ABSTRACT
Consider a random copolymer obtained by free radical copolymerization. The statistics of copolymerization and dyad probabilities can be calculated as follows. The propagation reactions can be of four types:
M M M M
M M M M
M M M M
+ →
+ →
+ → 1
* *M M M M k
+ →
(11.1)
The rate of irreversible reactions can be written as
d M
dt k M M k M M
d M
dt
[ ] = − [ ][ ]− [ ][ ]
[ ] = −
k M M k M M22 2 2 12 2 1[ ][ ]− [ ][ ]* * (11.2)
The free radical species formed may be assumed to be highly reactive and can be assumed to be consumed as rapidly as they are formed. This is referred to as the quasi-steady-state assumption (QSSA). Thus:
d M
dt k M M k M M
d M
d
. [ ]
= − [ ][ ]− [ ][ ] [ ] t
k M M k M M= − [ ][ ]− [ ][ ]22 2 2 21 2 1* * . (11.3)
d M M
dt k M M
d M M
dt k M M
. [ ]
= [ ][ ] [ ]
= [ ] 2 1 2
.
