Chemistry Reference
In-Depth Information
4.2 Kinetics of Ionic Chain-Growth Polymerization
The kinetic picture of
cationic chain polymerization
varies considerably. Much depends upon the
mode of termination in any particular system. A general scheme for initiation, propagation, and
termination is presented below [
1
,
2
]. By representing the coinitiator as A, the initiator as RH, and the
monomer as M, we can write:
Cationic Initiation Process
Rate of Initiation
R
I
= K k
i
[A][RH][M]
K
A + RH
H
(AR)
k
i
(AR)
HM
(AR)
H
+ M
Rate of Propagation:
Cationic Propagation Process:
k
p
R
P
= k
P
[HM
+
(AR) ][M]
+ M
HM
n
HM
n
M
(AR)
(AR)
Cationic Termination:
By Tra
ns
fer:
Rate of Termination
= k
t
[HM
+
R
t
(AR) ]
k
tr
M
HM
n
M
(AR)
+
M
M
n+1
+
H
M
(AR)
By Spont
a
neous T
er
mination:
HM
n
M
k
ts
(AR)
M
n+1
+ H
(AR)
By Rearrangement of the Kinetic Chain:
HM
n
M
HM
n
MAR
(AR)
In the above expressions, [HM
+
——(AR)
] represents the total concentration of all the propagating
ion-pairs; and
is the equilibrium constant for the formation of initiating cations. When a steady state
exists, the rates of initiation and termination are equal to each other:
K
2
HM
þ
...
::ð
AR)
¼Kk
i
½
½
A][RH][M
=k
t
The rate of propagation can be written as:
2
R
P
¼ Kk
i
k
t
½
A
½
RH
½
M
=k
t
The number average degree of polymerization is equal to:
¼
R
p
R
t
¼
k
P
½
M
DP
k
t
During the reaction terminations can occur by transferring to a monomer or to a chain transferring
agent S. Termination can also occur by spontaneous termination or by combination with the
counterion. If S is relatively small the number of propagating chains will remain unchanged. The
degree of polymerization will then be decreased by the chain-breaking reactions. The number average
degree of polymerization becomes:
R
p
R
t
þ R
ts
þ R
tr
;
M
þ R
tr
;
S
DP
¼
The rates of the two transfer reactions, to a monomer or to a transferring agent (S), as well as
spontaneous terminations can be written as:
