Chemistry Reference
In-Depth Information
Þ
½
HM
þ
-----(AR
R
tr
;
M
¼ k
tr
;
M
½
M
Þ
½
HM
þ
-----
R
tr
;
S
¼ k
tr
;
S
½
ð
AR
S
Þ
HM
þ
-----
R
ts
¼ k
ts
½
ð
AR
The number average degree of polymerization is then:
DP
¼ k
p
½
M
=ðk
t
þ k
tr
;
M
þ k
tr
;
S
½
S
þk
ts
Þ
The above can be rearranged to be written as follows:
=
¼ k
t
=k
p
½
þk
ts
=k
p
½
þ
C
M
þ
C
S
½
=½
1
DP
M
M
S
M
where C
M
and C
S
are the chain transferring constants for the monomer, and S is the chain transferring
agent. Here C
M
¼ k
tr,M
/
K
p
and C
S
¼ k
tr,S
/
k
p
. When a chain transferring agent is present and chain
growth is terminated,
2
R
p
¼ Kk
i
Kk
p
½
A
½
RH
½
M
=ðk
t
þ k
tr
;
S
½
S
Þ
The validity of the steady-state assumption in many cationic polymerizations may be questioned,
because many reactions occur at such high rates that a steady state is not achieved. Nevertheless, the
above equations were shown to be generally followed [
3
,
4
].
The kinetic picture of
also depends mostly upon the specific
reaction. For those that are initiated by metal amides in liquid ammonia the rate of initiation can be
shown to be as follows:
anionic chain polymerization
Anionic Initiation Process
Rate of Initiation
R
i
= k
i
[H
2
N: ][M]
K
KNH
2
K + NH
2
= Kk
i
[M][KNH
2
] [K
+
]
+ M
k
i
R
i
NH
2
H
2
N-M
Rate of Proagation
Anionic Propagation Process
H N-M
n
R
p
=
k
p
[M ][M]
+M
H
2
N-M n -M
where [M
] represents the total concentration of propagating anions. If there is a termination reaction
and it takes place by transfer to a solvent, the rate of transfer can be written:
M
½
R
tr
¼ K
tr
;
S
½
NH
3
When steady state conditions exist,
2
R
P
¼
Kk
i
k
p
½
M
½
KNH
2
K
þ
½
k
tr
;
S
½
NH
3
If the quantities of potassium and amide ions are equal, which is the normal situation, then a
somewhat different expression can be written:
1
=
2
1
=
2
R
i
¼ k
i
K
½
M
½
KNH
2
2
1
=
2
1
=
2
R
p
¼
k
i
K
k
p
½
M
½
KNH
2
k
tr
;
S
½
NH
3
In non-terminating or “living” polymerizations, the rate of propagation can be written as:
M
½
R
P
¼ k
p
½
M
