Biomedical Engineering Reference
In-Depth Information
where K j is the adsorption isotherm constant for species j for all layers above the first one
layer, c is ratio of the adsorption isotherm constant of the first layer to that of layers above
K 1j
K j ;
c ¼
(9.80)
and
X
N S
b ¼
K j C j
(9.81)
j ¼
1
The total number of species j molecules adsorbed is given by
i
1
N
n js;N ¼ n s1 P
1 q ij ¼ n s1 c P
N
N
b
b
1 K j C j
1
ð
1
cÞb cb
1
(9.82)
N
1
b
N
b Nb
N
1
½
1
þ Nð
1
bÞb
1
¼ n s1 c
1 K j C j ¼ n s1 c
K j C j
1
1
ð
1
cÞb cb
ð
1
bÞ½
1
ð
1
cÞb cb
which is the most general adsorption isotherm expression (valid for multilayer adsorption of
multispecies mixture on surfaces).
LHHW kinetics is derived from Langmuir adsorption isotherm. Table 9.3 shows some
examples of rates with different rate-controlling steps. The terms in the denominator of the
rate can tell the type of reaction and/or controlling step. If the concentration of one species
did not appear in the denominator, 1) either the rate-controlling step is the adsorption e
desorption of the species or 2) the particular species is not adsorbed on the surface. If square
root of a concentration appears, the adsorption of that particular species is dissociative. If an
adsorption e desorption step is rate controlling, the concentration of the particular species
does not appear in the denominator, however, its virtual concentration (equilibrium concen-
tration with other species) appear in its place. Rate control step has two active sites involved if
1
1
2 (same type of active sites) or
(two types of
ð
1
þ K A C A þ.Þð
1
þ K B C B þ.Þ
ð
1
þ K A C A þ.Þ
active sites) appears.
In kinetic analysis, PSSH (on all the intermediates) is more general and a better approxi-
mation than equilibrium step assumptions. PSSH can be traced back to the overall effect of all
the fluxes on the reaction network or pathway. However, the final rate expressions are quite
similar when the rate constants are lumped together. Therefore, there is no difference on the
quality of fit to experimental data one may obtain. The difference between the actual (or full
solution) and either one of the approximation methods (PSSH or LHHW) is noticeable if the
initial time period (at the onset of adsorption and reaction) is considered. After the onset or
the start of reaction, the difference between the approximation and full solutions is negligible.
Therefore, equilibrium step (or the opposite, rate-limiting step) assumptions are well suited
for kinetic analyses or simplification to complex problems.
The rate expression can also appear to be of power-law form if Freundlich isotherm
were used or Temkin approximation were applied to UniLan isotherms. The accuracy
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