Biomedical Engineering Reference
In-Depth Information
Integration of
Eqn (9.38)
yields
þ
P
N
s
m¼
1
K
m
C
m
e
Emax
RTK
j
C
j
E
max
P
N
s
ln
1
RT
q
j
¼
(9.39)
þ
P
N
s
m¼
1
K
m
C
m
1
1
K
m
C
m
m¼
For single species adsorption,
Eqn (9.39)
is reduced to
þ K
A
C
A
e
E
max
E
max
ln
1
RT
RT
q
A
¼
(9.40)
1
þ K
A
C
A
which is also know as the UniLan (
uni
form distribution
Lan
gmuir) model.
Fig. 9.6
shows the change of coverage with bulk phase concentration as predicted by the
three models: Langmuir, UniLan, and ExLan. One can observe that the general shape (or
qualitative behaviors) of the three models are quite similar. However, compared with the
ideal Langmuir isotherm, the nonideality introduced to the isotherms (either UniLan or
ExLan models) causes the isotherm to bend upward, i.e. coverage increases quicker at low
bulk phase concentration. This is due to the nonideal adsorption models we used: the inter-
action energy le
ve
l distributes from the base line of that corresponds to the ideal surfaces
(when equating
K
j
and
K
j
). Therefore, as one would expect, adsorbate molecules prefer to
adsorb to high interaction energy sites (with higher
D
H
ad
values) than lower ones (with
H
ad
values). The level of adsorption increases with nonideality (or introduction
of higher interaction energy sites).
D
lower
1.0
0.8
0.6
0.4
Langmuir
ExLan
UniLan,
0.2
E
max
=
RT
ExLan,
E
max
=
RT
0.0
0
2
4
6
8
10
K
A
C
A
FIGURE 9.6
The adsorption isotherms as predicted by ideal Langmuir adsorption, exponential interaction
energy distribution (ExLan) and uniform interaction energy distribution (UniLan).
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