Acta Universitatis Cibiniensis
Seria F Chemia 9(2006-1):81-88
Experimental Study about Molecular Diffusion in Porous
Structures
Diana Florescu1*, I. Stefanescu1 and V. Stanciu1
Abstract
The diffusion is a wide spread phenomenon, met in all mass transfer processes. In
this work we will present the adsorption phenomenon, i.e. the mass transfer between a
fluid phase and the surface of a solid substrate [1].
In this paper we present the experimental gas – chromatographic method for the
determination of the diffusion coefficient for oxygen and nitrogen molecules in two porous
mediums. As porous mediums we used two sorts of carbon - molecular sieve, the first from
underground deposits and the second from wooden extract, both prepared with original
methods in National Institute of R&D for Cryogenics Technologies and Isotopic
Separations– ICSI Rm. Valcea, Research & Development Department.
The diffusion coefficient is an important feature indicating the quality of a carbon
molecular sieve. It depends on the porosity of the sieve and on the porous diameter.
Keywords: molecular diffusion, porous structures, carbon molecular sieve, diffusion coefficient.
I. Introduction
The process on separation and purification of gases is based on selective
adsorption on materials and selective membranes, and it is developed in the last years. The
separation process is based on selectivity in sorption kinetic. The basic process is
1
National R&D Institute of Cryogenics and Isotopic Technologies – ICSI Rm. Valcea, Research &
Development Department – ICSI RM. VALCEA, Str. Uzinei, nr. 4 OP 4, CP 10, Rm. Valcea
Email:dianaf@icsi.ro
*
To whom the correspondence should be addressed.
81
Diana Florescu, I. Stefanescu and V. Stanciu
molecular diffusion of a component in microspores of porous materials or a porous
membrane, how to determine the self and preferential adsorption in determined conditions.
The diffusion represents the penetration of some molecules between other corp
molecules, in the contact region.
The diffusion occurs in almost all the mass transfer processes like: vaporization,
sublimation, boiling, adsorption and absorption.
Because the term of diffusion is so general, we want to specify that in this paper
we use the term of adsorption because we are referring to the mass transfer between a fluid
phase and the surface of a solid substrate.
II. Experimental
A. Experimental Methods
There are 3 methods of determination on the diffusion coefficient. These are
dynamic methods used in experimental determination of the effective coefficients of
diffusion, based on the transitory regime of one system. The methods are as follows: the
delay time’s method, the method of sorption’s speed and the gas – chromatographic
method.
We used the gas - chromatographic method as being the most appropriate for our
laboratory techniques and instrumentation. This procedure is based on the transitory
regime of one system.
The factors that influence the value of C constant are correlated in the next
relation, in which the only value unknown is D p :
F1 * d p2
C =
+
F1 * K * d p2
(1)
2π 2 (1 − F1 )D p
F1
1+ K *
1 − F1
2
75 (1 − F1 ) * D1, 2
Where:
D P - The effective coefficient of diffusion of the gas that is injected through solid pores
(cm/sec);
F – the empty fraction of the column;
d p - the equivalent diameter of granules from the studied material (cm);
D 1, 2 - the gas-gas diffusion coefficient (cm 2 /cm);
K – a measure who take count of the adsorption phenomenon and it is equal with
ε is the total porosity of the studied material.
1
ε
, where
The gas - gas diffusion coefficient D 1, 2 can be calculated with the Lenard – Jones
[2] relation:
2
D1, 2 =
0.0018583*T 3  1
1 


+
2
P *σ1, 2 * ΩD1, 2  M A M B 
82
1
2
(2)
Acta Universitatis Cibiniensis
Seria F Chemia 9(2006-1):81-88
where:
D1, 2 – the diffusion coefficient of substance 1 through substance 2, cm2/s;
0
– the collision diameter, it is Lennard-Jones parameter A ;
T – the temperature at which is determined the diffusion coefficient (K);
M 1 , M 2 - the molecular weight of the two gases;
Ω - the total collision; it depends on the temperature and the intermolecular potential
between a molecule from substance 1 and a molecule from substance 2.
1, 2
Table 1. Lennard-Jones forces calculated with the help of viscosity (from literature) [3].
Compound
Oxygen
Nitrogen
ε A / K , in 0K
Formula
O2
N2
113
91.5
0
σ, in A
3.433
3.681
There are many types of adsorbents:
a) Adsorbents on base of metallic oxides, for ex, activated alumina, 2 AlO 3 H 2O ; they
are used for drying gases or liquids, in chromatographic analyses and separation and in
catalysts preparation.
b) Adsorbents on base of silicate dioxide, silica gel - SiO 2 n H 2 O, with high capacity to
retain water vapors. The adsorption capacity for water vapors of silica gel is greater then of
the activated alumina and of the charcoal, but much lower than the adsorption capacity of
the molecular sieves.
c) Adsorbents on base of activated carbon. The activated carbon is prepared by various
special methods, depending on their utilization. From this point of view, there are two
types of activated carbon: carbon used for gases treatment and carbon used for liquid
treatment.
Microspores – they are pores usually smaller then 20; the main part of the
adsorption surface is composed 0from microspores. The transit pores (the so-called mezzopores) have rays of 20 – 500 A and they are contributing at total value of
0 the specific
surface with
Macrospores – have rays greater than 500 A , up to a few
0 no more than 5%.
thousand A . The contribution of these pores at the specific surface is very small,
practically negligible.
The diffusivity of a gas (or liquid) refers to its speed at the entrance and outlet
from carbon pores or molecular sieve pores. .
d) Molecular sieves – Both the artificial molecular sieves and the natural sieves are
crystalline aluminum-silicates or alkaline earth silicates; they are structured on SiO 22 −
units that form tetrahedral structures inside those there are cavities formed from the anions
specified in the previous paragraph.
e) Charcoals – molecular sieves – Due to the large distribution of the macrospores and
of the microspores, the usual charcoals don’t show any selectivity in the adsorption of
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Diana Florescu, I. Stefanescu and V. Stanciu
different molecules (regarding to their size). The artificial molecular sieves show this kind
of selectivity.
The selectivity is defined as the ratio between the values of diffusivity of two
gases.
A high selectivity indicates an easy separation between the compounds of the
gaseous mixture.
A high value of the capacity indicates the fact that a small quantity of CMS will adsorb
a higher volume of gases.
Here is a list with some gases, in the decrease order of their diffusivity:
H 2 , He , O 2 , CO , CO 2 , NH 3 , N 2 , Ar , CH 4 , H 2 S , ethylene, ethane, propylene,
ethanol, propane, n-butane, isobutene, n-pentane, isopentane, o-xylem, m-xylem, p-xylem,
n-hexane, n-heptanes, etc.
For light gases ( O 2 , CO , CO 2 , N 2 ), the values of diffusivity and selectivity will
be greater, while from heavy gases the diffusivity and selectivity values will be smaller.[4].
B. Materials and Equipments
The principal part of this equipment is the gas – chromatograph Hewlett-Packard
7624 A, at which in place of analytical column of separation there was installed a column
with the length of 48 cm and diameter of 4, 8 mm, in which the studied material was
introduced.
We follow the diffusivity, and the gaze pulse was injected at a volume of 500 l
with the help of a Hamilton syringe. The flowing of bear gas is measured at entrance and at
exit, with the flow meter with soap bubble, and the work pressure is read on a manometer
of 0-4 bar, with a precision of +/- 0, 05 bar. Before the measurements are made, the studied
material was activated through thermal treatment, under vide of 10-2 bar, in a time of 4
hours, at a temperature of 5000C. The material used is presented under form of cylindrical
extradite, with a length equal with the diameter.
III. Results and Discussions
For the measurements made with the gas – chromatographic method, we have used
new equipment improved in our Charcoal Materials Laboratory, in The National Institute
of R&D for Cryogenics Technologies and Isotopic Separations– ICSI Rm. Valcea. The
carbon was prepared after original methods.
Table 2. Few physical characteristics of adsorbents.
No.
Characteristics
1.
Total porosity εp (cm2/g)
2.
Equivalent diameter of granules dp (cm)
3.
Empty Fraction F
4.
Specific volume of pores (cm3/g)
5.
Density (cm3/g)
6.
Real density (cm3/g)
84
CMS-HP
0,33
0,24
0,69
0,33
0,434
1,42
CMS-LP
0,52
0,24
0,74
0,67
0,360
1,54
Acta Universitatis Cibiniensis
Seria F Chemia 9(2006-1):81-88
7.
8.
9.
10.
Apparent density (cm3/g)
Adsorption capacity for oxygen (cm3/g)
Specific surface (m2/gram)
Volume of pores with beam 5-300 A (cm3/g)
0,96
0,61
0,80
0,0171
0,78
0,65
0,86
0,0226
The principal part of this equipment is the gas – chromatograph Hewlett-Packard
7624 A, at which, the analytical column of separation was replaced with a column of 48
cm length and the diameter of 4, 8 mm, filled with the material for study. We follow the
diffusivity, and the gaze pulse was injected at a volume of 500 l with the help of a
Hamilton syringe. The flow carrier gas was measured at the entrance and at exit using a
flow meter with soap bubble and the work pressure was read with a manometer of 0-4 bar,
with a precision of +/- 0, 05 bar. The studied material was first activated through a thermal
treatment at 5000C under a 10-2 bar vacuum, for 4 hours. The material studied was in form
of cylindrical extruded, with a length equal with the diameter.
Fig. 1. Simplified diagram to the analytic route in the gas – chromatograph HP
7624 A, for determination of diffusion coefficient.1-gas cylinder; 2-drying trap; 3-debit
deliverer; 4, 5-injection orifice; 6-thermostat oven; 7-detector (TC); 8-valve to introduce
gaseous samples; 9-register.
Knowing that the diffusion may be considered a function of temperature, a
diagram Dp = f (1/T) was plotted after an equation of Arrhenius type. From the slopes of
the right lines obtained, we determined the energies of activation of the diffusion.
Their values confirm the fact that the diffusion occurs heavier with the molecular
weight increase.
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Diana Florescu, I. Stefanescu and V. Stanciu
Oxygen
Nitrogen
Oxygen
0.04390
0.06050
0.07791
0.09781
0.16108
0.13562
0.14714
0.15961
0.19484
0.23926
2.112
Oxygen
0.031160
0.032380
0.035880
0.041176
0.048310
Nitrogen
0.045602
0.057270
0.076980
0.101930
0.122180
Nitrogen
2.143
25
50
80
120
150
Oxygen
2.740
1
2
3
4
5
Nitrogen
1.993
Temp. 0C
Table 3. Experimental values obtained for the effective coefficients from diffusion and
activation energy from diffusion.
Adsorbent CMS-HP
Adsorbent CMS-LP
Activation
Activation
Deffectif (cm2/sec)
Energy
Deffectif (cm2/sec)
Energy
(kcal/mol)
(kcal/mol)
No
IV. Conclusions
In this paper we present the experimental gas – chromatographic method for the
determination of the diffusion coefficient for oxygen and nitrogen molecules in two porous
mediums. As porous mediums we used two sorts of carbon - molecular sieve, the first from
underground deposits and the second from wooden extracts, both prepared with original
methods in The National Institute of R&D for Cryogenics Technologies and Isotopic
Separations– ICSI Rm. Valcea, Research & Development Department.
The diffusion coefficient is an important feature indicating the quality of a carbon
molecular sieve. It depends on the porosity of the sieve and on the porous diameter. The
results of this work allow us to determine the quality of the sorts of carbon - molecular
sieve investigated.
86
Acta Universitatis Cibiniensis
Seria F Chemia 9(2006-1):81-88
a)
b)
Fig. 2. Types of chromatograms are obtained from diffusion of oxygen and nitrogen: a)
CMS-HP; T- 50oC; speed(v)-6,3cm/sec; for N2; b) CMS-LP; T- 25oC; speed (v) 3,5cm/sec, pour N2.
We have observed that:
- The value of the effective diffusion coefficient for oxygen in the case of CMSHP is approximately 4 times greater than for CMS-LP, showing the existence of pores
with smaller diameter in the second case;
- Nitrogen is a gas that passes easily and with the same speed through both types
of carbons;
- The value of the diffusion coefficient depends on the molecular weight of gas
and on the temperature;
- The adsorbent CMS-HP has smaller porosity and many pores in the diameter
0
range < 5 A , so the CMS-LP type is much more appropriate for the separation of oxygen
from nitrogen in the air by selective adsorption process;
- The gas - chromatographic method is a simple and efficient method and leads us
to discover, in the laboratory, the characteristics of the two types of CMS adsorbents. In
addition, it permits the determination of the values of the diffusion coefficient in the same
conditions as in industrial practice (granules of adsorbent with various geometry and
different shapes).
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Diana Florescu, I. Stefanescu and V. Stanciu
V. References
1. Bird R.B., Steward W.E., Lishtfoot E.N., Transport Phenomena, John Wiley and Sons,
New York, London, Sydney, 1980.
2. Treybal R.R., Mass Transfer Operation, Third Edition, McGraw, Ltd. 1980
3. Wilson R.E., Wicks C.E., Fundamentals of momentum, heat and mass transfer, John
Wiley and Sons, New York, London, Sydney, Toronto, 1989.
4. Dullien F.A.L. Porous Media Fluid Transport and Pore Structure, Academic Press, New
York, London, Sydney, Toronto, San Francisco, 1999.
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