Environmental Engineering Reference
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Kelvin equation could be extended significantly towards small mesopores and
large micropores when a proper t-curve was used to represent the film thickness
of nitrogen adsorbed on the carbon surface. The t-curve proposed in the work
gave the pore-size distribution functions for the carbons studied that reproduce
the total pore volume and show realistic behavior in the range at the borderline
between micropores and mesopores [1, 2, 16, 24, 37, 121, 145].
1.2.2.2 DUBININ-STOECKLI (DS) EQUATION
The adsorption of vapors by microporous carbons was described by the following
fundamental equation of Dubinin-Astakhov (DA):
n
A
��
(37)
WW
=
0
exp exp
−
-
€
ƒ„
E
-
Here, W (mmol·g
−1
) represents the amount adsorbed at relative pressure P
0
/P, W
0
denotes the limiting amount of micropores filling, and A is the differential mo-
lar work of adsorption defined as A = RT ln(P
0
/P) at temperature of T. One may
write that E = βE
0
, where β is the affinity coefficient depending on the adsorptive
only, and it has been assumed that for benzene as a reference β = 1. In general
case of heterogeneous microporous adsorbents, the adsorption is described by the
Dubinin-Stoeckli (DS) adsorption equation of:
�
22
�
�
�
W
mx A
x
W
=
0
exp
−
0
×+
1
erf
0
-
€
‚
€
‚
(38)
22
ƒ
12
+d
mA
„
22
ƒ
22
„
212
+d
mA
d +d
212
mA
-
which implies a normal half-width (
x
) distribution of micropore volume for the
slit-like pores as:
(
)
2
xx
−
dW
dx
W
0
=
0
exp
−
-
2
2
d
dπ
2
-
(39)
where, x
0
is the half-width of a slit shaped micropore, which corresponds to the
maximum of the distribution curve, and δ is the variance. The letter m is a con-
stant coefficient for a given vapor:
2
��
=
€‚
1
m
bƒ„
(40)
k
For benzene as the reference vapor, the constant k equals to 12 kJ·nm·mole
−1
. Us-
ing Eq. (38) to fit the experimental data, three parameters of W
0
, x
0
and δ, can be
extracted. Knowing these parameters, the micropore size distribution in terms of
volume can be calculated from Eq. (39) [1, 2, 19, 126, 133].
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