Accepted Manuscript
Quantitative relationships between molecular parameters and reaction rate of
organic chemicals in Fenton process in temperature range of 15.8 °C - 60 °C
Zhiwen Cheng, Bowen Yang, Qincheng Chen, Zhemin Shen, Tao Yuan
PII:
DOI:
Reference:
S1385-8947(17)32227-1
https://doi.org/10.1016/j.cej.2017.12.105
CEJ 18266
To appear in:
Chemical Engineering Journal
Received Date:
Revised Date:
Accepted Date:
27 October 2017
15 December 2017
20 December 2017
Please cite this article as: Z. Cheng, B. Yang, Q. Chen, Z. Shen, T. Yuan, Quantitative relationships between
molecular parameters and reaction rate of organic chemicals in Fenton process in temperature range of 15.8 °C - 60
°C, Chemical Engineering Journal (2017), doi: https://doi.org/10.1016/j.cej.2017.12.105
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Quantitative relationships between molecular parameters and reaction rate of organic
chemicals in Fenton process in temperature range of 15.8 °C - 60 °C
Zhiwen Cheng a, Bowen Yang a, Qincheng Chen b, Zhemin Shen a∗ , Tao Yuan a∗ ,
a. School of Environmental Science and Engineering, Shanghai Jiao Tong University, 800
Dongchuan Road, Shanghai 200240, China.
b. School of Agriculture and Biology, Shanghai Jiao Tong University, 800 Dongchuan Road,
Shanghai 200240, China.
ABSTRACT:
In order to have a better prediction for the degradation reaction rate constant of organic
compounds in Fenton process at different temperatures. A partial least squares (PLS) model was
established based on 116 lgk values for 24 organic compounds and quantum chemical parameters,
some basic information of molecules as well as the temperature of reaction system. The optimal
model was demonstrated as stable, robust and had good predictive ability, with the associate
statistical indices of adjusted squared correlation coefficient was 0.722, internal validation was
0.652, external validation was 0.512, cumulative cross-validation coefficient was 0.635, the
criterions indicated the developed model could be used to estimate the reaction rate of organic
compounds in Fenton process at different temperature. The model contains three components, the
most significant descriptors explaining the reaction rate are T and 1
for component 1, the
maximum charge in a carbon atom and minimum charge for nucleophilic attack for component 2,
the charge in a hydrogen atom, maximum charge for hydroxyl radical attack and minimum value
of bond order for component 3. The applicability domain (APD) of the proposed model was
∗
Corresponding author: E-mail: zmshen@sjtu.edu.cn (Zhemin Shen); taoyuan@sjtu.edu.cn (Tao Yuan)
1
calculated by the Euclidean distances. The results of APD showed that the predictions by the
derived PLS model were reliable. The proposed model not only offer a method to predict the
reaction rates, but also give some insights of the mechanism for the degradation of organic
compounds in Fenton process at different temperatures.
Key words: Reaction rate; PLS model; Temperature; Molecular parameters
1. Introduction
Organic compounds are widely used materials in chemical synthesis field [1]. But excess
organics in water often results in severe environmental problems [2, 3]. This kind of effluents are
highly resistant to be eliminated owing to the highly toxicity [4], strongly stability [5] and
diversely component [6]. Although various strategies have been reported, for example, catalysts
synergistic solar photocatalytic [7], ozonation oxidation [8] and sulfate oxidation method [9], etc..
These strategies are sometimes complex, high-cost and low efficiency. Therefore, it still remains a
great challenge to eliminate organic pollutions.
Classic homogeneous Fenton oxidation is one of the advanced oxidation processes (AOPs),
which is powerful and attractive technique in treatment of organic loading and non-biodegradable
wastewater [10, 11]. The oxidative potential of hydroxyl radical produced by Fenton reaction
could achieve 2.80 V and it has the advantage of high selectivity, easy operation and high
efficiency [12, 13]. Hydroxyl radicals can attack the most part of organics with rate constants
106-1012 times faster than ozone [14, 15]. The increase of temperature can produce more hydroxyl
radicals, which can significantly reduce TOC and COD [16-18]. The two indices represent the
content of organics in water and they are important indices for assessing the pollution level in
2
water. Zazo et al. (2011) demonstrated that increasing the temperature, up to 120 °C, clearly
improved the reduction of TOC, oxidation rate and the degree of mineralization of the pollutants
[16]. Munoz et al. (2014) found that increased the reaction temperature could achieve 60 % COD
reduction in sawmill wastewater [19]. Pi et al. (2015) studied the effect of temperature on
hydrolyzed polyacrylamide (HPAM) wastewater, they discovered that when the reaction system
above 30 °C, higher HPAM and CODCr removal ratios could be obtained in their study [20].
Therefore, temperature is an important parameter in Fenton/Fenton-like process.
Reaction rate is a crucial parameter index to the contaminants in evaluating the degradation
characteristics and behaviors [21, 22]. However, considering the increasing numbers (100,000
every year) [23] of chemicals used in global market which could be potential pollutants [24, 25], it
is of significance to investigate the reaction rate of the chemicals virtually. But the data of reaction
rate constants which are determined by experimental measurements are inefficient, laborious and
time-consuming for the large number of chemicals. The situation increases the importance of
seeking for an effective method to substitute traditional methods for obtaining reaction rate
constants of chemicals. Therefore, QSAR (quantitative-structure-activity-relationship) method as a
theoretical prediction method, has been widely used in the prediction of reaction rate constants in
oxidation systems [26, 27], it has the advantages of rapid and cost-effective and has attracted great
attentions in the last several years [28, 29]. To date, several QSAR/SAR models have been
developed for predicting the reaction rate and estimating the degradation behaviors in Fenton
process [30-33]. Jia et al. (2015) developed some MLR (multiple linear regression) models to
predict the reaction rate of 33 diverse compounds, results showed that the optimized model had a
good predictive ability [30]. Li et al. (2013) established an QSPR model for 28 azo dyes
3
compounds using MLR method, and found that the degradation percentage or TOC removal of azo
compounds had strongly relationship between MW/S and NN=N [31]. Gao et al. (2017) also
reported an SAR (Structure−activity relationship) between CL (chemiluminescence) and chemical
structure of 19 chlorophenolic persistent organic pollutants [32]. Peres et al. (2010) developed
some QSARs for the reaction rate of substituted phenolic in Fenton system [33]. However,
previous QSARs/SARs have the limitations for the prediction of reaction rate at the temperature of
25 °C-30 °C, while the temperature is an influential factor which will affect the reaction rate in
Fenton process. Thus, it is meaningful to supplement the reaction rate values covering different
temperature range. Indeed, Li et al. (2013) developed a QSAR model for predicting reaction rate
at different temperature in ozone system, and found 1 has the largest correlativity with lgkO3
[34]. Li et al. (2014) built a QSAR model for estimating the reaction rate of hydroxyl radicals at
different temperature, 1 was also an important parameter in the QSAR model [35]. Gupta et al.
(2016) developed a room-temperature QSAR model and temperature-dependent QSAR model for
the reaction rate of NO3 radicals respectively [36]. Therefore, it is desirable to establish some
QSAR models for the reaction rate at different temperature in Fenton process.
In this study, 116 lgk values were conducted and collected for 24 organic compounds at
different temperatures (15.8 °C-60 °C) in Fenton process. Then a series of quantum chemical
parameters were calculated by Gaussian 09 and Material Studio 7.0. Based on the lgk values and
quantum chemical parameters as well as some physicochemical indexes, a partial least-squares
(PLS) model with temperature dependence was developed subsequently. The proposed model was
then evaluated by the adjusted squared correlation coefficient (
), cumulative cross-validation
coefficient (
), internal validation (
), external validation (
4
)
and Y-randomization
validation. Furthermore, the applicability domain (APD) was also characterized by using the
Euclidean distances. It is our purpose to establish an appropriate model to predict the reaction rate
constants correctly and rapidly at different temperatures in Fenton process.
2. Materials and methods
2.1 Fenton experiments
18 organic compounds were selected as experimental materials for the reaction rate constants in
Fenton process. The experiments were carried out in 5 L beakers, the initial concentration of each
organic solution was 100 mg/L, for those of lowly soluble organic compounds, saturated solution
was prepared. 1 mol/L sulfuric acid was used for adjusting the pH to 3 ± 0.1 of each solution, then
4 mL (0.5 mol/L) ferrous sulfate solution and 2 mL (9.79 mol/L) H2O2 were added to each reactor.
Each reactor was stirred by using magnetic stirrers and the temperature was controlled at 25 °C,
30 °C, 40 °C, 50 °C and 60 °C by using constant temperature magnetic mixer (HJ-6A, Jiangsu
Jintan Huanyu Scientific Instrument Factory. Jiangsu, China). Sodium hydroxide was used for
terminating the reaction at different residence time. 0.25 µm filters were employed for removing
the precipitates subsequently. At last, UV-1600 spectrophotometer (Mapada Instruments Co., Ltd.
Shanghai, China) was used to analyze the concentration changes of each organic compound. All
the reagents were purchased from Aladdin Industrial Corporation (Shanghai, China).
2.2 Data set
The reaction rate constants of 18 organic compounds were calculated by the pseudo-first-order
kinetic [30, 37]. Besides, other lgk values for 6 organic compounds at different temperatures were
5
collected from the literatures [38-40]. The data set comprises 116 lgk values for 24 organic
compounds at different temperatures (15.8 °C - 60 °C). 116 lgk values were divided into training
set and validation set with the ratio of 4:1 [34, 41]. The detailed information of 116 lgk values for
24 organic compounds were listed in Table S1 (SI †).
2.3 Calculation methods
The quantum chemical parameters used in this study included dipole moment, total energy of a
molecule, energy of the highest occupied molecular orbital, energy of the lowest unoccupied
molecular orbital, the difference of and ( ), the sum of and (
), the square of , most positive partial charge on a hydrogen atom, minimum and
maximum negative partial charge on a carbon atom, minimum and maximum positive partial
charge on a hydrogen atom linked with a carbon atom, bond order and six kinds of fukui indices.
Bond order and fukui indices were calculated by Material Studio 7.0 (Dmol3/GGA-BLYP/DNP
(3.5) basis). The SCF convergence was set as 10-6 a.u. and the density mixing was chose at 0.2
charge and 0.5 spin [42]. In this work, bond order (BOx and BOn) represent the maximum and
minimum number of chemical bonds between a pair of coterminous atoms. Fukui indices
((+)/ ,(−)/ ,(0)/ ) stand for the maximum and minimum changes of an atom in a
molecule during the nucleophilic attack, electrophilic attack and hydroxyl radical attack. Other
quantum chemical parameters were computed by Gaussian 09 (DFT B3LYP/6-311G level). The
frequency of all the molecules were optimized to a minimum potential energy surface firstly,
HOMO and LUMO orbitals were selected to calculate the HOMO and LUMO levels secondly.
Finally, the values of the parameters were obtained from the Gaussian output files. Besides, we
6
summarized some basic information of the molecules, included the number of carbon atoms, the
ratio between the number of carbon atoms and hydrogen atoms, the ratio between the number of
oxygen atoms and carbon atoms. The reaction temperature () and the reciprocal of reaction
temperature (1) were also selected as parameters to build the model. The detailed information
and values of the parameters were listed in Table 1 and Table S1 (SI †), respectively.
Table 1
The interpretation of each abbreviation
Abbreviation
Interpretation
DFT
Density functional theory
SCF
Self-consistent field
PLS
Partial least-squares
VIP
Variable importance in the projection
RMSE
Root-mean-square error
OECD
Organisation for Economic Co-operation and development
QSAR
Quantitative Structure-Activity Relationship
APD
Applicability domain
k
Reaction rate constants
lgk
Logarithm of reaction rate constants
T
Temperature of reaction system
1
The reciprocal of reaction temperature
##
The number of carbon atom in a molecule
7
##: %
The ratio between the number of carbon atoms and hydrogen
atoms
#&: #
The ratio between the number of oxygen atoms and carbon atoms
µ
Dipole moment
('()*)
The total energy of a molecule
Energy of the highest occupied molecular orbital
Energy of the lowest unoccupied molecular orbital
The gap energy ( − )
Square of gap energy
The sum energy ( + )
(%)+
Most positive partial charge on a hydrogen atom
(# , ) / (# ,)
Minimum and maximum negative partial charge on a carbon atom
+
(#%)+
/ (#%)
Minimum and maximum positive partial charge on a hydrogen
atom linked with a carbon atom
-&
Bond order
(+), (−), (0)
Fukui indices
2.4 Model construction and validation
Partial least squares (PLS) regression was used to develop the model by using SIMAC-P+11.
The models produced by SIMAC software were evaluated by the adjusted squared correlation
coefficient (
) and cumulative cross-validation coefficient (
the robustness of a PLS model, when
). In general,
describes
> 0.5, the model could be considered as robust and
8
having a good predictive ability [34, 43]. The lgk values in training set were set as dependent
variables and the 25 parameters were set as independent variables. The method for selecting
parameters used in this study was according to the variable importance in the projection (VIP)
values given by the PLS models. The specific process for developing models was as follows.
Firstly, all the parameters were selected as variables to establish a PLS model (Model0). Secondly,
based on the ranking of the VIP value of each parameter in Model0 . The parameter was removed
in the light of VIP values from minimum to maximum one at a time. This process was repeated
until two parameters were remained and it would produce 23 models (Model1, Model2…Model23)
in this step. In other words, the remained two parameters had the largest VIP values. According to
the
value of each new model (Model1, Model2…Model23), the parameters which increased
the
value of the original PLS model (Model0 ) were removed. The rest parameters were
used for modeling in the next stage. Then repeat the first and second process using the rest
parameters until the model had the largest
largest
value. At last, the PLS regression with the
was considered as the optimal model. If several models had the same
values,
the model with a smaller number of parameters were selected as the optimal model. In addition,
the developed models were also validated by the internal validation (
error value (RMSE), the external validation (
)
), the root-mean-square
and Y-randomization validation.
2.5 Domain of applicability
According to the OECD (Organisation for Economic Co-operation and development) principles,
a QSAR model should have a defined domain of applicability [44]. The domain of application for
a QSAR model describes whether the model will predict an endpoint for a specific chemical with
9
a given reliability. It helps the users of the model to judge whether the prediction for a new
chemical is reliable or not, the predictions for only those compounds that fall into this domain
could be considered reliable [45]. The Euclidean distances were performed to define the APD in
this study. The distance of a compound in the test set to its nearest spot in the training set was
compared to the APD threshold, when the distance was smaller than the value of APD, the
prediction could be considered reliable [46]. The following equations was used to calculate the
APD.
APD =< 4 > +67
Equation 1
?
∑@
;AB(; ,<=> )
σ=9
Equation 2
Where < 4 > is calculated as follows : (1) calculate the distance between all pairs of compounds
in the training set; (2) the average value of all the distance values are calculated; (3) the values
lower than the average value are recorded as a new data set, and < 4 > is the average value of the
new data set [47]. CD and CE are the ith observation value of compound in the training set and
the average value of all the compounds in the training set, respectively. n is the number of
compounds in the new set. Generally, 6 is chosen equal to 0.5 [48].
3 Results and discussion
3.1 Experimental results
90 k values for 18 organic compounds at different temperature are evaluated by using a
pseudo-first-order kinetic model and listed in Table S1 (SI †). The k values have an increasing
tendency with the increasing of temperature (Table S1). The smallest value in 25 °C is 0.056 min-1
(Aniline), while the largest value is 2.386 min-1 (Orange G), it is nearly 42 times larger than that of
10
Aniline. The smallest and largest k values in 60 °C are 0.972 min-1 (Aniline) and 20.014 min-1
(Methyl orange), respectively. However, the k values of Aniline increase by nearly 17 times when
the temperature increase from 25 °C to 60 °C. Therefore, the increase of the reaction temperature
is beneficial to the improvement of the reaction rate of Aniline. On the contrary, the reaction rates
of Orange G at 25 °C and 60 °C are 2.386 min-1 and 3.493 min-1, respectively. It only improves
1.107 min-1 when the temperature increases to 60 °C. From the k values in Table S1, the
incremental extent of k values for different compounds are different at different temperatures. The
k values of Methyl orange have the biggest change from 0.351 min-1 to 20.014 min-1, which has
the improvement of 57 times. While the smallest change of k values is Acid orange 74, which only
improved from 1.249 min-1 (25 °C) to 1.658 min-1 (60 °C). The k values in Table S1 (SI †) also
suggest that with the increasing of temperature, the compound has slowly growth (increase rates
range 32.74 % - 77.90 %) when it has a higher reaction rate (k > 0.900) at 25 °C. Instead, for that
of compound who has lower reaction (k < 0.900) rate at 25 °C, increasing the reaction temperature
will increase the reaction rate obviously (increase rates range 181.28 % - 5601.99 %).
3.2 Results of QSAR model
116 lgk values were divided into training set and test set, with the number of 93 and 23,
respectively. Therefore, 93 lgk values were used for model construction and other 23 lgk values
were used for model validation. A PLS model was obtained subsequently by PLS-VIP method.
The optimal PLS model is as following:
11
lgH = −2.813 + 0.015 − 15.608 1 − 0.013 ## + 0.361 #&: # + 7.392 (#%)+
+ 1.181 (# ,)Q − 0.167 + 4.120 − 2.678 (%)+ + 1.475 -&
− 15.675 (+) + 0.383 (0)
n= 93, = 0.722,
= 0.652, p= 0.000, RMSE= 0.168,
=
0.512,
= 0.635
Where n is the number of compounds in training set; is the squared correlation coefficient;
is the internal validation,
is the external validation; RMSE is the root-mean-square-error;
is the cumulative variance of dependent variable; p is the significance level. The results of
the statistical indexes satisfy the estimate criterion.
model is stable,
=
= 0.652 > 0.5 indicates the developed
0.512 > 0.5 demonstrates the model has a good predictive ability,
=
0.635 > 0.5 describes the robustness of the PLS model [49]. Furthermore, based on the PLS model,
the predicted lgk values versus experimental lgk values are presented in Fig. 1. As can be seen
from Fig. 1, the predicted lgk values are almost closely and evenly distributed around the
regression line (y = x). The two dashed lines also show that the prediction residuals lie within
± 1.0 except the 2,7-Dihydroxynaphthalene at 25 °C. The experimental lgk value of
2,7-Dihydroxynaphthalene at 25 °C is 0.225 min-1, while the predicted lgk value of it is -0.811
min-1, with the difference of 1.036. It can be seen from the results, the developed PLS model is
suitable for predicting the reaction rate at different temperature in Fenton process.
12
2.0
1.5
Predicted lgk values
1.0
■ Training set
■ Test set
0.5
0.0
-0.5
-1.0
-1.5
-2.0
-2.5
-3.0
-3.0
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
Experimental lgk values
Fig. 1. Plots of predicted lgk versus observed lgk for PLS model
3.3 Discussion and mechanism interpretations
Fig. 2 shows the VIP value of each variable in the PLS model. VIP value reflects the influence
of independent variables on the dependent variable (lgk). The sequence for VIP value of each
variable is T (1.733) > 1 (0.711) > -& (1.294) > (+) (0.944) >
(0.939) >
(# ,)Q (0.799) >
(%)+
(#%)+
(0.747) > #&: # (0.709) > ## (0.602) > (0.573) > (0) (0.468) > (0.112) (Fig. 2). In this study, temperature is the most important
factor for the reaction rate with the largest VIP value of 1.733 and the temperature is the most
relevant for explaining the reaction rate. Fig. 3 is the plots w* (weights of independent variables)
and c (weights of dependent variable) of the PLS model. From the two figures, we can find how
the independent variables and dependent variable influence the PLS components, and the
relationship between independent variables and dependent variable [50]. The independent
13
variables will have greater contribution on the ith component when the independent variable has a
larger weight value (w*) along the ith PLS component. Similarly, the dependent variable will have
greater contribution on ith component when it has a larger weight value (c) along the ith PLS
component. Fig. 3 (a) shows that component 1 is dominated by T and 1. Temperature is an
important parameter in degrading the organic compounds [51]. Besides, the temperature is also an
crucial indices for the vapor pressure (Ps) which is of great importance to environmental behavior
assessment of organic pollutants [43]. Li et al. (2013) and Li et al. (2014) also found that 1 is
an influential factor for the degradation of organic chemicals in ozone process and hydroxyl
radical system, respectively [34, 35]. As for the temperature, it has the positive correlation with
lgk, while the forms of temperature (1) has the negative correlation with lgk. It has been
reported that increasing the reaction temperature leads to the increasing the reactivity of hydroxyl
radical [52, 53]. Thermally activation could improve the oxidative ability of hydrogen peroxide by
producing abundant hydroxyl radical with more strongly oxidative actives in Fenton process [54].
Besides, increase the temperature could enhance the concentration of hydroxyl radicals in the
reaction solution [55], increase the number of activated molecules and increase the effective
collisions between oxidant and organic compounds. The sufficient hydroxyl radical may offer
different possible ways for reaction with organic compounds. For instance, abstraction reaction,
substitution reaction, etc. [56]. It is helpful to the degradation of organic compounds. As a result,
the reaction rate increases with the temperature increases.
(# ,)Q and (+) are conclusive factors in component 2.
(# , )Q is the meaning of
maximum negative partial charge on a carbon atom and (+) represents the smallest changes of
charge in each atom during the nucleophilic attack. The two parameters are relevant to the changes
14
of charge in each atom during the oxidation process. The first two PLS component describe that
temperature and charge governing the reaction rate in Fenton process. Fig. 3 (b) illustrates that
component 3 is mainly dominated by
(%)+ , -& and (0) .
(%)+ signifies the most
positive partial charge on a hydrogen atom, the hydrogen atom with the largest
(%)+ value will
be attacked firstly by hydroxyl radical. (0) stands for the biggest changes of charge in each
atom during hydroxyl radical attack. From the value of (0) , we can find the easiest position for
hydroxyl radical attack. -& refers to the minimum number of chemical bonds between a pair of
coterminous atoms in the molecule. It is relevant to the position of bond breaking, suggesting the
stability of chemical bond. Moreover, from the optimal PLS model, seven parameters (, #&: #,
(#%)+
,
(# ,)Q , , -& , (0) ) have the positive correlation relationship with lgk, while
there is a negative correlation between other five parameters (1, ##, ,
(%)+ , (+) )
and lgk. As for ##, the lgk values decrease with the increase of the number of carbon atoms. The
structure of organic compound will be complicated when the ## increases, it is difficult for
hydroxyl radical to attack the complicated compounds. As for #&: # , it has the positive
correlation relationship with lgk. The lgk values increase with the increase of #&: #. The value of
#&: # will be larger when the number of carbon atoms are small and it is easy for hydroxyl
radical to degrade them.
(#%)+
and
(# , )Q represent the changes of charge on a hydrogen
atom linked with a carbon atom and carbon atoms, respectively. When
(#%)+
and
(# , )Q are
larger, it is easier for atoms to take place the electron transfer reaction and to be oxidized. As for
the gap energy ( = − ), it is difficult to lose electrons when the HOMO level of
a molecule is small. Similarly, it is difficult to obtain electrons when the LUMO level of a
molecule is large. Therefore, the gap energy has the negative correlation with lgk. (+) is a
15
measurement of the ability of nucleophilic attack. Compounds with high (+) values have
small lgk values because they have strong endurance to hydroxyl radical. On the other hand,
(0) has the positive correlation with lgk, it will provide much more chance for hydroxyl radical
to attack the compounds with high (0) values than those of small (0) values. In this study,
-& has the positive correlation with lgk. Generally, compounds whose bond order is under four,
the chemical bond in a molecule tends to be more stable if its -& is larger. Therefore, it can be
inferred that larger value of -& promote the degradation of compounds under our experimental
conditions. and
(%)+ seem to have the opposite tendency with previous work [37, 41].
Maybe the two factors just have the statistical significance in this study or need to discuss with
other factors together, we might consider it as a further study in the future.
1.8
1.6
1.4
VIP
1.2
1.0
0.8
0.6
0.4
Egap
f(0)x
2
E gap
#C
#O:C
+
q(CH )x
q(C-)x
f(+)n
BOn
1/T
T
0.0
q(H)+
0.2
Variables
Fig. 2. VIP value of each independent variable in the optimal model
16
0.8
(a)
q(C-)x
0.6
0.4
f(0)x
w*c[2]
0.2
+
q(CH )x
E
#C
#O:C
0.0
lgk
2
gap
BOn
Egap
1/T
-0.2
T
q(H)+
-0.4
f(+)n
-0.6
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
w*c[1]
0.6
(b)
BOn
f(0)x
0.4
q(C-)x
E2gap
lgk
0.2
w*c[3]
1/T
q(CH+)x
0.0
Egap
-0.2
f(+)n
T
#O:C
-0.4
#C
-0.6
q(H)+
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
w*c[1]
Fig. 3. The plot of weights, w* and c, of each variable in the PLS model. (a) is component 2
versus component 1, (b) is component 3 versus component 1
3.4 Y-randomization test of PLS model
Y-randomization test is also performed to validate the robustness of developed PLS model. The
17
lgk values were rearranged randomly twenty repetitions, and twenty new PLS models were
established by using original independent variables matrix. Based on the acceptance criterion, the
associated and
of the new twenty models were expected to be smaller than the optimal
PLS model. The results of Y- randomization can be seen in Fig. 4. The red plot stands for the
original and
values of PLS model, the violet plots represent the new and
values of twenty models. The result in Fig. 4 indicates that the original PLS model in this study
have no possibility of chance correlation and express good robustness.
0.7
0.6
0.5
q
2
0.4
0.3
0.2
0.1
0.0
■ original PLS model
twenty new models
-0.1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
2
R
Fig. 4. Plots of Y- randomization test for 20 repetitions
3.5 Applicability domain of the PLS model
To ensure the applicability domain of the developed model, Euclidean distances were used to
calculate the domain based on the equation 1. The APD threshold and the distances of 23 test
compounds to their nearest neighbor in the training set are listed in Table 2. The APD threshold of
the developed PLS model is 0.613. All the distance values of test compounds are much more
18
smaller than 0.613, which suggests the predictions for the test compounds by the PLS model are
reliable. For other compounds, we can use the developed model to predict the reaction rate when
the nearest distance to the compounds in the training set of this study fall into this threshold
(0.613).
Table 2
The APD and distances of test compounds to neighbors in the training set
Organic compounds
Euclidean distances
APD of PLS model
0.613
Blue 2B
0.235
Phloroglucinol anhydrous
0.021
m-Cresol purple
0.106
BPA
0.113
2,7-Dihydroxynaphthalene
0.333
Sulfanilic acid
0.193
3,4-Dichlorobenzeneamine
0.056
1,10-Phenanthroline
0.114
Nitrobenzene
0.037
Aniline
0.039
Eriochrome® Blue Black R
0.076
2-Nitroaniline
0.023
4-Nitroaniline
0.084
19
Isatin
0.312
Orange G
0.079
Methyl orange
0.174
o-Cresol
0.060
p-Cresol
0.025
Acid black 1
0.135
2,7-Dihydroxynaphthalene
0.197
o-Cresol
0.059
3,4-Dichlorobenzeneamine
0.123
p-Dimethylaminobenzaldehyde
0.078
4. Conclusion
In this study, 90 lgk values for 18 organic compounds were conducted in Fenton process at
different temperatures (25 °C - 60 °C), 26 lgk values for 6 organic compounds (15.8 °C - 50 °C)
were collected from published literatures. 116 lgk values were divided into training set (93) and
test set (23). A PLS model were subsequently developed by using the lgk value in training set as
dependent variables and 12 kinds of chemical parameters. The associated evaluation criterions
= 0.722,
= 0.652,
=
0.512,
= 0.635 and Y-randomization showed that the model
was stable, robust and had good predictive ability. APD analysis also suggested that the optimal
model could be used to estimate the reaction rate in Fenton process at different temperatures. The
main factors governing the reaction rate in Fenton process are temperature, minimum value of
bond order, the changes of charge of atoms in a molecule, the number of carbon atoms and the gap
20
energy between LUMO and HOMO of a molecule. The proposed model provides a theoretical
method to evaluate the reaction rate in Fenton process at the temperature of 15.8 °C - 60 °C, and
by using the model, we can obtain the reaction rate of organic compounds rapidly and accurately
in Fenton process.
Acknowledgement
This work was supported by the National Science Foundation of China (Project No. NSFC
21177083, NSFC key project 21537002), and National water pollution control key project
2014ZX07214-002.
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Highlights
The experimental materials covered 24 kinds of organics with different structures
Temperature is a crucial parameter for developing the model
A PLS model was established for reaction rate constants in Fenton process
The proposed model could accurately predict reaction rate from 15.8 °C - 60 °C
28
29