Measurements of Diffusion Coefficients in
Porous Solids by Inverse Gas Chromatography
J. Kapolos, N. Bakaoukas, A. Koliadima, and G. Karaiskakis
(Submitted July 20, 2005)
The relatively new methodology of reversed-flow gas chromatography has been applied to
measure the diffusion coefficients of gaseous species into porous solid material. The necessary
experimental arrangements and the theoretical analysis were described, and the appropriate
mathematical analysis which leads to equations describing the diffusion coefficients as a function
of the experimental data and other measurable experimental conditions was developed. All of
the calculations were performed using a simple software for a personal computer. The meth-
odology was applied to pentane, hexane, and heptane diffusing into porous a- and -alumina as
well as of sulfur dioxide diffusing into porous marble at various temperatures. The results were
compared with those obtained by the Knudsen formula or those given by other researchers.
1. Introduction
One of the most fascinating phenomena associated with
porous solids is the ability of the absorbed surface species to
diffuse into the porous solid. This phenomenon is of great
importance in catalysis, metallurgy, environmental studies,
and many other industrial and natural processes.
There are few experimental data referring to diffusion
into porous media, although for calculating diffusion coef-
ficients in porous solids theoretical approaches have been
adopted such as the well-known formula of Knudsen.
[1]
In
1997, Reyes et al.
[2]
reported a new application of fre-
quency-modulated perturbation methods for measuring dy-
namic parameters and capacities pertaining to diffusion and
adsorption within mesoporous solids. These methods
needed corrections to translate the apparent diffusion coef-
ficients into their true values due to adsorption uptakes. On
the other hand, the van’t Hoff equation and Henry’s law
constants were used for considering experimental enthalpies
and entropies of adsorption.
In contrast to the latter, a subtechnique of inverse gas
chromatography can be used without any perturbation of the
system (except in the sampling procedure taking place far
from the gas-solid interface) to show the time distribution of
adsorption energies, local monolayer capacities, and local
isotherm on heterogeneous solid surfaces
[3]
as well as to
determine the surface diffusion coefficients for physically
adsorbed or chemisorbed substances. This technique, which
is called reversed-flow gas chromatography (RF-GC), has
been reviewed recently for catalytic studies,
[4]
diffusion co-
efficients,
[5]
and isotherm determination.
[6]
In this work, the appropriate mathematical analysis and
experimental arrangements for the application of RF-GC for
the calculation of diffusion coefficients in porous solids are
developed.
The diffusion of hydrocarbons (i.e., pentane, hexane, and
heptane) into common porous absorbents (i.e., a- and -alu-
mina) at various temperatures was studied as a reference
model for evaluating the methodology. The developed
methodology was then applied to a more complicated sys-
tem such as sulfur dioxide-marble with great environmental
significance.
2. Theory
The experimental arrangement on which the following
theoretical analysis is based has already been published
[3-7]
and is repeated here in Fig. 1 for convenience.
The necessary mathematical model is based on three
mass balance equations, an adsorption isotherm, and an ini-
tial condition. These equations are as follows.
The mass balance equation of the solute gas A in the free
region y of the tube outside of the porous particles species
on heterogeneous surfaces
[7]
is:
c
1
t
= D
1
2
c
1
y
2
− D
1
2
c
1
r
2
+
2
r
c
1
r
(Eq 1)
where c
1
is the gaseous concentration (in moles per cubic
centimeter) in the free of solid region of section y, and D
1
is the diffusion coefficient (in square centimeters per sec-
ond) of the injected solute in the region filled with solid
particles, with r being the particle radius ranging from 0 (at
the surface) to R (in the center of the particles).
The mass balance equation of the solute inside the po-
rous volume is:
c
2
t
= D
1
2
c
2
r
2
+
2
r
c
2
r
+ k
R
a
s
a
y
c
s
− c*
s
(Eq 2)
This article is a revised version of the paper printed in the Proceedings
of the First International Conference on Diffusion in Solids and Liq-
uids—DSL-2005, Aveiro, Portugal, July 6-8, 2005, Andreas Öchsner,
José Grácio and Frédéric Barlat, eds., University of Aveiro, 2005.
J. Kapolos, Department of Agricultural Products Technology, Tech-
nological Educational Institute of Kalamata, 24100 Kalamata, Greece;
and N. Bakaoukas, A. Koliadima, and G. Karaiskakis, Department
of Chemistry, University of Patras, 26504 Rio, Patras, Greece. Contact
e-mail: jkapolos@teikal.gr.
JPEDAV (2005) 26:477-481
DOI: 10.1361/154770305X66574
1547-7037/$19.00 ©ASM International
Basic and Applied Research: Section I
Journal of Phase Equilibria and Diffusion Vol. 26 No. 5 2005 477