Environmental Engineering Reference
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where is the sum of the diameter of an adsorbent atom and an adsorbate
molecule (the remaining parameters of the above equation are defined in
list of abbreviation). Finally, the following two equations were obtained:
L
a
a
+ ×+
b
nc n
2
av (all)
1(all)
2(all)
2(all)
2(all)
=
+
d
1
+
b
exp
−
cn
E
A
0
1( all )
1( all )
(91)
not only for the micropore diameters (called the first range):
�
�
E
a
n
L
�
an
��
a n
�
0
3( mic )
3( mic )
€
‚
b
+
n
av ( mic )
1( mic )
2( mic )
ƒ
„
=
+
×
E
€
‚€
‚
(92)
0
d
b
+
n
b
+
n
ƒ
„ƒ
„
A
1( mic )
2( mic )
for calculations up to effective diameter equal to 2 nm (called the second range).
The additional details of all above-mentioned calculations were given previously,
therefore they are omitted in the current study. Taking into account the assump-
tions made during the derivation of Eq. (90), the main condition, which should
be fulfilled for the chosen molecules of adsorbates, is the absence of a dipole
moment and a spherical-like structure. Therefore, with chosen N
2
, Ar, CCl
4
, and
C
6
H
6,
for some of these adsorbates the Horvath-Kawazoe method was adopted.
Moreover, these adsorbates have been widely applied in the investigation of the
structural heterogeneity of microporous carbons. However, the choice of nitrogen
at its liquid temperature as the probe molecule may not be suitable for very nar-
row pores such as those in carbon molecular sieves, where the activated diffusion
effects might be important. These effects can be reduced by conducting the ex-
periment at higher temperatures. It is thus useful to investigate the MSD obtained
from adsorption of different adsorbates at temperature other than the boiling point
of nitrogen at 77.5 K, For example, at near ambient temperatures. The tempera-
tures chosen in the calculation were equal or very close to those applied in mea-
surements where the investigated adsorbates are used for the determination of
structural heterogeneity of carbons. Summing up, all the above results show that
the average pore diameter is a function not only of E
0
but also of n. Then, using
Eqs. (91) and/or (92), the average reduced effective diameter can be calculated
and multiplied by the adsorbate diameter. The typical plots (the lines) for chosen
adsorbates (C
6
H
6
and N
2
) and values of (1.50 and 3.25) are compared with re-
lationships proposed by the other others works. It should be pointed out that the
shape of this curves is similar to that observed for the empirical and/or semiem-
pirical relationships. This procedure was also applied previously to experimental
data of adsorption on different carbonaceous molecular sieves. The correlation
between suggested and calculated using Eqs. (91) and (92) pore diameters is very
good. On the other hand, we recently tried to answer the most general questions
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