Page 256 - Academic Press Encyclopedia of Physical Science and Technology 3rd Polymer

P1: GNH/GRI P2: GTV Final pages
Encyclopedia of Physical Science and Technology EN012B-596 July 27, 2001 18:18

Polymers, Synthesis 765

can be easily polymerized to 1005% conversion. However, shown in Table VII in terms of the radical concentration.
the ceiling temperature concept also has ramifications On substituting this value into the rate expression, one
for polymer degradation. For example, if polymethyl obtains a final rate expression that is quite useful. Basi-
methacrylate (PMMA) is exposed to free radicals at cally, it states that the rate of polymerization will depend
high temperatures, one can basically unzip the polymer on several constants, but that it will also be proportional
chain and regenerate nearly quantitatively the monomeric to the first power of the monomer concentration and to
species. The monomer α-methylstyrene has been widely the square root of the initiator concentration. Thus, as
studied, and it is well known that it is very difficult to one doubles the initiator concentration, the expected rated
polymerize this structure to high molecular weight unless should increase only by a factor of ∼1.4. If one plots the
one uses rather low temperatures. It is possible to use an rate of polymerization versus the log of the initiator con-
◦
anionic mechanism at −78 C and completely polymerize centration for a variety of monomers and initiators such
α-methylstyrene. as methyl methacrylate and AIBN or styrene and ben-
zyl peroxide, for example, one observes slopes equal to
1/2. An additional term in the rate of expression is f ,
2. Kinetics of Free-Radical Polymerization
the fraction efficiency of initiation: For 100% efficiency,
The propagation or the growth step involves the rapid ad- f has a value of 1.0. This is never achieved, although in
dition of additional monomer to the initiated species. If some cases, particularly with some azo initiators, many
this grows with a rate constant k p , where R now repre- people have reported values as high as 0.9. More recent
sents a long chain, one can define the propagation reaction work has tended to indicate that this value may be rather
by the equation shown. An important assumption here is high.
that all the chains have the same reactivity. Another rea- A fourth process in polymerization kinetics is called the
sonable assumption is that the initiation step involves the chain transfer reaction. This reaction is very important in a
reaction of only one monomer molecule and the propaga- variety of cases, as outlined in Scheme 15. Here, we depict
tion involves the addition of many monomer molecules. a growing chain interacting with a small molecule XY
The rate of the polymerization can be designated R p and in such a way that a portion of the small molecule can
may be shown to be basically equivalent to the rate of terminate the active radical chain and at the same time
propagation. The rate of propagation or polymerization, produce a new radical Y. Basically, this step regulates
then, will be given by the product of the rate constant k p , the molecular weight. It does not necessarily decrease
the monomer concentration, and the concentration of the the rate of polymerization if one assumes that the
growing species. Free radicals involve unpaired electrons, new radical Y will again reinitiate more monomer and
and hence their lifetime is rather short (e.g., a fraction
of a second). Therefore, the growth step is basically at
some stage quickly terminated, usually by one of the two
schemes shown in Scheme 16. Some typical rate constants
are summarized in Table VII. Moreover, it is easy to see
that the termination rate constant is much faster than that
of either of the other two steps. This allows one to make
a steady-state assumption in which one can set the rate of
initiation equal to the rate of termination. An advantage of
doing this is that it becomes possible to solve the equation

TABLE VII Typical Rate Constants
k I Low rate constant
3
2
k p = 10 –10 liters/mole sec
∼
9
7
∼
k T = 10 –10 liters/mole sec
Hence, a steady state of free radicals, e.g.,
R I = R T
2
2k d [I] = 2k t [M ]
1/2

k d
[M] = [I] (difficult to measure)
k T
1/2

k d
R p = k p [I] [M]
k T
SCHEME 15 Chain transfer.