Experimental adsorption isotherms based on inverse gas chromatography.

Abstract

A new chromatographic perturbation method is used for studying the adsorption-desorption equilibrium in various gas-solid heterogeneous systems. It is the reversed-flow method giving accurate and precise values of many physicochemical constants including the basic and necessary adsorption isotherm values. For four inorganic oxides, namely, Cr2O3, Fe2O3, TiO2 and PbO, and two aromatic hydrocarbons (benzene, toluene) these adsorption isotherms have been determined through a non-linear model.

Full text

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969 (2002) 81–86Journal of Chromatography A,
www.elsevier.com/locate/chroma
E xperimental adsorption isotherms based on inverse gas
chromatography
E. Kalogirou, I. Bassiotis, Th. Artemiadi, S. Margariti, V. Siokos,
F. Roubani-Kalantzopoulou
Department of Chemical Engineering, National Technical University of Athens, 9 Iroon Polytechniou St., 157 80 Zografou, Greece
*
Abstract
A new chromatographic perturbation method is used for studying the adsorption–desorption equilibrium in various
gas–solid heterogeneous systems. It is the reversed-flow method giving accurate and precise values of many physico-
chemical constants including the basic and necessary adsorption isotherm values. For four inorganic oxides, namely, Cr O ,
Fe O , TiO and PbO, and two aromatic hydrocarbons (benzene, toluene) these adsorption isotherms have been determined
232
through a non-linear model.
 2002 Elsevier Science B.V. All rights reserved.
23
Keywords: Adsorption isotherms; Inverse gas chromatography; Metal oxides; Benzene; Toluene
1 . Introduction
erties and the influence of air pollution on these
properties. In addition, traditional inverse gas–solid
chromatography [4] has roughly the same aims, but
as it is a classical chromatographic elution method, it
has several weak points: it does not take into account
the sorption effect, it neglects the mass-transfer
phenomena taking place, and is also influenced by
the carrier gas flow.
With the use of suitable personal computer pro-
grams [3,5], the study of the absorption–desorption
phenomena of many solutes on many solids becomes
possible, without specifying a priori an absorption
isotherm equation. Two significant advantages of this
method are simplicity and low cost in relation to the
time required.
In contrast to the work accomplished with the
same RF-GC method based on a linear model [6],
this study is based on a non-linear–adsorption iso-
therm model [2] which is appropriate for studying
Progress in many areas of material science and
engineering requires the development of new ad-
vanced methods for studying processes occurring at
phase boundaries. Reversed-flow gas chromatog-
raphy (RF-GC) [1] is used to study gas–solid
interfaces [2,3].
The RF-GC method differs from the classical
chromatographic methods in that the stationary phase
properties rather than the solute properties are of
interest. Thus, it provides information about the
nature and behavior of the material surface in various
environments, including individual material prop-
*Corresponding author. Tel.: 130-1-772-3277; fax: 130-1-
202-7691.
E-mail address: roubanif@central.ntua.gr (F. Roubani-Kalan-
tzopoulou).
0021-9673/02/$ – see front matter
PII: S0021-9673(02)00371-0
 2002 Elsevier Science B.V. All rights reserved.

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969 (2002) 81–86
82
E. Kalogirou et al. / J. Chromatogr. A
oxides and non-metals in general. The failure of a
linear model in this case is attributed to surface
heterogeneity of these substances [7].
This work focuses on the experimental examina-
tion of some powders which are used in processing
in the paint and ceramic industries as well as in
catalyst preparation and utilization, namely Cr O ,
Fe O , TiO and PbO.
232
and flow restorations are indicated on the chart
recorder strip (Fig. 2).
The chromatograph used was a Shimadzu 8A,
slightly modified, with a flame ionization detection
(FID) system. The experimental arrangement was
analogous to that used in catalytic studies [8], and is
very different from those used in the past [3]. Here
the L section (20.5–23.4 cm) did not contain any
1
solid material, while the L
contained the solid bed. Both sections, L and L ,
were made of Pyrex glass with I.D. 3.5 mm. The
sampling column l91l (40 cm140 cm) was a
stainless steel chromatographic tube of 4.0 mm I.D.
A small quantity of liquid benzene (4.0 ml) or
toluene (4.7 ml) was injected into the end of column
containing the solid bed (PbO, Fe O , TiO , Cr O ).
After the appearance of the continuously rising
concentration–time curve, the reversing procedure
for the nitrogen carrier gas flow started, each reversal
lasting 10 s. The narrow fairly symmetrical sample
peaks created by the flow reversals were recorded
and their height was printed as a function of time t.
Conditioning in situ at 473.2 K, under a continu-
ous flow of nitrogen, for 24 h, is necessary, followed
each time by adjustment of the working temperature
(363.2 K for benzene and 393.2 K for toluene).
Toluene was a Mallinckrodt analytical reagent and
benzene a special laboratory reagent for chromatog-
raphy from BDH (UK). The inorganic oxides (PbO,
23
(4.0–5.0 cm) section
2
12
2 . Experimental
The RF-GC technique involves perturbation of the
flow-rate of the carrier gas, simply achieved ex-
perimentally by using a four- or six-port gas sam-
pling valve and reversing the direction of flow of the
carrier gas, usually for a short time interval. If pure
carrier gas passes through the sampling column,
nothing happens on reversing the flow. If a solute
comes out of the diffusion column at z50 (Fig. 1) as
a result of its diffusion into the carrier gas, filling the
column z and also running along the sampling
column, the flow reversal records the concentration
of the solute at the junction of the sampling and
diffusion columns at the moment of reversal. This
recording of concentration has the form of extra
chromatographic peaks superimposed on the other-
wise continuous detector signal (Fig. 2). The mo-
ment of injection is time 0 and some flow reversals
23223
Fig. 1. Outline for the experimental arrangement for the study of adsorption isotherms.

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969 (2002) 81–86
83
E. Kalogirou et al. / J. Chromatogr. A
Fig. 2. Sample peaks from the chromatograph Shimadzu 8A with FID.
Fe O , TiO , Cr O ) were Merck analytical re-
23223
agents, and were used as such. The external porosity
and the specific surface of the solids are shown in
Table 1. The volumetric flow rate of the nitrogen
carrier gas was equal to 26.0 cm min
chromatographic peaks in relation to time). Only the
absolutely necessary mathematical equations are
quoted here to help the reader understand how the
parameters in the tables and figures were extracted
from the experimental data.
Four basic equations are mentioned.
First, the local adsorption isotherm of the solute
studied is:
a
m
y
S]]
*
c 5?d y 2L 1
sd
S2
aa
SS
*
where c
is equilibrium adsorbed concentration of
S
21
the solute at time t, mol g
amount of this solute, mol; a
material per unit length of column bed, g cm
d y 2L
is Dirac’s delta function for the initial
sd
2
condition of the bed, when the solute is introduced as
an instantaneous pulse at point y 5L , cm
length coordinate along section L , cm; a is cross-
sectional area of the void space in region y, cm ; k1
is local adsorption parameter, s
concentration of the solute as a function of time t
and coordinate y along the column, mol cm
is dummy variable for time.
3
21
.
3 . Calculations
t
The theoretical analysis relevant to the present
work, dealing with physicochemical parameter de-
termination under non-steady-state conditions, has
been published elsewhere [9,10]. All the calculations
have been made with a GW-Basic personal computer
program using the experimental data (heights of
?k E c (t)dt
0
(1)
1
y
; m is initially adsorbed
S
is amount of solid
S
21
;
Table 1
External porosity (e) and specific surface area (SSA) of the four
solids used
21
; y is
2
2
y
2
21
2
Solid
e
SSA (cm g)
21
; c
is gaseous
Cr O
2
Fe O
2
PbO
TiO
0.7252
0.7988
0.5551
0.5459
33400
23400
300
31100
y
3
3
23
; and t
2

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969 (2002) 81–86
84
E. Kalogirou et al. / J. Chromatogr. A
Secondly, the mass balance equation for the solute
in the gaseous region z of the diffusion column is:
The explicit calculation of the isotherm can be
carried out as described elsewhere [2]. However, the
following equations are improved [11], as they are
based on Eq. (5), rather than Eq. (6), as done
originally [2]:
5gc(l9,t)5O A exp(B t)
i51
a OA exp(B t)
*
≠cS
i51
]]]]]]]
5k ?
14
≠cG
S
ii
i51
?O A exp B t 21 /B
gaS
i51
?O A exp(B t)
g
i51
2
≠c
]
≠t
≠ c
]]
≠z
zz
5D ?5kc
(2)
12app z
where c is gaseous concentration of the solute as a
z
function of time t and length coordinate z along the
23
column, mol cm; D is diffusion coefficient of this
1
solute into the carrier gas (nitrogen), cm s
k
is apparent rate constant of a first-order or
app
pseudofirst-order reaction of the solute in the gas
21
phase, s.
Next, the mass balance equation of the same
solute in the region y of the diffusion column, filled
with the solid material under study is:
3
1/M
H
(6)
ii
2
21
; and
4
yii
(7)
a OA B exp(B t)
i
4
k a
1
]]
y
*
S
c 5
(8)
fsdg
iii
2
≠c
]
≠t
≠ c
]]
≠y
a
]
a
yy
S
4
*
S
5D ?2k
??(c 2c )2kc
(3)
22
21Sapp y
1
]
y
c 5
G
(9)
ii
where D is diffusion coefficient of this solute into
2
the gas phase in section y, cm
constant for desorption of the solute from the solid
21
bulk, s; and c
is concentration of the solute
S
adsorbed on the solid at time t, mol g
Finally, the rate of change of the adsorbed con-
centration is given by the equation:
≠cS
]
*
5kc 2c 2k c
sd
21SS2 S
≠t
2
21
where c
solute (mol/cm ), and A and B are the pre-ex-
ponential factors and the exponential coefficients of
Eq. (5). One can consider t in the above equations as
a dummy independent variable and calculate, for
chosen arbitrary values of t, both the differential
isotherm ≠c* /≠c
and c*
SG
sponding values of c . Plotting ≠c* /≠c
G
against c
for each chosen t, independent ex-
G
perimental isotherms are obtained.
is the gaseous concentration of the probe
3
i
s; k
is rate
G
21
i
21
.
together with the corre-
S,
or c*
(4)
SGS
21
where k
first-order or pseudofirst-order surface reaction of the
adsorbed solute.
With the initial conditions
m]
c (0,y)5?d(y 2L ),
y
2
a
y
(s) is the rate constant of a possible
2
4 . Results and discussion
The differential isotherms for the four oxides and
the two aromatic hydrocarbons are shown in Tables
2 and 3, while the integrated isotherms are plotted
and shown in Figs. 3 and 4.
From Figs. 3 and 4, it is obvious that characteriza-
tion of the adsorptive properties of the different
solids is possible. It is shown for example that PbO
behaves very differently from the other oxides used.
That is, among TiO , Cr O , Fe O and PbO studied
22
with benzene or toluene, the isotherms of the last
oxide have the lowest c* values. The shapes of all
S
isotherms remain unchanged.
As a result, safe and accurate conclusions about
chemical reactivity and kinetics can be made to-
and c (0,y)50, m being the amount (mol) of the
S
solute introduced as a pulse at y 5L , the solution of
the system of differential Eqs. (1)–(4) leads to the
function [9]:
5gc(l9,t)5O A exp(B t)
i51
2
4
1/M
H
(5)
ii
323
where H is height of sample peaks resulting from the
flow reversal, cm; M is response factor of the
detector, dimensionless; g is calibration factor of the
3
detector, cm per mol/cm ; and c(l9,t) is measured
sampling concentration of the solute, mol cm
23
.

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969 (2002) 81–86
85
E. Kalogirou et al. / J. Chromatogr. A
Table 2
The differential isotherms for the adsorption of benzene on four
oxides at 363.2 K
3
21
Dummy
variable (min)
(≠c* /≠c ) (cm g
SG
)
PbOFe O
2
Cr O
2
TiO
332
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
0.3086
0.2359
0.2159
0.2151
0.2261
0.2474
0.2792
0.3225
0.3781
0.4463
0.5258
0.6136
0.7051
0.7948
0.8775
3.086
2.442
2.411
2.570
2.823
3.136
3.487
3.860
4.241
4.617
4.977
5.310
5.611
5.877
6.106
4.473
2.538
2.213
2.207
2.351
2.602
2.944
3.371
3.873
4.435
5.036
5.649
6.248
6.807
7.310
171.7
5.501
3.974
3.687
3.769
4.049
4.473
5.017
5.660
6.381
7.154
7.948
8.731
9.474
10.15
Fig. 3. Adsorption isotherms for PbO, Fe O , TiO , and Cr O
with benzene.
23223
which are elution techniques. This method has the
following advantages [2]: (a) it does not need an a
priori isotherm equation; (b) it accounts for the mass
transfer phenomena; (c) it takes desorption into
account; (d) a sorption effect is absent; and (e) it
produces isotherms in the presence of a possible
heterogeneous and also an homogeneous reaction in
the gas-phase.
In addition further advances have been achieved:
(a) explicit calculation of the isotherms was not
carried out as described in Ref. [2] but was based on
further improved equations; (b) the adsorption and
kinetic measurements were rendered independent of
the diffusion coefficient of the gas injected, which
until now was determined independently, found in
gether with correct explanations about the studied
systems based on these experimentally obtained
isotherms, since the kinetic parameters are closely
related to the existing adsorption isotherm, depend-
ing strongly on the adsorption–desorption phenom-
ena. Many other systems can be examined with the
same method.
We believe that this method is to be preferred to
the classical inverse gas chromatographic methods,
Table 3
The differential isotherms for the adsorption of toluene on four
oxides at 393.2 K
3
21
Dummy
variable (min)
(≠c* /≠ ) (cm g
SC
)
PbO Fe O
2
Cr O
2
TiO
332
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
0.3660
0.1899
0.1484
0.1322
0.1257
0.1248
0.1278
0.1344
0.1448
0.1594
0.1786
0.2030
0.2331
0.2687
0.3094
1.750
0.9990
0.8467
0.7984
0.7994
0.8350
0.9024
1.003
1.140
1.315
1.530
1.778
2.049
2.329
2.599
230.21
2.147
1.327
1.082
0.9804
0.9378
0.9286
0.9423
0.9739
1.021
1.082
1.158
1.246
1.345
1.453
23.702
9.302
3.326
2.501
2.252
2.205
2.272
2.425
2.653
2.951
3.314
3.731
4.185
4.655
5.116
Fig. 4. Adsorption isotherms for PbO, Fe O , TiO , and Cr O
with toluene.
23223