Chemistry Reference
In-Depth Information
Table 3.1
Illustration of a free radical polymerization
1. Initiation
2. Propagation
3. Termination
a. By combination
b. By disproportionation
c. By transfer
respectively. S stands for the chain transferring agent.
R
I
denotes the decomposition rate of the
initiator and
R
P
the rate of polymerization. The rate constants, for the initiator decomposition is
k
d
, for
the initiation reaction is
k
I
, for the propagation
k
P
, and for the termination is
k
T
. The above is based on
an assumption that
k
I
are independent of the sizes of the radicals. This is supported by
experimental evidence that shows that radical reactivity is not affected by the size, when the chain
length exceeds dimer or trimer dimensions [
3
]. The reactions involved in a typical free-radical
polymerization process, as stated above, are illustrated in Table
3.1
The equation for the rate of propagation, shown above in the kinetic scheme, contains the term [M]. It
designates radical concentration. This quantity is hard to determine quantitatively because its concen-
tration is usually very low. A
steady state
assumption is, therefore, made to simplify the calculations. It is
assumed that while the radical concentration increases at the very start of the reaction, it reaches a
constant value almost instantly. This value is maintained from then on, and the rate of change of free-
radical concentration is assumed to quickly become and remain zero during the polymerization. At
steady state, the rates of initiation and termination are equal, or
k
P
and
R
i
¼ R
t
¼
2
k
i
[M] [
4
]. This assumption
makes it possible to solve for [M] and can then be expressed as:
1
=
2
½
M
¼ðk
d
½
I
=k
t
Þ
The rate of propagation is
1
=
2
R
P
¼ k
P
½
ðk
d
½
=k
t
Þ
M
I
The rate of propagation is approximately equal to the total rate of polymerization. The total rate
can be designated as
R
pol
. Because all but one molecule are converted during the step of propagation,
we can write:
h
i
ð
R
P
¼ k
P
X
n
RM
n
M
Þ
This rate of propagation applies if the kinetic chain length is large and if the transfer to monomer is
not very efficient. The rate of monomer disappearance can be expressed as
