Chemistry Reference
In-Depth Information
There is an important difference between the distributions calculated for equi-
librium, bifunctional step-growth polymerization in Chapter 7 and for the free-
radical polymerizations with termination by disproportionation or chain transfer
that are being considered here. The distribution functions in the step-growth case
apply to the whole reaction mixture; in the free-radical polymerization this distri-
bution describes only the polymer which has been formed. There is obviously a
strong parallel between the probability
S
of this section and the extent of reaction
p
used in the step-growth calculations in Chapter 7. Many authors use the same sym-
bol for both parameters. Different notations are used here, however, for clarity.
When termination occurs by combination as well as disproportionation, the
initial instantaneous distribution of molecular weights is given by
[18,19]
:
2
S
i
2
1
3
S
i
2
2
ω
i
5
F
i
ð
1
2
SÞ
1
ð
1
2
AÞi ði
2
1
Þð
1
2
SÞ
=
2
(8-109)
where
F
is the fraction of product formed by chain disproportionation and/or
transfer and
C
I
½
I
1
C
M
½
M
1
C
½
TH
1
2
k
td
R
p
=
k
p
2
½
M
A
5
(8-110)
2
C
I
½
I
C
M
½
M
1
C
½
TH
1
2
ð
k
tc
1
k
td
Þ
R
p
=
k
p
2
½
M
Equation (8-109)
reduces to
Eq. (8-105)
when
k
tc
5
0(
F
1) and to
Eq. (8-
5
111)
when
k
td
5
0 and transfer is negligible (
A
0):
5
1
2
i
3
S
i
2
2
ω
i
5
ð
i
2
1
Þð
1
2
S
Þ
(8-111)
In the latter case
DP
n
5
2
=ð
1
S
Þ
(8-112)
2
DP
w
5
ð
2
S
Þ=ð
1
S
Þ
(8-113)
1
2
and
1
2
ð
DP
w
=
DP
n
5
S
Þ
2
1
(8-114)
The ratio in
Eq. (8-114)
has a limiting value of 1.5 at high polymer molecular
weights when
S
approaches 1. This is narrower than the instantaneous distribution
produced in the absence of termination by coupling.
8.14.2
High-Conversion Polymerization
Molecular weight distributions in high-conversion polymerizations are not nearly
as predictable as those in low-conversion reactions, and they will vary with the
particular monomer and polymerization conditions.
A number of factors combine to make high conversion molecular weight dis-
tributions broader than those calculated in
Section 8.14.1
. Since autoacceleration
results from a reduced termination rate, it is always accompanied by an increase
