Biomedical Engineering Reference
In-Depth Information
H
E
ad
E
des
A
H
ad
A
Closeness of A to the surface active site
FIGURE 9.3
Interaction potential between molecule A and the active site
s
on the surface.
frequency,
Z
cT
(A, B), of Eqn (6.20). If we designate
E
as the activation energy required for
chemisorption,
C
s
as the total concentration of sites available for chemisorption,
q
the fraction
of free sites available for chemisorption, and
q
A
the fraction of sites on the surface covered by
the adsorbate molecule A, the following analog to Eqn (6.21) may be written as
s
RT
2pM
A
E
ad
RT
C
s
qe
Z
cT
ð
A
;
a
dsÞ¼N
AV
C
A
(9.3)
We may also include a term analogous to the steric factor to be used as a measure of the devi-
ation of chemisorption rates from this ideal limit.
s
RT
2pM
A
E
ad
RT
e
Z
cT
ð
A
;
a
dsÞ¼N
AV
C
A
C
s
qx
(9.4)
where
is commonly termed the
sticking probability.
The adsorption rate constant is thus pre-
dicted from
Eqn (9.4)
.
A potential-energy diagram for the adsorption
e
desorption process
x
A
þ s
%
A
$s
(9.1a)
is shown in
Fig. 9.3
. As illustrated, the chemisorption is exothermic, which is, in general, the
case. Also, since adsorption results in a more ordered state (similar to solid state) compared
to the bulk gas or liquid, we can argue in thermodynamic terms that entropy changes on
chemisorption are negative. This fact is a useful fact in testing the reasonableness of rate
expressions for reactions on surfaces. Eqn
(9.1a)
as we written implies that
Eqn (9.2)
is valid,
for which we will call the Langmuir adsorption rate.
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