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In the next section we shall consider an attempt to combine both
resonance and polarity effects.
7.5 The Price-Alfrey Equation
In the last two sections we have considered-separately-the effects of
resonance and polarity on copolymerization. While these concepts provide
some insights into various observations, it is artificial to consider
either one of them operating exclusively. In fact, resonance and polarity
features are both active in most molecules. A method for merging their
contributions is clearly desirable.
Another troublesome aspect of the reactivity ratios is the fact that
they must be determined and reported as a pair. It would clearly simplify
things if it were possible to specify one or two general parameters for
each monomer which would correctly represent its contribution to all
reactivity ratios. Combined with the analogous parameters for its
comonomer, the values rj and r2 could then be evaluated. This situation
parallels the standard potential of electrochemical cells which we are
able to describe as the sum of potential contributions from each of the
electrodes that comprise the cell. With x possible electrodes, there are
x(x - l)/2 possible electrode combinations. If x = 50, there are 1225
possible cells, but these can be described by only 50 electrode
potentials. A dramatic data reduction is accomplished by this device.
Precisely the same proliferation of combinations exists for monomer
combinations. It would simplify things if a method were available for
data reduction such as that used in electrochemistry.
An approach to copolymerization has been advanced by Price and Alfrey
which attempts to both combine resonance and polarity considerations and
accomplish the data reduction strategy of the last paragraph. It should
be conceded at the outset that the Price-Alfrey method is only
semiquantitative in its success. Its greatest usefulness is probably in
providing some orientation to a new system before launching an
The Price-Alfrey Equation
The Price-Alfrey approach begins by defining three parameters-P, Q,
and e- for each of the comonomers in a reaction system. We shall see
presently that the parameter P is rapidly eliminated from the theory. As
a result, the Price-Alfrey system is also called the Q-e scheme for со
For the reaction of radical i with monomer j, Price and Alfrey
assume that the cross-propagation rate constant can be written as
In this equation P and Q are parameters that describe the reactivity of
the radical and monomer of the designated species, and the values of e
measure the polarity of the two components without distinguishing between
monomer and radical.
From Eqs. (7.13) and (7.14), the reactivity ratios can be written
That these expressions do combine resonance and polarity effects can
be seen as follows:
1. If molecules 1 and 2 differ widely in polarity, then the
exponent in Eq.
(7.28) will be large and the exponential will be small. We saw in
Sec. 7.3 that alternation is favored by large differences in polarity and
is described by small values of rjr2.
2. If molecules 1 and 2 are identical in polarity, then - e2 in
and (7.27) is zero and rj = Qi/Q2 and r2 = Q2/Qi . Comparing
with Eqs. (7.23) and (7.24) leads to the result
Finally, Eqs. (7.26) and (7.27) can be combined to give
rjr2 = exp [(e1 - e2)(e2 -e^)] = exp [-(ej - e2)2]
3. This last identification makes the Q's strictly a matter of
resonance, whereas the general concept of "reactivity" also includes
steric effects. The effects
Polymers with Microstructure
of polarity are explicitly handled by the e's and are not therefore
lumped together with these other concepts.
4. There are no inherent restrictions on Q and e; hence the individual
reactivity ratios can take on a wide range of values.
An advantage of the Price-Alfrey system is that each monomer is
characterized by its own values for Q and e, which are assumed to be
independent of the nature of the comonomer. Thus if Q and e values were
available for all monomers, then these could be combined at will to
generate the parameters rj and r2 which define copolymer composition and
microstructure. This feature makes data reduction and predictions about
new systems feasible. The only problem is that Q and e cannot be
evaluated independently for a particular monomer any more than the
potential of a single electrode can be measured. In electrochemistry we