Environmental Engineering Reference
In-Depth Information
of micropores of considerably different sizes. For microporous solids with a great
number of micropores of different sizes, the summation in Eq. (21) should be
replaced by integration and then a
mi
is given by:
2
∞
��
A
( )
0
∫
a
=
a
exp
−
B
-
F
B dB
€‚
mi
mi
ƒ„
(22)
-
0
where F(B) is the distribution function of the structural parameter B normalized
to unity. The integral Eq. (22) was first proposed by Stoeckli. Expressing in this
integral the structural parameter B by means of the half-width
x
:
2
Bx
=ς
(23)
Where is the proportionality constant; we have:
∞
(
)
( )
0
∫
22
a
=
a
exp
−
mx A
J
x dx
(24)
mi
mi
0
where is the micropore size distribution and m is defined by:
ς
=
b
m
(25)
2
Comparison of the integral Eqs. (22 and (24) gives the following relationship
between the distribution functions F(B) and J(
x
):
( )
( )
J
x
=ς
2
xF
B x
(26)
∞
( )
( )
∫
X
A
=b −
2
A
−
2
m x
2
exp
mx A
22
J
x dx
mi
(27)
0
Eqs. (26) and (27) define the relationship between distribution function X
mi
(A),
F(B) and J(
x
).The average adsorption potential associated with Eqs. (26) and (27)
is given by:
1
2
∞
∞
−
bπ
FB
( )
1
��
Jx
()
∫
∫
A
=
dB
=
€
ƒ„
dx
2
2
m
x
(28)
B
0
0
The dispersion for the distribution function X
mi
(A)may be expressed as follows:
1
1
( )
∞
2
∞
2
FB
dB
()
2
1
Jx
2
−
−
∫
∫
2
s=b
− =
A
dx
−
A
-
-
A
(29)
B
mx
0
0
where A is defined by Eqs. (28) and (29) have general character and permit calcu-
lation of A and for arbitrary micropore distributions F(B) and J(
x
)[1, 2].
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