Chemistry Reference
In-Depth Information
from terminating by their low mobilities. Bulk polymerization of vinyl chloride
provides an example of this.
Autoacceleration is also known as the
gel effect
or as the
Tromsdorff effect
or
Norrish
Smith effect
after pioneering workers in this field.
Note in the bulk polymerization example in
Fig. 8.3
that
R
p
increases rapidly
at low conversions and then effectively ceases before all the monomer in the
system has been consumed. This occurs when the polymerization mixture
becomes glassy and even the propagation step becomes subject to diffusion con-
trol. Most monomers will solvate and soften their own polymers so that the sys-
tem does not become rigid until a high proportion of the monomer has been
converted.
8.14
Molecular Weight Distribution
8.14.1
Low-Conversion Polymerization
It is convenient to focus separately on the cases in which termination is entirely
by disproportionation or by combination. When both modes of termination occur,
the size distribution of the polymer that is formed is described by a weighted
average of the distribution functions for the individual modes.
We assume here that the concentrations of monomer and initiator remain sen-
sibly constant during the polymerization and that any dependence of termination
rate constants on macroradical size and concentration or autoacceleration effects
can be neglected. This means that the molecular weight distributions to be derived
can be expected to apply to low-conversion polymers. Commercial macromole-
cules, whose polymerizations are often finished at high conversions, may have
distributions that differ from those calculated here.
Section 8.14.2
discusses the
size distributions of such polymers.
A given monomer-ended radical may add monomer or undergo chain transfer
or termination. The probability
S
that it will grow by monomer addition is
R
p
S
5
(8-99)
R
p
1
R
tr
1
R
t
Now
M
R
p
5
k
p
½
½
M
(8-13a)
M
1
M
½
M
R
tr
5
C
I
k
p
½
I
½
C
M
k
p
½
M
1
Ck
p
½
TH
½
(8-100)
from Eqs.
(8-76) and (8-77)
. Also,
M
2
R
t
5
ð
k
tc
1
k
td
½
Þ
(8-101)
from
Eqs. (8-20) and (8-23)
. Insertion of the last three relations into
Eq. (8-100)
and simplification give
2
