Environmental Engineering Reference
In-Depth Information
one, decreasing and increasing exponential distributions and Rayleigh distribu-
tion. Some of these equations have rather complex mathematical form; however,
the decreasing exponential and Rayleigh distributions may be considered as spe-
cial cases of the gamma-type distribution, which generate a very simple isotherm
equation. General integral equation similar to integral equation for the adsorption
isotherm on heterogeneous microporous solids can be written as follows:
∞
=
∫
(
)
0
(51)
a
a
zAFzdz
,
()
mi
mi
mi
0
where a
mi
is the equilibrium amount adsorbed in micropores, is the maximum
amount adsorbed in micropores, is the local isotherm describing adsorption in
uniform micropores;
z
is the quantity associated with the micropore size; A = RT
In (p/p
o
) is the adsorption potential, F(
z
) is the distribution function characterizing
heterogeneity of microporous structure. Jaroniec and co-workers proposed the
following gamma-type distribution function:
n
r
v
(52)
( )
-
v
−
1
exp
n
Fz
=
z
−r
(
z
)
(
)
-
v
n
Γ
whereis the inverse value of the characteristic energy E
o
for the reference adsor-
bate, p > 0 and v > 0 are parameters for the gamma distribution function. It was
shown elsewhere that the Jaroniec-Choma (JC) equation, which was obtained by
generalization of the DA equation for n = 2 or n = 3, gives good description of gas
and vapor adsorption for many microporous active carbons. A general form of the
JC equation can be written as:
−
v
n
n
��
A
(53)
0
aa
=
1
+
-
€‚
bƒ„
mi
mi
-
Here a
mi
and denote respectively the amount and the maximum amount adsorbed
in micropores, p and v are parameters of the gamma distribution function. Eq. (53)
with n = 2 was proposed by Jaroniec and Choma on the basis of the assumption
that mention before with n = 2 [Dubinin-Radushkevich (DR) equation] governs
adsorption in uniform micropores. This assumption was justified experimentally
by Stoeckli and Dubinin and others. Later, Stoeckli carried out careful adsorp-
tion and calorimetric experiments for benzene on molecular carbon sieves, and
showed that DA equation with n = 3 gives a better representation of adsorption
in uniform micropores than that with n = 2. These experimental studies suggest
that the DA equation with n = 2 describes adsorption in nearly uniform micro-
pores and its generalized from [Eq. (53) with n = 2] gives a good description of
adsorption on microporous active carbons with large structural heterogeneity. For
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