Chemistry Reference
In-Depth Information
This extra monomer supplied is sufficient for equilibrium swelling of the particles [
298
]. As a result, the
rate of polymerization becomes zero order with respect to time.
When conversion reaches about 70%, all the remaining monomer is absorbed in the polymer
particles and there are no more monomer droplets left. At this point the reaction rate becomes first
order with respect to time.
The qualitative approach of Harkins was put on a quantitative basis by Smith and Ewart
[
314
-
316
]. Because 10
13
radicals are produced per second and can enter between 10
14
and
10
15
particles, Smith felt that a free radical can enter a particle once every 10-100 s. It can cause
the polymerization to occur for 10-100 s before another free radical would enter and terminate chain
growth [
317
]. A period of inactivity would follow that would last 10-100 s and then the process
would repeat itself. Such a “stop and go” mechanism implies that a particle contains a free radical
approximately half of the time. It can also be said that the average number of radicals per particle is
0.5. This is predicted on conditions that (a) the rate of chain transfer out of the particle is negligible
and (b) the rate of termination is very rapid compared with the rate of radical entry into the particle.
The kinetic relationships derived by Smith and Ewart for the system are as follows:
The rate of primary radical entering a particle
¼ r
i
¼ R
i
=N
Rate of polymerization
¼ R
P
¼ k
P
½
M
N=
2
Average degree of polymerization
¼
DP
¼ Nk
P
½
M
=R
i
where,
k
P
is the constant for propagation, [M] is the concentration of monomer,
N
is the number of
particles containing
n
radicals (~0.5) and the expression for the number of particles formed:
0
:
4
0
:
6
N ¼ Kðr=mÞ
ðA
S
SÞ
where,
m
is the volume increase of the particles,
A
S
is the area occupied by one emulsifier molecule.
S
is the amount of emulsifier present.
0.37 (based on the assumption that the micelles
and polymer particles compete for free radicals in proportion to their respective total surface areas).
K
is a constant
¼
K
can also be equal to 0.53 (based on the assumption that the primary radicals enter only micelles, as
long as there remain micelles in the reaction mixture).
r
is the rate of entry into the particles. The
kinetic chain length can be written as:
RM
=
u ¼ k
p
N
p
½
M
=
2d
½
d
t
The Smith-Ewart mechanism does not take into account any polymerization in the aqueous phase.
This may be true for monomers that are quite insoluble in water, such as styrene, but appears unlikely
for more hydrophilic ones such as methyl methacrylate or vinyl acetate. In addition, it was calculated
by Flory that there is insufficient time for a typical cation-radical (such as a sulfate ion radical) to add
to a dissolved molecule of monomer such as styrene before it becomes captured by a micelle [
317
].
This was argued against, however, on the ground that Flory's calculations fail to consider the
potential energy barrier at the micelle surfaces from the electrical double layer. This barrier would
reduce the rate of diffusion of the radical-ions into the micelles [
316
].
Considerably different mechanisms were proposed by several groups [
317
,
318
]. They are based
on a concept that most polymerizations must take place at the surface of the particles or in their outer
“shell” and not within the particles. It is claimed that the interiors of the particles are too viscous for
free radicals to diffuse inside at a sufficiently fast rate. Two different mechanisms were proposed to
explain why polymerization takes place preferentially in the shell layer. One of them suggests that the
