Chemistry Reference
In-Depth Information
k
t
R
p
2
k
p
½
½
5
(8-86)
2
fk
d
M
from
Eq. (8-29)
for polymerizations initiated by thermal decomposition of an ini-
tiator. For such systems
Eq. (8-85)
becomes
1
DP
n
5
k
tc
R
p
k
p
½
2
k
tc
R
p
k
p
½
k
t
R
p
2
k
p
fk
d
½
C
M
1
C
I
(8-87)
2
1
2
1
3
M
M
M
R
p
can be varied by changing [M] and [I] and corresponding values of 1
=
DP
n
plot-
ted against
R
p
. The equation above is a quadratic in
R
p
, but the initial portion of the
plot at low
R
p
is linear with intercept
C
M
at zero
R
p
. The slope of this linear portion
gives
2
k
td
)
1/2
can be derived at known [M]
[6]
.
The technique descri
bed
relies implicitly on the assumption that termination
rates are independent of DP
n
. More recent work has shown that this is not strictly
true (see
Section 8.13
) and neglect of this effect may account for much of the
scatter in
C
M
values reported in the polymer literature.
2
from which
k
p
/k
tc
1
ð
k
tc
1
2
k
td
Þ=
k
p
½
M
8.8.3
Transfer to Solvent and Chain Transfer Agents
The chain transfer agent in some laboratory polymerizations is the solvent.
Industrial free-radical polymerizations are not normally run in solution, for eco-
nomic reasons, and the chain transfer agents in these reactions are ingredients that
are
add
ed deliberately to limit the molecular weight of the polymer. Although
R
p
and DP
n
are inextricably linked in ideal radical polymerizations, the use of transfer
agents
per
mits the independent adjustment of these two parameters as long as the
desired DP
n
is less than that for the corresponding transfer-free reaction
(Eq. 8-64)
.
To define a useful new symbol, consider a solvent
free-radical polymeriza-
tion. The number average degree of polymerization of the polymer made at any
instant in the absence of a transfer agent is given by
Eq. (8-77)
as
1
DP
n
5
k
tc
R
p
k
p
½
2
k
td
R
p
k
p
½
C
I
½
I
1
2
1
2
1
C
M
1
5
(8-77a)
½
M
M
M
ð
DP
n
Þ
0
where
DP
n
Þ
0
is the number average degree of polymerization produced in the
absence of any optional reactants like solvent or chain transfer agent. It depends
only on the nature and concentrations of monomer and initiator as well as the
reaction temperature.
There are a number of methods for measuring
C
(or
C
s
). The most readily
obvious procedure involves the insertion of
Eq. (8-77a) into (8-77)
to yield
1
ð
1
C
½
Ta
(8-77b)
DP
n
Þ
5
DP
n
Þ
0
1
ð
ð
½
M
Experimentally, the polymerization is carried out under conditions where the
rate of transfer to initiator is negligible (e.g., by using an azo initiator) and where
