Q and e values

This system was developed to take account of the tendency of monomers to form alternating copolymers, llie Q and e values can be taken to represent the relative rates of reaction of various monomers to each type of fiee radical after correction is made for differences in general monomer reactivity. 

The reciprocal of the monomer reactivity ratio l/r can be considered as the monomer reactivity which relates the relative reactivity of like and unlike monomers with the propagating species. 

The structure of a monomer has a profound effect on its reactivity, e.g. a phenyl group adjacent to a double bond increases the reactivity more than that for a methyl group. This is due to the greater degree of resonance stabilisation obtained. The contribution made by the structure and steric factors, to the overall reactivity of the monomer, is represented by Pi and Qi. 

The polarity of the double bond also influences the monomer reactivity and is represented by ei and Cj. 

El and E2 represent charges on Mi and M2 D is the di-electric constant K is the Boltzman constant 

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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 ri and 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 ... 

Table 7.4 Values of the Price-Alfrey Q and e Values for a Few Common Monomers...

Use the Q and e values listed in Table 7.4 for each of the comonomers to give five independent estimates of Q and e for acrylonitrile. Compare the average of these four with the values given for acrylonitrile in Table 7.4. 

The Q and e values of VP are 0.088 and —1.62, respectively (125). This indicates resonance interaction of the double bond of the vinyl group with the electrons of the lactam nitrogen, whence the electronegative nature. With high e+ monomers such as maleic anhydride, VP forms alternating copolymers, much as expected (126). With other monomers between these Q and e extremes a wide variety of possibiHties exist. Table 14 Hsts reactivity ratios for important comonomers. 

Regrettably, Q and e values are imprecise and tend to vary with the reactivity ratios used in their calculation (115). An attempt has been made to improve the Price-Alfrey equation by the assignment of different values of e to the monomer and to the radical derived from it (116). Schwan and Price (117) have reexamined the Price-Alfrey equation, and they write it in the form ... 

The order of radical reactivities can be obtained by multiplying the I /r values by the appropriate propagation rate constants for homopolymerization (fen). This yields the values of fei2 for the reactions of various radical-monomer combinations (Table 6-4). The fei2 values in any vertical column in Table 6-4 give the order or monomer reactivities—as was the case for the data in Table 6-3. The data in any horizontal row give the order of radical reactivities toward a reference monomer. (The Q and e values in the last two vertical columns should be ignored at this point they will be considered in Sec. 6-3b-4.)... 

Greenley, R. Z., Q and e Values for Free Radical Copolymerizations of Vinyl Monomers and Telogens, pp. 267-274 in Chap. II in Polymer Elandbook, 3rd ed., J. Brandrup and E. H. Immergut, eds., Wiley-Interscience, New York, 1989b. 

Using the Q and e values in Table 6-7, calculate the monomer reactivity ratios for the comonomer pairs styrene-1,3-butadiene and styrene-methyl methacrylate. Compare the results with the r and rx values in Table 6.2. 

On this basis, values of Q and e can be calculated for each monomer, so long as two arbitrary reference values are assumed. For this purpose Price took the values for styrene as Q = 1.0 and e = -0.8. Q and e values can then be obtained for all monomers that are copolymerizable with styrene. These monomers in their turn can serve as reference compounds for further determinations with other monomers that do not copolymerize with styrene. One of the main advantages of the so-called Q,e scheme is that the data can be presented in the form of a diagram instead of very complex tables of reactivity ratios. 

Obviously the precision of this procedure is not very great, since the assumptions underlying the calculations of Q and e values can be regarded at best as semiquantitative. However, it has been shown that when the reactivity ratios are back-calculated from the Q,e values, quite good agreement is obtained with the experimental values, so that it is possible to make useful predictions of reactivity... 

VEs can also copolymerize by free-radical initiation with a variety of comonomers. According to the Q and e values of 0.023 and —1.77 (isobutyl vinyl ether), VEs are expected to form ideal copolymers with monomers of similar and e values or alternating copolymers with monomers such as maleic anhydride (MAN) that have high values of opposite sign (Q = 0.23 e = +2.25). 

The most significant observation in the radical copolymerization of methyl methacrylate with vinylidene chloride in the presence of zinc chloride is the increase in the Q and e values of methyl methacrylate, the increase in the rx value of methyl methacrylate, and the decrease in the r2 value of vinylidene chloride (30). Although it has been proposed that these results arise from the increased reactivity of the complexed methyl methacrylate monomer, a more likely explanation is the homopolymerization of a methyl methacrylate-complexed methyl methacrylate complex accompanied by the copolymerization of methyl methacrylate with vinylidene chloride. 

The application of NMR spectroscopy data to estimate the reactivity ratios is regarded to be very promising [272]. The Q and e values of the Alfrey-Price scheme may be immediately calculated analyzing the shifts of the corresponding bands in carbon-NMR spectra Such data obtained for more than fifty pairs of monomers are tabulated in Ref. [273]. A quite different method based on the application of the trivial expressions ... 

The Q and e scheme has been the subject of considerable attention. It promised new possibilities of monomer classification, calculation of copolymerization parameters from known values of Q and and predictions about the behaviour of copolymerizing systems. However, to such ends the Q and e values should be known, and they are not directly measurable. In order to calculate them from copolymerization parameters, the easily copolymerized styrene has been selected as the reference monomer, with the assigned values Q = 1 and e = -0.8. Data on the Q and e factors of practically all copolymerizing monomers are now available (see Tables 3 and 3A) some kinetic significance is ascribed to monomer position in the Q — e plane (see Fig. 21). Monomers with a high Q value are expected to form poorly reactive radicals with a low tendency to add further monomer units monomers with widely differing e values usually copolymerize easily, etc. 

For a growing radical chain that has monomer 1 at its radical end, its rate constant for combination with monomer 1 is designated kn and with monomer 2, k1T Similarly, for a chain with monomer 2 at its growing end, the rate constant for combination with monomer 2 is k22 and with monomer 1, k2V The reactivity7 ratios may be calculated from Price-Alfrey Q and e values, which are given in Table 8 for the more important acrylic esters (87). The sequence distributions of numerous acrylic copolymers have been determined experimentally utilizing linn techniques (88,89). Several review articles discuss copolymerization (84,85). 

These equations show the individual steps connected with the propagation reaction, i.e. the sums in the numerator or denominator are the sums of all possible propagation reactions in which a given monomer adds to the growing chains ending in every monomer unit. The Q and e values were obtained from binary copolymerization studies. The calculated and experimental results are compared in Table 4. 

The value of KgJKg can be determined also from Q and e values (36). The basic relationship (11) of the Q—e scheme (76) yields... 

Reactivity of itaconic add in copolymerization is dependent upon pH and degrees of ionization of the add. Acid reactivity has been studied most carefully in acrylonitrile copolymerization 33, 37). Under acidic conditions an increase in itaconic concentration greatly decreases the polymerization rate, while at pH s of 7—9.8 moderate increases of itaconate do not reduce the rates so strongly. Monomer reactivity ratios and Q and e values have been calculated for the various states of ionization of the acid as reported in Table 5. As the pH rises, drops from 1.57 to 0.1 suggesting, as stated earlier, that the dianion undergoes little homopolymerization. The change in is less than 2-fold which indicates appreciable copolymerization of the dianion. The much greater decrease... 

These results suggest that of the two copolymerization parameters, and e, only the e values are aflFected appreciably by an increase in pressure. Calculations have been made obtaining relative Q and e values which bear out this thesis. The decreasing radical selectivity found in these experiments implies an increased radical reactivity. This offers further support to Walling s suggestion that the ally acetate radical increases in reactivity with increasing pressure. 

These are simply the equations of Alfrey and Price (1 j, which relate monomer reactivity ratios to Q and e values, and in which the reasonable values of 2 = and 2 = 1 re substituted, with the convention that the reference standard, ethylene, is monomer 2. In Equation 6 it is seen that the Qi value is simply a ratio of propagation rate constants unmodified by the presence of differences in e values, as is the case in the styrene-based scheme. This would seem to be a more desirable type of parameter to deal with, simply because its meaning is perfectly straightforward. 

Table III. Reactivity Ratios and Q and e Values for Ethylene-Vinyl Chloride and Ethylene-Vinyl Acetate Copolymerizations...

Some data recently obtained on high pressure ethylene copolymerizations illustrate the quantitative aspects of an ethylene-based Q-e scheme (6). In Figures 3 and 4 copolymer composition curves for the ethylene-vinyl chloride and the ethylene-vinyl acetate copolymerizations are given. The monomer reactivity ratios for these two systems are tabulated in Table III along with Q values and e values for vinyl chloride and vinyl acetate calculated using ethylene as the standard (Q = 1.0 and g = 0). These Q and e values may be compared with those obtained using styrene as the standard. 

These ethylene-based Q and e values may be used to calculate the reactivity ratios for the copolymerization of vinyl acetate with vinyl chloride. Agreement is good when these values are compared with experimental values. In Table IV reactivity ratios calculated from ethylene- and styrene-based Q and e values are shown. 

It appears that these ethylene-based Q and e values are capable of forming an internally consistent correlation scheme. It will be interesting to see whether this scheme is capable of yielding good results over the wide variety of monomers for which the styrene-based scheme has been so successful. 

Thus r and T2 can be calculated from Q and e values of monomers forming the pair. 

Using the tabulated Q and e values for any two monomers, one can calculate the and values from Eqs. (7.39) and (7.40) for this monomer pair whether or not they have ever been polymerized. 

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