Biomedical Engineering Reference
In-Depth Information
Noting that
K
ji
¼ K
j
e
D
H
ad
;
ji
(9.33)
RT
Substituting
Eqn (9.32)
into
Eqn (9.33)
, we obtain
DH
ad
;j0
Es
RT
¼ K
j
e
E
s
K
ji
¼ K
j
e
(9.34)
RT
Now applying the exponential surface energy distribution to
E
s
, similar to the steps in
Eqns
(9.19) through (9.23)
, we obtain
K
j
C
j
ln
e
!
E
max
Z
E
max
K
j
C
j
e
E
s
X
N
s
1
n
s
d
E
s
¼RT
f
s
0
n
s
RT
E
s
RT
E
s
RT
f
s0
e
q
j
¼
þ
K
m
C
m
þ
P
N
s
m¼
1
K
m
C
m
e
E
s
1
RT
m¼
1
0
0
where
E
max
is the maximum (upper limit) of the “surface energy” deviation from the
minimum. Thus,
þ
P
N
s
m¼
K
j
C
j
1
1
K
m
C
m
q
j
¼
ln
(9.35)
þ
P
N
m¼1
K
m
C
m
E
max
RT
E
max
RT
e
e
1
Assuming whole spectrum of energy distribution, i.e.
E
max
/ N
,
Eqn (9.35)
is reduced to
ln
"
1
X
!
1
#
N
s
q
j
¼ K
j
C
j
þ
K
m
C
m
(9.36)
m¼
1
Therefore, the generalization of multiple component and dissociative adsorption to nonideal
adsorption would be straightforward.
9.1.2.2. UniLan Isotherm
We have seen how the “surface energy” distribution using an exponential expression can
be treated elegantly for adsorption of multiple species mixture based on Langmuir adsorp-
tion isotherm. One other simplistic distribution is the uniform distribution, i.e. all the avail-
able active centers (sites) are distributed linearly along the surface energy rise:
n
s
E
max
d
E
s
d
n
si
¼
(9.37)
where
E
s
varies between 0 and
E
max
. The fractional coverage by species
j
is then
Z
n
s
E
max
Z
K
j
e
Es
RT
C
j
1
n
s
1
E
max
q
j
¼
q
ji
d
n
si
¼
d
E
s
(9.38)
þ
P
N
s
m¼
1
K
m
C
m
e
Es
1
RT
0
0
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