Environmental Engineering Reference
In-Depth Information
1.2.2.3 STOECKLI MODEL
Another approach for the determination of PSD of porous adsorbents which is
also based on the Dubinin's TVFM is Stoeckli method. It had been shown by
scientists, that for the ideal slit-shaped microporous materials, a good estimate of
the adsorption isotherm can be obtained by:
a
WW
=
-
(41)
0
(
)
3
a AK
+b
/
-
0
(
)
3
W a L
vv
31
−
exp exp
Ã
−
aL
3
dW
dL
0
=
( )
v
(42)
The a and ν are constant parameters that are related to the mean and width of the
distribution, respectively. K
0
is calculated using Eq. (42). This is applicable over a
range of pore size from0.4 to 2.0 nm. After obtaining the model parameters using
Eq. (41), pore size distribution can be determined using the following gamma type
distribution of the mean pore width (L = 2x) [1, 126, 133]:
(
)
3
W a L
vv
31
−
exp exp
Ã
−
aL
3
dW
dL
0
=
( )
v
(43)
1.2.2.4 HORVATH-KAWAZOE (HK) METHOD
Horvath and Kawazoe developed a rather simple means of characterizing the pore
structure of porous materials. This model provides a simple, one-to-one corre-
spondence between the pore size and relative pressure at which the pore is filled.
Using thermodynamic arguments and applying the potential obtained by Horvath
and Kawazoe derived the following expression:
��
4
10
4
10
P
RT
1
NA
+
NA
d
d dd
+− =
RT
ln ln
RT
ln ln
1
N
aa
AA
× − −+
-
€‚
-
AV
P
q
−q
d
4
(
L d
−
2
)
3(
Ld
−
)
3
9(
Ld
−
)
9
3
d
3
9
d
9
ƒ„
0
0
0
0
0
0
(44)
where L represents the micropore width (L = 2x), N
AV
denotes Avogadro's num-
ber, and R and T are gas constant and temperature, respectively. A
a
and A
A
are
dispersion constant characterizing adsorbate-adsorbent and adsorbate adsorbate
interactions, N
a
and N
A
are the number of atoms per unit area of adsorbent and
the number of molecules per unit area of adsorbate, d
0
is the arithmetic mean of
the adsorbate molecular diameter and the adsorbent atomic diameter, and δ is the
distance between a gas molecule and an adsorbent atom at zero interaction energy
at relative pressure of P/P
0
. From the amount adsorbed at relative pressure of P/
P
0
, Eq. (44) yields the corresponding slit-pore width, L. Thus, a plot of adsorbed
volume versus L is a cumulative pore-volume curve, the slopes of which give the
differential PSD [133].
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