# Polymer Chemistry. The Basic Concepts - Himenz P.C.

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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

experimental investigation.

The Price-Alfrey Equation

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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

polymerization.

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

Eqs. (7.26)

and (7.27) is zero and rj = Qi/Q2 and r2 = Q2/Qi . Comparing

these limits

with Eqs. (7.23) and (7.24) leads to the result

(7.25)

(7.26)

and

(7.27)

Finally, Eqs. (7.26) and (7.27) can be combined to give

rjr2 = exp [(e1 - e2)(e2 -e^)] = exp [-(ej - e2)2]

(7.28)

(7.29)

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

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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

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