Chemistry Reference
In-Depth Information
K
-
+
-
+
RM
j
L
i
RM
j
L
i
+
k
p
-
k
p
M
M
(11-16)
K
-
+
-
+
RM
j + 1
+
L
i
RM
j + 1
L
i
solvated free
ions
solvated
ion pairs
Here
k
p
and
k
p
are rate constants for ion pair and free ion propagation, respec-
tively, and
K
is the equilibrium constant for dissociation of ion pairs into solvated
free ions.
h
i
h
i
2
P
j
RM
j
P
j
RM
j
Li
"
½
K
h
i
5
h
i
5
(11-17)
P
j
RM
j
P
j
RM
j
Li
"
Li
"
==
==
5
½
P
j
RM
j
since [Li
"
] must
for electrical neutrality. If the polymer molecular
weight is high, the consumption of monomer in initiation reactions will be negli-
gible and the overall rate of reaction can be expressed as
"
#
"
#
M
dt
5
R
p
5
k
p
X
j
½
1
k
p
X
j
d
½
M
RM
j
RM
j
==
Li
"
½
(11-18)
2
Then, combining Eqs. (11-17) and (11-18),
"
#
"
#
1
=
2
k
p
X
j
k
p
K
1
=
2
X
j
R
p
½
RM
j
RM
j
Li
"
Li
"
==
==
(11-19)
5
1
M
½
P
j
RM
j
Li
"
can be set equal to the total initi-
ator concentration [RLi] so that
Eq. (11-19)
becomes
If there is little dissociation
==
k
p
K
1
=
2
½
R
p
k
p
1
(11-20)
5
½
M
½
RLi
1
=
2
RLi
A plot of the left-hand side of
Eq. (11-20)
against [RLi]
1/2
yields a straight line
with intercept
k
p
and slope
k
p
.
K
can be determined independently by measuring
the conductivity of solutions of low-molecular-weight living polymers and
k
p
can
therefore also be estimated
[1]
. Such experiments show that free ions are generally
present only in concentrations about 10
2
3
those of the corresponding ion pairs. The
free ions are, however, responsible for a significant proportion of the polymeriza-
tion, since
k
p
values are of the order of 10
4
10
5
liter/mol sec compared to
k
p
magnitudes 10
2
liter/mol sec which are of the same order as free radical
k
p
's.
Hydrocarbon Solvents
. Hydrocarbon solvents do not solvate the metal coun-
terions. The rate of polymerization depends directly on the monomer concentra-
tion as in the case of solvating media, but
the rate dependence on initiator
