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get around the latter problem by assigning to the hydrogen electrode
under standard conditions a potential contribution of 0.0000 V. The
choice of this electrode and this assignment of potential are arbitrary,
but, once accepted, they permit other electrode potentials to be
evaluated relative to the standard. A similar procedure is followed for
the Q and e values. The reference monomer is chosen to be styrene and the
parameters are assigned the following values: Qsty = 1.0 and esty = -0.8.
In their original work Price and Alfrey assigned styrene an e value of-
1.0, but this was revised to the present value, which gives better
agreement with experimental reactivity ratios.
This last statement shows that expressing Q and e values relative to
the values for styrene is not identical to the procedure for electrode
potentials. In the latter, cell potentials are calculated correctly from
electrode potentials, regardless of the value assigned to the reference.
The Price-Alfrey system is only semiquantitative; values are assigned
which give the best average fit to the largest number of monomers. This
is accomplished more effectively by assigning styrene an e value of -0.8.
In this respect the Q-e values are like bond dissociation energies in
which the properties of a variety of different compounds are considered
to find the strength of an "average" bond. Both bond energies and Q-e
values fall short of expectations when specific effects are present which
separate a particular system from the "average."
Table 7.4 lists the Q and e values for an assortment of common
monomers. The extremes in the column of e values in Table 7.4-which are
listed in order-quantify the range of donor-acceptor properties which is
used as the basis for ranking in Fig. 7.2. The Q values perform a similar
ranking with respect to resonance effects. The eight different Q-e
combinations in Table 7.4 allow the estimation of Ã! and r2 values for 28
different copolymers. Of course, in these systems Q and e values were
assigned to give the best fit to r values which had already been
measured. As an illustration of the predictive values of the Q-e scheme,
consider the following example:
The Price-Alfrey Equation
Table 7.4 Values of the Price-Alfrey Q and e Values for a Few Common
Monomer Q e
Acrylonitrile 0.60 1.20
Methyl vinyl ketone 1.0 0.7
Methyl acrylate 0.42 0.60
Methyl methacrylate 0.74 0.40
Vinyl chloride 0.044 0.20
Vinyl acetate 0.026 -0.22
Styrene (standard) 1.0 -0.8
Butadiene 2.39 -1.05
Source: L. J. Young in Ref. 4.
Reactivity ratios for the TV-vinylphthalimide (molecule 1)-styrene
(molecule 2) system were measured, and foundt to be r! = 0.075 and r2
=8.3. Use these values to estimate values of Q and e for jV-
vinylphthalimide; then estimate the parameters rj and r2 for system in
which molecule 2 is vinyl acetate.
Since styrene is used as the standard in the Price-Alfrey system, Q2
=1.0 and e2 = -0.8. Use these values and the experimental rj and r2
values for the styrene-jV-vinylphthalimide system to evaluate Qj and ej:
Using Eq. (7.28), we have rir2 = e-(ei"e2)2 = 0.075(8.3) = 0.623, In
0.623 =-[el - (-0.8)] 2, and ej + 0.8 = ±0.688. The phthalimide
substituent is expected to be more electronegative than phenyl, so we
choose the negative root; therefore ej = -0.688 - 0.8 = -1.49. Using Eq.
(7.26), we have rj = (Qi/Q2) e-ei(ei-e2),
0.075 = (Qi/1) e_(_1-49)(-°-688), Qj = 0.21. Next we let vinyl acetate
be monomer 2 and obtain the Q and e values for this monomer from Table
7.4: Q2 = 0.026 and e2 = -0.22. Using the Q and e values for TV-
vinylphthalimide calculated above, we find from Eq. (7.26), rj = (Qi/Q2)
e-ei(ei-e2) = (0.21/0.026) å-Ñ-1.49)1-149-Ñ-î.22)] = l .22, and, from Eq.
(7.27), r2 = (Q2/Qi) e-e2(e2- ei) = (0.026/0.21) e-^-0-22)!-0-22-^1-49)!
= 0.16. The experimental values of the reactivity ratios in this system
are rj = 2.4 and r2 = 0.07. Working backward from these data gives Qj =
0.50 and ej = -1.56 for TV-vinylphthalimide.
This example also illustrates that "best-fit" values of Q and e are not
t Data from Ref. 4.
Polymers with Microstructure
7.6 A Closer Look at Microstructure
In Sec. 7.3 we noted that variations in the xxx2 product led to
differences in the microstructure of the polymer, even when the overall
composition of two compared systems is the same. Structures [I]-[III] are
examples of this situation. In this section we shall take a closer look
at this variation, using the approach which is best suited for this kind
of detail: statistics.
Suppose we define as p^ the probability that a unit of type i is
followed in the polymer by a unit of type j, where both i and j can be
either 1 or 2. Since an i unit must be followed by either an i or a j,