Biomedical Engineering Reference
In-Depth Information
active center balance when the adsorption is at equilibrium, or the net adsorption rate
is zero.
Isotherms directly obtained from
Eqns (9.2) or(9.12)
are termed Langmuir isotherms as
uniform surface activity is assumed so that all the rate constants are not functions of the
coverage,
K
A
C
A
q
A
¼
(9.9)
1
þ K
A
C
A
and
p
K
A
2
C
A
2
q
A
¼
p
K
A
2
C
A
2
(9.14)
1
þ
Since the dissociative adsorption is a special case of the adsorption where the concentration is
replaced by the square root of concentration as noted from
Eqns (9.14) and (9.9)
, we shall now
focus on the nondissociative adsorption.
k
A
k
0
E
ad
E
des
RT
¼ K
A
e
D
H
ad
e
K
A
¼
(9.5a)
RT
A
For adsorption of multiple component mixture at the same active center, Langmuir
adsorption isotherm is given by
K
j
C
j
q
j
¼
(9.17)
þ
P
N
m¼1
K
m
C
m
1
Nonideal surfaces can be modeled by a distribution of interaction energy (adsorption heat
D
H
ad
, and/or
E
ad
and
E
des
). An exponential distribution of available sites with an excess
adsorption heat between 0 and
E
max
leads to
þ
P
N
s
m¼
K
j
C
j
1
1
K
m
C
m
q
j
¼
ln
(9.35)
þ
P
N
s
m¼
E
max
RT
E
max
RT
e
e
1
1
K
m
C
m
Eqn
(9.35)
may be referred to as ExLan (
Ex
ponential energy distribution
Lan
gmuir)
adsorption isotherm. For adsorption of single species,
K
A
C
A
1
þ K
A
C
A
q
A
¼
ln
(9.26)
E
max
RT
E
max
RT
e
e
1
þ K
A
C
A
Assuming whole spectrum of energy distribution, i.e.
E
max
/ N
,
Eqn (9.35)
is reduced to
q
j
¼ K
j
C
j
ln
"
1
X
!
1
#
N
s
þ
K
m
C
m
(9.36)
m¼
1
For single species adsorption,
Eqn (9.36)
is reduced to
þðK
A
C
A
Þ
1
q
A
¼ K
A
C
A
ln
½
1
(9.27)
Search WWH ::
Custom Search