.70
0.708
11
-1
-1
1
-1
0.60
0.624
12
-1
1
-1
-1
0.69
0.701
13
-1
-1
-1
1
0.61
0.619
14
-1
1
1
1
0.62
0.634
15
1
1
1
1
0.57
0.576
16
0
0
0
0
0.74
0.754
17
0
0
0
0
0.75
0.754
18
1
-1
1
-1
0.64
0.642
19
1
-1
-1
1
0.56
0.582
20
1
-1
1
1
0.60
0.600
21
2
0
0
0
0.64
0.651
22
0
0
0
0
0.76
0.754
23
-2
0
0
0
0.73
0.691
24
0
0
0
0
0.75
0.754
25
0
2
0
0
0.63
0.635
26
0
-2
0
0
0.71
0.677
27
0
0
0
-2
0.64
0.640
28
0
0
-2
0
0.68
0.675
29
0
0
2
0
0.57
0.547
30
0
0
0
2
0.59
0.562
tion up to 3 g/l. The optimal conditions of (NH4)2SO4,
KH2PO4, MgSO4⋅7H2O and yeast extract for maximum
xylitol production were determined by response surface analysis and estimated by regression equation.
The predicted results are shown in Table 6 and values
from the regression equation closely agreed with
experimental values.
Table 6. Analyses of variance (ANOVA) for response surface
quadratic model for the production of xylitol; R2 - 94.88%; R2
(predicted) - 78.15%; R2 (adjusted) - 89.38%
Term
Coefficient SE Coefficient
Constant
0.748000
0.009461
T
P
79.058
0.000
Block
0.006000
A
-0.010000
0.004904
1.223
0.241
0.004660
-2.146
B
0.050
-0.010667
0.004731
-2.255
0.041
C
-0.031833
0.004731
-6.729
0.000
D
-0.019333
0.004731
-4.087
0.001
A×A
-0.020625
0.004359
-4.732
0.000
B×B
-0.024375
0.004359
-5.592
0.000
C×C
-0.035625
0.004359
-8.173
0.000
D×D
-0.038125
0.004359
-8.747
0.000
A×B
-0.004750
0.005837
-0.814
0.429
A×C
-0.000250
0.005837
-0.043
0.966
A×D
-0.014000
0.005837
-2.399
0.031
B×C
-0.012500
0.005707
-2.190
0.046
B×D
0.016250
0.005707
2.848
0.013
C×D
0.028750
0.005707
5.038
0.000
0.7
C10
The above model is used to predict the xylitol
production within the limits of the experimental factors
that the actual response values agree well with the
predicted response values.
The production of xylitol with variable interactions were studied by plotting surface curves against
any two independent variables, while keeping another
variable at its central (0) level. The curves of calculated response (xylitol production) and contour
plots from the interactions between the variables are
shown in Figures 2-11. Figures 2 and 3 show the
dependency of xylitol on yeast extract and KH2PO4.
The xylitol production increased with increasing in
yeast extract to about 4 g/l and then xylitol production
is decreased with further increase in yeast extract.
Similar results were observed in Figures 4-11. Increase
in KH2PO4 resulted in the increase in xylitol produc-
CI&CEQ 19 (3) 377−384 (2013)
0.6
2
0.5
0.4
0
D
-2
0
B
2
-2
Figure 2. Plot showing the effect of yeast extract and KH2PO4 on
xylitol production; hold values: A = 0, C = 0.
Validation of the experimental model
Validation of the experimental model was tested
by carrying out the batch experiment under optimal
operation conditions: (NH4)2SO4 – 3.94 g/l, KH2PO4 –
2.74 g/l, MgSO4⋅7H2O – 1.02 g/l and yeast extract –
3.45 g/l established by the regression model. Four
repeated experiments were performed and the results
are compared. The xylitol production (0.76 g/g) obtained
381
S. RAMESH et al.: RESPONSE SURFACE OPTIMIZATION OF MEDIUM COMPOSITION…
CI&CEQ 19 (3) 377−384 (2013)
2
0.45
0.50
0.55
0.60
0.65
0.70
D
1
0
C10
<
–
–
–
–
–
–
>
0.45
0.50
0.55
0.60
0.65
0.70
0.75
0.75
Hold Values
A 0
C 0
-1
-2
-2
-1
0
B
1
2
Figure 3. Plot showing the effect of yeast extract and KH2PO4 on xylitol production.
2
C 10
<
0.4 –
0.5 –
0.6 –
>
1
C10
C
0.7
0.4
0.5
0.6
0.7
0.7
Hold Values
A 0
D 0
0
0.6
0.5
-1
2
0.4
0
C
-2
0
B
2
-2
-2
-2
Figure 4. Plot showing the effect of MgSO4⋅7H2O and KH2PO4
on xylitol production; hold values: A = 0, D = 0.
-1
0
B
1
2
Figure 5. Plot showing the effect of MgSO4.7H2O and KH2PO4 on
xylitol production.
2
C 10
<
0.4 –
0.5 –
0.6 –
>
1
C10
D
0.7
Hold Values
B 0
C 0
0
0.6
0.5
2
0.4
0
0
A
2
-1
D
-2
-2
Figure 6. Plot showing the effect of yeast extract and (NH4)2SO4
on xylitol production; B = 0, C = 0.
from experiments was very close to the actual response (0.754 g/g) predicted by the regression model,
which proved the validity of the model.
382
0.4
0.5
0.6
0.7
0.7
-2
-2
-1
0
A
1
2
Figure 7. Plot showing the effect of yeast extract and (NH4)2SO4 on
xylitol production.
CONCLUSION
In this work, Plackett-Burman design was used
to determine the relative importance of medium com-
S. RAMESH et al.: RESPONSE SURFACE OPTIMIZATION OF MEDIUM COMPOSITION…
CI&CEQ 19 (3) 377−384 (2013)
2
0.45
0.50
0.55
0.60
0.65
0.70
1
C1 0
C
0.7
0
-1
2
0.4
0
C
-2
0
A
2
0.45
0.50
0.55
0.60
0.65
0.70
0.75
0.75
Hold Values
B 0
D 0
0.6
0.5
C 10
<
–
–
–
–
–
–
>
-2
-2
Figure 8. Plot showing the effect of MgSO4⋅7H2O and (NH4)2SO4
on xylitol production; hold values: B = 0, D = 0.
-2
-1
0
A
1
2
Figure 9. Plot showing the effect of MgSO4⋅7H2O and (NH4)2SO4 on
xylitol production.
2
C 10
<
0.52 –
0.56 –
0.60 –
0.64 –
0.68 –
>
B
1
0.7
0.52
0.56
0.60
0.64
0.68
0.72
0.72
Hold Values
C 0
D 0
0
C1 0
0.6
2
0.5
0
B
-2
0
A
2
-1
-2
-2
-2
-1
0
A
1
2
Figure 10. Plot showing the effect of KH2PO4 and (NH4)2SO4 on Figure 11. Plot showing the effect of KH2PO4 and (NH4)2SO4 on xylitol
xylitol production; C = 0, D = 0.
production.
ponents for xylitol production. Among the variables,
(NH4)2SO4, KH2PO4, MgSO4⋅7H2O and yeast extract
were found the most significant variables. From
further optimization studies the optimized values of
the variables for xylitol production were as follows:
(NH4)2SO4 – 3.94 g/l, KH2PO4 – 2.74 g/l, MgSO4⋅7H2O –
1.02 g/l and yeast extract – 3.45 g/l. This study showed
that corncob is a good source for the production of
xylitol. Using the optimized conditions, the production
reaches 0.76 g/g. The results show a close agreement between the expected and obtained production
level.
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Acknowledgment
The authors wish to express their gratitude for
the support extended by the authorities of Annamalai
University, Annamalainagar, India, in carrying out the
research work in Bioprocess laboratory, Department
of Chemical Engineering.
383
S. RAMESH et al.: RESPONSE SURFACE OPTIMIZATION OF MEDIUM COMPOSITION…
CI&CEQ 19 (3) 377−384 (2013)
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S. RAMESH
R. MUTHUVELAYUDHAM
R. RAJESH KANNAN
T. VIRUTHAGIRI
Department of Chemical Engineering,
Annamalai University, Annamalainagar,
Tamilnadu, India
NAUČNI RAD
OPTIMIZACIJA SASTAVA HRANLJIVE PODLOGE
SA HIDROLIZATOM HEMICELULOZE
KUKURUZNOG KLIPA ZA PRODUKCIJU KSILITOLA
POMOĆU Debaryomyces hansenii var. Hansenii
PRIMENOM METODE POVRŠINE ODZIVA
Izvršeno je optimizovanje hranljive podloge za produkciju ksilitola pomoću Debaryomyces
hansenii var. hansenii. Ova optimizacija produkcije ksilitola na podlozi sa hidrolizatom
hemiceluloze kukuruznog klipa je izvršena primenom statističke metode zasnovane na
planiranju eksperimenata. Uticaj devet nutrienata na produkciju ksilitola je ocenjen Plackett-Burman-ovim dizajnom. Pozitivan uticaj na produkciju ksilotola imali su MgSO4⋅7H2O,
KH2PO4, (NH4)2SO4 i ekstrakt kvasca. Ove komponente su optimizovane metodom površine odziva. Optimalni uslovi su MgSO4⋅7H2O – 1,02 g/l, (NH4)2SO4 – 3,94 g/l, KH2PO4 –
2,74 g/l i ekstrakt kvasca – 3,45 g/l. Ovi uslovi su potvrđeni eksperimentalno, a prinos
ksilitola je bio 0,76 g/g.
Ključne reči: ksilitol, kukuruzni klip, Debaryomyces hansenii var. hanseni, optimizacija, metoda površine odziva.
384
Available on line at
Association of the Chemical Engineers of Serbia AChE
www.ache.org.rs/CICEQ
Chemical Industry & Chemical Engineering Quarterly 19 (3) 385−388 (2013)
SAŠA Ž. DRMANIĆ1
JASMINA B. NIKOLIĆ1
ALEKSANDAR D.
MARINKOVIĆ1
GAVRILO M. ŠEKULARAC1
BRATISLAV Ž. JOVANOVIĆ2
1
Department of Organic Chemistry,
Faculty of Technology and
Metallurgy, University of Belgrade,
Belgrade, Serbia
2
Institute of Chemistry, Technology
and Metallurgy, University of
Belgrade, Belgrade, Serbia
SCIENTIFIC PAPER
UDC 547.821:543.4
DOI 10.2298/CICEQ120326073D
CI&CEQ
THE EFFECTS OF SOLVENTS AND
STRUCTURE ON THE ELECTRONIC
ABSORPTION SPECTRA OF THE ISOMERIC
PYRIDINE CARBOXYLIC ACID N-OXIDES
The ultraviolet absorption spectra of the carboxyl group of three isomeric
pyridine carboxylic acids N-oxides (picolinic acid N-oxide, nicotinic acid
N-oxide and isonicotinic acid N-oxide) were determined in fourteen solvents in
the wavelength range from 200 to 400 nm. The position of the absorption
maxima (λmax) of the examined acids showed that the ultraviolet absorption
maximum wavelengths of picolinic acid N-oxide are the shortest, and those of
isonicotinic acid N-oxide acid are the longest. In order to analyze the solvent
effect on the obtained absorption spectra, the ultraviolet absorption frequencies of the electronic transitions in the carboxylic group of the examined acids
were correlated using a total solvatochromic equation of the form νmax = v0 +
+ sπ* + aα+ bβ, where νmax is the absorption frequency (1/λmax), π* is a
measure of the solvent polarity, β represents the scale of solvent hydrogen
bond acceptor basicities and α represents the scale of solvent hydrogen bond
donor acidities. The correlation of the spectroscopic data was carried out by
means of multiple linear regression analysis. The solvent effects on the ultraviolet absorption maximums of the examined acids were discussed.
Keywords: picolinic acid N-oxide, nicotinic acid N-oxide, isonicotinic acid
N-oxide, ultraviolet absorption maximum, protic and aprotic solvents,
solvatochromic effects.
Pyridine N-oxides, the group of compounds that
pyridine carboxylic acids belong to, have applications
in a wide range of fields including industry, medicine,
biochemistry and even nano-tecnology [1-7]; therefore, there is interest in studying the structural and
spectrochemical information about them.
The connection that exists between the compound structure, solvent effect and the ultraviolet
absorption spectra has been a subject of many studies [8-13]. The absorption of UV light can raise the
electrons in the molecule to a higher energy level.
The possible electronic transition under UV light are
n → π* (lone electron from the pair in a nonbonding
orbital to higher level antibonding orbital), π → π*
(electron from a π bond to higher level antibonding
orbital) and σ → σ* (electron from a σ bond into a
higher level antibonding orbital) [14,15]. The part of
molecule with an ability to absorb the UV light is
called the chromophore. This part of the molecule has
a characteristic value of the wavelength of the absorbed UV radiation, called the absorption maximum
(λmax).
The π → π* transition in the carboxylic group of
the three isomeric pyridine carboxylic acids (Figure
1), dissolved in a set of solvents, was analyzed in this
study.
COOH
COOH
N
Correspondence: S.Ž. Drmanić, Department of Organic Chemistry, Faculty of Technology and Metallurgy, University of Belgrade, Karnegijeva 4, Belgrade, Serbia.
E-mail: drmana@tmf.bg.ac.rs
Paper received: 26 March, 2012
Paper revised: 15 June, 2012
Paper accepted: 14 July, 2012
COOH
N
O
O
(1)
(2)
N
O
(3)
Figure 1. Picolinic acid N-oxide (1), Nicotinic acid N-oxide (2),
Isonicotinic acid N-oxide (3).
385
S.Ž. DRMANIĆ et al.: THE EFFECTS OF SOLVENTS AND STRUCTURE…
During the excitation process, π → π* of the one
electron from the π bond in the carbonyl (C=O) group
of the carboxylic group is promoted from to an antibonding orbital which contains higher energy. The
molecular structure or the present solvent can influence the wavelength of the absorption maximum: if
λmax increases it is a batochromic shift, while if it
decreases it is a hypsochromic shift. Also, batochromic shift signifies the lower energy of the electronic
π → π* transition, while the hypsochromic shift means
higher energy.
The effects of solvent polarity and hydrogen
bonding on the absorption spectra of the examined
compounds are interpreted by means of the linear
solvation energy relationships (LSER) concept, developed by Kamlet and Taft [16], using a general solvatochromic equation of the form:
νmax = v0 + sπ* + aα+ bβ
(1)
where α, β and π* are solvatochromic parameters; s,
a and b are solvatochromic coefficients; νmax = 1/λmax
is the maximum absorption frequency; and v0 is the
reference value, which is taken to be in the solvent
cyclohexane, for which all the solvent parameters
have the value zero [16].
In Eq. (1), π* is the index of the solvent dipolarity/polarizability, which is a measure of the ability of
a solvent to stabilize a charge or a dipole by its own
dielectric effects. The π* scale was selected to range
from 0.00 for cyclohexanone to 1.00 for dimethyl
sulfoxide. The α coefficient represents the solvent
hydrogen bond donor (HBD) acidity, in other words it
describes the ability of a solvent to donate a proton in
a solvent-to-solute hydrogen bond. The α scale
CI&CEQ 19 (3) 385−388 (2013)
extends from 0.00 for non-HBD solvents to about 1.00
for methanol. The β coefficient is a measure of the
solvent hydrogen bond acceptor (HBA) basicity, and
describes the ability of a solvent to accept a proton in
a solute-to-solvent hydrogen bond. Theβ scale was
selected to extend from 0.00 for non-HBA solvents to
about 1.00 for hexamethylphosphoricacid triamide.
EXPERIMENTAL
Picolinic acid N-oxide, nicotinic acid N-oxide and
isonicotinic acid N-oxide were commercial product
(Fluka) of p.a. quality.
Spectroscopic measurements
The UV spectra of the examined compounds
were recorded using a Shimadzu 1700A spectrophotometer. The wavelength range was 200-400 nm. The
concentrations of the examined solutions were 10-4
mol/dm3. The solvents used were of high purity,
designed for spectroscopic measurements.
RESULTS AND DISCUSSION
The absorption maxima of the examined pyridine carboxylic acids N-oxides in a set of fourteen
solvents are given in Table 1.
It can be noticed that the values of wavelengths
of the absorption maxima increase with the number of
C-atom between the carboxylic group and the N-oxy
group in the ring. This batochromic shift is a consequence of the compounds structure. The negative
inductive effect of the N-oxy group in the molecule of
the picolinic acid N-oxide is strong on the substituent
next to it, which is the carboxylic group. This effect
Table 1. The absorption maxima for the examined pyridine carboxylic acids N-oxides in various solvent
Solvent
Picolinic acid N-oxide
λmax / nm
νmax / 103 cm-1
Nicotinic acid N-oxide
λmax / nm
νmax / 103 cm-1
Isonicotinic acid N-oxide
λmax / nm
νmax / 103 cm-1
Methanol
260.41
38.4
267.37
37.4
286.53
34.9
Ethanol
261.78
38.2
268.81
37.2
288.18
34.7
Propan-1-ol
263.85
37.9
271.00
36.9
289.85
34.5
Propan-2-ol
264.55
37.8
271.73
36.8
291.54
34.3
2-Methylpropan-2-ol
266.66
37.5
273.97
36.5
290.69
34.4
Ethylene glycol
250.62
39.9
257.07
38.9
282.48
35.4
Butan-1-ol
262.46
38.1
269.54
37.1
291.54
34.3
Pentan-1-ol
263.15
38.0
270.27
37.0
289.85
34.5
2-Methylnutan-2-ol
263.85
37.9
269.54
37.1
289.85
34.5
Butan-2-ol
263.85
37.9
271.74
36.9
290.69
34.4
N-Methylformamide
258.39
38.7
264.55
37.8
266.66
37.5
Dioxane
247.52
40.4
250.62
39.9
251.30
39.8
Methyl acetate
250.62
39.9
258.39
38.7
263.85
37.9
Chloroform
250.62
39.9
257.06
38.9
258.39
38.7
386
S.Ž. DRMANIĆ et al.: THE EFFECTS OF SOLVENTS AND STRUCTURE…
can change the electronic density and the electronic
disposition in the carboxylic group and therefore
cause the need for higher energy of the π → π* transition. Furthermore, the intramolecular hydrogen bond
can be formed between the carboxylic hydrogen and
the oxygen from the N-oxy group (Figure 2) in the
molecule of picolinic acid N-oxide, which additionally
increases the negative inductive effect of the N-oxy
group. This hydrogen bond has been proved and
analyzed by X-ray, FTIR and NMR spectra [17]. The
final electron acceptor in the system, oxygen, attracts
the electrons from the σ bond strongly in order to
keep the hydrogen bond.
O
N
C
O
O
H
Figure 2. The inductive effect of the N-oxy group and the
hydrogen bond in the molecule of picolinic acid N-oxide.
In the case of nicotinic acid N-oxide there is only
the negative inductive effect of the N-oxy group that
can influence the carbonyl group, somewhat weaker
than for picolinic acid N-oxide and there is hardly any
possibility for the formation of the intramolecular
hydrogen bond. This compound therefore has longer
λmax and the lower energy of the examined π → π*
transition. Even weaker negative inductive effect and
no possibility for an intramolecular hydrogen bond
exists in the case of the isonicotinic acid N-oxide.
There the maximum wavelengths are the longest and
the π → π* transition energy the lowest, as it is free
from the described effects.
In order to discuss the effect of solvents on the
absorption spectra of the examined isomeric pyridine
carboxylic acids N-oxide, the absorption frequencies
(νmax) were correlated with the Kamlet-Taft solvatochromic parameters, Table 2 [18].
The obtained correlation equations were as follows:
Picolinic acid N-oxide:
νmax = 39.61 + (1.98±0.62)π* – (2.26±0.48)β –
- (0.86±0.35)α, (R = 0.957, s = 0.32, n = 14)
(2)
Nicotinic acid N-oxide:
νmax = 38.66 + (2.06±0.80)π* – (2.28±0.60)β –
- (1.09±0.46)α, (R = 0.937, s = 0.41, n = 14)
Isonicotinic acid N-oxide:
CI&CEQ 19 (3) 385−388 (2013)
νmax = 37.64 + (3.47±1.46)π* – (2.56±1.13)β –
- (3.48±0.84)α, (R = 0.938, s = 0.75 n = 14)
(4)
Table 2. Solvent parameters
Solvent
π*
β
α
Methanol
0.60
0.62
0.93
Ethanol
0.54
0.77
0.83
Propan-1-ol
0.52
0.83
0.78
Propan-2-ol
0.48
0.95
0.76
2-Methylpropan-2-ol
0.41
1.01
0.68
Ethylene glycol
0.92
0.52
0.90
Butan-1-ol
0.47
0.88
0.79
Pentan-1-ol
0.40
0.86
0.84
2-Methylbutan-2-ol
0.40
0.93
0.28
Butan-2-ol
0.40
0.80
0.69
N-Methylformamide
0.90
0.80
0.62
Dioxane
0.55
0.37
0.00
Methyl acetate
0.60
0.42
0.00
Chloroform
0.58
0.10
0.20
From the given equation it can be seen that the
here applied solvent set has a similar effect on all
three examined isomeric acids. For all the examined
compounds the solvent polarity/polarizability effect
causes the hypsochromic shift, while the HBA and
HBD solvent effects cause the batochromic shift. In
other words, the energy of the π* electronic transition
in the carboxylic group of the examined pyridine carboxylic acids N-oxides is raised by the solvent polarity, but lowered by its proton-donor and protonacceptor effects. When a dipolar molecule is dissolved in a polar solvent, as it is a case in this study, the
hypsochromic shift appears when the molecule is a
higher dipole in the ground state, than in the excited
state. With the increase of solvent polarity the more
dipolar structure is better stabilized, so it can be concluded that the molecules of the examined acids are
higher dipoles in the ground state and that the π* transition in the carbonyl group decreases their polarity.
From the highest values of the coefficients for all
three parameters (π*, β and α) in the case of the
isonicotinic acid N-oxide it can be seen that the solvent effect on the π* transition of the C=O group of
this compound is the strongest, i.e., that it is the most
sensitive to solvent properties.
CONCLUSION
(3)
From the analysis of the absorption spectra of
the π* transitions of the carbonyl group in the carboxyl
group of picolinic acid N-oxide, nicotinic acid N-oxide
and isonicotinic acid N-oxide in the chosen solvent
set it can be concluded that the both the structure and
387
S.Ž. DRMANIĆ et al.: THE EFFECTS OF SOLVENTS AND STRUCTURE…
the solvent effect can influence the position of the
absorption maxima. The examined transition demands
the highest energy in the case of picolinic acid
N-oxide, where it is hardened by the negative inductive effect of the N-oxy group, and the intramolecular
hydrogen bond, and the lowest energy in the case of
isonicotinic acid N-oxide, where there is no possibility
for such a hydrogen bond, and the negative inductive
effect is the lowest. The analysis of solvent effects,
expressed quantitatively by the Kamlet-Taft total solvatochromic equation, showed that for all three examined compounds the π* transition energy increases
with the solvent polarity, meaning that they are lower
dipoles in the excited than in the ground state.
Acknowledgements
Authors are grateful to the Ministry Education,
Science and Technological Development of The
Republic of Serbia for financial support (Project
172013).
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[17]
J. Stare, J. Mavri, G. Ambrožič, D. Hadži, J. Mol. Struct.
(Theochem) 500 (2000) 429
[2]
F. Bardak, A. Ataç, M. Kurt, Spectrochim. Acta 71 (2009)
1896
[18]
A.F. Lagalante, R.J. Jacobson, T.J. Bruno, J. Org. Chem.
61 (1996) 6404.
[3]
N. Can, A. Ataç, F. Bardak, Ş.E.S. Can, Turk. J. Chem.
29 (2005) 589
SAŠA Ž. DRMANIĆ1
JASMINA B. NIKOLIĆ1
ALEKSANDAR D. MARINKOVIĆ1
GAVRILO M. ŠEKULARAC1
BRATISLAV Ž. JOVANOVIĆ2
1
UTICAJ RASTVARAČA I STRUKTURE NA
ELEKTRONSKE ABSORPCIONE SPEKTRE
IZOMERNIH PIRIDIN-KARBOKSILNIH KISELINA NOKSIDA
Katedra za organsku hemiju,
Tehnološko-metalurški fakultet,
Univerzitet u Beogradu, Beograd,
Srbija
2
Institut za hemiju, tehnologiju i
metalurgiju, Univerzitet u Beogradu,
Beograd, Srbija
UV apsorpcioni spektri pikolinske kiseline N-oksida, nikotinske kiseline N-oksida i
izonikotinske kiseline N-oksida određeni su u 14 protičnih i aprotičnih rastvarača u opsegu
od 200-400 nm. Položaji maksimuma apsorpcije bili su najniži za pikolinsku kiseline
N-oksid, a najviši za izonikotinsku kiseline N-oksid. Da bi se analzirao uticaj ratvarača,
apsorpcione frekvence su korelisane Kamlet-Taftovom jednačinom, kojom se uticaj polarnosti/polarizabilnosti, proton-donorskog i proton-akceptorskog dejstva rastvarača može
kvantiativno izraziti.
NAUČNI RAD
Ključne reči: pikolinska kiselina N-oksid, nikotinska kiselina N-oksid, izonikotinska kiselina N-oksid, apsorpcioni spektri, protični i aprotični ratvarači, solvatohromni efekti.
388
Available on line at
Association of the Chemical Engineers of Serbia AChE
www.ache.org.rs/CICEQ
Chemical Industry & Chemical Engineering Quarterly 19 (3) 389−398 (2013)
HADI BASERI
ALI HAGHIGHI-ASL
MOHAMMAD NADER
LOTFOLLAHI
School of Chemical, Gas and
Petroleum Engineering, Semnan
University, Semnan, Iran
SCIENTIFIC PAPER
UDC 66.06/.071:546.264-31
DOI 10.2298/CICEQ120203074B
CI&CEQ
THERMODYNAMIC MODELING OF SOLID
SOLUBILITY IN SUPERCRITICAL CARBON
DIOXIDE: COMPARISON BETWEEN MIXING
RULES
In this paper, the Peng-Robinson equation of state is used for thermodynamic
modeling of the solubility of various solid components in supercritical carbon
dioxide. Moreover, the effects of three mixing rules (van der Waals, Panagiotopoulos and Reid, and modified Kwak and Mansoori mixing rule) on the
accuracy of calculation results were studied. Good correlations between calculated and experimental data were obtained in a wide temperature and pressure range. A comparison between the used models showed that modified
Kwak and Mansoori mixing rules gave better correlations in comparison with
the other mixing rules.
Keywords: solid solubility; supercritical carbon dioxide; equation of
state; mixing rules.
In recent years, there has been increasing interest in the use of clean technologies that reduce
pollution or waste, as well as energy or material use
compared traditional technologies. Supercritical fluid
technology is one of the most important clean technologies that can be used in many important industries,
such as in chemical and biochemical reactions,
extraction and purification processes, particle production or more recently in material and polymer processing [1-4].
To develop or improve these processes for producing better products, it is necessary to know the
phase behavior of the solute component in supercritical or pressurized fluid. Experimental methods were
used to determine the solubility of solids in supercritical fluids (SCF). Since these methods are very
costly and time consuming, models are often used to
provide correlations.
Several models have been developed in order to
correlate and predict solubility data at various pressures and temperatures. Some of these models are
empirical, while others have fundamental basis [5].
Correspondence: A. Haghighi-Asl, School of Chemical, Gas and
Petroleum Engineering, Semnan University, P.O. Box: 3519645399, Semnan, Iran.
E-mail: ahaghighi@semnan.ac.ir; alihaghighiasl@yahoo.com
Paper received: 3 February, 2012
Paper revised: 16 July, 2012
Paper accepted: 16 July, 2012
Generally, for prediction of solid solubilities in supercritical fluids, an equation of state (EOS) approach, a
density-based approach or a solubility parameter
approach is used.
Density-based models and solubility parameter
based models are used because of their relative ease
of application in comparison to models based on
equations of state. But equations of state based
models have been used because of their proper
abilities to predict the phase properties [6].
Equation of state based models are applied in
many industries including oil and gas industries,
separation and purification industries and some
supercritical assisted industries. Van der Waals [7]
developed the first two-parameter cubic equation of
state. In this equation, the effect of intermolecular
forces and size of molecules are considered in two
terms of repulsive and attractive terms. Redlich and
Kwong [8], Soave [9] and Peng and Robinson [10]
modified the repulsive and attractive terms of van der
Waals EOS and proposed new equations of state in
which parameters were defined as functions of
reduced temperature and acentric factor. These models
were proposed for pure substances; however, for
mixtures, mixing rules must be used.
Cubic equations of state are valuable engineering tools for process design of any complex system.
These equations are remarkably successful in mode-
389
H. BASERI et al.: THERMODYNAMIC MODELING OF SOLID SOLUBILITY…
ling of phase equilibrium with supercritical components. The Peng-Robinson equation of state (PREOS) is a well-known cubic EOS that gives a good
qualitative picture of all types of SCF phase behavior
and reasonably it gives good quantitative fits for a
wide variety of systems [11,12]. For example, many
researchers used the PR-EOS for modeling of vapor
liquid equilibrium or solid vapor equilibrium which
contains supercritical carbon dioxide [13,14]. Moreover, PR-EOS has also been attempted to model the
solubility of polar solutes in supercritical CO2 in the
presence of a polar co-solvent with some degree of
success [15,16].
Mixing rules are used for modeling of phase
equilibrium in the mixtures. Conventional mixing rules
such as van der Waals mixing rules or Panagiotopoulos and Reid mixing rules were used in many literatures for modeling of phase equilibrium of various
systems in solid, liquid or gas phase [17]. Kwak and
Mansoori [18] proposed new mixing rules based on
statistical mechanical arguments. They presented
new mixing rules by making relevance between the
parameters of EOS and the parameters (energy and
volume) of potential function in which the constants
used for the mixing rules are temperature independent.
Valderrama and Alvarez [19] have considered
the application of the original Kwak and Mansoori
mixing rules and a simplification of the combining
rules for bij and dij. They presented new simplified
mixing rules based on original Kwak and Mansoori
mixing rules and they modeled the solubility of some
solid components in supercritical carbon dioxide.
In the present report, we study temperature
independent mixing rules for PR-EOS, i.e. the van der
Waals one fluid mixing rules, Panagiotopoulos and
Reid mixing rules, and MKM mixing rules to predict
the solubility of various solutes in supercritical carbon
dioxide. The solutes studied here have a very different molecular structure and have been used in many
important industries, e.g., textile, polymer, food and
cosmetic industries.
Thermodynamic model
When equilibrium between a fluid mixture
(solute i + solvent j) and a solid (i) is reached, the
general condition of equilibrium is as follows (it is
assumed that the solid phase is pure and does not
contain solvent):


fi S = fi F
(1)
F
f i is the fugacity of solute i in the fluid mixtur,
where

f i S is the fugacity of pure solute i at the same
390
CI&CEQ 19 (3) 389−398 (2013)
temperature and pressure in the solid phase. Since
the solid phase is pure, the fugacity of solute i is given
by [20]:


v isat
dP 
P sat RT


f i S = Pi sat (T ) φisat exp 

P

(2)

i
The solubility of solute i can be expressed as
[20]:



 Vi S 

d
P


P sat  R T 

i

Pi sat (T ) φi sat (T ) exp 
yi =

P
φi F P
(3)
By supposing that the molar volume of the solid
is independent of pressure and the fugacity coefficient
of pure solid is unity, a simplified equation can be
obtained:
V i S P − Pi sat (T ) 
Pi sat (T )



yi = F
exp 


RT
φi P

F
(4)

In Eq. (4), φi is the fugacity coefficient of solute

component i in the fluid phase, in this paper, φi F was
calculated by using of PR EOS (5) plus three different
mixing rules: van der Waals one fluid mixing rules,
Panagiotopoulos and Reid mixing rules and MKM
mixing rules.
The PR-EOS combined with VDW mixing rules
gives Eq. (6) for fugacity coefficient [20]:
P =
RT
a
−
V − b V (V + b ) + b (V − b )
 b (i )
 bP
ln φiF =
(Z − 1) − ln(Z −
b
 RT

) −


 bP  
 2 y j aij
  Z + (1+ 2)

b
(
i
)
 RT  
 j
 ln 
−
−
a
b  
 bP  
 bP  
2 2
  Z − (1− 2) RT  

RT





aP
(RT )
2
a ij = a i a j (1 − k ij ) and a =  i  j y i y j a ij
b =   yi y j
i
j
bi + b j
2
(5)
(6)
(7)
(8)
In these equations ai and bi are the attraction
and repulsion parameters for the pure substances,
but aij and bij are the unlike interaction parameters.
For PR EOS these parameters can be calculated by
the following equations:
H. BASERI et al.: THERMODYNAMIC MODELING OF SOLID SOLUBILITY…
 
R 2TC i 2 
1−  T
ai = 0.45724
k
1
+

 TCi
Pc i 







k = 0.37464 + 1.5422 ω − 0.26922 ω
0.5

 


2
(9)
CI&CEQ 19 (3) 389−398 (2013)
 bi + b j 

 2 
bm =   y i y j 
i
j
and
2
(10)
i
RT
bi = 0.07780 c i
PC i
di +d j 

 2 
dm =   yi y j 
(11)
A=
j
cP
(RT )2
and B =
(15)
bm P
RT
The Panagiotopoulos and Reid mixing rules are
as follow [21]:
and
a =   y i y j (1 − K ijPan ) ai a j
c = am + d mRT − 2 amd mRT
with
Ai =  y j (1 − k ij ) ai a j and Bi =  y j
i
j
K ijPan = k ij − (k ji − k ij )y i
(12)
Detailed method for calculation of the fugacity
coefficient by PR-EOS and Panagiotopoulos and Reid
mixing rules was presented in our last work [22]. The
fugacity coefficient for a component (i) in a mixture
can be obtained by equation (13):

RT  ∂ (nb ) 
lnφi F =
( Z − 1)) −


b  ∂ni  T ,n
j
a
(
(
)
)

−


(13)
where n is the total number (moles) of molecules, ni is
the number of molecule (i) in the mixture and V is the
total volume of mixture. For calculation of the fugacity
coefficient by this equation, energy parameter for the
mixture (a) and the volume parameter for the mixture
(b) must be calculated by Eqs. (8) and (12).
Valderrama and Alvarez [19] modified the Kwak
and Mansoori mixing rules and a new equation for
fugacity coefficient was derived:

(2Bi − bm )(Z − 1)
lnφi F =
− ln(Z − B ) −
bm
×(
A
2 2B
×
2 Ai + 2RTDi − 2 RT (am Di + d m Ai ) / amd m
c
2Bi − bm
bm
 Z + B (1 + 2) 
)ln 

 Z + B (1 − 2) 
am =   y i y j (1 − k ij ) ai a j
i
and
j
j
bi + b
j
2
and
Di =  y j
di +d j
(17)
2
j
In these
d j = d j (1 − δ j ) .
equations,
b j = b j (1 − β j )
and
RESULTS AND DISCUSSION
RT 1  1  ∂(n 2a ) 
 b
+
(  


 2 2 a  n  ∂ni  T ,n j

V + 1 − 2 b 


1 1  ∂(nb ) 



−  
×
RT
ln

V + 1 + 2 b 
b  n  ∂ni  T ,n 

j 



 (V − b ) Z
RT ln 
 V
j
(16)
−
(14)
The solubility of various solid components, with
different molecular weights, like climbazole, cinnamic
acid and spiroindolinonaphthoxazine photochromic
dye have been successfully predicted by using a thermodynamic model which consisted of the PR-EOS
with various mixing rules.
The experimental data of the solubility of solid
components in supercritical CO2 used in this paper
have been given from various literatures. The critical
constants, acentric factors, molar volume of solids
and constants for Antoine equation of these components are listed in Table 1 (for Irgacure 2959 photoinitiator and spiroindolinonaphthoxazine photochromic
dye, the estimated vapor pressure at required temperatures were reported).
Table 2 shows a comparison of the results of
PR-EOS with three various mixing rules: van der
Waals one fluid, Panagiotopoulos and Reid, and
MKM mixing rules. Comparison between the used
models is based on Average Absolute Relative Deviation (AARD) between calculations and experimental
solubility data (Eq. (18)).
AARD =
1
N
N

i =1
exp
calc
y solid
− y solid
exp
y solid
(18)
In this paper, solubility of nine different solid
components in supercritical CO2 was predicted by
391
H. BASERI et al.: THERMODYNAMIC MODELING OF SOLID SOLUBILITY…
CI&CEQ 19 (3) 389−398 (2013)
Table 1. Properties of the solids which were studied in this paper
a
Substance
TC / K
PC / MPa
ω
Vm / cm3 mol–1
Climbazole
872.0
2.37
0.819
Triclocarbon
935.8
3.49
1,5 Naphtaline diamine
886.3
4.339
4-Methoxyphenylacetic acid
827.30
3.485
Naphtalin
748.2
Cinnamic acid
Phenoxyacetic acide
Irgacure 2959 photoinitiator
Sublimation vapor
B
223.8
10.382
5479.6
[23]
0.760
206.3
10.533
5588.4
[23]
0.714
113
11.854
4453.7
[24]
0.808
127.9
55.95
21101.81
[25]
4.05
0.302
110.3
13.583
3733.9
[19]
803.94
3.858
0.688
118.8
40.92
14527.28
[25]
802.61
3.991
0.760
113.0
43.78
14557.64
[25]
840.6
2.89
0.60
151.1
At 318.2 K:
At 328.2 K:
[26]
4.63×10 Pa
0.134 Pa
0.361 Pa
At 308 K:
at 318 K
At 308 .2 K:
-2
Spiroindolinonaphthoxazine
photochromic dye
Reference
A
1446.2
1.436
1.169
344.9
0.72×10
-13
pa 3.81×10
-13
At 328 K:
Pa
18.3×10
-13
[27]
Pa
a
A and B are the constants in the sublimation pressure expression: log P (105 Pa) = A − B/T (K)
Table 2. Average absolute relative deviations between the experimental data and calculation results of CO2-solid systems by using the
PR EOS with three temperature independent mixing rules
No.
1
System: CO2 +
T/K
P / MPa
Range of y2×10
Climbazole
313-333
10-40
6-48
-4
Parameters
a
Kij = 0.1483
Kij = 0.1466
Kji = -0.1816
K = -0.155
β = -0.0398
δ = 0.4868
17.47
Kij = 0.1933
Kij = 0.1466
Kji = -0.1816
K = -0.1193
β = -0.1395
δ = 0.3889
16.79
Kij = 0.2606
Kij = 0.2606
Kji = 0.1551
K = 0.7931
β = 0.1835
δ = 1.1452
55.79
Kij = 0.2079
Kij = 0.2079
Kji = 0.1331
K = 0.2015
β = -0.4538
δ = 0.7818
17.6
Kij = 0.2219
Kij = 0.2219
Kji = 3.44
K = 0.4711
β = 0.2545
δ = 0.9563
33.0
PR_VDW1
PR_Pa.& Reid
MKM
2
Triclocarbon
313-333
10.9-39
0.9-8.7
b
c
PR_VDW1
PR_Pa.& Reid
MKM
3
Spiroindolinonaphthoxazine
photochromic dye
308-328
10-26
0.0022-0.05
PR_VDW1
PR_Pa.& Reid
MKM
4
1,5 Naphtaline diamine
313-333
11-20
0.02-0.16
PR_VDW1
PR_Pa.& Reid
MKM
5
Irgacure 2959 photoinitiator
308-328
10-26
0.05-2.8
PR_VDW1
PR_Pa.& Reid
MKM
392
AARD / % Ref.
Mixing rules
[23]
16.5
2.34
[23]
16.5
3.20
[27]
54.0
13.6
[24]
17.3
6.00
30.0
10.0
[26]
H. BASERI et al.: THERMODYNAMIC MODELING OF SOLID SOLUBILITY…
CI&CEQ 19 (3) 389−398 (2013)
Table 2. Continued
No.
6
System: CO2 +
T/K
P / MPa
Range of y2×10
Naphtalin
308-318
15-35
70-300
-4
Parameters
PR_VDW1
Kij = 0.1012
Kij = 0.0987
Kji = -0.4032
K = 0.1440
β = -0.1130
δ = 0.6456
7.20
Kij = 0.0248
Kij = 0.0238
Kji = 2.0528
K = 0.0415
β = 0.0772
δ = 0.5908
6.28
Kij = 0.1449
Kij = 0.1439
Kji = 2.3006
K = 0.2482
β = 0.3003
δ = 0.7191
12.23
Kij = -0.1426
Kij = -0.1458
Kji = 2.5298
K = -0.2610
β = -0.3224
δ = 0.5174
14.43
PR_Pa.& Reid
MKM
7
Cinnamic acid
308-328
15-24
0.3-4.3
PR_VDW1
PR_Pa.& Reid
MKM
8
Phenoxyacetic acide
308-328
12-23
0.5-8
PR_VDW1
PR_Pa.& Reid
MKM
9
4-Methoxyphenylacetic acid
308-328
11-24
0.4-6.3
PR_VDW1
PR_Pa.& Reid
MKM
a
b
AARD / % Ref.a
Mixing rules
[19]
3.60
3.40
[25]
6.20
4.21
[25]
11.86
3.74
[25]
14.0
4.79
c
PR EOS with Panagiotopoulos and Reid mixing rules; PR EOS with modified Kwak and Mansoori mixing rules; reference of experimental data
using of PR-EOS with three various mixing rules.
Moreover, calculation results are compared with the
experimental data which were reported in various
literatures. Good estimating results are achieved by
using of this calculating method. For example, climbasole is one of the solids which were studied in this
paper. The results of calculations for this component
are plotted in Figure 1. As can be seen in this figure,
the best calculation results in comparison with
experimental data are the results of calculations
obtained using PR-EOS with MKM mixing rules.
Experimental solubility of triclocarbon in supercritical CO2 at various temperatures of 313.2, 323.2,
333.2 K [23], and the results of calculations by the
proposed model are shown in Figure 2. These figures
show the experimental and calculation solubility data
from 10 to 35 MPa. These figures show that by
increasing pressure, deviation between experimental
data and calculation results of the model by two mixing rules of Panagiotopoulos & Reid and van der
Waals mixing rules increased. But MKM mixing rules
show good results at all ranges of pressure.
For Irgacure 2959 photoinitiator a comparison
between experimental data and the results of calculations by the proposed models with three mixing rules
of Van der Waals one fluid mixing rules, Panagioto-
poulos and Reid mixing rules, and MKM mixing rules
are shown in Figure 3. This figure shows that at
pressures higher than 20 MPa, deviation between
experimental data and calculation results by two mixing rules of Van der Waals one fluid mixing rules and
Panagiotopoulos and Reid mixing rules becomes very
large. The MKM mixing rule showed good calculation
results in all pressure ranges.
Based on the results reported in Figures 1-3 it
can be concluded that the performance of MKM
mixing rules in comparison with other applied models
is the best. The reported values of AARD show that
for the MKM mixing rules, the deviation between calculated results and experimental data is very small.
PR-EOS with Kwak-Mansoori mixing rules is an
equation of state with three temperature independent
parameters. In this equation, the thermodynamic variables were separated from constants of PR-EOS [18].
MKM mixing rules are based on original Kwak-Mansoori mixing rules but they have been simplified by
[19]. As can be shown in Figures 1-3, by using MKM
mixing rules, the accuracy of calculated results
increased in comparison with other mixing rules such
as Panagiotopoulos and Reid mixing rules.
The calculated results of other researchers (by
different models) are reviewed in Table 3. The used
393
H. BASERI et al.: THERMODYNAMIC MODELING OF SOLID SOLUBILITY…
CI&CEQ 19 (3) 389−398 (2013)
Figure 1. Solubility of Climbasole in supercritical CO2 at various temperatures (A: 313.2, B: 323.2 and C: 333.2 K). (- - -): Calculation
results by PR-EOS and van der Waals one fluid mixing rules, (⋅⋅⋅): calculation results by PR-EOS and Panagiotopoulos and Reid mixing
rules, (─): calculation results by PR-EOS and MKM mixing rules and (●): experimental data [23].
thermodynamic models, number of adjustable parameters (that were used in the proposed model), number of used experimental data for estimation of adjustable parameters and the AARD between experimental and calculated values are reported in this table.
Comparison between the reported AARD in
Table 2 and those in Table 3 can be useful for comprehension of accuracy of different models. It can be
shown from Tables 2 and 3 that for climbazole and
triclocarbon, the values of AARD by MKM mixing
394
rules are about half in comparison with those for other
proposed models.
For Irgacure 2959 photoinitiator and spiroindolinonaphthoxazine photochromic dye, AARD of PR and
SRK models in combination with temperature dependent mixing rules with six adjustable parameters are
about 0.1 and 0.13. These values with MKM mixing
rules are also about 0.1 and 0.13 but by use of three
adjustable parameters.
H. BASERI et al.: THERMODYNAMIC MODELING OF SOLID SOLUBILITY…
CI&CEQ 19 (3) 389−398 (2013)
Figure 2. Solubility of Triclocarbon in supercritical CO2 at various temperatures (A: 313.2, B: 323.2 and C: 333.2 K). (- - -): Calculation
results by PR-EOS and van der Waals one fluid mixing rules, (⋅⋅⋅): calculation results by PR-EOS and Panagiotopoulos and Reid mixing
rules, (─): calculation results by PR-EOS and MKM mixing rules and (●): experimental data [23].
For other components, the values in Tables 2
and 3 show that the PR-EOS in combination with
MKM mixing rules gives better results in comparison
with other models.
CONCLUSIONS
This paper studies the performance of different
thermodynamic models for calculation of solid solubility in supercritical fluids. The results showed that
the type of mixing rules and the number of adjustable
parameters used in the mixing rules have major
effects on the accuracy of model. Based on the comparison between experimental data and calculation
results for nine studied components it can be concluded that MKM mixing rules with three adjustable
parameters show better results for modeling of solid
solubility in SCF in comparison with the van der
Waals mixing rules and Panagiotopoulos and Reid
mixing rules.
395
H. BASERI et al.: THERMODYNAMIC MODELING OF SOLID SOLUBILITY…
CI&CEQ 19 (3) 389−398 (2013)
Figure 3. Solubility of Irgacure 2959 photoinitiator in supercritical CO2 at various temperatures (A: 308.2, B: 318.2 and C: 328.2 K).
(- - -): calculation results by PR-EOS and van der Waals one fluid mixing rules, (⋅⋅⋅): calculation results by PR-EOS and Panagiotopoulos
and Reid mixing rules, (─): calculation results by PR-EOS and MKM mixing rules and (●): experimental data [26].
Table 3. Comparison between different thermodynamic models
No.
1
2
3
396
Number of
experimental data
Mean of reported
Reference
AARDa / %
System: CO2 +
Used model
Number of adjustable parameter
Climbazole
PR-VDW 1
3
Temperature dependent
24
7.70
QLF
3
Temperature dependent
24
6.33
PR-VDW 1
3
Temperature dependent
24
15.20
QLF
3
Temperature dependent
24
7.67
PR
6
Temperature dependent
27
5.03
Triclocarbon
1,5 Naphtaline diamine
[23]
[23]
[24]
H. BASERI et al.: THERMODYNAMIC MODELING OF SOLID SOLUBILITY…
CI&CEQ 19 (3) 389−398 (2013)
Table 3. Continued
No.
4
Number of
experimental data
Mean of reported
Reference
AARDa / %
System: CO2 +
Used model
Number of adjustable parameter
4-Methoxyphenylacetic acid
PR-VDW 1
1
Temperature independent
22
14.04
PR-VDW 2
2
Temperature independent
22
4.80
SRK-VDW 1
1
Temperature independent
22
13.48
SRK-VDW 2
2
Temperature independent
22
5.15
[25]
5
Naphtalin
PR-MKM
3
Temperature independent
22
4.70
[19]
6
Cinnamic acid
PR-VDW 1
1
Temperature independent
19
6.16
[25]
7
8
9
Phenoxyacetic acide
Irgacure 2959 photoinitiator
PR-VDW 2
2
Temperature independent
19
5.37
SRK-VDW 1
1
Temperature independent
19
6.57
SRK-VDW 2
2
Temperature independent
19
5.48
PR-VDW 1
1
Temperature independent
22
12.14
PR-VDW 2
2
Temperature independent
22
4.41
SRK-VDW 1
1
Temperature independent
22
12.92
SRK-VDW 2
2
Temperature independent
22
4.73
PR-VDW 1
3
Temperature dependent
3
31.20
PR-VDW 2
6
Temperature dependent
6
9.20
6
Temperature dependent
6
12.33
6
Temperature dependent
6
13.17
Spiroindolinonaphthoxazine PR-VDW 2
photochromic dye
SRK-VDW 2
[25]
[26]
[27]
a
Mean value of the average absolute relative deviation between experimental data and calculation results which reported in various papers for each
component
Nomenclature
A, A
a
B, B
b
d
fi
kij, Kij
P
R
T
V
yi
Z
α
parameters used in MKM mixing rules
EOS interaction energy parameter
parameters used in MKM mixing rules
EOS volume parameter
EOS constants for KM mixing rules
fugacity of component i
binary interaction parameter
pressure
universal gas constant
thermodynamic temperature
volume
mole percent of component i
compressibility factor
temperature-dependent parameter for calculation of a(T)
parameters used in MKM mixing rules
β, δ
fugacity coefficient
φ
Superscripts
c
m
critical point
parameters of MKM mixing rules for the mix-
tures
s
F
Pan
Sat
VDW
solid phase
fluid phase
Panagiotopoulos and Reid
saturation
Van der Waals
REFERENCES
[1]
J. Yuanhui, J. Xiaoyan, F. Xin, L. Chang, L. Linghong, L.
Xiaohua, Chin. J. Chern. Eng. 15(3) (2007) 439-448
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[3]
B. Subramaniam, R.A. Rajewski, K. Snavely, J. Pharm.
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[8]
O. Redlich, J.N.S. Kwong, Chem. Rev. 44 (1949) 233-244
[9]
G. Soave, Chem. Eng. Sci. 27 (1972) 1197–1203
[10]
D.B. Robinson, D.Y. Peng, Ind. Eng. Chem. Fund. 15
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[11]
M.A. McHugh, V.J. Krukonis, Supercritical Fluid Extraction: Principles and Practice, Butterworth, Boston, MA,
1994
[12]
Z. Huang, S. Kawi, Y.C. Chiew, Fluid Phase Equilib. 216
(2004) 111–122
[13]
H. Baseri, M.N. Lotfollahi, J. Chem. Thermodynamics 43
(2011) 1535–1540
[14]
S. Colussi, N. Elvassore, I. Kikic, J. Supercritical Fluids
39 (2006) 118–126
[15]
K. Tamura, T. Shinoda, Fluid Phase Equilib. 219 (2004)
25–32
[16]
S. Raeissi, C.J. Peters, J. Supercrit. Fluids 33 (2005)
115–120
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[17]
K.R. Hall, G.A. Iglesias-Silva, G.A. Mansoori, Fluid Phase
Equilibria, 91 (1993) 67-76
[22]
M.N. Lotfollahi, H. Baseri, A. Haghighi Asl, Iran. J. Chem.
Chem. Eng. 27 (2008) 97-105
[18]
T.Y. Kwak , G.A. Mansoori, Chem. Eng. Sci. 41(5) (1986)
1303–1309
[23]
C.I. Park, M.S. Shin, H. Kim, J. Chem. Thermodynamics
41 (2009) 30-34
[19]
J.O. Valderrama, V.H. Alvarez, J. Supercritical Fluids 32
(2004) 37–46
[24]
K. Khimeche, P. Alessi, I. Kikic, A. Dahmani, J. Supercritical Fluids 41 (2007) 10-19
[20]
J.M. Prausnitz, R.N. Lichtenthaler, E.G. De Azevedo,
rd
Molecular thermodynamic of fluid phase equilibria, 3
ed., Prentice-Hall, Inc., Upper Saddle River, NJ, 1999
[25]
Y.P. Chen, Y.M. Chen, M. Tang, Fluid Phase Equilibria
275 (2009) 33–38
[26]
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A.Z. Panagiotopoulos, D.B. Reid, Fluid Phase Equilibria,
29 (1986) 525-534
P. Coimbra, D. Fernandes, P. Ferreira, M.H. Gil, H.C. de
Sousa, J. Supercritical Fluids 45 (2008) 272-281
[27]
P. Coimbra, M.H. Gil, C.M.M. Duarte, B.H. Heron, H.C.
de Sousa, Fluid Phase Equilibria 238 (2005) 120–128.
HADI BASERI
ALI HAGHIGHI-ASL
MOHAMMAD NADER
LOTFOLLAHI
School of Chemical, Gas and
Petroleum Engineering, Semnan
University, Semnan, Iran
NAUČNI RAD
TERMODINAMIČKO MODELOVANJE
RASTVORLJIVOSTI ČVRSTIH JEDINJENJA U
NATKRITIČNOM UGLJEN-DIOKSIDU: POREĐENJE
PRAVILA MEŠANJA
U ovom radu, Peng-Robinson-ova jednačina stanja je korišćena za termodinamičko
modelovanje rastvorljivosti različitih čvrstih komponenti u natkritičnom ugljen-dioksidu.
Takođe, proučavan je uticaj tri pravila mešanja: Van der Waals-ovo, PanagiotopoulosReid-ovo i modifikovano Kwak-Mansoori-ovo, na tačnost dobijenih rezultata. Dobijena je
dobra korelacija između izračunatih i eksperimentalnih podataka u širokom opsegu temperature i pritiska. Modifikovano Kwak-Mansoori-jevo pravilo mešana daje bolju korelaciju u odnosu na ostala pravila mešanja.
Ključne reči: rastvorljivost čvrstih jedinjenja; natkritični ugljen-dioksid; jednačina
stanja; pravila mešanja
398
Available on line at
Association of the Chemical Engineers of Serbia AChE
www.ache.org.rs/CICEQ
Chemical Industry & Chemical Engineering Quarterly 19 (3) 399−409 (2013)
S. NADEEM1
ARSHAD RIAZ2
R. ELLAHI2
1
Department of Mathematics,
Quaid-i-Azam University,
Islamabad, Pakistan
2
Department of Mathematics and
Statistics, FBAS, IIU Islamabad,
Pakistan
SCIENTIFIC PAPER
UDC 5/6:519:51-3
DOI 10.2298/CICEQ120402075N
CI&CEQ
PERISTALTIC FLOW OF A JEFFREY FLUID IN
A RECTANGULAR DUCT HAVING
COMPLIANT WALLS
In this article, the theoretical and mathematical study of peristaltic transport of
a Jeffrey fluid in a rectangular duct with compliant walls is discussed. The
constitutive equations are simplified under the implementation of low Reynolds
number and long wavelength approximations. The analytical solution of the
resulting equations is evaluated by Eigen function expansion method. The graphical aspects of all the parameters of interest are also analyzed. The graphs
of velocity for two and three dimensional flow are plotted. The trapping bolus
phenomenon is also discussed though streamlines.
Keywords: peristaltic flow, Jeffrey fluid, rectangular duct, compliant walls.
The study of peristaltic flows is quite useful in
physiology and industry because of its large number
of applications and in mathematics due to its complicated geometries and solutions of nonlinear equations. In physiology, it is used by many systems in the
living body to propel or to mix the contents of a tube.
The peristaltic mechanism usually occurs in urine
transport from the kidney to the bladder, swallowing
food through the esophagus, chyme motion in the
gastrointestinal tracts, vasomotion of small blood
vessels, movement of Spermatozoa and the human
reproductive tract. Theoretically and mathematically,
the complete exact solutions of peristaltic flow problems are quite difficult to determine even in viscous
fluid theory. However, after using certain physical
simplifications such as long wavelength and low Reynolds number approximations, the authors successfully calculate only limited exact and analytical solutions. Some interesting studies are given in the references [1-11]. The study of peristaltic flows of Newtonian and non-Newtonian fluids in two-dimensional
symmetric and asymmetric channels is also very
useful in a number of applications, specially the study
of inter-uterine fluid flow in a nonpregnant uterus [1221]. Recently, Reddy et al. [22] have given the idea
that the sagittal cross-section of the uterus may be
better approximated by a tube of rectangular cross
section than a two dimensional channel and presented the influence of lateral walls on peristaltic flow
in a rectangular duct. More recently, this idea has
been extended by Nadeem and Akram [23] for nonNewtonian fluids. More studies on the peristaltic flow
in three-dimensional rectangular channel are cited in
the references [24-25]. A large number of analytical
and numerical studies on the peristaltic flow of Newtonian and non-Newtonian fluids in different flow geometries are discussed by Tripathi [26-33]. However,
the peristaltic flows of three dimensional non-Newtonian fluids in a rectangular duct having compliant
walls have to the best of our knowledge not been
explored. The aim of the present work is to discuss
the peristaltic flow of a Jeffrey fluid in a rectangular
duct with compliant walls. The governing equations of
a Jeffrey fluid for three dimensional flows are simplified under the assumptions of long wavelength and
low Reynolds number approximation. The exact solutions of the reduced equations having the compliant
wall properties are found with the help of the Eigen
function expansion method. The physical features of
the pertinent parameters are measured with the help
of graphs. The circulating bolus scheme is also
described with the help of streamlines graphs.
Correspondence: Arshad Riaz, Department of Mathematics and
Statistics, FBAS, IIU Islamabad 44000, Pakistan.
E-mail: arshadriaz26@gmail.com
Paper received: 2 April, 2012
Paper revised: 9 July, 2012
Paper accepted: 17 July, 2012
MATHEMATICAL FORMULATION
Consider the peristaltic flow of an incompressible non-Newtonian Jeffrey fluid in a cross section of
399
S. NADEEM, A. RIAZ, R. ELLAHI: PERISTALTIC FLOW OF A JEFFREY FLUID…
rectangular channel having the width 2d and height
2a. In the present geometry, the Cartesian coordinate
system is taken in such a way that the x-axis is taken
along the axial direction, the y-axis is taken along the
lateral direction and the z-axis is along the vertical
direction of rectangular channel (Figure 1). The walls
of the channel are assumed to be flexible and are
taken as compliant, on which waves with small amplitude and long wave length are considered.
CI&CEQ 19 (3) 399−409 (2013)
β 2 ∂ 2u
∂p
1 ∂ 2u
=
+
∂x 1 + λ1 ∂y 2 1 + λ1 ∂z 2
(4)
Here β = a/d is the aspect ratio. The corresponding non-dimensional boundary conditions for
compliant walls are stated as:
u ( x , y , z ,t ) = −1 at y = ±1
(5)
u ( x , y , z ,t ) = −1 at z = ±h ( x ,t ) = ±1 ± η ( x ,t )
(6)
where η(x,t) = ϕcos2π(x-t), ϕ = b/a (amplitude ratio)
and 0≤ ϕ ≤1. The governing equation for the flexible
wall may be specified as:
L (η ) = p − p 0
where L is an operator, which is used to represent the
motion of stretched membrane with viscosity damping
forces such that [22]:
L =m
Figure 1. Schematic diagram for the peristaltic flow in a
rectangular duct.
The geometry of the channel wall is given by:
 2π
( x − ct ) 
λ

z = h ( x ,t ) = ±a ± b cos 
(1)
where b is the amplitude of the wave, λ is the
wavelength, c is the velocity of propagation, t is the
time and x is the direction of wave propagation. The
walls parallel to the xz-plane remain undisturbed and
do not measure any peristaltic wave motion. We
assume that the lateral velocity is zero as there is no
change in lateral direction of the duct cross section.
Let (u,0,w) be the velocity for a rectangular duct. The
stress tensor for the Jeffrey model is defined by [3134]:
S =
.. 
.
 γ + λ2 γ 

1 + λ1 


μ
(2)
In the above equation, λ1 is the ratio of
relaxation to retardation times, λ2 is the delay time, γ
is shear stress and double dots denote the differentiation with respect to time. Under the assumption
of long wave length and low Reynolds number, the
governing equations in non-dimensional form for the
considered flow problem are stated as [23]:
∂u ∂w
+
=0
∂x ∂z
400
(3)
∂2
∂
∂4
∂2
+D
+B
−T
+K
2
4
∂t
∂t
∂x
∂x 2
(7)
In the above equation, m is the mass per unit
area, D is the coefficient of the viscous damping
membrane, B is the flexural rigidity of the plate, T is
the elastic tension in the membrane, K is spring stiffness and p0 is the pressure on the outside surface of
the wall due to tension in the muscle, which is
assumed to be zero here. The continuity of stress at
z=±1±η and using the x-momentum equation yield:
∂p
∂ 3η
∂ 2η
∂ 5η
∂ 3η
∂η
= E1 2 + E 2
+E3 5 −E4 3 +E5
(8)
∂x
∂t ∂x
∂x
∂t ∂x
∂x
∂x
∂ 3η
∂ 2η
∂ 5η
∂ 3η
∂η
+E2
+E3 5 −E4 3 +E5
=
2
∂t ∂x
∂x
∂t ∂x
∂x
∂x
1 ∂ 2u
β 2 ∂ 2u
=
+
2
1 + λ1 ∂y
1 + λ1 ∂z 2
E1
(9)
at z = ±1 ± η , in which E1 = ma3c/λ3µ, E2 = Da3/λ2µ,
E3 = Ba3/cλ5µ, E4 = Ta3/cλ3µ and E5 = Ka3/cλµ are the
non-dimensional elasticity parameters. Now we differentiate Eq. (4) with respect to z as follows:
β 2 ∂3u
1 ∂ 3u
+
=0
2
1 + λ1 ∂z ∂y
1 + λ1 ∂z 3
(10)
The expressions for stream function satisfying
Eq. (3) are defined as (u = ∂ψ/∂z, w = -∂ψ/∂x).
Solution of the problem
The solution of Eq. (10) with boundary conditions (5), (6) and (9) is computed by the eigenfunction expansion method and is directly defined as:
S. NADEEM, A. RIAZ, R. ELLAHI: PERISTALTIC FLOW OF A JEFFREY FLUID…
u = −1 +
RESULTS AND DISCUSSIONS
 cosh α z  16C ( −1)
π
+ 1−
cos ( 2n − 1) y

2
 cosh α h  ( 2n − 1) π β
n
(11)
n
3
3
2
n
where:
α = ( 2n − 1)
n
π
2
β
(12)
C = 2π (1 + λ ) ϕ [2E π cos 2π ( x − t ) −
1
2
− (E + 4π ( −E + E + 4E π
2
5
CI&CEQ 19 (3) 399−409 (2013)
1
4
3
2
) ) sin 2π ( x − t )]
(13)
The detailed calculation is given in the appendix.
It is noted that limiting λ1→0 results in reversing the
present problem to the viscous fluid case. It is also
observed from the above analysis that employing β→0
and β→1 reduces the discussed geometry to the twodimensional channel and square duct, respectively.
(a)
In this section, the effects of different physical
parameters of a Jeffrey fluid model on the velocity
profile of the fluid under discussion are examined
graphically and the trapping phenomenon is also illustrated by plotting streamlines for different pertinent
parameters. Figures 2-7 are plotted to see the variation of the velocity profile with the emerging parameters β, λ1, E1, E2, E3 and E4. The streamlines are
sketched in Figures 8-13, which show the flow
behavior with various values of all the observing parameters. In Figures 2, 4 and 5, the velocity profile is
plotted with different values of the parameters β, E1
and E2. From these figures, we can observe that the
magnitude of the velocity profile is a decreasing function of the above three parameters. The effects of
(b)
Figure 2. Velocity profile for different values of β for fixed ϕ = 0.2, x = 0.5, t = 0.4, λ1 = 0.5, E1 = 0.1, E2 = 0.2, E3 = 0.01, E4 = 0.2, E5 = 0.3.
a) For 2-dimensional, b) for 3-dimensional.
(a)
(b)
Figure 3. Velocity profile for different values of λ1 for fixed ϕ = 0.2, x = 0.5, t = 0.4, β = 2.5, E1 = 0.1, E2 = 0.1, E3 = 0.05, E4 = 0.2, E5 = 0.5.
a) For 2-dimensional, b) for 3-dimensional.
401
S. NADEEM, A. RIAZ, R. ELLAHI: PERISTALTIC FLOW OF A JEFFREY FLUID…
(a)
CI&CEQ 19 (0) 000−000 (2013)
(b)
Figure 4. Velocity profile for different values of E1 for fixed ϕ = 0.2, x = 0.5, t = 0.4, β = 1.5, λ1 = 0.5, E2 = 0.1, E3 = 0.05, E4 = 0.2, E5 = 0.5.
a) For 2-dimensional, b) for 3-dimensional.
(a)
(b)
Figure 5. Velocity profile for different values of E2 for fixed ϕ = 0.2, x = 0.5, t = 0.4, β = 2.5, λ1 = 0.5, E1 = 0.1, E3 = 0.01, E4 = 0.2, E5 = 0.5.
a) For 2-dimensional, b) for 3-dimensional.
(a)
(b)
Figure 6. Velocity profile for different values of E3 for fixed ϕ = 0.2, x = 0.5, t = 0.4, β = 2.7, λ1 = 0.5, E1 = 0.1, E2 = 0.1, E4 = 0.2, E5 = 0.5.
a) For 2-dimensional, b) for 3-dimensional.
402
S. NADEEM, A. RIAZ, R. ELLAHI: PERISTALTIC FLOW OF A JEFFREY FLUID…
CI&CEQ 19 (3) 399−409 (2013)
(a)
(b)
Figure 7. Velocity profile for different values of E4 for fixed ϕ = 0.2, x = 0.5, t = 0.4, β = 3, λ1 = 0.5, E1 = 0.1, E2 = 0.1, E3 = 0.2, E5 = 0.5.
(a) For 2-dimensional, (b) For 3-dimensional.
(a)
(b)
(c)
(d)
Figure 8. Streamlines for different values of β. a) For β = 0.4, b) for β = 0.6, c) for β = 0.8 d) for β = 1. The other parameters are y = 0.5,
λ1 = 1, ϕ = 0.2, t = 0.5, E1 = 1, E2 = 0.2, E3 = 0.05, E4 = 0.1, E5 = 0.3.
403
S. NADEEM, A. RIAZ, R. ELLAHI: PERISTALTIC FLOW OF A JEFFREY FLUID…
CI&CEQ 19 (3) 399−409 (2013)
(a)
(b)
(c)
(d)
Figure 9. Streamlines for different values of λ1. a) For λ1 = 0.5, b) for λ1 = 1, c) for λ1 = 1.5, d) for λ1 = 2. The other parameters are y = 0.5,
β = 1, ϕ = 0.2, t = 0.5, E1 = 1, E2 = 0.2, E3 = 0.01, E4 = 0.2, E5 = 0.3.
(a)
(b)
(c)
(d)
Figure 10. Streamlines for different values of ϕ. a) For ϕ = 0.1, b) for ϕ = 0.2, c) for ϕ = 0.3, d) for ϕ = 0.4. The other parameters are
y = 0.5, β = 1, λ1 = 1, t = 0.5, E1 = 1, E2 = 0.2, E3 = 0.01, E4 = 0.2, E5 = 0.3.
404
S. NADEEM, A. RIAZ, R. ELLAHI: PERISTALTIC FLOW OF A JEFFREY FLUID…
CI&CEQ 19 (3) 399−409 (2013)
(a)
(b)
(c)
(d)
Figure 11. Streamlines for different values of E1. a) For E1 = 1, b) for E1 = 2, c) for E1 = 3, d) for E1 = 4. The other parameters are y = 0.5,
β = 1, λ1 = 1, t = 0.5, ϕ = 0.2, E2 = 0.2, E3 = 0.05, E4 = 0.2, E5 = 0.3.
(a)
(b)
(c)
(d)
Figure 12. Streamlines for different values of E2. a) For E2 = 0.5, b) for E2 = 1, c) for E2 = 1.5, d) for E2 = 2. The other parameters are y =
0.5, β = 1, λ1 = 1, t = 0.5, ϕ = 0.2, E1 = 0.2, E3 = 0.05, E4 = 0.2, E5 = 0.3.
405
S. NADEEM, A. RIAZ, R. ELLAHI: PERISTALTIC FLOW OF A JEFFREY FLUID…
CI&CEQ 19 (3) 399−409 (2013)
(a)
(b)
(c)
(d)
Figure 13. Streamlines for different values of E3. a) for E3 = 0.01, b) for E3 = 0.05, c) for E3 = 0.09, d) for E3 = 0.13. The other parameters
are y = 0.5, β = 1, λ1 = 1, t = 0.5, ϕ = 0.2, E1 = 0.2, E2 = 0.05, E4 = 0.2, E5 = 0.3.
different values of the physical parameters λ1, E3 and
E4 are mentioned in Figures 3, 6 and 7. From these
plots, it is seen that velocity profile rises directly with
increasing the magnitude of λ1, E3 and E4. From Figures 2-7, it can also be seen that the velocity attains
its maximum value at the centre of the channel and
remains symmetric throughout the channel. The
streamlines for different values of the emerging parameters are drawn in Figures 8-13 to lookout for the
trapping bolus phenomenon. From Figure 8, it can be
seen that number of the trapped bolus is reduced
when increasing the value of parameter β. Figure 9 is
plotted to show the streamlines with the λ1 being
increased. From this plot, it is clear that the size of the
trapping bolus rises with increasing magnitude of λ1.
The streamlines for different values of the parameter
ϕ are shown in Figure 10. It is clear from this graph
that the number of boluses is decreasing monotonically with increasing ϕ, but the size of the bolus is
increasing with ϕ. Figure 11 reveals that the number
of trapped boluses is decreasing with E1. In Figure 12,
the number of trapped boluses remains unchanged,
but increases in size with increasing values of E2 on
the left side of the channel and has the opposite
406
behavior on the other side. The streamlines for E3 are
shown in Figure 13. It is easy to see from this figure
that the boluses decrease in number, but their size
changes with the increase of E3.
CONCLUDING REMARKS
In the present study, the mathematical and
graphical results of the peristaltic flow of a Jeffrey
fluid in a compliant rectangular duct were discussed.
The governing equations were simplified by employing the long wavelength and low Reynolds number
approximations. The resulting equations were then
solved by using the method of Eigen function expansion. The following main results were observed:
• The profile of the velocity is decreasing
function of the parameters β, E1 and E2.
• The influence of the pertinent parameters λ1,
E3 and E4 is totally opposite to that of β, E1 and E2.
• The fluid flows more rapidly at the central
part of the channel.
• The number of boluses is reduced with the
increasing effects of the parameters β, ϕ, E1 and E3,
while increased in case of λ1.
S. NADEEM, A. RIAZ, R. ELLAHI: PERISTALTIC FLOW OF A JEFFREY FLUID…
• The size of the bolus changes randomly with
the variation of all the physical parameters.
• The results for the viscous fluid case can be
obtained by taking λ1→0.
Nomenclature
u, w
b
a
d
x, y, z
λ
μ
p
c
t
λ1
λ2
γ
γ
β
ϕ
ψ
m
D
B
T
K
p0
velocity components
amplitude of the wave
height of the channel
width of the channel
Cartesian coordinates
wavelength
viscosity
pressure
velocity of propagation
time
relaxation time
delay time
shear stress
derivative of shear stress
aspect ratio
amplitude ratio
stream function
mass per unit area
coefficient of the viscous damping membrane
flexural rigidity of the plate
elastic tension in the membrane
spring stiffness
pressure on the outside surface
REFERENCES
[1]
S. Nadeem, S. Akram, Commun. Nonlinear Sci. Numer.
Simul. 15 (2010) 312-321
[2]
S. Nadeem, N.S. Akbar, Commun. Nonlinear Sci. Numer.
Simul. 14 (2009) 3844-3855
[3]
M.A. Abd Elnaby, M.H. Haroun, Commun. Nonlinear Sci.
Numer. Simul. 13 (2008) 752-762
CI&CEQ 19 (3) 399−409 (2013)
[9]
N.S. Akbar, S. Nadeem, Int. J. Heat Mass Tran. 55 (2012)
375-383
[10]
N.S. Akbar, S. Nadeem, Int. Commun. Heat Mass Tran.
38 (2011) 154-159
[11]
T. Hayat, S. Abelman, E. Momoniat, F. M. Mahomed,
Math. Comput. Appl. 15 (2010) 638-657
[12]
S. Nadeem, S. Akram, Math. Comput. Model. 52 (2010)
107-119
[13]
S. Nadeem, S. Akram, Commun. Nonlinear Sci. Numer.
Simul. 15 (2010) 1705-1716
[14]
A. Ebaid, Phys. Lett., A 372 (2008) 4493-4499
[15]
S. Nadeem, N.S. Akbar, Commun. Nonlinear Sci. Numer.
Simul. 15 (2010) 2860-2877
[16]
S. Srinivas, V. Pushparaj, Commun. Nonlinear Sci.
Numer. Simul., 13 (2008) 1782-1795
[17]
E.F. Elshehawey, N.T. Eladabe, E.M. Elghazy, A. Ebaid,
App. Math. Comput. 182 (2006) 140-150
[18]
S. Nadeem, S. Akram, Z. Naturforsch, A 64 (2009) 559–
–567
[19]
S. Tsangaris, N.W. Vlachakis, J. Fluid. Eng-T. ASME 125
(2003) 382-385
[20]
S. Nadeem, S. Akram, Arch. Appl. Mech. 81 (2011) 97–109
[21]
S. Nadeem, S. Akram, Int. J. Numer. Methods Fluids 63
(2010) 374-394
[22]
M.V. Subba Reddy, M. Mishra, S. Sreenadh, A. R. Rao,
J. Fluid. Eng. 127 (2005) 824-827
[23]
S. Nadeem, S. Akram, Nonlinear Anal. Real World Appl.,
11 (2010) 4238-4247
[24]
S. Nadeem, S. Akram, T. Hayat, A.A. Hendi, J. Fluids
Eng. 134 (2012)
[25]
R. Ellahi, A. Riaz, S. Nadeem, M. Ali, Math. Probl. Eng.
329639 (2012) 24 pages
[26]
D. Tripathi, Int. J. Therm. Sci. 51 (2012) 91-101
[27]
D. Tripathi, O. A. Beg, Proc. Inst. Mech. Eng. H. J. Eng.
Med. 226 (2012) 631-644
[28]
D. Tripathi, ASME J. Fluid. Eng. 133 (2011) 121104
[29]
D. Tripathi, Comput. Math. Appl. 62 (2011) 1116-1126
[30]
D. Tripathi, Int. J. Numer. Meth. Biomed. Eng. 27 (2011)
1812–1828
[4]
K.S. Mekheimer, Phys. Lett., A. 372 (2008) 4271-4278
[5]
J.J. Lozano, M. Sen, Chem. Eng. Process. 49 (2010)
704-715
[31]
[6]
S. Nadeem, N.S. Akbar, Commun. Nonlinear Sci. Numer.
Simul. 15 (2010) 3950-3964
D. Tripathi, N. Ali, T. Hayat, M.K. Chaube, A.A. Hendi,
Appl. Math. Mech. -Engl. Ed. 32 (2011) 1231–1244
[32]
S.K. Pandey, D. Tripathi, Int. J. Biomath. 3 (2010) 453–472
[33]
D. Tripathi, T. Hayat, N. Ali, S.K. Pandey, Int. J. Modern
Phys., B 25 (2011) 3455-3471
[34]
M. Kothandapani, S. Srinivas, Int. J. Non-Linear Mech. 43
(2008) 915-924.
[7]
D. Tripathi, Math. BioSci. 233 (2011) 90-97
[8]
A.M. Siddiqui, W.H. Schwarz, J. Non-Newton Fluid Mech.
53 (1994) 257-284
APPENDIX
Eq. (10) can be written as:
C=
1 ∂ 2u
β 2 ∂ 2u
+
1 + λ1 ∂y 2 1 + λ1 ∂z 2
(14)
407
S. NADEEM, A. RIAZ, R. ELLAHI: PERISTALTIC FLOW OF A JEFFREY FLUID…
CI&CEQ 19 (3) 399−409 (2013)
Now let us introduce a transformation:
u ( x , y , z ,t ) = v 1 ( x , y , z ,t ) + w 1 ( y )
(15)
After using the above equation in Eq. (14) we get system of two equations:
2
d w1
=0
dy 2
(16)
with B.Cs:
w 1 ( ±1) = −1
(17)
and
C=
1 ∂ 2v 1
β 2 ∂ 2v 1
+
1 + λ1 ∂y 2 1 + λ1 ∂z 2
(18)
with B.Cs:
v 1 ( x , ±1, z ,t ) = 0, v 1 ( x , y , ±h ,t ) = −1 − w 1 ( y )
(19)
Now we solve Eq. (18) with B.Cs (19) by Eigen function expansion method. The Eigen functions for the above
problem are defined as:
ϕn ( y ) = cos ( 2n − 1)
π
2
y , n = 1,2,3...
(20)
Now we define a series solution of the form:
∞
v 1 = ϕn ( y ) φn ( z )
(21)
n =1
Now using the above equation in Eq. (18) and after using the orthogonality condition we obtained:

φn ( z ) =  1 −

n
cosh α n z  16C ( −1)

cosh α n h  ( 2n − 1)3 π 3 β 2
(22)
Using Eqs. (20) and (22), Eq. (21) can be written as:
∞

v 1 ( x , y , z ,t ) =    1 −
n =1 

n

cosh α n z  16C ( −1)
π
 cos ( 2n − 1) y

3 3 2
cosh α n h  ( 2n − 1) π β 
2

(23)
Now from Eqs. (15), (16) and (23) we have the final solution:
∞

u ( x , y , x ,t ) = − 1 +    1 −
n =1 

n

π
cosh α n z  16C ( −1)
 cos ( 2n − 1) y

3 3 2
cosh α n h  ( 2n − 1) π β 
2

where αn and C are defined in Eqs. (12) and (13).
408
(24)
S. NADEEM, A. RIAZ, R. ELLAHI: PERISTALTIC FLOW OF A JEFFREY FLUID…
S. NADEEM1
ARSHAD RIAZ2
R. ELLAHI2
CI&CEQ 19 (3) 399−409 (2013)
PERISTALTIČKO STRUJANJE JEFFREY-OVOG
FLUIDA U PRAVOUGAONOM KANALU SA
POPUSTLJIVIM ZIDOVIMA
1
Department of Mathematics, Quaid-iAzam University, Islamabad, Pakistan
2
Department of Mathematics and
Statistics, FBAS, IIU Islamabad,
Pakistan
NAUČNI RAD
Rad se bavi teorijskim i matematičkim izučavanjem peristaltičkog strujanja Jeffrey-evog
fluida u pravougaonom kanalu sa popustljivim zidovima. Konstitutivne jednačine su
pojednostavljena uvođenjem pretpostavkama o malom Rejnolds-ovom broju i velikoj
talasnoj dužini. Analitičko rešenje rezultujućih jednačina je dobijeno primenom metode
Eigen-ve funkcije širenja. Takođe, grafički su analizirani svi značajni parametri. Prikazani su grafici brzine za dvo- i trodimenzionalno strujanje.
Ključne reči: peristaltičko strujanje, Jeffrey-ev fluid, pravougaoni kanal, popustljivi zidovi.
409
Available on line at
Association of the Chemical Engineers of Serbia AChE
www.ache.org.rs/CICEQ
Chemical Industry & Chemical Engineering Quarterly 19 (3) 411−422 (2013)
MOHAMMAD RAMEZANI
NAVID MOSTOUFI
MOHAMMAD REZA MEHRNIA
School of Chemical Engineering,
College of Engineering, University
of Tehran, Iran
SCIENTIFIC PAPER
UDC 66.069.82:544.4
DOI 10.2298/CICEQ120407076R
CI&CEQ
EFFECT OF HYDRODYNAMICS ON KINETICS
OF GLUCONIC ACID ENZYMATIC
PRODUCTION IN BUBBLE COLUMN
REACTOR
Oxidation of glucose by homogeneous glucose oxidase was performed in rectangular bubble column reactor at 40 °C, ambient pressure and pH of 5.5 while
superficial gas (oxygen) velocity was varied in the homogeneous and transition
regime in the range of 0.0014–0.0112 m s-1. Effect of superficial gas (oxygen)
velocity on the apparent reaction rate and its parameters was determined and
it was observed that the apparent reaction rate on the basis of volume of the
liquid increased with increasing the superficial gas (oxygen) velocity. The
apparent reaction rate was assumed to be in the form of Michaelis-Menten
equation and its apparent kinetic parameters were evaluated by the nonlinear
regression method.
Keywords: bubble column; kinetics; hydrodynamics; Michaelis-Menten
equation; oxygen velocity.
Bubble columns are gas-liquid contactors in
which a gas consisting of one or more reactants is
distributed into the column by a sparger and reacts
with the liquid phase itself or with a component dissolved or suspended in it [1]. With their simple
construction, no mechanically moving parts, efficient
mixing and low shear stress and good heat and mass
transfer properties, these reactors are becoming more
popular in biological processes compared with stirred
reactors [2,3].
Bioconversion of glucose to gluconic acid is one
of the well known processes in the biological industries. Gluconic acid and its salts are important materials used in pharmaceutical, food, textile, detergent,
leather, photographic and other biological industries
[4]. In fact, gluconic acid and D-gluconolactone are
simple dehydrogenation products of oxidation of Dglucose obtained by glucose oxidase (E.C.1.1.3.4) [5–7]. A detailed description of kinetics of gluconic acid
production has been published in several papers [8–10]. The mechanism of this bioconversion can be
given by three steps:
Correspondence: N. Mostoufi, School of Chemical Engineering,
College of Engineering, University of Tehran, Iran.
E-mail: mostoufi@ut.ac.ir
Paper received: 7 April, 2012
Paper revised: 22 July, 2012
Paper accepted: 22 July, 2012
GOD
glucose + O2 ⎯⎯⎯
→ D-gluconolactone + H2O2
CAT
H2O2 ⎯⎯⎯
→ H2O +
1
O2
2
LAC
D-gluconolactone + H2O ⎯⎯⎯
→ gluconic acid
(1)
(2)
(3)
where GOD is glucose oxidase, CAT is catalase and
LAC is lactonase. The overall reaction can be
considered as follows:
glucose +
1
GOD,CAT
O2 ⎯⎯⎯⎯→
gluconic acid
2
(4)
Nakamura and Ogura [11] proposed the kinetics
of the oxidation of glucose by the glucose oxidase
from Penicillium amagaskiense. They expressed that
semiquinoid intermediates do not affect the reactive
mechanism of glucose oxidase. Thereafter, Gibson et
al. [5] determined the kinetics and mechanism of glucose oxidase in two different ways, including monometric and stopped flow experiments. They measured
the kinetics of glucose oxidase reaction with diverse
substrates such as glucose, mannose, xylose and
2-deoxyglucose and concluded that the rate of glucose oxidation is considerably faster than other reactions. Furthermore, they mentioned that the rate of
oxidation of glucose depends on oxygen concentration as well as temperature.
411
M. RAMEZANI, N. MOSTOUFI, M.R. MEHRNIA: EFFECT OF HYDRODYNAMICS ON KINETICS…
Despite sufficient amount of surveys conducted
on kinetics of reaction and mass transfer characteristics of immobilized glucose oxidase [12,13], there
are rather fewer studies focused on homogeneous
glucose oxidase. Nakao et al. [14] investigated mass
transfer characteristics and optimal operating conditions for producing gluconic acid with immobilized glucose oxidase in airlift and bubble column reactors.
They concluded that bubble column reactor provides
higher gluconic acid productivity and lower glucose
oxidase activity decay compared to other type of
reactors due to its better mass transfer properties.
Afterwards, Bang et al. [15] investigated glucose
oxidation in a three-phase stirred airlift reactor. They
highlighted the influence of oxygen concentration and
gas velocity on the reaction rate and concluded that
the reaction rate noticeably increases with oxygen
concentration in gas phase as well as gas velocity.
Furthermore, Klein et al. [16] and Znad et al. [17]
demonstrated the positive influence of air flow rate on
the reaction rate of gluconic acid production.
Although the effect of temperature on the reaction rate of glucose oxidation has been studied, there
are limited surveys dedicated to thorough investi-
gations of the effect of gas velocity on this rate.
Accordingly, the aim of this work is to investigate the
effect of gas velocity and hydrodynamics of the bubble column on the rate of enzymatic oxidation of glucose by glucose oxidase. The reason for choosing the
bubble column reactor is that considerably higher
amounts of gluconic acid can be produced, glucose
oxidase activity decay is lower, and mass transfer
properties are better in this reactor compared to other
types of reactors [14]. In the present work, glucose
was oxidized by homogeneous glucose oxidase at
various gas velocities at 40 °C. Considering the
Michaelis-Menten equation, the apparent reaction
rate parameters were determined. The results of this
work can be used in future studies concerning the
modeling of bubble columns used in bioprocesses,
taking into account reaction and hydrodynamic parameters.
EXPERIMENTS AND METHODS
Bioreactor set-up
The schematic of the experimental setup used in
this work is shown in Figure 1. The rectangular bub-
Figure 1. Schematic of the experimental set-up.
412
CI&CEQ 19 (3) 411−422 (2013)
M. RAMEZANI, N. MOSTOUFI, M.R. MEHRNIA: EFFECT OF HYDRODYNAMICS ON KINETICS…
ble column was made of Plexiglas with dimensions of
0.12 m width, 0.7 m height and 0.05 m depth. The
oxygen was introduced through a Plexiglas perforated
plate sparger located 0.03 m above the base of the
reactor. The sparger was rectangular with the
dimensions of 0.12 m length and 0.05 m width. It
contained 14 orifices with diameter of 0.0006 m and
0.01 m square pitch. The design of the reactor and
sparger was based on the findings of Buwa and
Ranade [18] who showed that the sparger design has
an insignificant effect on the turbulence and flow
regime (for this kind of sparger, with this pitch and
hole diameter). A rectangular bubble column was utilized in order to improve the accuracy of measuring
bubble sizes as in cylindrical bubble column reactors
the curvature of the reactor introduces error when
determining bubble size through photographic method.
Materials
The D-Glucose monohydrate (99% pure) from
Fluka was used as reactant in different concentrations
of 0.0555, 0.222, 0.3885 and 0.555 mol/ L. Distilled
water was used as solvent in all experiments. Glucose oxidase produced by Aspergillus niger (SigmaAldrich Company) fermentation which was claimed to
contain 1 mg g-1 of flavine-adenine dinucleotide (FAD)
and with activity of 24,800 units g-1 (unit definition:
required amount of enzyme to oxidize 1 μmol of glucose to gluconic acid and H2O2, per minute at 25 °C
and pH 7). The catalase was produced by bovine liver
with activity of 3940 units mg-1. Acetate buffer with pH
5.5 was used for adding the glucose oxidase and
catalase to the solution of glucose. The physical properties of glucose solution with two enzymes used in
this work are listed in Table 1.
Methods
All experiments were carried out at controlled
temperature (±0.1 K) and pH value (±0.1) using a
Mettler Toledo DL28 titrator using 1 M NaOH. The pH
of the solution was maintained at 5.5 (maximum GOD
activity) by NaOH, which was automatically added to
the solution in order to neutralize gluconic acid. The
catalase and glucose oxidase with concentration of
0.0101 g/L were added to the aqueous solution of glucose at various concentrations. Since oxygen was
CI&CEQ 19 (3) 411−422 (2013)
dissolved in the liquid, nitrogen gas was passed
through the column to remove the oxygen. The gas
was then changed to oxygen and oxygen concentration in the liquid phase was measured by a Mettler
Toledo oxygen sensor connecting to a PC and recorded
online. Oxygen was introduced into the column
through a sparger at superficial velocities of 0.0014,
0.0028, 0.0056 and 0.0112 m/s. All experiments were
carried out in the homogeneous and transition regime
at atmospheric pressure and 40 °C.
For highlighting the effect of gas hold-up and
specific gas-liquid interfacial area on reaction rate,
this hydrodynamic parameter were determined by the
following equations [1]:
εG =
H G − HL
HG
(5)
 i d i3
 i d i2
(6)
d 32 =
a=
6ε G
(7)
d 32
In order to determine the Sauter mean diameter
(d32), the equivalent sphere diameter of bubble (di) is
evaluated by Eq. (8) and photographic method:
d i = 3 E 2e
(8)
For evaluating the bubble size distribution, the
resulting data from Eq. (8) and number of bubbles in
each size acquired from photographs were considered. The fraction of each bubble size in the total
length of reactor was obtained from the proportion of
number of bubbles in each size to the total number of
bubbles.
In order to assess the volumetric mass transfer
coefficient (kLa), non-stationary or dynamic method
was used. Under the assumptions of ideal mixing in
gas and liquid phases, constant interfacial area and
no significant change in oxygen concentration in the
gas phase, the volumetric mass transfer coefficient
can be determined from [19]:
−t
c ∗ − c L  ( −k Lat )
τp 
τ
e
k
a
e
=
−

 (1 − k Laτ p )
L
p
∗
c − c0 

(9)
Table 1. Physical properties of glucose solution used at 40 °C
ρ / kg m-3
μ×103 / Pa s
σ×103 / N m-1
0.05551
982.6
0.6891
69.79
0.2220
993.7
0.7463
69.64
0.3885
1000
0.8124
69.47
0.5551
1017
0.8870
69.30
Glucose concentration, mol L
-1
413
M. RAMEZANI, N. MOSTOUFI, M.R. MEHRNIA: EFFECT OF HYDRODYNAMICS ON KINETICS…
In Eq. (9) τp represents the response time of the
oxygen probe which was evaluated as the time
needed to reach 63% of the value finally approached
when exposed to a step change in concentration
[19,20]. In the present work, this constant can be
assessed by transferring the oxygen probe kept in a
solution of sodium sulfite for 0.5 min (wherein the
oxygen concentration is zero) to another solution
saturated with oxygen (which in this work was glucose solution). The response time (τp) of the oxygen
probe used in this work was evaluated to be 25 s at
40 °C.
Due to the fact that hydrogen peroxide has the
inhibition effect on GOD and reaction rate [9,21-23], it
was necessary to prevent its production by adding
sufficient amount of catalase, thus, no free hydrogen
peroxide was observed. In order to determine the
reaction rate, the concentration of gluconic acid was
measured by titration with NaOH. The rates of gluconic acid production at various gas velocities were
evaluated by measuring the slope of lines showing
the time courses of gluconic acid production while the
zero time was taken after 700 s from the enzyme
addition.
0.035
u= 0.0014 m/s
u= 0.0028 m/s
u= 0.0056 m/s
u= 0.0112 m/s
CI&CEQ 19 (3) 411−422 (2013)
RESULTS AND DISCUSSION
Effect of gas velocity
The quantitative determination of gluconic acid
production, evaluated by titration with NaOH, is illustrated in Figure 2 at glucose concentration of 0.0555
mol L-1. The error bars represent standard deviations
of the observed values and are presented only for
oxygen velocity of 0.0056 m s-1 as an example. The
error bars for other oxygen velocities were fairly in the
same range and are not displayed to make the figure
easy to understand. It can be seen in these figures
that variations of gluconic acid concentrations vs. time
are linear with the correlation coefficient greater than
0.985. These slopes determine the apparent rate of
gluconic acid production. It can be seen that oxygen
velocity has a positive effect on producing of gluconic
acid and the reaction rate.
The determined reaction rate versus oxygen
velocity is illustrated in Figure 3. It can be easily
recognized that gas velocity has a positive effect on
reaction rate and with increasing gas velocity, the
reaction rate increases. The results of this study are
in agreement with those in literature [15,16]. Bang et
0.03
y = 0.003x + 0.000
R² = 0.994
Gluconic Acid [mol L-1]
0.025
y = 0.002x + 0.000
R² = 0.985
0.02
0.015
y = 0.002x + 0.000
R² = 0.997
0.01
y = 0.001x + 0.000
R² = 0.995
0.005
0
0
1
2
3
4
5
6
7
8
Time [hr]
Figure 2. Gluconic acid concentration at various different oxygen velocities. Reaction conditions: [GOD] = 0.0101 g L -1;
[CAT] = 0.0101 g L-1; temperature = 313.15 K, pH 5.5 and 0.0555 mol L-1 glucose (error bars are standard deviations).
414
9
M. RAMEZANI, N. MOSTOUFI, M.R. MEHRNIA: EFFECT OF HYDRODYNAMICS ON KINETICS…
0.0045
0.004
C glucose = 0.0555 mol/L
C glucose = 0.222 mol/L
C glucose = 0.3885 mol/L
C glucose = 0.555 mol/L
CI&CEQ 19 (3) 411−422 (2013)
0.0035
r [mol L-1 hr-1]
0.003
0.0025
0.002
0.0015
0.001
0.0005
0
0
0.002
0.004
0.006
uG [m
0.008
0.01
0.012
s-1]
Figure 3. Reaction rate versus oxygen velocity at various glucose concentrations (error bars are standard deviations).
al. [15] concluded that the reaction rate depended on
gas velocity for uG < 1.17 cm s-1 while it was independent of gas velocity for uG > 1.17 cm s-1. In the
present work, the range of gas velocity was between
0.14-1.12 cm s-1 which is less than 1.17 cm s-1 and
the reaction rate was found to be affected by the gas
velocity. Higher oxygen velocity amplifies significantly
supply of oxygen into the bioreactor and increases
gas hold-up which assists to raise the intensity of
mixing and leads to boosting the oxygen transfer rate
and increases the reaction rate as a result. Figure 3
also shows that the reaction rate is nearly constant in
the range of gas velocity of 0.0028 to 0.0056 m s-1.
This trend can be related to the available interfacial
area in the reactor. The effect of glucose concentration on the reaction rate can also be comprehended
from this figure. It is obvious that with increasing
glucose concentration the apparent reaction rate is
increased.
Figure 4 demonstrates the bubble size distribution at various gas velocities considered in this
work. It can be seen in this figure that the bubbles at
0.0028 m s-1 are slightly smaller than that at 0.0056 m
s-1. It is worth mentioning that according to Buwa and
Ranade [18] at the gas velocity of 0.0112 m s-1 there
was a transition regime in the bubble column reactor.
While higher gas velocity provides more bubbles in
the reactor, presence of larger bubbles reduces the
inter-phase mass transfer area. As a result, it is suggested that gas velocities of 0.0028 and 0.0056 m s-1
provide almost the same concentration of oxygen in
the liquid phase. Consequently, the reaction rates at
these gas velocities become the same. In fact, below
0.0028 m s-1 the bubbles are small and relatively far
separated each other. Therefore, increasing the gas
velocity below this limit only increases the number of
bubbles (corresponding to increase in inter-phase
mass transfer area). At gas velocities higher than
0.0028 m s-1 the number of bubbles becomes so high
that they become closer to each other and coalescence of bubbles begins. Although coalescence of
bubbles still exists at gas velocities higher than
0.0056 m s-1, the increase in the number of bubbles
outweighs the decrease in the interfacial area, thus,
the concentration of oxygen in the liquid phase
increases with increasing the gas velocity and the
reaction rate increases accordingly.
Figure 5 illustrates the effect of glucose concentration on gas hold-up. This figure demonstrates that
the gas hold-up decreases with increasing the glucose concentration. In fact, the viscosity of solution
increases with increasing the glucose concentration,
resulting in formation of larger bubbles. Consequently, the number of bubbles decreases and their
rise velocity increases, which makes the gas hold-up
decrease. Figure 5 also shows that the gas hold-ups
415
M. RAMEZANI, N. MOSTOUFI, M.R. MEHRNIA: EFFECT OF HYDRODYNAMICS ON KINETICS…
CI&CEQ 19 (3) 411−422 (2013)
0.5
uG = 0.0014 m/s
uG = 0.0028 m/s
uG = 0.0056 m/s
uG = 0.0112 m/s
0.45
0.4
0.35
Fraction
0.3
0.25
0.2
0.15
0.1
0.05
0
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
7.5
Bubble size [mm]
Figure 4. Bubble size distribution at various gas velocities and glucose concentration of 0.555 mol L-1.
0.14
uG = 0.0014 m/s
uG = 0.0056 m/s
uG = 0.0028 m/s
uG = 0.0112 m/s
0.12
Gas Hold-up (εG)
0.1
0.08
0.06
0.04
0.02
0
0
0.1
0.2
0.3
Glucose concentration
0.4
0.5
0.6
[mol L-1]
Figure 5. Gas hold-up at various superficial gas velocities as a function of glucose concentration (error bars are standard deviations).
416
M. RAMEZANI, N. MOSTOUFI, M.R. MEHRNIA: EFFECT OF HYDRODYNAMICS ON KINETICS…
140
uG = 0.0014 m/s
uG = 0.0056 m/s
CI&CEQ 19 (3) 411−422 (2013)
uG = 0.0028 m/s
uG = 0.0112 m/s
120
100
a [m-1]
80
60
40
20
0
0
0.1
0.2
0.3
0.4
0.5
0.6
Glucose concentration [mol L-1]
Figure 6. Effect of glucose concentrations on specific gas-liquid interfacial area at various superficial gas velocities.
for gas velocities of 0.0028 and 0.0056 m s-1 are reasonably close to each other.
Variation of specific gas-liquid interfacial area
with glucose concentration at various gas velocities is
shown in Figure 6. It can be seen in this figure that
the specific gas-liquid interfacial area decreases with
increasing the glucose concentration. In fact, with
increasing the glucose concentration, the gas hold-up
decreases which results in decreasing the specific
gas-liquid interfacial area (see Eq. (7)). Figure 6 also
reveals that the specific gas-liquid interfacial area at
both gas velocities of 0.0028 and 0.0056 m s-1 are
very close. This also can be attributed to close values
of gas hold-up and mean bubble size at these velocities.
Figure 7 shows the effect of glucose concentration on volumetric oxygen transfer coefficient. This
figure reveals that the mass transfer coefficient
decreases with increasing the glucose concentration.
This negative effect of glucose concentration on mass
transfer coefficient can be attributed to the viscosity of
solution. Increasing the glucose concentration
increases the viscosity of solution, thus, the turbulent
intensity and gas hold-up decrease. As a result, the
specific gas-liquid interfacial area decreases and
does the oxygen transfer coefficient. It can be seen in
Figure 7 that oxygen transfer coefficient for gas velocities of 0.0028 and 0.0056 m s-1 are close. As stated
before, the specific gas-liquid interfacial areas for
these velocities are significantly close which is the
reason for observing almost the same values of oxygen transfer coefficients at these velocities. The
experimental results of this work were compared with
existing experimental correlations for volumetric mass
transfer coefficient. Among the correlations, the
correlation proposed by Akita and Yoshida [24]:
k LaDc2
=
D AB
 μL 
= 0.6 

 ρLD AB 
0.5
 gDc2 ρL 


 σ 
0.62
 gDc3 ρL2 


2
 μL 
(10)
0.31
ε
1.1
G
is in satisfactory agreement with the experimental
data as demonstrated in Figure 8. The relative disparity between these results with Akita and Yoshida
[24] is attributed to difference in dimension of bubble
column reactor, kind and diameter of sparger, physical properties of materials and superficial gas velocity.
Since the reaction rate depends on the gas
hold-up, the reaction rate should be presented as a
function of this hydrodynamic parameter. Therefore,
the apparent reaction rate obtained in Figure 2 with
the unit of mol/m3 of liquid/h should be converted into
mol/m2 of interfacial area/h through the following
expression:
417
M. RAMEZANI, N. MOSTOUFI, M.R. MEHRNIA: EFFECT OF HYDRODYNAMICS ON KINETICS…
0.03
uG = 0.0014 m/s
uG = 0.0056 m/s
CI&CEQ 19 (3) 411−422 (2013)
uG = 0.0028 m/s
uG = 0.0112 m/s
0.025
kLa [s-1]
0.02
0.015
0.01
0.005
0
0
0.1
0.2
0.3
0.4
Glucose concentration
0.5
0.6
[mol L-1]
Figure 7. Effect of glucose concentration on volumetric mass transfer coefficient at various superficial gas velocities (error bars are
standard deviations).
0.05
+30 %
Calculated kLa from correlation [s-1]
0.045
0.04
0.035
0.03
-30 %
0.025
0.02
0.015
0.01
0.005
0
0
0.005
0.01
0.015
0.02
0.025
0.03
Experimental kLa
0.035
0.04
0.045
[s-1]
Figure 8. Comparing the experimental results with the correlation proposed by Akita and Yoshida [24].
418
0.05
M. RAMEZANI, N. MOSTOUFI, M.R. MEHRNIA: EFFECT OF HYDRODYNAMICS ON KINETICS…
r′
×
mol
mol
=r 3
×
m Interfacial area.hr
m Liq.hr
2
(11)
(1− ε G ) m3Liq 1
r
m3Gas
×
=
3
2
ε G m Gas aG m Interfacial area aL
where a = aGεG and aL = a/(1-εG). Converted reaction
rate against glucose concentration is illustrated in
Figure 9 at various gas velocities. It can be seen in
this figure that the reaction rate decreases with
increasing the gas velocity at various glucose concentrations. The reason for this change in trends of r’ with
gas velocity is related to gas hold-up and specific
gas-liquid interfacial area (aG) included in the converted reaction rate. With increasing the gas velocity,
gas hold-up (εG) and specific gas-liquid interfacial
area (aG) increase and the reaction rate decreases
when the rate r is almost constant irrespective of the
superficial gas velocity, i.e., when r is nearly equal to
the chemical reaction rate.
The parameter aL is in fact the specific interfacial
area per unit volume of the liquid and is a function of
the properties of gas and liquid. The variation of aL
with glucose concentration is almost the same as that
of a, which is shown in Figure 6. Therefore, it is
related to the concentration of glucose in the solution.
The parameter aL is a strong function of the glucose
concentration at low gas velocity while with increasing
the gas velocity becomes almost independent of the
14
CI&CEQ 19 (3) 411−422 (2013)
glucose concentration. The reason for such a trend
can be explained by the change in the physical properties of the solution with glucose concentration. The
viscosity of the solution increases with increasing the
concentration of glucose. As a result, larger bubbles
are formed at higher glucose concentration which
reduces the gas holdup and the specific interfacial
area. This is the reason for observing the decreasing
trend in aL with increasing the concentration of glucose. It is worth mentioning that the same effect of
gas velocity on the reaction rate has been already
pointed out by Bang et al. [15]. This factor can explain
dependence of the reaction rate on the oxygen velocity at low superficial gas velocities and its independence at high gas velocities.
Evaluation of apparent kinetic parameters
The mechanism of glucose oxidation by GOD
was proposed by Nakamura and Ogura [11] and in
more details by Gibson et al. [5]. They proposed that
oxidation of glucose consists of the following two
steps with four apparent kinetic parameters:
k
k
1
2
Eox +G ⎯⎯
→ Ered ⋅ Glu ⎯⎯→
Ered +Glu
k
(12)
k
3
4
Ered +O2 ⎯⎯→
Eox ⋅ H2O2 ⎯⎯→
Eox +H2O2
(13)
Duke et al. [25] developed a rate equation for
this mechanism with the hypothesis of steady state
uG = 0.0014 m/s
uG = 0.0028 m/s
uG = 0.0112 m/s
uG = 0.0056 m/s
12
r' [mol m-2 hr-1]
10
8
6
4
2
0
0
0.1
0.2
0.3
0.4
0.5
0.6
Glucose concentration [mol L-1]
Figure 9. Reaction rate per unit interfacial area vs. glucose concentration at various gas velocities (error bars are standard deviations).
419
M. RAMEZANI, N. MOSTOUFI, M.R. MEHRNIA: EFFECT OF HYDRODYNAMICS ON KINETICS…
condition. With the assumption that the observed rate
r is the chemical reaction rate, the proposed rate
equation is expressed as follows:
C E,0 t
1
1
1
1
=
+
+
+
r
k 1C G k 2 k 3C O2 k 4
r
2
According to Beltrame et al. [26], the following
composite coefficient kc:
kc
=
1
k2
+
1
k 3CO2
+
1
(15)
k4
can be substituted into Eq. (14) and the equation of
apparent reaction rate would be converted into the
Lineweaver-Burk form:
1
r
=
2
1  1
1
+ 

kc 
(16)
CE,0 t  k 1C G
k cCE,0 t C G
k c k1 + CG
(17)
In order to determine the apparent kinetic parameters of Michaelis-Menten rate equation (kc and k1),
a least square nonlinear regression technique was
utilized. Calculated rate constants are given in Table
2. It should be noted that the results in Table 2 are
valid only for the limited ranges of enzyme concentration, partial pressure of oxygen and glucose concentration employed in this study. For comparison of these
results with other publications, it is necessary to compromise the resulting units with the reported units. For
attaining this purpose, the enzyme concentration should
be reported in molar. Thereby, the results should be
divided by 1.27×10-6, as our enzyme contains 1 mgFAD
g-1GOD that is 1.27×10-6 molFAD g-1GOD. The converted
values are illustrated in Table 2. These apparent kinetic parameters are compared with those reported in
literature [25,26] as described below. Figure 10
demonstrates the variation of apparent reaction rate
(14)
2
1
=
CI&CEQ 19 (3) 411−422 (2013)
or the analogous form of Michaelis-Menten equation:
Table 2. Evaluation of kc and k1 for different oxygen velocity examined with two kinds of units
Gas velocity, m s
-1
kc
-1
mol g h
k1
-1
s
-1
-1
Lg h
-1
-1
L mol s
0.0014
0.0758
16.58
2.456
537.3
0.0028
0.1351
29.56
17.33
3791
0.0056
0.1424
31.16
16.25
3555
0.0112
0.2015
44.08
17.76
3884
0.005
Modeling apparent reaction rate [mol L-1 hr-1]
+5%
0.004
-5%
0.003
0.002
0.001
0
0
0.001
0.002
0.003
Experimental apparent reaction rate [mol
0.004
L-1
hr-1]
Figure 10. Parity plot of calculated apparent reaction rate vs. experimental data.
420
0.005
-1
M. RAMEZANI, N. MOSTOUFI, M.R. MEHRNIA: EFFECT OF HYDRODYNAMICS ON KINETICS…
(calculated based on the constants reported in Table
2) as a function of superficial gas velocity and compared with experimental data. It can be seen in this
figure that the calculated results are in satisfying
agreement with the experimental data with correlation
coefficient geater than 0.9436.
Beltrame et al. [26] estimated kc and k1 in the
range of 0–30 °C. At 30 °C, they reported 0.6606 mol
g-1 h-1 and 28.10 L g-1 h-1 for kc and k1, respectively.
According to their results, larger values of kc and k1
would be expected at 40 °C. However, k1 and kc in
this study are smaller than those reported by Beltrame et al. [26]. One possible reason for this difference is oxygen concentration which in this work is
considerably less than that reported by Beltrame et al.
[26]. In their research, C0, was equal to 1.18×10-3 mol
L-1 while in this work C0 was between 4.27×10-5–
–1.37×10-4 mol L-1. As kc is related to steps containing
the oxidization of reduced enzyme, lower values
resulted in this study compared to those in Beltrame
et al. [26]. The lower amount of oxygen dissolved in
the liquid phase leads to increase in the amount of
reduced enzyme which is converted to Eox.H2O2 (Eq.
(13)) and apparent kinetic parameter related to this
step is decreased as a consequence. It is worth noting
that the reaction rate is a weak function of oxygen
velocity. In accordance with Beltrame et al. [26] and
results of this work, it can be concluded that the
reaction rate depends more on temperature than oxygen velocity. The values of k1 are between 537-3884
s-1 while in the literatures, those are fairly higher.
Gibson et al. [5] reported 2100 s-1 for 0 °C and 16000
s-1 for 38 °C. It is followed by Duke et al. [25] who
disclosed 3700 s-1 at 0 °C and 23800 at 30 °C. These
discrepancies between the results are related to an
assumed enzyme concentration and activity which
was mentioned about 10-8 mol L-1 [25] as well as the
oxygen transfer limitation. However, the difference is
within one order of magnitude which seems plausible.
CONCLUSIONS
The effect of oxygen velocity on the apparent
reaction rate of oxidation of glucose by homogeneous
glucose oxidase was investigated. It was observed
that increasing the gas velocity results in increasing
the apparent reaction rate due to higher oxygen
transfer from gas phase to liquid phase. At two gas
velocities of 0.0028 and 0.0056 m s-1 the apparent
reaction rates are noticeably close due to the similarity of the gas hold-ups, specific gas-liquid interfacial
areas and the volumetric oxygen transfer coefficients
in these two velocities. To emphasize effects of the
CI&CEQ 19 (3) 411−422 (2013)
hydrodynamic parameters on the apparent reaction
rate, the apparent reaction rate was expressed on the
basis of the available interfacial area which includes
gas hold-up and specific interfacial area. With assuming the apparent reaction rate in the form of MichaelisMenten equation, a satisfactory agreement between
the experimental and calculated apparent reaction
rates was observed. The apparent constants of the
Michaelis-Menten equation were determined by the
nonlinear regression method.
Nomenclature
aG
specific gas-liquid interfacial area per unit gas
volume (m-1)
aL
specific gas-liquid interfacial area per unit
liquid volume (m-1)
a
specific gas-liquid interfacial area based on the
dispersion volume (m-1)
CAT catalase
c*
equilibrium dissolved oxygen concentration
(mol L-1)
CE,t initial total enzyme concentration (g L-1)
CG
glucose concentration (mol L-1)
cL
dissolved oxygen concentration for physical
oxygen absorption (mol L-1)
CO2 dissolved oxygen concentration for glucose
oxidation (mol L-1)
C O* 2 equilibrium dissolved oxygen concentration for
glucose oxidation (mol L-1)
c0
initial dissolved oxygen concentration for physical oxygen absorption (mol L-1)
di
sphere equivalent diameter (m)
d32
mean bubble size (Sauter mean diameter) (m)
E
major axis of the ellipsoid (m)
e
minor axis of ellipsoid (m)
Eox
oxidized enzyme
Ered reduced enzyme
G
glucose
GOD glucose oxidase
HG
dispersion height (m)
HL
static liquid height (m)
kc
kinetic parameter of Michaelis-Menten equation (mol g-1 h-1)
k1
kinetic parameter of Michaelis-Menten equation (L g-1 h-1)
k2
kinetic parameter related to glucose oxidation
(mol g-1 h-1)
k3
kinetic parameter related to glucose oxidation
(L g-1 h-1)
k4
kinetic parameter related to glucose oxidation
(mol g-1 h-1)
421
M. RAMEZANI, N. MOSTOUFI, M.R. MEHRNIA: EFFECT OF HYDRODYNAMICS ON KINETICS…
volumetric oxygen transfer coefficient (s-1)
LAC lactonase
r
apparent rate of gluconic acid production per
unit liquid volume (mol L-1 h-1)
r’
apparent rate of gluconic acid production per
unit interfacial area (mol m-2 h-1)
t
time (s)
uG
superficial gas (oxygen) velocity (m s-1)
kLa
CI&CEQ 19 (3) 411−422 (2013)
[9]
J. Mirón, M.P. Gonzalez, J.A. Vázquez, L. Pastrana, M.
Murado, Enzyme Microb. Technol. 34 (2004) 513-522
[10]
H. Kojima, S. Suzuki, J. Chem. Eng. Jpn. 39 (2006) 1050–1053
[11]
T. Nakamura, Y. Ogura, J. Biochem. 52 (1962) 214-220
[12]
A. Blandino, M. Macı́ as, D. Cantero, Process Biochem.
36 (2001) 601-606
[13]
D. Mislovicova, E. Michalkova, A. Vikartovska, Process
Biochem. 42 (2007) 704-709
Greek letter
[14]
εG
τp
K. Nakao, A. Kiefner, K. Furumoto, T. Harada, Chem.
Eng. Sci. 52 (1997) 4127-4133
[15]
W. Bang, X. Lu, A. Duquenne, I. Nikov, A. Bascoul, Catal.
Today 48 (1999) 125-130
Subscripts
[16]
G
L
J. Klein, M. Rosenberg, J. Markos, O. Dolgos, M. Kroslák,
Biochem. Eng. J. 10 (2002) 197-205
[17]
H. Znad, J. Markos, V. Bales, Process Biochem. 39
(2004) 1341-1345
gas hold-up
response time of the oxygen probe (s)
gas
liquid
REFERENCES
[1]
W.D. Deckwer, R.W. Field, Bubble column reactors,
Wiley, New York, 1992
[2]
A. Sánchez Mirón, M.C. Cerón García, F. García Camacho, E. Molina gima, Y. Chisti, Enzyme Microb. Technol.
31 (2002) 1015-1023
[18]
V.V. Buwa, V.V. Ranade, AIChE J. 50 (2004) 2394-2407
[19]
F. Garcia-Ochoa, E. Gomez, Biotechnol. Adv. 27 (2009)
153-176
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K. Van't Riet, Ind. Eng. Chem. Process Des. Dev. 18
(1979) 357-364
[21]
J. Bao, K. Furumoto, K. Fukunaga, K. Nakao, Biochem.
Eng. J. 8 (2001) 91-102
[3]
C.C. Fu, W.T. Wu, S.Y. Lu, Enzyme Microb. Technol. 33
(2003) 332-342
[22]
J. Bao, K. Furumoto, M. Yoshimoto, K. Fukunaga, K.
Nakao, Biochem. Eng. J. 13 (2003) 69-72.
[4]
D.T. Sawyer, Chem. Rev. 64 (1964) 633-643
[23]
[5]
Q.H. Gibson, B. Swoboda, V. Massey, J. Biol. Chem. 239
(1964) 3927-3934
C.M. Wong, K.H. Wong, X.D. Chen, Appl. Microbiol. Biotechnol. 78 (2008) 927-938
[24]
H.J. Bright, M. Appleby, J. Biol. Chem. 244 (1969) 3625–3634
K. Akita, F. Yoshida, Ind. Eng. Chem. Process Des. Dev.
12 (1973) 76-80
[25]
M.K. Weibel, H.J. Bright, J. Biol. Chem. 246 (1971) 2734–2744
F.R. Duke, M. Weibel, D. Page, V. Bulgrin, J. Luthy, J.
Am. Chem. Soc. 91 (1969) 3904-3909
[26]
P. Beltrame, M. Comotti, C.D. Pina, M. Rossi, J. Catal.
228 (2004) 282-287.
[6]
[7]
[8]
M. Mattey, Crit. Rev. Biotehnol. 12 (1992) 87-132
MOHAMMAD RAMEZANI
NAVID MOSTOUFI
MOHAMMAD REZA MEHRNIA
School of Chemical Engineering,
College of Engineering, University of
Tehran, Iran
NAUČNI RAD
UTICAJ HIDRODINAMIKE NA KINETIKU ENZIMSKE
PRODUKCIJE GLUKONSKE KISELINE U
BARBOTAŽNOJ KOLONI
Oksidacija glukoze slobodno suspendovane glukozo oksidaze je izvršena u pravougaonoj
barbotažnoj koloni na 40 °C, atsmosferskom pritisku i pH 5,5, dok je površinska brzina
kiseonika varirana u homogenom i prelaznom režimu u opsegu 0,0014–0,.0112 m/s. Određen je uticaj površinske brzine kiseonika na prividnu brzinu reakcije i njene parametre.
Uočeno je da se prividna brzina reakcije po jedinici zapremine povećava sa povećanjem
površinske brzine kiseonika. Pretpostavljeno je da prividna brzina reakcije sledi Michaelis-Menten-ovu jednačinu, čiji su parametri izračunati metodom nelinearne regresije.
Ključne reči: barbotažna kolona, kinetika, hidrodinamika, Michaelis-Menten-ova
jednačina, površinska brzina kiseonika.
422
Available on line at
Association of the Chemical Engineers of Serbia AChE
www.ache.org.rs/CICEQ
Chemical Industry & Chemical Engineering Quarterly 19 (3) 423−433 (2013)
WEI LI1,2
JINHUI PENG1
SHENGHUI GUO1
LIBO ZHANG1
GUO CHEN1
HONGYING XIA1
1
Key Laboratory of Unconventional
Metallurgy, Ministry of Education,
Kunming University of Science and
Technology, Yunnan, China
2
Faculty of Science, Kunming
University of Science and
Technology, Yunnan, China
SCIENTIFIC PAPER
UDC 544.47/.478
DOI 10.2298/CICEQ120421077L
CI&CEQ
CARBOTHERMIC REDUCTION KINETICS OF
ILMENITE CONCENTRATES CATALYZED BY
SODIUM SILICATE AND MICROWAVEABSORBING CHARACTERISTICS OF
REDUCTIVE PRODUCTS
Carbothermic reduction kinetics of ilmenite concentrates catalyzed by sodium
silicate were investigated; the reduction degree of ilmenite concentrates
reduction reaction was determined as R = 4/7(16y + 56x)(ΔWΣ - fA-PW)/(16y +
+ 56x + 112). The results show that the reaction activation energy of initial
stage and later stage is 36.45 and 135.14 kJ/mol, respectively. There is a great
change in the reduction rate at temperatures of 1100 and 1150 °C; the catalysis effect and change of reduction rate were evaluated by TG and DSC curves
of sodium silicate. Microwave-absorbing characteristics of reduction products
were measured by the method of microwave cavity perturbation. It was found
that microwave absorbing characteristics of reduction products obtained at
temperatures of 900, 1100 and 1150 °C have significant differences. XRD
characterization results explained the formation and accumulation of reduction
product Fe, and pronounced changes of microwave absorbing characteristics
due to the decrease of the content of ilmenite concentrates.
Keywords: sodium silicate; ilmenite concentrates; catalytic reduction;
kinetics; microwave absorbing characteristics.
The mineral ilmenite (FeTiO3) is the main source
of titanium dioxide which is widely used as a white
pigment. The common treatment method is thermal
reduction of ilmenite to form TiO2 and elemental iron
followed by a leach to remove the iron. The reduction
of ilmenite concentrate plays an important role in the
titanium industry. It has been well documented that
ilmenite concentrate usually needs high reductive
temperature or needs additives to improve its reactivity when it is directly reduced [1,2]. Over the past
several decades, many research studies have been
done on the mechanism and kinetics of the reduction
of different ilmenite. Wouterlood [3] investigated the
reduction of ilmenite with carbon at temperatures of
900 to 1200 °C and found the reaction consisted of
two stages: the fast first stage indicating the reduction
of ferric to ferrous iron, and a slower second stage in
which ferrous iron was reduced to metallic iron.
Correspondence: J. Peng, Faculty of Science, Kunming University of Science and Technology, Yunnan,650093, China.
E-mail: jhpeng_ok@yeah.net
Paper received: 21 April, 2012
Paper revised: 10 August, 2012
Paper accepted: 13 August, 2012
Researches have shown that carbothermic reduction
of ilmenite at temperatures below 1200 °C produces
metallic iron and reduced form of oxides (TinO2n-1)
[4,5]. Carbothermic reduction of ilmenite and rutile
was investigated by Welham and Williams [6] at temperatures up to 1500 °C, indicating that the reduction
of rutile was found to proceed through a series of
oxides TinO2n-1 until the formation of Ti3O5. Kucukkaragoz [7] investigated the reduction of ilmenite
concentrate with graphite under argon gas between
1250 and 1350 °C, showing that reduction rates
increased with increasing temperature and decreasing particle size. Dewan [8] studied carbothermal
reduction of ilmenites of different grades and synthetic rutile in different gas atmospheres. The carbothermal reduction of primary ilmenite concentrate was
faster in hydrogen and occurred at a lower temperature than in argon and helium. The reduction in
argon and helium had about the same rate and extent
[8]. Eungyeul [9,10] researched the reduction of titania-ferrous ore by H2 and CO; Satoshi [11] also investigated the reduction kinetics of natural ilmenite ore
with carbon monoxide and found the reduction rate
423
W. Li et al.: CARBOTHERMIC REDUCTION KINETICS OF ILMENITE…
increased with increasing temperature, the rate and
the degree of reduction depended on the formation of
a metallic shell of iron [9-11]. The reactivity of ilmenite
can also be improved by using a pre-oxidization
process, increasing the rate of ilmenite reduction and
the rate of leaching [12-15]. Zhang and Ostrovski [15]
investigated the effects of pre-oxidation and sintering
on the phase composition, specific surface area, morphology and reducibility of ilmenite concentrates. It
was demonstrated that both pre-oxidation and sintering increased the temperature required to reduce
titanium oxides. Pre-oxidization is now a broadly
adopted practice in the processing of ilmenite ore for
production of TiO2 pigment and metallic titanium.
Wang and Yuang [16] described the reduction degree
and rate of Bama ilmenite concentrate by graphite at
temperatures from 850 to 1400 °C. The reduction
degree and reaction rate of the ilmenite increased
with increasing temperature. The higher the temperature was, the faster the reaction rate was. The
reduction degree of the ilmenite decreased due to the
presence of impurities.
The ilmenite deposit in Panzhihua region,
Sichuan, China accounts for 35% of the titanium
resource in the world, and for approximately of 92% in
China [17]. So, it is very important to utilize the ilmenite resources efficiently for the development of the
titanium industry. However, due to the higher contents
of CaO and MgO and complex mineralogy in ilmenite
in Panzhihua region, it is very difficult to upgrade the
ilmenite to titanium-rich slag, which limits the development and utilization of ilmenite deposit in Panzhihua
region; it is urgent to develop new processing technologies of ilmenite concentrates [13,18-20].
In recent years there has been a growing interest in microwave heating in mineral treatment.
Advantages in utilizing microwave technologies for
processing materials include penetrating radiation,
controlled electric field distribution and selective and
volumetric heating [21]. Because of these advantages, a number of potential applications of microwave processing materials have been investigated,
such as microwave assisted ore grinding, microwave
assisted carbothermic reduction of metal oxides, microwave assisted drying and anhydration, microwave
assisted mineral leaching, microwave assisted roasting and smelting of sulphide concentrate, microwave
assisted pretreatment of refractory gold concentrate,
microwave assisted spent carbon regeneration, coke
CI&CEQ 19 (3) 423−433 (2013)
making and activated carbon production, and microwave assisted waste management, etc. [22-31].
For microwave processing of ilmenite, Itoh et al.
described the microwave oxidation of rutile extraction
process, in which rutile is extracted from a natural
ilmenite ore by oxidation and magnetic separation
followed by leaching with diluted acid [32]. Kelly and
Rowson investigated microwave reduction of oxidized
ilimenite concentrate [33]. Tong et al. evaluated the
economic values of industrial applications of carbothermic reduction of metals oxide by microwave heating, showing that the cost is lowered about 15-50%
compared to that of conventional method [34]. Cutmore et al. investigated dielectric properties of some
minerals [35]. Microwave absorbing characteristics of
ilmenite concentrate with different proportions of carbonaceous reduction agents were investigated by the
authors’ group [20], which further confirms the feasibility of microwave reduction of ilmenite concentrate.
All of these investigations present encouraging results.
However, to the best of our knowledge, there is
little information about carbothermic reduction kinetics
of ilmenite concentrate by using catalyst and microwave absorbing characteristics of reactants and products during microwave irradiation, resulting in difficulty of investigations on the interaction mechanism
between microwaves and materials, which limits the
application of microwave heating technology in industry. So, there is an urgent need to investigate microwave-absorbing characteristics of materials and accumulation of data of dielectric properties, in order to
prompt applications of microwave heating in all different kind of fields.
The objective of the present study is to investigate carbothermic reduction kinetics of ilmenite concentrate synergistic catalyzed by sodium silicate and
microwave-absorbing characteristics of reductive products measured by the method of microwave cavity
perturbation.
EXPERIMENTAL
Materials
The raw material, ilmenite, was obtained from
Panzhihua (Sichuan province, PR China). The chemical compositions of ilmenite and proximate analysis of
coke were listed in Tables 1 and 2, respectively.
It can be seen from Tables 1 and 2 that both
ilmenite and coke contain volatiles; especially for
Table 1. Chemical compositions of ilmenite concentrate
Component
Content, mass%
424
TFe
TiO2
CaO
MgO
SiO2
Al2O3
S
32.18
47.85
1.56
6.56
5.6
3.16
≤0.1
W. Li et al.: CARBOTHERMIC REDUCTION KINETICS OF ILMENITE…
CI&CEQ 19 (3) 423−433 (2013)
Table 2. Proximate analysis of coke
Water content
Ash
Volatile
Fixed carbon
Total sulfur
Calorific value
1.93%
27.80%
1.41%
70.80%
2.68%
23.64 MJ/Kg
coke, the amount content of volatile, sulfur and water
is more than 6.02%. If this amount were also calculated as weight of oxygen loss, it would lead to
calculation errors of reduction degree by using the
method of weight loss. So, calibrations of weight loss
fraction at different reduction temperatures by using
coke as reduction agent were investigated, in order to
increase the calculation accuracy of reduction degree
of ilmenite concentrate.
Experimental set up
The set-up of kinetics of reduction experiment
was illustrated in Figure 1 which consists of a vertical
carborundum furnace, a computer monitor system for
monitoring the weight change of the reacting sample
and a temperature controller. The balance is on the
top of furnace and is connected through a suspending
thread. The kinetics experimental conditions were as
follows: ilmenite concentrate 2 g; addition amount of
coke (particle size 180-200 mesh) 15 mass%; ratio of
adhesive of sodium silicate 5 mass%. The weighed
ilmenite concentrate and coke were thoroughly mixed
by stirring over 30 min. Pellets of ilmenite concentrate
containing coke were dried at temperature of 500 °C
for 6 h in a muffle furnace.
Measuring principles of microwave absorbing
characteristics
The measuring principle and equipment referred
to our preciously published paper, in which the
method of microwave cavity perturbation and equipment has been described in detail [20].
Reduction degree of ilmenite concentrates
The weight loss of pellets containing coke during
reduction process included: the evaporation of water,
emission of volatiles in coke, reduction of Fe oxide
and carbon gasification. According to the definition of
basic reduction degree, the following equation could
be obtained:
R=
ΔW 0
× 100% =
M0
Δ W Σ − ΔW C − Δ W V − Δ W W
=
× 100%
M0
(1)
where ΔW0 is the removing amount of oxygen of iron
oxides in ilmenite concentrates (g); M0 is total amount
of oxygen in ilmenite concentrates (g); ΔWv is the
emission amount of volatiles (g); ΔWw is the emission
amount of water (g); ΔWΣ is the total weight loss
amount (g); ΔWc is the amount of carbon loss (g).
In order to eliminate the effects of release of
volatile components and water on reduction degree,
pellets of aluminum oxide powder containing coke
were prepared using the same method as for pellets
of ilmenite concentrates. The emission ratio of volatiles and water of pellets was calculated using the following equation:
Figure 1. Schematic diagram of the reductive experimental setup.
425
W. Li et al.: CARBOTHERMIC REDUCTION KINETICS OF ILMENITE…
f A-P = 100
ΔW V + ΔW W
W A-P
(2)
where fA-P is ratio of weight loss for pellets of aluminum oxide powder containing coke and WA-P is the
mass of pellets of aluminum oxide powder containing
coke.
When replacing the mass of pellets of aluminum
oxide powder containing coke by using pellets containing carbon (W), W = W A-P , reduction degree was
obtained as:
R = 100
ΔW Σ − ΔW C − f A-PW
M0
(3)
Assuming the reaction process of the carbon
reduction of iron oxides under the high temperature
is:
Fe x O y + C = Fe x O y −1 + CO
(4)
equation:
ΔW C =
12
ΔW 0
16
was obtained; so the calculating formula for reduction
degree was deduced as:
R = 100
4( ΔW Σ − f A-PW )
7M 0
(5)
For carbothermic reduction of ilmenite concentrates within the appropriate reduction temperature,
only the reduction process of iron oxides occurs; the
reduction process of TiO2 to low-valence titanium will
occur accompanying the reduction process only at a
higher temperature. So, carbothermic reaction of
ilmenite concentrates can be considered as:
Fe x O y ⋅ TiO2 + C = Fe x O y −1 + CO + TiO2
(6)
If controlling the appropriate temperature,
assuming TiO2 formed during the carbothermic
reduction process of ilmenite concentrates is not
reduced, the reduction degree for ilmenite concentrates can be simplified according to Eq. (5), where M0
should be corrected, if M0r is the ratio of O in FexOy:
M 0r =
16 y
16 y + 56 x
R = 100
64 y (ΔW Σ − f A-PW )
7(16 y + 56 x )
(7)
(8)
The oxygen amount of Fe x O y ⋅ TiO2 is:
M 0• =
426
16 y
16 y + 56 x + 112
(9)
CI&CEQ 19 (3) 423−433 (2013)
At this point, the calculating equation for reduction degree for pellets of ilmenite concentrates containing carbon was finally obtained as:
R = 100
4(16 y + 56 x )(ΔW Σ − f A-PW )
7(16 y + 56 x + 112)
(10)
RESULTS AND DISCUSSION
Calibrations of weight-loss fraction of coke and
ilmenite concentrates
It can be seen from Tables 1 and 2 that ilmenite
and coke contain volatiles. The amount content of
volatile, sulfur and water, especially for coke, is more
than 6.02%. If this amount were calculated as weight
of oxygen loss, it would lead to errors in calculation of
reduction degree by using the method of weight loss.
So, calibrations of weight loss fraction at different
reduction temperatures by using coke as reduction
agent were investigated, in order to increase the calculation accuracy of reduction degree of ilmenite concentrate.
Calibration conditions: coke mass 0.3 g, ilmenite
concentrates 2 g, the others were the same as
defined in “Experimental set up”. The upper deck of
coke and ilmenite concentrates were covered by
Al2O3, which had been calcined to constant weight, in
order to prevent coke injection and oxidation of
ilmenite concentrates. Furthermore, the process was
performed under a protective atmosphere of N2,
preventing weight loss of coke oxidation or weight
gain of oxidation of ilmenite concentrates. Figures 2
and 3 show the relationship between reduction time
and weight loss fraction of coke at different reduction
temperatures and the relationship between reduction
time and weight loss fraction of ilmenite at different
reduction temperatures, respectively.
It can be found that the weight loss of both coke
and ilmenite concentrates increases with increasing
of temperature at the same heating time. Under the
same constant temperature, weight loss of coke and
ilmenite concentrates increases with increase in time
and ilmenite concentrates, losing weight faster at
early stage, while weight loss of volatiles is slower at
final stage. Therefore, increasing constant temperature and heating time will enhance the weight loss of
coke and ilmenite concentrates; if calibrations of
weight-loss fraction of coke and ilmenite concentrates
were not carried out, it would cause a large calculation error for the reduction degree.
The sum of weight losses of coke and ilmenite
concentrates at different reduction temperature for
carbothermic reduction of ilmenite concentrate were
W. Li et al.: CARBOTHERMIC REDUCTION KINETICS OF ILMENITE…
obtained from Figures 2 and 3, and the results are
listed in Table 3.
30
1473
1423
1373
1323
20
1273
15
1073
1173
1123
1223
10
12
2g
1g
4g
8
0
300
600
900
Time/s
1200
Figure 2. Relationship between reduction time and weight loss
fraction of coke at different reduction temperatures.
1423K
1373K
1323K
1273K
1223K
1173K
1123K
1073K
2.5
2.0
1.5
1.0
0.5
0.0
6g
6
7g
5g
8g
4
2
3.0
Percent mass loss/%
3g
10
5
0
of chemical reaction. If the diameter of pellets were
small, it would cause the difficulty of follow-up sample
characterization. The weight of pellets was investigated in the present study. The conditions were as
follows: sodium silicate 3%; coke 15%, ilmenite concentrate 1-8 g (results shown in Figure 4); other set of
conditions: sodium silicate 5%, others the same as
defined in “Experimental set up” (results shown in
Figure 5).
R(%)
Percent mass loss/%
25
CI&CEQ 19 (3) 423−433 (2013)
0
300
Time/s
600
900
Figure 3. Relationship between reduction time and weight loss
fraction of ilmenite at different reduction temperatures.
Carbothermic reduction of ilmenite concentrates
catalyzed sodium silicate
Generally speaking, the larger the diameter of
pellets (weight of pellets), the lower the performance
0
0
500
1000
1500
2000
Time/s
2500
3000
3500
Figure 4. Relationships between reduction degree and different
ball weights at 1050 °C.
It can be seen from Figure 4 that the reaction
rate and weight loss for pellets of 2 g are the highest,
the maximum reduction degree is 10.73%, so the
weight of pellet was chosen to be 2 g. From Figure 5
it can be seen that the reduction rate becomes faster
at temperatures above 1423 K, the reduction degree
is 22.74%, being larger compared to that in Figure 4
at the same conditions, while the corresponding
amount of sodium silicate has increased only 2%,
indicating that sodium silicate has a catalytic effect on
the reduction process.
If nuclei formation and growth are the controlling
steps during the carbothermic reduction of ilmenite
concentrates, the rate expression can be given by
Table 3. Total weight loss of pellets; coke, 0.30 g; ilmenite concentrate, 2.00 g
Temperature, °C
Weight loss of coke, g
Weight loss of ilmenite concentrate, g
Total weight loss, g
800
0.048
0.035
0.083
850
0.052
0.041
0.093
900
0.054
0.042
0.096
950
0.057
0.043
0.10
1000
0.060
0.045
0.105
1050
0.066
0.048
0.114
1100
0.072
0.05
0.122
1150
0.078
0.054
0.132
427
W. Li et al.: CARBOTHERMIC REDUCTION KINETICS OF ILMENITE…
Avrami-Erofeev Equation [36-38], which is one of the
equations often used to describe the nucleation kinetics and subsequent crystal growth:
1
( − ln(1 − α )n ) = kt or α = 1 - exp(-ktn)
(11)
where α is conversion value, n the reaction order, k
the rate constant and t the time.
30
1473K
25
1423K
Table 4 that multiples of reaction rate increase from
4.43 to 9.0 rapidly, reaching stabilization at temperature of 1473 K.
The linear equation y = −4.3841x − 8.0708 is
obtained by fitting the data in Figure 6. The initial
apparent activation energy for reduction of ilmenite
concentrates catalyzed by Na2SiO3·9H2O was 36.45
kJ/mol; the pre-exponential factor was 60e-8.0708 min-1.
By fitting Figure 7, the linear equation y = −16.254x +
+ 1.3425 was also obtained. The initial apparent activation energy for reduction of ilmenite concentrates
catalyzed by Na2SiO3·9H2O was 135.14 kJ/mol; the
pre-exponential factor was 60e-1.3425 min-1.
-11.4
15
1373K
10
1273k
5
1073K
0
-11.5
1323K
0
1000
2000
3000
Time/s
4000
-11.6
1223K
1173K
1123K
-11.7
lnK
R/%
20
CI&CEQ 19 (3) 423−433 (2013)
5000
-11.9
Figure 5. Relationships between reduction degree and
reduction time.
-12.0
Rate equation described by the oxygen weight
loss of reactants of TiO2 ⋅ Fe x O y (assumed random
nucleation and its subsequent growth, n = 1) could be
obtained as:
-12.2
ln(1 − α ) = −kt
y=-4.3841x-8.0708
-11.8
Experimental data
Linear fit of experimental data
-12.1
(12)
where k is the reaction rate (1/min); α is the oxygen
weight loss of reactants of TiO2 ⋅ Fe x O y , being the
reduction degree of pellets containing carbon (%); t is
reduction time (min).
Making a plot by using the equation above and
reduction degree data in Figure 5, reaction rate constants at different constant temperatures can be obtained
(Table 4), and by making a plot of ln K vs. 1/T. Figures 6 and 7 can be obtained. It can be found from
0.78 0.80 0.82 0.84 0.86 0.88 0.90 0.92 0.94
1/T×10-3(K-1)
Figure 6. Plot of ln K vs. 1/T (1023–1273 K range).
The TG and DSC curves of Na2SiO3·9H2O were
used to confirm its catalytic effect for carbothermic
reduction process of ilmenite concentrates.
It can be seen from TG curves of sodium silicate
in Figure 8 that the temperature range of 348.5–494.3
K is attributed to the weight loss of crystallization
water, of which the weight loss ratio being bigger
more than 50%, losing almost all crystallization water,
and appears as an endothermic peak in DSC curves
shown in Figure 9. The melting point of sodium silicate is 1326 K, indicating that melting endothermic
Table 4. Reduction temperature and corresponding reaction rate constant
Temperature, K
-6
-1
Reaction rate constant, 10 min
Reaction rate multiplier
1073
5.41
1.00
1123
6.08
1.12
1173
7.51
1.39
1223
8.25
1.52
1273
10.36
1.91
1323
18.47
3.41
1373
23.96
4.43
1423
48.70
9.00
1473
58.50
10.81
428
W. Li et al.: CARBOTHERMIC REDUCTION KINETICS OF ILMENITE…
reaction for sodium silicate occurs, prompting the
enhancement of activation of alkali metal of sodium
ions, which are absorbed by coke, prompting the
reaction of carbon gasification, in agreement with the
great changes of reaction rate constant in the temperature range of 1373–1423 K.
-9.6
-9.8
-10.0
lnK
-10.2
y=-16.254x+1.3425
-10.4
-10.6
-10.8
Experimental data
Linear fit of experimental data
-11.0
0.67 0.68 0.69 0.70 0.71 0.72 0.73 0.74 0.75 0.76
-3
1/T×10 (K)
Figure 7. Plot of ln K vs. 1/T (1323–1473 K range).
Changes of microwave-absorbing characteristics and
XRD characterization
Figure 10 shows the microwave spectra of
reduction products of ilmenite concentrates catalyzed
by sodium silicate, and Table 5 lists the correspondence microwave absorbing characteristics parameters. Relative frequency shift, attenuations and quality
factors (Q) at the first wave crest of microwave
CI&CEQ 19 (3) 423−433 (2013)
spectra were computed by computer software. From
these parameters, the microwave-absorbing characteristics of reduction products at different conditions
were compared (Figures 11 and 12).
Through analyses of microwave-absorbing characteristics such as attenuation voltage, frequency,
bandwidth and quality factor, combined with Table 5
and Figures 10-12, it can be concluded that there are
great changes for microwave-absorbing characteristics of reduction products obtained at temperatures of
900 and 1100 °C. In order to confirm the changes for
microwave-absorbing characteristics, reduction products obtained at temperatures of 900, 1100 and
1150 °C were also characterized by XRD (Figures 13
and 14).
It can be seen from Figure 13 that the phases of
reduction products at 1100 °C are FeTiO3 (artificial
ilmenite), iron and salts of silicate and very small
amount of Fe3O4. A characteristic peak of Fe at
44.68° is 683 cps, showing that the formation of Fe
accumulates, and reduction reaction reaches to some
extent. The FeTiO3 phase indicates that sodium silicate catalytic reaction is not complete. The Fe3O4
phase shows that mechanism of reduction reaction of
ilmenite concentrates catalyzed by sodium silicate is
similar to that of common iron ore.
It is shown that the intensity of characteristic
peak of Fe at 44.68° is 176, 683 and 933 cps from low
temperature to high temperature, indicating that the
intensity of Fe increases with increasing temperature,
resulting in the increase of iron content (under the
Figure 8. TG Curves of sodium silicate.
429
W. Li et al.: CARBOTHERMIC REDUCTION KINETICS OF ILMENITE…
CI&CEQ 19 (3) 423−433 (2013)
Figure 9. DSC Curves of sodium silicate.
Figure 10. Microwave spectra of reduction products.
2.440
Attenuation/v
1.90
2.435
1.85
2.430
1.80
Attenuation
Frequency of microwave
1.75
2.425
1.70
2.420
1.65
1.60
2.415
800
900
1000
1100
Reduction temperature/℃
Frequency of microwave/Ghz
2.445
1.95
1200
Figure 11. Relationships between reduction temperature and attenuation, frequency of microwave.
430
W. Li et al.: CARBOTHERMIC REDUCTION KINETICS OF ILMENITE…
CI&CEQ 19 (3) 423−433 (2013)
0.09
54
0.08
42
B andwidth
Q uality fact
0.06
36
Quality fact
Bandwidth
48
0.07
0.05
30
0.04
800
900
1000
1100
R eduction tem perature/ ℃
1200
Figure 12. Relationships between reduction temperature and bandwidth, quality factor.
Table 5. Microwave-absorbing characteristic parameters of reduction products
Product
Quality factor (Q)
Attenuation voltage, V
Frequency, GHz
Bandwidth, GHz
Empty cavity
2.2135
2.4755
0.0320
77.36
NZ800
1.9342
2.4379
0.0453
53.82
NZ850
1.9241
2.4373
0.0459
53.10
NZ900
1.9081
2.4401
0.0458
53.28
NZ950
1.9303
2.4391
0.0454
53.72
NZ1000
1.9288
2.4385
0.0438
55.67
NZ1050
1.9406
2.4418
0.0438
55.75
NZ1100
1.7955
2.4356
0.0539
45.18
NZ1150
1.6351
2.4234
0.0852
28.44
NZ1200
1.6341
2.4164
0.0782
30.90
Intensity(CPS)
1500
1000
500
0
29-0733> Ilmenite - Fe+2TiO3
35-0796> MgTi2O5 - Magnesium Titanium Oxide
06-0696> Iron - Fe
46-1473> Aenigmatite - Na2Fe5+2TiSi6O20
24-0203> Augite - Ca(Mg,Fe)Si2O6
19-0629> Magnetite - Fe+2Fe2+3O4
10
20
30
40
50
60
70
80
90
2θ / °
Figure 13. XRD Pattern of reductive product at 1100 °C.
431
W. Li et al.: CARBOTHERMIC REDUCTION KINETICS OF ILMENITE…
CI&CEQ 19 (3) 423−433 (2013)
6000
Itensity(CPS)
5000
900 ℃
4000
△
▲
3000
1150 ℃
2000
1000
1100 ℃
0
10
20
30
40
50
60
70
80
90
2-theta( °
Figure 14. XRD Patterns of reductive product at different reduction temperatures (△: FeTiO3, ▲: Fe).
same measuring conditions). The intensity of the
reduction product at temperature of 900 °C is low,
which can be considered the initial formation of Fe,
demonstrating that the reduction reaction of ilmenite
concentrates catalyzed by sodium silicate starts at
temperature of 900 °C. The intensity of characteristic
peak of FeTiO3 at 32.58° is 1859, 1652 and 908 cps
from low temperature to high temperature, showing
that the content of FeTiO3 decreases with increasing
reaction temperature, however, even though the temperature reaches 1150 °C, the reduction reaction of
ilmenite concentrates is not complete. The sharp
change of intensity becomes small at temperature
range of 1100 to 1150 °C, indicating that reaction rate
of carbothermic reduction of ilmenite concentrates
becomes faster, which agrees with the results of
multiples of rate increasing from 4.43 to 9.0 listed in
Table 4. Therefore, the formation of reduction production iron and Fe accumulation and the decrease of
content of ilmenite concentrates are the main reasons
for the large changes of microwave-absorbing characteristics of reduction products.
CONCLUSIONS
The reduction degree of ilmenite concentrates
reduction reaction has been deduced as R = 4/7(16y
+ 56x)(ΔWΣ - fA-PW)/(16y + 56x + 112) from reduction
degree expression R = 100ΔW0/M0.
Kinetics experimental results show that activation energies of initial and later stage are 36.45 and
135.14 kJ/mol, respectively. There is a great change
for reduction rate at temperatures of 1100 and 1150
°C; the catalysis effect and great change for reduction
rate were evaluated by TG and DSC curves of sodium
silicate.
Microwave-absorbing characteristics of reduction products were measured by the method of microwave cavity perturbation. It was found that mic-
432
rowave absorbing characteristics of reduction products obtained at temperatures of 900, 1100 and
1150 °C have significant differences. XRD characterization results explained the formation and accumulation of reduction product Fe, and pronounced
changes of microwave absorbing characteristics due
to the decrease of the content of ilmenite concentrates.
Acknowledgments
The authors would like to express their gratitude
for the financial support of the Major Program of
National Natural Science Foundation of China (Grant
No. 51090385), the International S&T Cooperation
Program of China (No. 2012DFA70570), the Yunnan
Provincial International Cooperative Program (No.
2011IA004) and Reserve Talents of Middle-aged and
Young Academic Technology Leaders in Yunnan Province (2011CI010).
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117-120 (in Chinese)
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H.S. Ku, F. Siu, E. Siores, J.A.R. Bal, A.S. Blicblau, J.
Mate. Process. Technol. 113 (2001) 184-188
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Stoddard, Miner. Eng. 13 (2000) 729-736
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[22]
M. Al-Harahsheh, S.W. Kingman, Hydrometallurgy 73
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K.E. Haque, Int. J. Miner. Process. 57 (1999) 1-24
WEI LI1,2
JINHUI PENG1
SHENGHUI GUO1
LIBO ZHANG1
GUO CHEN1
HONGYING XIA1
1
Key Laboratory of Unconventional
Metallurgy, Ministry of Education,
Kunming University of Science and
Technology, Yunnan, China
2
Faculty of Science, Kunming
University of Science and Technology,
Yunnan, China
NAUČNI RAD
KINETIKA KARBOTERMALNE REDUKCIJE
KONCENTRATA ILMENITA KATALIZOVANE
NATRIJUM-SILIKATOM I MIKROTALASNO-APSORPCIONE KARAKTERISTIKE
PROIZVODA REDUKCIJE
U ovom radu je ispotivana kinetika karbotermalne redukcije koncentrata ilmenita katalizovane natrijum-silikatom. Stepen redukcije koncentrata ilmenita je određen kao R =
= 4/7(16y + 56x)(ΔWΣ - fA-PW)/(16y + 56x + 112). Rezultati pokazuju da su vrednosti
energije aktivacije početne i krajnje faze 36,45 i 135,14 kJ/mol, redom. Na temperaturama
od 1100 i 1150 °C primećena je velika promena u brzini redukcije. Uticaj katalize i velika
promena brzine redukcije je određena pomoću TG i DSC krive natrijum-silikata. Mikrotalasno-apsorpcione karakteristike proizvoda redukcije su merene metodom mikrotalasnih
kavitacionih perturbacija. Ustanovljeno je da se mikrotalasne apsorpcione karakteristike
proizvoda redukcije dobijenih na temperaturama 900, 1100 i 1150 °C jako menjaju i u
kombinaciji sa XRD objašnjavaju stvaranje i akumulaciju proizvoda redukcije Fe. Velike
promene mikrotalasnih apsorpcionih karakteristika se javljaju i zbog smanjenja sadržaja
koncentrata ilmenita.
Ključne reči: natrijum-silikat; koncentrati ilmenita; katalitička redukcija; kinetika;
mikrotalasne apsorpcione karateristike.
433
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Chemical Industry & Chemical Engineering Quarterly 19 (3) 435−440 (2013)
CI&CEQ
YU SUN1,2
SHUANGSHUANG XU1
YANLING GENG1
XIAO WANG1
TIANYOU ZHANG2
ISOLATION AND PURIFICATION OF LIGNANS
FROM Schisandra chinensis BY COMBINATION
OF SILICA GEL COLUMN AND HIGH-SPEED
COUNTER-CURRENT CHROMATOGRAPHY
Shandong Analysis and Test
Center, Shandong Academy of
Sciences, Jinan, China
2
Shandong MingRen Freda
Pharmaceutical co., LTD, Jinan,
Shandong, China
Silica gel column combined with high-speed counter-current chromatography
separation was successfully applied to the separation of schizandrin (I), angeloylgomisin H (II), gomisin A (III), schisantherin C (IV), deoxyschizandrin (V),
γ-schisandrin (VI) and schisandrin C (VII) from the fruits of Schisandra chinensis (Turcz.) Baillon. The petroleum ether extracts of the fruits of S. chinensis
were pre-separated first on a silica gel column and divided into two fractions as
sample 1 and sample 2. 260 mg of sample 1 was separated by HSCCC using
petroleum ether–ethyl acetate–methanol–water (10:8:10:8, v/v) as the two-phase
solvent system and 18.2 mg of schizandrin, 15.7 mg of angeloylgomisin H,
16.5 mg of gomisin A and 16.7 mg of schisantherin C were obtained. 230 mg
of sample 2 was separated using petroleum ether–ethyl acetate–methanol–water
(10:0.5:10:1, v/v) as the two-phase solvent system and 19.7 mg of deoxyschizandrin, 23.4 mg of γ-schisandrin and 18.2 mg of schisandrin C were obtained.
The purities of the separated compounds were all over 94% as determined by
HPLC. The chemical structures of these compounds were confirmed by ESIMS and 1H-NMR.
1
SCIENTIFIC PAPER
UDC 582.678.2:543.544:615.89
DOI 10.2298/CICEQ120504078S
Keywords: Schisandra chinensis (Turcz.) Baillon., lignans, high-speed
counter-current chromatography.
Schisandra chinensis fructus (Wuweizi in
Chinese), the dried fruits of Schisandra chinensis
(Turcz.) Baillon, is officially listed in the Chinese Pharmacopoeia and one of the most famous traditional
Chinese medicine [1]. It is distributed in northeastern
China, Russia, Japan and Korea [2]. Traditionally, the
fruits of S. chinensis are used for the treatment of
chronic cough, nocturnal emission, spermatorrhea,
enuresis, frequent urination, protracted diarrhea, night
sweating, spontaneous sweating, palpitation and
insomnia [1]. It is also widely used as a functional
ingredient and nutritional in foods, such as beer, wine,
beverages, jam and other products [3]. Additionally, it
is known to be a rich source of lignans with a dibenzo[a,c]cyclooctadiene skeleton [4,5], which have
attracted considerable interest because of their bipheCorrespondence: X. Wang, Shandong Analysis and Test Center, Shandong Academy of Sciences, 19 Keyuan Street, Jinan,
250014, China.
E-mail: wxjn1998@126.com
Paper received: 4 May, 2012
Paper revised: 13 August, 2012
Paper accepted: 19 August, 2012
nyl-type structures and multiple pharmacological activities. In particular, pharmacological research indicated that these lignans can inhibit LTB4 production
[6], afford protection against hepatic damage induced
by CCl4 [7] and protect the liver from injury after
administration of acetaminophen [8].
Due to these particular pharmacological and
clinical effects of lignans separated from S. chinensis,
it is necessary to establish an efficient method for the
preparative separation and purification of these compounds from this plant. Recently, several extraction,
isolation and purification methods of S. chinensis lignans have been reported, such as ionic liquid-based
ultrasonic-assisted, ionic liquid based microwave
simultaneous, macroporous resins and ion exchange
resin [9–12]. High-speed counter-current chromatography (HSCCC) is a liquid-liquid partition chromatographic technique that can eliminate irreversible
adsorption of sample onto the solid support [13]. It
has been widely used in preparative separation and
purification of various natural products [14–17]. In the
previous studies, Peng et al. [18] obtained schizandrin and gomisin A from S. chinensis by HSCCC and
435
Y. SUN et al.: ISOLATION AND PURIFICATION OF LIGNANS FROM S. chinensis…
Huang et al. [19] separated deoxyschizandrin and
γ-schisandrin from S. chinensis using this method too.
In order to get more pure compounds, a simple and
feasible method needs to be established. In this
paper, an efficient method, combination of silica gel
column and HSCCC, was reported. Seven lignans
were successfully isolated and purified from S. chinensis by HSCCC.
EXPERIMENTAL
Reagents and materials
Chromatographic grade methanol (Tedia Company Inc, Fairfield, USA) was used for HPLC analysis.
Organic solvents including petroleum ether (60–90
°C), ethyl acetate, ethanol and methanol were all of
analytical grade (Damao Chemical Factory, Tianjin,
China). The water used in solutions and dilutions was
treated with a Milli–Q water purification system (Millipore, USA).
The fruits of S. chinensis were purchased from a
local drug store. The botanical identification was made
by Dr. Zongyuan Yu, Shandong Academy of Chinese
Medicine, China. Silica gel (200–300 mesh, Haiyang
Chemical Factory, Qingdao, China) was used for
sample preparation.
Apparatus
A model GS10A–2 Preparative HSCCC (Beijing
Emilion Science & Technology Co., Beijing, China)
equipped with a PTFE multilayer coil (1.6 mmI.D.×110
m, with a total capacity of 230 mL). The β values of
this preparative column range from 0.5 at internal to
0.8 at the external (β = r/R, where r is the distance or
the rotation radius from the coil to the holder shaft,
and R (R = 8 cm), the revolution radius or the distances between the holder axis and central axis of the
centrifuge). The rotation speed is adjustable from 0 to
1000 rpm, and 800 rpm was used in this experiment.
The two-phase solvent was pumped into the column
with a model NS–1007 constant-flow pump. Continuous monitoring of the effluent was achieved with a
model 8823A–UV monitor at 254 nm. A model 3057–
11 portable recorder was employed to record the
chromatogram.
The HPLC equipment used was a Waters Empower system (Milford, MA, USA) including a model
600 system controller, a model 600 pump, a model
600 multisolvent delivery system, a model 996 photodiode array detector.
Preparation of crude extract
About 500 g of the dried fruits of S. chinensis
were milled to powder (about 40 mesh) and extracted
436
CI&CEQ 19 (3) 435−440 (2013)
with 3 L 95% ethanol for three times (2 h each time)
at the temperature of 70 °C. The extracts were combined and evaporated to dryness with a rotary evaporator at 50 °C. Then the ethanol extracts were dissolved in water and extracted with petroleum ether for
3 times. The petroleum ether extraction solutions
were concentrated to dryness, which yielded 36.8 g of
crude extract. Then the petroleum ether extract was
further subjected to the silica gel column (200 g of
silica gel H, 200–300 mesh) eluted stepwise with petroleum ether–ethyl acetate (5:1 and 2:1, v/v) to obtain
two fractions. The petroleum ether–ethyl acetate (2:1,
v/v) effluent was collected and evaporated to dryness
with a rotary evaporator at 50 °C and about 28.6 g of
powder was obtained (sample 1). The petroleum
ether–ethyl acetate (5:1, v/v) effluent was also collected and evaporated to dryness with a rotary evaporator at 50 °C and about 4.2 g of powder was
obtained (sample 2). All these samples were stored in
a refrigerator until subsequent HSCCC separation.
Selection of the two-phase solvent systems
Approximately 2 mg of the test sample was
weighed in a 10 ml test tube to which 2 ml of each
phase of the equilibrated two-phase solvent system
was added. The tube was capped and shaken vigorously for 1 min to equilibrate the sample thoroughly
with the two phases. Equal volumes of each phase
were then analyzed by HPLC to obtain the partition
coefficients (KD). The KD value was expressed as the
peak area of compound in the upper phase divided by
the peak area of compound in the lower phase.
HSCCC Separation
In each separation process, the multilayer coiled
column was first entirely filled with the upper phase
(stationary phase) of the solvent. The apparatus was
then rotated at 800 rpm, while the lower phase
(mobile phase) was pumped into the column at a flow
rate of 2 mL/min. After hydrodynamic equilibrium was
reached, as indicated by a clear mobile phase eluting
at the tail outlet, the sample solution was injected
through the sample port. The effluent from the outlet
of the column was continuously monitored with a UV
detector at 254 nm. The chromatogram was recorded
for 50 min after sample injection. Each peak fraction
was manually collected according to the UV absorbance profile and analyzed by HPLC.
Analysis and characterisation of HSCCC fractions
The two samples and each peak fraction from
HSCCC were analyzed by HPLC. The analyses were
accomplished by a Shim–Pack VP–ODS column (250
mm×4.6 mm I.D., 5 μm) at a column temperature of
Y. SUN et al.: ISOLATION AND PURIFICATION OF LIGNANS FROM S. chinensis…
25 °C. Mobile phase was performed with methanol–
water (75:25, v/v). The flow rate was 1.0 mL/min.
Detection wave was 254 nm.
The HSCCC fractions were all analyzed by ESI–
MS on an Agilent 1100/MS–G1946 (Agilent, Santa
Clara, CA, USA) and NMR spectra on a Varian–600
NMR spectrometer (Varian, Palo Alto, CA, USA) with
chloroform (CDCl3) as solvent.
RESULTS AND DISCUSSION
In HSCCC separation, the choice of a suitable
two-phase solvent system, which can provide an ideal
range of the KD for the targeted compounds, is the
first and critical step. In general, the most suitable
range of the KD value is close to 1 [13]. Too large KD
values tend to produce excessive sample band
broadening, while too small KD values usually result in
poor peak resolution. Several two-phase solvent
systems were tested and the KD values were measured, and summarized in Table 1.
It was found that no two-phase solvent system
was suitable for separation of the target compounds
by one-step HSCCC separation according to the KD
values shown in Table 1. Thus, the petroleum ether
extracts of the fruits of S. chinensis were pre-separated first on a silica gel column. Different kinds of
solvent systems such as petroleum ether–ethyl acetate, petroleum ether–diethyl ether, trichlormethane–
methanol were tested for the separation. Different elution gradients were also investigated. It was found
that when petroleum ether–ethyl acetate (5:1 and 2:1,
v/v) was used for the separation, the crude extract
was separated into two fractions. Sample 1 (2:1
fraction) mainly contained compounds I–IV, and sample
2 (5:1 fraction) mainly contained compounds V–VII.
Meanwhile, these compounds were largely enriched
after the separation of silica gel column. Thus, sample
1 was used for HSCCC separation of compounds I–IV,
CI&CEQ 19 (3) 435−440 (2013)
and sample 2 for compounds V–VII. The HPLC chromatograms of sample 1 and sample 2 are shown in
Figure 1.
In accordance with the KD values of compounds
I–IV shown in Table 1, it can be seen that both petroleum ether–ethyl acetate–methanol–water with volume
ratios of 10:8:10:8 and 10:8:9:8 were suitable for
separation of compounds I–IV. So these solvent systems were tested for HSCCC separation. When
petroleum
ether–ethyl
acetate–methanol–water
(10:8:10:8, v/v) was used as the two-phase solvent
system, the separation result was better than that of
petroleum
ether–ethyl
acetate–methanol–water
(10:8:9:8, v/v) was used. So 260 mg of sample 1 was
separated by HSCCC with the solvent system of
petroleum
ether–ethyl
acetate–methanol–water
(10:8:10:8, v/v). The HSCCC chromatogram of sample
1 is shown in Figure 2A. The fractions of HSCCC
were collected according to HPLC analysis. 18.2 mg
of schizandrin (I), 15.7 mg of angeloylgomisin H (II),
16.5 mg of gomisin A (III) and 16.7 mg of schisantherin C (IV) were obtained with the purities of 98.5,
94.4, 97.7 and 95.6%, respectively. The HPLC chromatograms of compounds I–IV are shown in Figure
1a–d.
From Table 1, it can be seen that petroleum
ether–ethyl acetate–methanol–water with volume ratios
of 10:1:10:1, 10:0.5:10:1 and 10:0.5:10:0.5 were all
suitable for separation of compounds V–VII. When
petroleum
ether–ethyl
acetate–methanol–water
(10:1:10:1 and 10:0.5:10:0.5, v/v) were used as the
two-phase solvent system, compounds VI and VII
were successfully separated, however, compound V
could not be obtained. While when petroleum ether–
ethyl acetate–methanol–water (10:0.5:10:1, v/v) was
chosen as the two-phase solvent system, compounds
V–VII could all be obtained. So petroleum ether–ethyl
acetate–methanol–water (10:0.5:10:1, v/v) was chosen
to be the two-phase solvent system for the separation
Table 1. Partition coefficient (KD) values of target compounds in different two-phase solvent systems
Solvent system composition (petroleum
ether–ethyl acetate–methanol–water), v/v
Compound
I
II
III
IV
V
VI
VII
1:1:1:1
1.38
2.73
3.72
5.23
15.40
—
—
10:8:10:10
1.14
2.31
3.10
4.15
14.63
—
—
10:8:12:8
0.25
0.62
0.97
1.28
5.74
13.14
10.84
10:8:10:8
0.65
1.11
1.48
1.96
11.62
—
13.76
10:8:9:8
0.92
1.65
2.02
2.43
10.01
17.21
14.66
10:5:10:5
0.24
0.35
0.57
0.96
3.37
8.73
6.68
10:2:10:2
0.13
0.17
0.29
0.62
1.77
3.02
2.17
10:1:10:1
0.06
0.07
0.10
0.11
0.43
1.55
1.00
10:0.5:10:1
0.06
0.07
0.13
0.15
0.74
1.98
1.28
10:0.5:10:0.5
0.02
0.02
0.06
0.07
0.36
1.03
0.70
437
Y. SUN et al.: ISOLATION AND PURIFICATION OF LIGNANS FROM S. chinensis…
CI&CEQ 19 (3) 435−440 (2013)
Figure 1. HPLC Chromatograms of the ethyl acetate fraction of Magnolia sprengeri and HSCCC peak fractions (I–VII). Experimental
conditions: column, Shim–pack VP–ODS column (250 mm×4.6 mm i.d., 5μm); column temperature, 25 °C; mobile phase, methanol–water
(25:75, v/v); flow rate, 1 mL/min; detection, 254 nm; injection volume, 20 µL.
438
Y. SUN et al.: ISOLATION AND PURIFICATION OF LIGNANS FROM S. chinensis…
CI&CEQ 19 (3) 435−440 (2013)
Figure 2. HSCCC Chromatograms. A) Sample 1. HSCCC Conditions: Two-phase solvent system: petroleum ether–ethyl acetate–
methanol–water (10:8:10:8, v/v); mobile phase: lower phase; flow rate: 2 mL/min; detection, 254 nm; sample size: 260 mg dissolved in
5 mL of the upper phase and 5 mL of the lower phase. B) Sample 2. HSCCC Conditions: Two-phase solvent system: petroleum ether–
ethyl acetate–methanol–water (10:0.5:10:1, v/v); mobile phase: the lower phase; flow rate: 2 mL/min; detection, 254 nm; sample size:
230 mg dissolved in 5 mL of the upper phase and 5 mL of the lower phase.
and purification of compound V–VII. The HSCCC
chromatogram of sample 2 was shown in Figre 2B.
19.7 mg of deoxyschizandrin (V), 23.4 mg of γ-schisandrin (VI) and 18.2 mg of schisandrin C (VII) were
obtained from 230 mg of sample 2 with the purities of
94.3, 95.6 and 98.2%, respectively. The HPLC chromatograms of compounds V–VII are shown in Figure
1e–g.
The chemical structure of each peak fraction of
HSCCC was identified according to its ESI-MS and
1
H-NMR data. Compared with the data given in [20–
-27], peaks I–VII in Figure 2 were indentified as schizandrin, angeloylgomisin H, gomisin A, schisantherin
C, deoxyschizandrin, γ-schisandrin and schisandrin C.
CONCLUDING REMARKS
The results of our studies described above clearly
demonstrated that the combination of silica gel column
chromatography and HSCCC was successfully used
in the separation and purification of schizandrin,
angeloylgomisin H, gomisin A, schisantherin C,
deoxyschizandrin, γ-schisandrin and schisandrin C
from the fruits of S. chinensis. It is proved that the
combined use of silica gel column chromatography
and HSCCC is a good separation strategy that can
also be used for the separation and purification of
other lignans from natural products.
Acknowledgments
Financial supports from the Natural Science
Foundation of China (20872083), scientific and technological major special project (2010ZX09401-302-512) and the Key Science and Technology Program of
Shandong Province (BS2009SW047) are gratefully
acknowledged.
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YU SUN1,2
SHUANGSHUANG XU1
YANLING GENG1
XIAO WANG1
TIANYOU ZHANG2
1
Shandong Analysis and Test Center,
Shandong Academy of Sciences,
Jinan, China
2
Shandong MingRen Freda
Pharmaceutical co., LTD, Jinan,
Shandong, China
NAUČNI RAD
IZOLACIJA I PREČIŠĆAVANJE LIGNINA IZ
Schisandra chinensis KOLONSKOM
HROMATOGRAFIJOM NA SILIKAGELU
KOMBINOVANOM SA HSCCC
HROMATOGRAFIJOM
Kolonska hromatrografija na silikagelu kombinovana sa HSCCC hromatrografijom je uspešno primenjena za razdvajanje šizandrina (I), angeloilgomisina H (II), gomisina A (III),
šisanderina C (IV), deoksišizandrina (V), γ-šisandrina (VI) i šisandrina C (VII) iz ploda
Schisandra chinensis (Turcz.) Baillona. Petroletarski ekstrakti ploda S. chinensis prethodno razdvojeni na koloni sa silikagelom su podeljeni na dve frakcije: uzorak 1 i uzorak 2.
Uzorak 1 (260 mg) je razdvojen HSCCC hromatografijom koristeći petroletar-etil acetat–metanol-voda (10:8:10:8, v/v) kao dvofazni sistem rastvarača, pri čemu je dobijeno 18,2
mg šizandrina, 15,7 mg angeloilgomisina H, 16,5 mg gomisina A i 16,7 mg šisanderina C.
Uzorak 2 (230 mg) je razdvojen HSCCC hromatografijom koristeći petroletar-etil acetat–metanol-voda (10:0.5:10:1, v/v) kao dvofazni sistem rastvarača, pri čemu je dobijeno 19,7
mg deoksišizandrina, 23,4 mg γ-šisandrina i 18,2 mg šisandrina C. Čistoća izdvojenih
jedinjenja je veća od 94%, što je određeno HPLC metodom. Hemijske strukture ovih jedinjenja su dokazane ESI-MS i 1H-NMR metodama.
Ključne reči: Schisandra chinensis (Turcz.) Baillon., lignin, HSCCC hromatografija.
440
Available on line at
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Chemical Industry & Chemical Engineering Quarterly 19 (3) 441−448 (2013)
HUSEIN DIBAEI ASL1
MAJID ABDOUSS2
MAHMOUD TORABI ANGAJI3
AMINODDIN HAJI4
1
R&D Department, Asia
Technology Pioneers Co. Ltd.,
Tehran, Iran
2
Department of Chemistry,
Amirkabir University of
Technology, Tehran, Iran
3
Polymers and Chemical
Engineering Group, Faculty of
Engineering, Tehran University,
Tehran, Iran
4
Department of Textile
Engineering, Birjand Branch,
Islamic Azad University, Birjand,
Iran
SCIENTIFIC PAPER
CI&CEQ
SURFACE AND MECHANICAL PROPERTIES
OF POLYPROPYLENE/CLAY
NANOCOMPOSITE
Huge consumption of polypropylene in the industries like automotive motivates
academic and industrial R&Ds to find new and excellent approaches to
improve the mechanical properties of this polymer, which has no degradation
effect on other required performance properties like impact resistance, controlled crystallinity, toughness and shrinkage. Nowadays, nanoparticles play a
key role in improving the mechanical and surface properties of polypropylene.
In this study, three compositions of polypropylene/nanoclay, containing 0, 2
and 5% of nanoclay were prepared in an internal mixer. For characterizing the
nanoclay dispersion in polymer bulk, TEM and XRD tests were used. For
scratch resistance testing, scratch lines were created on the load of 900 grain
on sheets and SEM images were taken and compared with neat PP scratch
image. Crystallinity and mechanical behavior were studied. The results showed
that mechanical properties and scratch resistance of the composites were
improved.
Keywords: nanocomposite, nanoclay, polypropylene, mechanical behavior.
UDC 678.742.3
DOI 10.2298/CICEQ120226079D
Polypropylene (PP) is an important thermoplastic material because of its good processing ability,
high strength, chemical resistance, and low cost [1]. It
has been used as the material of choice for interior
auto parts and other component applications. However, the surface of polypropylene and its copolymers
are generally very susceptible to damage [2]. Beside
the improvement of stiffness and strength of polypropylene, its scratch resistance improvement is critical.
A better understanding of the role of additives
and fillers in the scratch behavior of thermoplastic
polyolefins (TPOs) is needed for the maximum utilization of TPOs for automotive applications. A wide
range of inorganic materials, such as glass fibers,
talc, calcium carbonate and clay minerals have been
successfully used as additives or reinforcement to
improve the stiffness and strength of polypropylene,
but scratch susceptibility has not been improved [3,4].
Correspondence: M. Abdouss, Department of Chemistry, Amirkabir University of Technology, Hafez Ave., Tehran, Iran.
E-mail: phdabdouss44@aut.ac.ir
Paper received: 26 February, 2012
Paper revised: 30 August, 2012
Paper accepted: 30 August, 2012
Nanocomposites are a new growing generation
of polymer-composites, which can give us a good
solution for this problem. Nanocomposites are able to
play a magical role in the polymer industry [5,6].
Polymer nanocomposites are a new class of
multiphase materials containing a dispersion of an
ultrafine phase, typically in the range of 1–100 nm.
Among the different nanoparticles, nanoclay has
attracted significant attention because it provides two
distinct opportunities for dispersion in the polymer
matrix that include intercalation and exfoliation. These
studies indicated that polymer nanocomposites exhibit enhanced strength, modulus, and flame retardancy
that are not exhibited by the individual phases or conventional composites containing micrometer size particles or fibers [1,7-14].
Automakers such as Ford and General Motors
Corp. are beginning to use nanocomposites, made by
the conventional process, in nonstructural applications. For example, GM is using the material in the
step-assist on the GMC Safari/Chevrolet Astro minivans [15].
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H.D. ASL et al.: SURFACE AND MECHANICAL PROPERTIES OF POLYPROPYLENE/CLAY …
In this study, scanning electron microscopy
(SEM) is used to characterize the scratch patterns on
the polymer surface, and other changes on mechanical properties of polypropylene were investigated.
EXPERIMENTAL
The polypropylene (PI0800) used in the experiments was a product of Bandar Imam Co. Nanoclay
(Nanoline DK1) was provided by Fenghong Clay
Chem. Co. (China). PP-MAH, as a compatibilizer
(trade name Fusabond-MD353D) was purchased
from Dupont Chem. Co.
An internal mixer (Haake HBI system 90, 300cc,
fill factor 0.8) was used to prepare the required composites (Table 1). Initially PP-MAH and nanoclay were
mixed with ratio of 2:1 and then PP was added to the
mixer. The mixing temperature was kept at 180 °C,
the rotation speed set at 100 rpm. The mixing time
was 8 min. In order to prepare the film of desirable
dimensions, 2.5 g of composite were pressed under
12 atm. at 220 °C for 5 min. The sample was then
cooled to room temperature. Films with thickness of
1.5 mm were obtained.
CI&CEQ 19 (3) 441−448 (2013)
used for the measurement of notched impact strength
according to ASTM D256.
Differential scanning calorimetry (DSC) curves
were recorded on a DSC 2010 machine (TA Instruments, New Castle, DE, USA) to examine the thermal
behavior of samples. Approximately 5 mg of each
sample was used and the measurements of the
samples were performed by heating from 20 to 200
°C at a rate of 10 °C/min under nitrogen atmosphere.
For the transmission electron microscopy (TEM)
analysis, the specimen was microtomed to an ultra
thin section of 70 nm thickness using an ultracryomicrotome with a diamond knife. The structure was
observed under a Phillips CM 12.
Scratch resistance and hardness of the specimens were tested following the procedure previously
described [16]. To evaluate the depth of the scratches,
SEM investigations were done using a Cambridge
S-360 instrument.
X-ray diffraction (XRD) data were collected on a
Siemens D5000 XRD with a 2θ range of 1.2–12°.
RESULTS AND DISCUSSIONS
Mechanical properties
Table 1: composition of the compounds
Compound
PP
Nanoclay
PP-gr-Ma
D1
100
0
0
D2
96
2
2
D3
90
5
5
The tensile properties were determined in accordance with ASTM D-638 using Instron 6025 tensile
testing equipment. A Zwick 5102 impact tester was
The tensile and flexural strength of the samples
are shown in Tables 2 and 3, and the impact resistance is presented in Table 4. As can be seen from
these results, the strength and modulus were substantially increased compared with the neat PP without significant variations in toughness or impact
strength as measured by standard nothed Izod Test.
Beside the mechanical properties, XRD patterns
of nanoclay D2 and D3 and have been achieved
(Figure 1). Curve analysis for these three samples
Table 2. Tensile strength test results of specimens
Speciemen
Width/thickness Strain at peak Elongation at break Peak stress Stress at yield Break stress Strain at yield Modulus
mm
%
mm
MPa
MPa
MPa
%
MPa
D1
9.85/3.9
8.144
9.07
28.8
28.72
27.25
6.926
1100
D2
9.8/3.9
6.512
8.2
35.1
34.8
34.6
5.73
1450
D3
9.8/3.9
6.08
7.2
38.3
38.2
38
5.6
1720
Table 3. Flexural strength test results
Speciemen
Width/thickness, mm
Strain at break, %
Modulus, MPa
Strain at peak, %
D1
10.55/9.95
0.105
1094.41
0.095
Stress at yield, MPa
39.2
D2
9.9/9.65
0.081
1415.52
0.081
44.55
D3
9.9/9.65
0.076
1650.15
0.062
49.98
Table 4. Impact resistance results
Sample
Impact resistance; Izod, N m/m
442
D1
D2
D3
20.2
19
18
H.D. ASL et al.: SURFACE AND MECHANICAL PROPERTIES OF POLYPROPYLENE/CLAY…
CI&CEQ 19 (3) 441−448 (2013)
Figure 1. XRD Pattern of: a) nanoclay; b) nanocomposite D2; c) nanocomposite D3.
indicates that the interlayer platelet spacing of nanoclay is about 21 Å. Dissapearance of the d001 diffraction peak in D2 and D3 indicates the exfoliated structure of layers in nanocomposite. TEM images (Figure
2) were taken in order to obtain visible evidence of
nanoclay layers in the polymer matrix.
Mechanical tests, TEM and XRD results and
their comparison with other nanocmposite researches
led us to conclude that D2 and D3 have mechanical
properties expected from a nanocomposite [5,7,15].
The strong interaction in the polypropylene–clay system is responsible for significant changes in physical
and mechanical properties [8].
Scratch resistance properties
In typical studies of scratch behavior of polypropylene, many factors such as filler type, additive,
lubricant, impact modifier and surface morphology
have been considered but in nanocomposites scratch
studies, filer-matrix adhesion, positioning and orientation of nanolayers and polymer chains in the matrix
have appeared as new factors [17]. Here we discuss
these factors.
For characterizing the scratch patterns of
sample surface, SEM images were taken (Figure 3)
and the hardness of the surfaces was determined
(Table 2). The crystallinity behavior of the samples
was studied by DSC technique (Figure 4). There is a
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H.D. ASL et al.: SURFACE AND MECHANICAL PROPERTIES OF POLYPROPYLENE/CLAY…
D2
CI&CEQ 19 (3) 441−447 (2013)
D3
Figure 2. TEM Images of D2 and D3.
Figure 3. SEM Micrographs of the scratch damage region at load of 900 g on the surface of each sample.
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H.D. ASL et al.: SURFACE AND MECHANICAL PROPERTIES OF POLYPROPYLENE/CLAY…
CI&CEQ 19 (3) 441−448 (2013)
Figure 4. Differential scanning calorimerty (DSC) graphs of samples; TmD1 = 165.81 °C, TmD2 = 167.2 °C, TmD3 = 169.3 °C.
direct relation between the hardness and scratch
resistance of polypropylene nanocomposites.
Under load, plastic deformation and stress
whitening appear when scratch resistance is not high
enough; this is due to the formation of voids, microcrazing and debonding in polymer surface [3,17].
These fracture features of the surface lead to intense
scattering of light from the surface and, in turn,
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H.D. ASL et al.: SURFACE AND MECHANICAL PROPERTIES OF POLYPROPYLENE/CLAY …
CI&CEQ 19 (3) 441−448 (2013)
increase the scratch visibility. We can visually compare the fracture features of the specimen surfaces,
but for a comprehensive study, visibility factor of the
surfaces, was used for the comparison of scratch
lines in D1, D2 and D3.
To calculate the visibility factor, the gray value of
every pixel in scratch image was determined using
image analyzing software. The G function was as
below:
(scratch visibility). This bonding restricts the microcrazing and formation of voids and plastic deformation. The compatibilizer effect is considerable in better
bonding strength. Also it could offset the positive
effect from the increased clay dispersion and has
shielding, plasticizing and miscibility effects [10].
For the rest of the paper, we describe the effective parameters, which have more influences on
scratch resistance of nanoclay-filled polyolefin.
G (image − pixel) = Gray value (0-255) in an image
pixel (0 = black, 255 = white)
Polymer chains positioning near the surface
The fracture feature of the scratched surface of
the polymer lead to increase of diversity of G on the
image. So, the average value of G' (image differentiation) was considered as a visibility factor:
n
 G′(image − pixel) n = visibility factor (n = number
of pixels in image)
The comparison in Table 5 suggested the
sequence of visibility factor as D1 < D2 < D3. High
visibility factor indicates weak scratch resistance.
Therefore, the nanocomposite had more scratch
resistance than neat polypropylene (Table 4) and D3
is fairly better than D2.
The improvement of scratch resistance and
mechanical properties of polypropylene without more
destruction in other required properties can be a revolutionary development in the auto parts industry.
Better bonding strength between the surfaces of
nanoclay layers and the polymer is another important
factor that determines the amount of fracture features
Layered structure of clay is determined as a key
factor in improving the properties of polymers. Difusion of polymer chains to basal spacing of layers
and its interaction with layer surfaces lead to a new
structure in polymer bulk with lower entanglements of
the chains (Figure 5). In this situation, the chains had
a more elastic behavior when they were under stress.
Also, the high aspect ratio of layers leads to damp the
stress down and restrict the advance of stress to
depth of polymer.
Crystallinity and nucleation
The crystallinity percentage and morphology
strongly influence the scratch behavior and have
direct effects on scratch resistance. Incorporating
nanoclay and pure montmorillonite in the polymer
matrix provides additional nucleation sites, thereby
increasing the crystallinity.
In this study, the crystallinity of specimens
increased according to χcD3 < χcD2 <χcD1, in which χcD3
is the percentage of crystallinity and is calculated as
ΔHrev/ΔH°; where ∆Hrev is the endothermic melting
enthalpy (Figure 4) and ∆H° is the melting enthalpy of
Table 5. Comparison of visibility parameters and hardness of the specimens
Specimen
Visibility factor (image differentiation)
Hardness (Shore D)
D1
143.1
71
D2
97.2
74
D3
70.9
77
Figure 5. Schematics of chains and layers positioning near the surface.
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H.D. ASL et al.: SURFACE AND MECHANICAL PROPERTIES OF POLYPROPYLENE/CLAY…
100% crystalline polypropylene [18]. High percentage
of crystallinity increases the resistance of cracking
and void creation under the scratch load. Nanoclay
affects the crystallization behavior by increasing the
equilibrium melting point of α and γ crystals indicative
of thermodynamic interaction with the host matrix and
is corroborated by the shift in the glass transition
temperature [10].
CI&CEQ 19 (3) 441−448 (2013)
REFERENCES
[1]
Y. Yang, J. Chen, Q. Yuan, R.D.K. Misra, Mater. Sci.
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S. Zokaei, R. Lesan Khosh M.R. Bagheri, Mater. Sci.
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Other parameters which may be considered
[5]
J. W. Cho, D.R. Paul, Polymer 42 (2001) 1083-1094
• Damping of stresses due to the layer structure of clay is the most influential factor in improving
surface properties of D3.
• Quality of organic modification of the montmorillonite, lubricant and other surface modifiers.
[6]
K. Friedrich, S. Fakirov, Z. Zhang, Polymer composites:
from nano- to macro-scale, Springer, New York, 2005, p.
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C. Deshmane, Q. Yuan, R.D.K. Misra, Mater. Sci. Eng., A
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Mater. Sci. Eng., A 458 (2007) 150-157
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S.M. Lai, W.C. Chen, X.S. Zhu, Composites, A 40 (2009)
754-765
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R.D.K. Misra, Q. Yuan, J. Chen, Y. Yang, Mater. Sci.
Eng., A 527 (2010) 2163-2181
[11]
R.D.K. Misra, Q. Yuan, P.K.C. Venkatsurya, Mech. Mater.
45 (2012) 103-116
[12]
V. Ramuni, Q. Yuan, J. Chen, R.D.K. Misra, Mater. Sci.
Eng., A 527 (2010) 4281-4299
[13]
Q. Yuan, S. Awate, R.D.K. Misra, Eur. Polym. J. 42
(2006) 1994-2003
[14]
Q. Yuan, R.D.K. Misra, Polym. 47 (2006) 4421-4433
[15]
S. Sinha Ray, M. Okamoto, Prog. Polym. Sci. 28 (2003)
1539-1641
[16]
T. Koch, D. Machl, Polym. Test. 26 (2007) 927-936
[17]
R.D.K. Misra, H. Nathani, A. Dasari, Mater. Sci. Eng., A
386 (2004) 175-185
[18]
Ph. H. Nam, P. Maiti, M. Okamoto, Polym. 42 (2001)
9633-9640.
CONCLUSION
Addition of nanoclay in small amounts (2 and
5%) improves the scratch resistance and mechanical
properties of polypropylene. This case does not credit
for typical additives such as talc; they increase susceptibility for plastic deformation in the polymer surface.
The layered structure of clay is an important
factor that affects the damping of stresses. Because
of the non-polar backbone of PP, a suitable compatibilizer is essential for the interaction of polypropylene
and organo-layers.
The nanoclay/polypropylene nanocomposite is a
potential material for automotive industry with a wide
range of usages and it can be a choice of substitution
for other polymers in automotives.
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H.D. ASL et al.: SURFACE AND MECHANICAL PROPERTIES OF POLYPROPYLENE/CLAY …
HUSEIN DIBAEI ASL1
MAJID ABDOUSS2
MAHMOUD TORABI ANGAJI3
AMINODDIN HAJI4
1
R&D Department, Asia Technology
Pioneers Co. Ltd., Tehran, Iran
2
Department of Chemistry, Amirkabir
University of Technology, Tehran, Iran
3
Polymers and Chemical Engineering
Group, Faculty of Engineering, Tehran
University, Tehran, Iran
4
Department of Textile Engineering,
Birjand Branch, Islamic Azad
University, Birjand, Iran
NAUČNI RAD
CI&CEQ 19 (3) 441−448 (2013)
POVRŠINSKE I MEHANIČKE OSOBINE
NANOKOMPOZITA POLIPROPILEN/GLINA
Ogromna potrošnja polipropilena u automobilskoj industriji motiviše akademska i industrijska istraživanja i razvoj radi pronalaženja novih pristupa u poboljšanju mehaničkih
osobina ovog polimera, koji nema degradacioni efekat na druge tražene performance,
kao što su otpornost na udar, kontrolisana kristalnost, žilavosti i skupljanje. Danas,
nanočestice imaju ključnu ulogu u poboljšanju mehaničkih i površinskih osobina polipropilena. U ovom radu, mikserom su pripremljene tri kompozicije polipropilen/nanoglina
koje sadrže 0, 2 i 5% nanogline. Karakterizacija nanogline dispergovane u polimeru je
izvršena pomoću TEM i XRD analiza. Za test otpornosti na grebanje, ogrebotine su
formirane pri opterećenju od 900 linija po ploči, nakon čega su snimljene SEM slike i
poređene sa PP scratch slikama. Takođe je proučavana kristalnost i mehaničko ponašanje kompozita. Rezultati su pokazali da su mehaničke osobine i otpornost na grebanje
kod kompozita znatno poboljšani.
Ključne reči: nanokompoziti, nanoglina, polipropilen, mehaničko ponašanje.
448
Available on line at
Association of the Chemical Engineers of Serbia AChE
www.ache.org.rs/CICEQ
Chemical Industry & Chemical Engineering Quarterly 19 (3) 449460 (2013)
A. ABDALLAH EL HADJ1
C. SI-MOUSSA1
S. HANINI1
M. LAIDI2
1
Laboratoir de BioMatériaux et
Phénomène de Transfert (LBMPT),
Université de Médéa, Quartier Ain
D’heb, Médéa, Algérie
2
Unité de Développement des
Equipement Solaires, Tipaza,
Algérie
SCIENTIFIC PAPER
UDC 544:615:661.12
DOI 10.2298/CICEQ120407005E
CI&CEQ
APPLICATION OF PC-SAFT AND CUBIC
EQUATIONS OF STATE FOR THE
CORRELATION OF SOLUBILITY OF SOME
PHARMACEUTICAL AND STATIN DRUGS IN
SC-CO2
In this work, the solubilities of some anti-inflammatory (nabumetone, phenylbutazone and salicylamide) and statin drugs (fluvastatin, atorvastatin, lovastatin, simvastatin and rosuvastatin) were correlated using the Perturbed-Chain
Statistical Associating Fluid Theory (PC-SAFT) with one-parameter mixing rule
and commonly used cubic equations of state Peng-Robinson (PR) and SoaveRedlich-Kwong (SRK) combining with van der Waals 1-parameter (VDW1) and
van der Waals 2-parameter (VDW2) mixing rules. The experimental data for
the studied compounds were taken from literature at temperature and pressure
in ranges of 308–348 K and 100–360 bar, respectively. The critical properties
required for the correlation with PR and SRK were estimated using Gani and
Noonalol contribution group methods whereas, PC-SAFT pure-component
parameters: segment number (m), segment diameter (σ) and energy parameter (ε/k) have been estimated by Tihic’s group contribution method for nabumetone. For phenylbutazone and salicylamide those parameters were determined using a linear correlation. For statin drugs, PC-SAFT parameters were
fitted to solubility data, and binary interaction parameters (kij and lij) were
obtained by fitting the experimental data. The results were found to be in good
agreement with the experimental data and showed that the PC-SAFT approach
can be used to model solid-SCF equilibrium with better correlation accuracy
than cubic equations of state.
Keywords: solid solubility, cubic equation of state, PC-SAFT, anti-inflammatory, supercritical carbon dioxide, correlation.
The chemical industry conducts constant
research in new technologies where the main objective is to satisfy the customer expectations by offering
high-efficiency products and to comply with international standards, which are becoming more and
more severe in terms of hygiene and environment
protection.
Super critical fluids are one of the most interesting technologies that became the target of several
research studies in recent years. Such importance is
related to the development of new cheap-priced pro-
Correspondence: A.A. El Hadj, Laboratoir de BioMatériaux et
Phénomène de Transfert (LBMPT), Université de Médéa, Quartier Ain D’heb, 26000, Médéa, Algérie.
E-mail: a_abdallahelhadj@yahoo.fr
Paper received: 7 April, 2012
Paper revised: 27 January, 2013
Paper accepted: 31 January, 2013
ducts without pollution constraints related to the environment. One of their major trumps is to be a plausible alternative to the organic solvents. In many
cases, they offer some solutions that cannot be provided by traditional techniques in terms of efficient
operation, non-toxicity, availability, low-cost and the
easiness of separation compared to classic process.
Thus, many works have been published on the application of this technology [1-3].
Carbon dioxide is the most commonly used
supercritical fluid because of its ability to replace
organic solvents with more advantages (its availability, inertness, non-toxicity, low critical temperature
and pressure).
Modelling of solubility of solids in supercritical
fluids is needed for the separation process design,
development and optimization. Undoubtedly, the most
used models are the cubic equations of state, such as
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A.A. EL HADJ et al.: APPLICATION OF PC-SAFT AND CUBIC EQUATIONS OF STATE…
Peng-Robinson (PR) [4] and Soave-Redlich-Kwong
(SRK) [5]. Although those models are the basic tools
for supercritical fluid-solid equilibrium calculations,
their application is associated with some drawbacks,
mainly the non-availability of the solids properties for
pharmaceutical compounds, polymers and bio-molecules (critical properties, molar volume and sublimation pressure). For this reason, and in order to perform the estimation of those parameters, several studies [6-7] have been carried out based on the socalled group contribution techniques, but their prediction ability is limited to classes of components with
simple structures. Therefore, the sensitivity of solubility correlations to solids’ properties can add a factor
of uncertainly to the approach. For example, Coimbra
[8] and Valderrama and Zavaleta [9] found that the
variations of 10% in the sublimation pressure estimation of solute might produce deviations between 5
and 19% in solubility calculations. To surpass this
problem, more accurate methods were developed,
such as the Marrero and Gani [10] and Nannoolal
method [11].
More theoretical equations of state were developed based on Werthiem’s perturbation theory [12–14] such as Statistical Associating Fluid Theory
(SAFT) [15-17], Lennard-Jones (SAFT-LJ) [18-19],
soft-SAFT [20-21], Variable Range (SAFT-VR) [22–23], Hard-Sphere (SAFT-HS) [24-26], and PerturbedChain (PC-SAFT) [27-28], and recently SAFT + Cubic
equation of state [29], etc. In the last decade, attempts
were carried out in order to model the phase equilibrium with the latter SAFT-EOS where numerous applications were reported in the literature and have been
recently reviewed by McCabe and Galindo [30].
SAFT models require five pure associating-component parameters and three parameters for nonassociating fluids: the segment number (m), the interaction energy (ε/k) and the segment diameter (σ). The
application of PC-SAFT-EOS for modeling of solid
compounds-SCF phase equilibrium is limited because
of the non-availability of pure component parameters
for multifunctional molecules. Several works treating
this subject can be found in the literature [31-33].
The purpose of this work is the application of
both PC-SAFT equation of state, Peng-Robinson (PR)
and Soave-Redlich-Kwong (SRK) cubic equations of
state for correlating the solubility of some anti-inflammatory drugs (compounds that are non-steroidal antiinflammatory drugs (NSAIDs) with analgesic and antipyretic properties and are used to treat fever, headache and pain associated with cold influenza and arthritis) and statin drugs in supercritical CO2 (components are used to reduce cholesterol and risk of heart
attack [34]). The chemical structures of the studied
solid drugs are shown in Figure 1.
THERMODYNAMIC MODELS
In this work, the PC-SAFT, PR and SRK equations of state were used for correlating of solid drugs
in the supercritical carbon dioxide.
The PR and SRK equation of state
The PR equation of state
The explicit form of PR equation of state for
mixture can be written as:
P 
am T 
RT

v  bm  v v  bm   bm v  bm 
Figure 1. Chemical structures of the studied drugs.
450
CI&CEQ 19 (3) 449460 (2013)
(1)
A.A. EL HADJ et al.: APPLICATION OF PC-SAFT AND CUBIC EQUATIONS OF STATE…
where P is the pressure, T is the temperature, R is the
gas constant, v is the molar volume of the component,
and am and bm are van der Waals energy and volume
parameters for mixture, respectively. The latter parameters can be obtained using mixing rules. In this
work, the van der Waals 1-parameter (VDW1) and
van der Waals 2-parameter (VDW2) rules were
applied:
VDW1 mixing rule:
CI&CEQ 19 (3) 449460 (2013)
The SRK equation of state
SRK cubic equation of state for mixture is given
by the following expression:
P 
RT
v  bm 

am (T )
v v  bm 
For pure components, ai and bj are expressed as
follows:
am   y i y j ai a j 1  k ij 
(2)
a (T )  0.42747
bm   y i bi
(3)
with:
i
j
i
am   y i y j a i a j 1  k ij 
(4)
bm   y i y j bij
(5)
i

(6)
where k ij and l ij are the binary interaction parameters; ai and bj are energy and volume parameters
for pure components defined as:
R 2Tc2
ai  0.45724
 (Tr ,w )
Pc
(7)
with  Tr ,   being a temperature-dependent function
in the attractive parameter of EOS defined as:
 Tr ,  

 

2
 1 0.37464  1.5422  0.26992 2  1Tr 0.5  (8)


bi  0.077796
RTc
Pc
(9)
where  is the acentric factor, Tc and Pc are the critical constants, and Tr is the reduced temperature.
The expression for the fugacity coefficient for a
mixture can be written as:
ln i 

 
b  0.08664
j

(12)
bi
( Z  1)  ln(Z  B ) 
bm
 n

 2 y j a ij

A  j 1
bi   Z  (1  2)B 


ln 

am
bm   Z  (1  2)B 
2 2B 




(10)

 1  0.480  1.574  0.176 2  1 Tr 0.5 


j
 b  bj 
bij   i
 1  l ij
 2 
R 2Tc2
 (Tr ,w )
Pc
 (Tr ,w ) 
VDW2 mixing rule:
i
(11)
RTc
Pc
2
(13)
(14)
It should be mentioned that am and bm for SRKEOS can be obtained using the van der Waals 1parameter (VDW1) and 2-parameter (VDW2) rules
cited in the PR-EOS section.
The expression of fugacity coefficient is given
by:
ln i 
bi
(Z  1)  ln( Z  B ) 
bm
ai bi
A
B
 (2
 )ln(1  )
B
b
Z
am
m
(15)
The PC-SAFT equation of state
The Perturbed-Chain Statistical Associating Fluid
Theory (PC-SAFT) is an equation of state that is
expressed in terms of Helmholtz energy for mixtures
of non-associating molecules:
ǎ = A /NkT = aid + ahc + adisp
(16)
id
where a is the ideal gas contribution that is considered as unit, ahc is the contribution of hard sphere
chain reference system and adisp is the contribution of
dispersion force.
As it can be seen, this equation consists of the
hard-chain reference contribution and the dispersion
contribution, and it can be expressed in terms of
Helmholtz energy for N-component of non-associating
chains as:
ãres = ãhc + ãdisp
(17)
The hard-chain reference contribution is given
by:
451
A.A. EL HADJ et al.: APPLICATION OF PC-SAFT AND CUBIC EQUATIONS OF STATE…
N
a hc  ma hs   y i (mi  1)ln g iihs ( ii )
(18)
i 1
where m is the mean segment number in the mixture:
N
m   y i mi
(19)
i 1
where yi is the mole fraction of chains of component i,
mi is the number of segments in a chain of component i.
Dispersion contribution
a disp  2 I 1,xk m 2 3  I 1(m 2 3 )xk  


 { mk C1I 2  mC1,xk I 2  mC1I 2,xk  
(20)
CI&CEQ 19 (3) 449460 (2013)
 a res 
kres (T ,v )  res
 a   Z  1  


kT
 x k T ,v ,xj  k
   res 
a
  y i 

  x T ,v ,x
ij





(27)
Modeling solid-SCF phase equilibrium
The solubility of a non-volatile pure solid (2) in a
supercritical fluid (1), y2, is determined from standard
thermodynamic relationships by equating fugacities in
the solid phase and in the supercritical phase for each
component (the isofugacity condition):
f 2solid  f 2SCF
(28)
m 2 2 3  mC1I 2 (m 2 2 3 )xk }
The fugacity of component (2) in the supercritical phase is expressed by:
Pairs of unlike segments are obtained by using
conventional combining rules:
f 2solid  y 22SCFP
 ij 
1
i   j
2


 ij   i  j 1  k ij 
(21)
The solubility can be expressed as the solute
mole fraction:
(22)
y2  
where kij is a binary interaction parameter that is
introduced to correct the segment-segment interactions of unlike chains.
The density to a given system pressure, Psys, is
determined iteratively by adjusting the reduced density of molecules, , until Pcalc = Psys. For a converged
value of , the number density of molecules, ρ (Å-3), is
calculated from:


6 N
   y i mi d i3 
  i 1

1
(23)
Equation for the compressibility factor is derived
from the relation:
 a

 1  Z hc  Z disp

  T ,x i
Z  1  
res
(24)
The pressure can be calculated in units of Pa by
applying the relation:


P  ZkT   1010
A
m 
3
(25)
The expression for the fugacity coefficient is
given by:
ln k 
kres (T ,v )
 ln Z
kT
(26)
The chemical potential can be obtained from:
452
(29)
 P2sub 
E
 P 
(30)
where E is the enhancement factor defined as:
 v 2s
2sub exp 
E 

(P  P sub )
RT


2SCF
(31)
where P is the equilibrium pressure, T is the equilibrium temperature, v 2s is the molar volume of the
pure solid, 2sub is the fugacity coefficient of pure solid
at its sublimation pressure, and 2SCF is the fugacity
coefficient of pure solid in the supercritical phase.
Physical properties
The Pitzer acentric factor and the molar volume
of solutes have been estimated by the Lee-Kesler
correlation using PE software [35] and the Fedors
method [36], respectively. Values of the required physical properties for all compounds using in the calculation and estimation methods are displayed in the
Tables 1 and 2.
PC-SAFT pure-component parameters
PC-SAFT pure-component parameters for nabumetone have been estimated by the Tihic group contribution method. For the other compounds (phenylbutazone, salicylamide and statin drugs), it is shown
that this method cannot be applied for missing functional groups (i.e., this method does not offer the
values of contributions for all group-assignments of
those compounds). The solution was the use of a
A.A. EL HADJ et al.: APPLICATION OF PC-SAFT AND CUBIC EQUATIONS OF STATE…
CI&CEQ 19 (3) 449460 (2013)
Table 1. Required physicals properties of anti-inflammatory drugs used
Compound
T ca / K
Pca / bar
w
3
–1
Vsb / cm mol
Carbon dioxide
304.2
73.76
0.225
-
23.68
0.602
d
0.412
d
1.348
d
843.93
Nabumetone
984.71
Phenylbutazone
Salicylamide
13.39
796.95
a
56.03
b
Psub / barc
308.2 K
318.2 K
-
-7
195.8
1.46210
266.9
-10
79.9
9.210
5.83310
c
328.2 K
-
4.58610
-7
1.31310
-6
3.48810
-9
1.35710
-8
6.21610
-7
-8
210
-7
d
Estimated by Gani Method [10]; estimated by Fedors method [36]; estimated by Nannoolal method [11]; estimated by Lee-Kesler correlation [35]
Table 2. Required physicals properties of statin drugs used
Tc / K
Compound
Pc / bar
Atorvastatine
1028.89
Lovastatine
901.80
a
a
c
Rosuvastatine
1065.21
Simvastatine
878.52
a
921.70
a
Fluvastatine
3
–1
Vs / cm mol
Psub / bar
308 K
12.08
a
1.1616
368.9
2.0010
13.49
a
1.295
335.4
5.9010
c
0.7648
293.3
13.01
a
1.2803
350.7
15.40
a
18.92
a
w
1.4726
288.1
b
318 K
-16b
1.7310
-8b
1.7110
4.2410
-13b
1.1910
-11a
8.4110
-16b
328 K
-15b
1.2910
-7b
4.6110
338 K
-15b
8.3510
-7b
1.1610
2.3110
-12b
1.1110
6.5410
-11a
7.8310
-15b
4.7710
-6b
2.7410
-11b
4.8610
3.1210
-10a
1.3110
6.2110
-14b
4.2510
348 K
-14b
-13b
-6b
-11b
-10b
1.9210
-9a
4.9410
-9a
-13b
2.5510
-12
c
Estimated by Nannoolal method [11]; estimated by Ambrose–Walton corresponding method [7]; estimated by Gani Method [10]
linear correlation developed by Tihic et al. [37] for
estimating phenylbutazone and salicylamide parameters. While for statin drugs, PC-SAFT-parameters
were considered adjustable parameters and were fitted
to solubility data (Table 3). This is because the Tihic’s
linear correlations gave very large values for the
segment number (m) and the segment diameter (σ),
and small values for the segment energy parameter
(ε/k) that lead to an overestimate of the solubility.
Such a result is expected because the statin molecules are characterized by multiple functional groups
(aromatic nitrogen, alcohol and acid functions, fluorine, sulfone, etc.) which makes it difficult to have a
good representation with those correlations or the
right classification into families that have been adopted
by Tihic and his co-workers [37].
Table 3. PC-SAFT pure component parameters for all compounds used
m
σ/Å
ε /k , K
2.07
2.78
169.21
Nabumetone
6.29
3.66
319.18
Phenylbutazone
6.86
4.14
312.05
Compound
Carbon dioxide
a
Salicylamide
3.39
3.86
334.30
Atorvastatine
9.40
4.20
309.10
Lovastatine
5.60
4.10
233.10
Rosuvastatine
7.70
4.20
299.90
Simvastatine
6.40
4.17
299.60
Fluvastatine
8.90
4.19
342.00
a
Pure component parameters for CO2 is taken from literature [27]
RESULTS AND DISCUSSION
In this work, the solubilities of three anti-inflammatory and five statin drugs in sc-CO2 were correlated. The experimental data were taken from literature [38,39]. The correlation was performed by minimizing the objective function, which is the absolute
average relative deviation (AARD) usually defined as:
OF  AARD (%) 
100
N
n
y calc  y exp
1
y exp

(32)
The absolute average relative deviation (AARD
,%) values along with values of regressed binary
interaction parameters for studied equations of state
for CO2 + nabumetone, CO2 + phenylbutazone and
CO2 + salicylamide are shown in Table 4 at various
temperatures.
This table shows that AARD values obtained
with PR-VDW1 model varied from 4.7% at 308.2 K for
the nabumetone-CO2 system to 34.3% at 328.2 K for
the salicylamide-CO2 system, whereas with the PRVDW2 model the AARD values varied from 4.5 to
32.3% for the same binary system at the same temperatures, respectively. Also, the application of SRKVDW1 model gave deviations that range from 3.8% at
328.2 K for nabumetone-CO2 system to 32.2% found
at 328.2 K for the salicylamide-CO2 system. Meanwhile, with SRK-VDW2 model the deviation varied
from 3.4 to 32.1% for the same binary systems at the
same temperatures, respectively. For PC-SAFT, the
deviation varied between 1.4% obtained for nabumetone-CO2 system at 318.2 K to 22% found in correlating of salicylamide-CO2 system at 328.2 K. It is also
453
A.A. EL HADJ et al.: APPLICATION OF PC-SAFT AND CUBIC EQUATIONS OF STATE…
CI&CEQ 19 (3) 449460 (2013)
Table 4. Correlation results for solubility of nabumetone, phenylbutazone and salicylamide in sc-CO2 with PR, SRK EoS’s using VDW1
and VDW2 and PC-SAFT with BR1 mixing rules at various temperatures
T = 308.2 K
Model
PR-vdw1
PR-vdw2
SRK-vdw1
SRK-vdw2
PC-SAFT
T = 318.2 K
T = 328.2 K
Parameter
Nabumetone
Phenylbutazone
Salicylamide
Nabumetone
Phenylbutazone
Salicylamide
Nabumetone
Phenylbutazone
Salicylamide
0.1098
k12
0.1076
0.0154
0.1501
0.1017
0.0123
0.1331
0.095
0.0101
AARD / %
4.7
6.6
21.2
7.1
11.62
8.6
5.1
15.0
32.3
k12
0.1057
0.013
0.15
0.098
0.0068
0.13 3
0.101
-0.002
0.1095
-0.45
l12
-0.65
-0.50
-0.3868
-0.717
-0.70
-0.2911
0.81
-0.72
AARD / %
4.5
6.2
21.2
6.8
10.7
28.6
5.0
10.7
32.3
k12
0.1191
0.0269
0.0174
0.1124
0.0222
0.1559
0.1024
0.0188
0.1323
AARD / %
6.3
8.8
20.7
7.7
12.0
27.9
3.8
14.4
32.2
k12
0.1169
0.024
0.1738
0.11
0.0173
0.1558
0.11
0.11
0.1319
l12
-0.59
-0.54
-0.12
-0.47
-0.69
-0.70
0.80
-0.70
-0.67
AARD / %
6.1
8.5
20.7
7.6
11.3
27.9
3.4
13.1
32.1
k12
0.1123
0.0921
0.0048
0.095
0.0871
0.0996
0.083
0.0109
AARD / %
1.6
3.9
8.8
1.4
6.4
1.9
16.0
22.0
worth mentioning that the values of AARD increased
with the increase of temperature. For example, AARD
values obtained with PR-VDW1 for salicylamide-CO2
system at 308.2 K (21.2%) were higher for the same
system at 328.2 K (32.3%).
The correlation results for five statin drugs (Tables 5 and 6) confirm the superiority of PC-SAFT in
predicting of the solubility compared to cubic equation
of state.
AARD values obtained with the PC-SAFT model
ranged between 2.9 and 27.3%. However, very important deviations were observed by applying the cubic
equations of state. For example, the values of AARD
obtained with PR-VDW1 varied from 10.3% at 308 K
for RV-CO2 system to 74.7% found at 328 K for LVCO2 system, whereas with SRK-VDW1 model the devi-
-6.53.10
-4
14.9
ations ranged from 16.2 to 75% for the same binary
system at the same temperatures, respectively.
Fitting the experimental solubility data provided
best-fit values to the binary interaction parameter k12
that is introduced to correct energetic interaction
between the solute-SCF (it ranges between -0.0091
obtained in (FV + CO2) system with PR-VDW2 at 348
K to 0.437 obtained in (LV + CO2) system with SRKVDW2 model). However, high and negative values for
interaction parameter, l12, were obtained, the highest
one being for the (AV + CO2) system at 348 K with
SRK-VDW2 model. Such results are not surprising
since l12 is introduced in the bm parameter to correct
the volumetric interaction between the solute and solvent. An analysis of the treated binary systems shows
that they consist of small solvent molecules (molar
Table 5. Correlation results for solubility of statin ( AV, LV and RV) in sc-CO2 with PR, SRK EoS’s using VDW1 and VDW2 and PCSAFT with BR1 mixingrules at various temperatures
Model
Parameter
PRvdw1
k12
308 K
AV
PRvdw2
AARD / %
SRKvdw2
454
AV
LV
RV
AV
LV
338 K
RV
AV
LV
348 K
RV
AV
LV
RV
0.0537 0.353 0.1014 0.0418 0.3627 0.0975 0.03 0.3802 0.0932 0.0146 0.3977 0.0885 0.0017 0.4115 0.081
44.6
64.7
10.3
35.4
70.3
11.9
30.6
74.7
12.2
28.9
72.9
18.1
24.4
68.4
23.9
0.053 0.353 0.1016 0.0424 0.3628 0.098 0.031 0.3804 0.093 0.0269 0.3977 0.0882 0.0058 0.4115 0.0817
l12
-0.79 -0.493 -0.793 0.856
-0.85
0.97
0.9
-0.77 -0.545
0.88
44.7
70.1
12.0
29.9
74.7
27.5
k12
AARD / %
k12
l12
AARD / %
PCSAFT
RV
328 K
k12
AARD / %
SRKvdw1
LV
318 K
k12
AARD / %
64.6
10.3
35.3
12.2
-0.745 -0.63
72. 4
18.0
0.88
-0.788
0.88
22.5
68.3
23.6
0.0807 0.3861 0.1187 0.0774 0.395 0.1135 0.063 0.411 0.1079 0.0499 0.426 0.1006 0.029 0.4368 0.09
51.4
68.2
16.2
42.6
72.9
14.8
36.7
75.0
14.4
34.0
72.0
18.3
27.7
66.8
21.9
0.086 0.3864 0.1186 0.0757 0.395 0.1131 0.0625 0.4112 0.1076 0.045 0.426 0.1011 0.031 0.437 0.0911
-0.1574 -0.88 -0.778 0.852
51.4
68.3
16.2
42.7
-0.75
-0.80
0.89
-0.80 -0.796
0.88
-0.79
0.88
0.90
-0.79
-0.79
72.9
14.8
35.8
75.6
31.5
72.1
18.4
24.6
66.8
21.9
0.0377 0.0785 0.0558 0.0293 0.0784 0.055
11.6
4.9
9.0
9.4
4.1
8.5
14.4
0.02 0.3977 0.046 0.0113 0.085 0.0405 0.023 0.0878 0.0345
13.4
4.2
8.3
20.0
6.6
15.1
28.0
7.4
20.5
A.A. EL HADJ et al.: APPLICATION OF PC-SAFT AND CUBIC EQUATIONS OF STATE…
CI&CEQ 19 (3) 449460 (2013)
Table 6: Correlation results for solubility of Statin (FV and SV) in sc-CO2 with PR, SRK EoS’s using VDW1 and VDW2 and PC-SAFT
with BR1 mixing rules at various temperatures
Model
Parameter
SV
FV
SV
FV
SV
FV
SV
FV
SV
FV
PR-vdw1
k12
AARD / %
k12
0.1485
0.0355
0.1537
0.0263
0.1592
0.0165
0.165
0.006
0.1758
-0.0062
49.5
14.3
51.8
20.8
56.5
24.4
55.8
29.2
55.4
36.3
0.148
0.0357
0.1533
0.0263
0.1592
0.0157
0.1653
0.0044
0.1743
-0.0091
l12
-0.88
0.4553
-0.80
0.0978
0.0313
-0.769
0.894
-0.789
0.74
-0.875
49.2
14.3
51.7
20.8
56.5
24.3
55.7
28.7
55.4
34.7
0.1824
0.0745
0.1865
0.0645
0.1908
0.0518
0.1949
0.0408
0.1948
0.0274
PR-vdw2
AARD / %
k12
SRK-vdw1
AARD / %
k12
SRK-vdw2
PC-SAFT
308 K
318 K
328 K
338 K
348 K
56.5
15.5
57.9
20.0
60.4
23.7
56.2
28.0
56.9
33.8
0.1845
0.0746
0.1834
0.0643
0.1908
0.051
0.195
0.0404
0.1961
0.0247
l12
-0.80
0.1922
-0.79
-0.3895
0.238
-0.87
0.90
-0.228
0.89
-0.736
AARD / %
k12
AARD / %
56.7
15.5
57.9
20.0
60.4
23.6
56.0
28.1
56.7
32.3
0.0526
0.0783
0.0529
0.0727
0.0508
0.0667
0.0485
0.06
0.0473
0.054
9.5
13.7
7.9
15.2
5.0
19.9
2.9
24.3
19.4
27.3
is usually close to zero (mole fraction, y2), and that of
the solvent is usually on the order of 0.999. Consequently, the behaviour of solid-SCF is governed by
the energetic interaction (due to the nature of atoms
and liaisons formed the complex) more than the
relative number of solute molecules in sc-CO2.
2. Some important deviations for both cubic
equation of state and PC-SAFT models may be the
result of either the formation of aggregates that need
to be taken into account in the application of any
model with more experimental studies about this phenomenon for correlating solubility, or the fluctuation of
the density of solvent close to the critical region.
Figures 2 and 3 show the solubility curves of
nabumetone and phenylbutazone in sc-CO2. These
include a comparison between experimental data and
weight of carbon dioxide is 44 g/mol) and very large
solute molecules (molar weight values vary between
137 for salicylamide to 540 g/mol for AV) providing
highly asymmetric systems. In this case, large values
of l12 are expected for well representing the complex
forming as a result of the association of solute-solvent. Despite these large values, there is no remarkable influence on AARD values when the two-parameter mixing rule VDW2 was used instead of the oneparameter mixing rule VDW1. This can be explained
by the following:
1. The binary interaction parameter, l12, is related
to the volumetric interaction between supercritical
fluid (CO2) and solid solute. Such correction has a
small effect on the correlation of the solubility of solid
in SCF since the concentration of solid in the solvent
0.0030
Solubility (mole fraction)
0.0025
0.0020
Experimental 308.2 K
SRK 308.2 K
PC-SAFT 308.2 K
Experimental 318.2 K
PR 318.2 K
SRK 318.2 K
PC-SAFT 318.2 K
Experimental 328.2 K
PC-SAFT 328.2 K
0.0015
0.0010
0.0005
0.0000
100
120
140
160
180
200
220
Pressure (bar)
Figure 2. Experimental solubility in sc-CO2 of nabumetone and correlation results obtained by PC-SAFT and PR-VDW2 at various temperatures.
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0.0030
Experimental 308.2 K
PR 308.2 K
PC-SAFT 308.2 K
Experimental 318.2 K
PR 318.2 K
PC-SAFT 318.2 K
Experimental 328.2 K
PR 328.2 K
PC-SAFT 328.2 K
Solubility (mole fraction)
0.0025
0.0020
0.0015
0.0010
0.0005
0.0000
100
120
140
160
180
200
220
Pressure (bar)
Figure 3. Experimental solubility in sc-CO2 of phenylbutazone and correlation results obtained by
PC-SAFT and SRK-VDW2 at various temperatures.
solubility predicted by PC-SAFT, PR and SRK equations.
For the three experimental temperatures, the
figures show an excellent agreement between experimental literature data (shown as circles, squares and
upward-triangles), and the solubility estimated by PCSAFT more than those estimated by cubic-EOS
(shown as solid and dashed lines, respectively).
For the correlation results of lovastatin and rosuvastatin, it is clear from the graphical analysis considered in Figures 4 and 5 that the solubility predicted
by PC-SAFT (shown as lines) follows the trend of the
experimental data (shown as circles, triangles and
squares), which suggests a good predictive ability of
this equation at various temperatures.
CONCLUSION
In this work, PC-SAFT EOS were used with
conventional combining rule to evaluate the capability
of this approach for modeling the solubility of solid
solutes in SCFs and the commonly used PR and SRK
0.00012
0.00011
0.00010
Slubility (mole fraction)
0.00009
0.00008
Experimental 308 K
Experimental 328 K
Experimental 348 K
PC-SAFT 308 K
PC-SAFT 328 K
PC-SAFT 348 K
0.00007
0.00006
0.00005
0.00004
0.00003
0.00002
0.00001
0.00000
100
150
200
250
300
350
Pressure(bar)
Figure 4. Experimental solubility in sc-CO2 of lovastatin and correlation results obtained by PC-SAFT.
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0.00026
0.00024
0.00022
slubility (mole fraction)
0.00020
0.00018
0.00016
Experimental 308 K
Experimental 328 K
Experimental 348 K
PC-SAFT 308 K
PC-SAFT 328 K
PC-SAFT 348 K
0.00014
0.00012
0.00010
0.00008
0.00006
0.00004
0.00002
0.00000
-0.00002
100
150
200
250
300
350
(Pressure (bar)
Figure 5. Experimental solubility in sc-CO2 of rosuvastatin and correlation results obtained by PC-SAFT.
cubic equations of state along with VDW1 and VDW2
mixing rules for correlating the solubility of NSAIDs
and statin drugs in supercritical carbon dioxide. The
obtained results show that PC-SAFT has an advantage over cubic EOS and gives a good correlative
accuracy than the cubic-EOS. Also, it should be mentioned that the use of the VDW2 (two binary interaction parameters, k ij and l ij ) mixing rule does not substantially improve the results of the modeling obtained
with the VDW1 (one binary interaction parameter, k ij )
mixing rule for both the SRK and PR equations of
state.
The accurate values of physical properties are
very important to the success of the correlation of
solubility data using equation of state, mainly the sublimation pressure. One of the most critical factors that
can influence the ability of estimation is the complexity of the molecules’ structure, including poly-functional groups and several cycles and aromatic cores.
It can be the origin of an important deviation in its
estimating as well as in the calculated solubility (case
of statin drugs) as it has been confirmed in previous
works [40].
Special attention was paid to the estimation of
PC-SAFT pure component parameters for non-associating substances because of the non-availability and
the complexity of structure. Tihic’s method used for
estimating PC-SAFT parameters for nabumetone
gave good correlation results of solubility in terms of
relative deviations, AARD. The Tihic linear correlation
for polyaromatic family used for calculating phenylbutazone and salicylamide gave accurate values and
could describe well the PC-SAFT component parameters, as well as the solubility estimate, compared
to those found using cubic-EOS. More complicated
systems were treated (CO2 (1) + statins (2)) where the
results obtained by PC-SAFT were obviously more
accurate than cubic EOSs. The PC-SAFT pure component parameters were determined by fitting the
solubility data, as it was done by Spyriouni et al. [41].
Despite the complexity of their structures, the nonavailability of parameters and the limitation of the
available estimation techniques, this approach can
represent the experimental data of solubility of solid
drugs in supercritical fluid with more accuracy than
the other models.
Nomenclature
AARD average absolute relative deviation
a
attractive term in PR and SRK-EOS
ǎ
Helmoltz free energy
AV
am, bm
EOS
FV
atorvastatin
EOS mixture parameter
equation of State
fluvastatin
k
Boltzmann constant, J/K
kij
binary interaction parameter
lij
binary interaction parameter
LV
lovastatin
NC
number of compounds
NSAID non steroidal anti-inflammatory drug
OF
objective Function
P
pressure (bar)
Pc
critical pressure
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Psub
sublimation pressure (bar)
PCSAFT
perturbed chain statistical associated fluid
theory
PR
Peng-Robinson
RV
rosuvastatin
SAFT statistical associated fluid theory
SCF
super-critical fluid
SRK
Soave-Redlich-Kwong
SV
simvastatin
T
equilibrium temperature (K)
Tc
critical temperature (K)
VDW1 Van-der-Waals mixing rule with one adjustable parameter
VDW2 Van-der-Waals mixing rule with two adjustable parameters
V
volume
v 2s
molar volume of solid
y2
mole fraction solubility of the solid, in supercritical phase
Z
compressibility factor
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[16]
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Greek letters
ε
η
ρ
σ
Φi
ω
depth of pair potential, J
packing fraction
total number density of molecules
segment diameter, Ǻ
fugacity coefficient of component i
Pitzer’s acentric factor
Superscripts
calc
disp
exp
hc
hs
id
s
sub
calculated property
contribution due to dispersive attraction
experimental property
residual contribution of hard-chain system
residual contribution of hard-sphere system
ideal gas contribution
solid
sublimation
Subscripts
2
c
i,j
m
solute (solid)
critical property
components i, j
constant for mixtures
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A. ABDALLAH EL HADJ1
C. SI-MOUSSA1
1
S. HANINI
2
M. LAIDI
1
Laboratoir de BioMatériaux et
Phénomène de Transfert (LBMPT),
Université de Médéa, Quartier Ain
D’heb, Médéa, Algérie
2
Unité de Développement des
Equipement Solaires, Tipaza, Algérie
NAUČNI RAD
CI&CEQ 19 (3) 449460 (2013)
PRIMENA PC-SAFT I KUBNE JEDNAČINE STANJA
ZA KOERELISANJE RASTVORLJIVOSTI NEKIH
FARMACEUTSKIH I STATINSKIH AKTIVNIH
SUPSTANCI U SUPEKRITIČNOM CO2
U ovom radu su rastvorljivosti nekih antiinflamatornih (nabumeton, phenilbutazon i salicilamid) i statinskih (fluvastatin, atorvastatin, lovastatin, simvastatin I rosuvastatin) aktivnih
supstanci korelisani PC-SAFT (sa jednoparametarskim pravilom mešanja) i uobičajenim
kubnim jednačinama Peng-Robinson-a (PR) i Soave-Redlich-Kwong-a (SRK) kombinovanim sa van-der Waals-ovim jedno- i dvo-parametarskim pravilima mešanja (VDW1 i
VDW2). Eksperimentalni podaci za ispitivana jedinjenja u opsegu temperature 308-348 K i
pritiska 100-360 bar su uzeti iz literature. Kritična svojstva potrebna za korelisanje pomoću
PR i SRK jednačina su izračunate Gani-Noonalol-ovom metodom doprinosa grupa, dok su
u slučaju nabumetona parametri PC-SAFT jednačine za čiste komponente (segmentni
broj, segmentni prečnik i energetski parameter, ε/k) izračunati metodom doprinosa grupa.
U slučaju fenilbutazona i salicilamida, ovi parametri su određeni linearnom korelacijom.
PC-SAFT parameteri statinskih jedinjenja su određeni iz podataka za rastvorljivost, a
parametri binarne interakcije su dobijeni fitovanjem eksperimentalnih podataka. Dobijeni
rezultat je bio u saglasnosti sa eksperimentalnim podacima. Pokazano je da se PC-SAFT
jednačina može upotrebiti za modelovanje ravnoteže čvrsto-superkritični fluid boljom korelacionom tačnošću od kubnih jednačina stanja.
Ključne reči: rastvorljivost čvrstih jedinjenja, kubna jednačina stanja, PC-SAFT,
antiinflamatoran, supekritičan CO2, korelacija.
460