Biomedical Engineering Reference
In-Depth Information
Thus, the extraction is of first order with respect to the extractable monomer units. At start,
the degree of polymerization is high, resulting in a lower rate constant. Toward the end of
extraction, the degree of polymerization is low, resulting in a higher rate constant.
In the liquid phase, the formation rate of monomers is given by
2
X
N
X
N
k
E
n
q
n
ð
r
1
¼
k
H
C
n
þ
2k
H
þ k
D
ÞC
1
(9.189)
n¼
1
n¼
1
where
k
D
is the rate constant for the decomposition of monomers, reaction
(9.165)
. As shown
in
6.6, the composition in the liquid phase may be described by two pseudo-components to
lump all the oligomers. Let
x
X
N
C
Si
¼
iC
i
(9.190)
i¼
1
X
N
C
S
¼
C
i
(9.191)
i¼
1
The lumped rates are given by
X
N
2
X
N
k
E
r
Si
¼
ir
i
¼
1
ðn þ
1
Þq
n
k
D
C
1
(9.192)
i¼
1
n¼
X
r
i
¼ k
H
ðC
Si
C
S
Þþk
E
X
N
N
r
S
¼
1
q
n
k
D
C
1
(9.193)
i¼
1
n¼
where
r
i
is the rate of formation of total number of monomer units in the solution (
C
i
) and
S
S
r
is the rate of formation of total number of molecules in monomer and oligomer forms in the
solution (
C
S
). Substitute
Eqns (9.191)
into
Eqn (9.189)
, we obtain
S
X
N
k
E
n
q
n
ð
r
1
¼
2k
H
C
S
þ
2k
H
þ k
D
ÞC
1
(9.194)
n¼
1
9.6. DECLI
NE OF SURFACE ACTIVITY: CATALYST DEAC
TIVATION
One particular aspect of solid catalysis that is not encountered in reactions that are not
catalytic is a progressive decrease in the activity of the surface with its time of utilization.
The reasons for this are numerous, but we will divide them into three general categories.
Poisoning:
loss of activity due to strong chemisorption of a chemical impurity on the active
sites of the surface, denying their access by reactant molecules. This should not be confused
with inhibition as expressed by adsorption terms in the denominator of LHHW rate
expressions.
Coking
or
fouling:
loss of activity, normally in reactions involving hydrocarbons or carbon-
based substrates, due to reactant or product degradation, producing a carbonaceous residue
on the surface blocking reactants from accessing the active centers on the catalyst surface.
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