Alfrey-Price Q and e-values

Copolymerization studies demonstrated that aminimide, 1,1-dimethyl-l-(2-hydroxypropyl)amine methacrylimide (DHA) copolymerizes readily with 4-vinylpyridine (4VP) and N-vinylpyr-rolidone (NVP). These copolymers could he thermolyzed in solution to give soluble poly(4-vinylpyridine-co-isopropenyl isocyanate) and poly(N-vinylpyrrolidone-co-isopropenyl isocyanate) materials. The reactivity ratios of each monomer pair were determined, and the Alfrey-Price Q and e values for DHA were calculated for DHA (Mt)-4VP (M2), r, = 0.41, r = 0.77, Q = 0.68, and e = 0.58 and for DHA (Mt)-NVP (Mg), r2 = 0.15, r2 = 0.35, Q = 0.14, and e = 0.58. The DHA-4VP copolymers quaternized readily to give a new family of water-soluble polyelectrolyte materials. The various copolymers were examined as adhesion promoters for rubber-tire cord composites. 

The Alfrey-Price Q and e values (17) were calculated from the monomer reactivity ratios in the copolymerization with 4VP = 0.68 and ex = 0.58. 

In Table 6.1 some of the most often-used monomers are shown with their reactivity, expressed in terms of the Alfrey-Price Q and e values [4] (see Section 1.6.4 of Chapter 1), their water solubilities, boiling points and the homopolymer Tg values. The table is arranged in order of decreasing polymer Tg values, splitting the list into two, with the upper half representing glassy polymers at room temperature and rubbery polymers taking the bottom half. 

The semiempirical Alfrey-Price Q and e values for vinyl acetate are, respectively, 0.026 and —0.22 [226]. With some exceptions, the reactivity of the higher vinyl esters is similar to that of vinyl acetate and is reflected in similarity of their Q and e values. From these values one can qualitatively conclude that compared to styrene, the vinyl acetate double bond is slightly more electron rich and that there is comparatively little resonance interaction... 

Table 10.14. Alfrey-Price Q and e Values of Vinyl Ethers and Equilibrium Constants...

Alfrey-Price Q and e-values, 304, 307, 309, 310, 314, 334, 337, 342, 352, 353, 389, 393-395, 400, 416, 419, 424 MA monomer, 247, 272 Alkali cyanide, addition to fumarates, 64 Alkenyl benzyl ethers, MA copolymerization, 532 Alkenylsuccinic anhydride applications, 147, 175 double bond migration, 174 hydrolysis, 175 isomerization catalysts, 174 MA polymerization, 342 MA-olefin adducts, 147-151, 163-165, 172, 173 Alkoxysuccinic acids, preparation, 46 Alkyd resins, MA applications, 44, 479, 499 Alkyl acetoacetates... 

The electron richness of vinylferrocene as a monomer has been demonstrated in its copolymerization with maleic anhydride, in which 1 1 copolymers were obtained over a wide range of feed ratios and ri r2 = 0.003 [13]. Subsequent copolymerization of vinylferrocene with classic organic monomers, such as styrene [13], Ai-vinyl-2-pyrrolidone [15], methyl methacrylate [13] and acrylonitrile [13] were carried out and the Alfrey-Price Q and e parameters [16] determined. The value of e is a semiempirical measure of the electron richness of the vinyl group. The best value of e for vinylferrocene is about —2.1, which, when compared with the e values of maleic anhydride (-H 2.25), p-nitrostyrene (-1-0.39), styrene (—0.80), p-Ai,Ai -dimethyl-aminostyrene ( — 1.37) and l,T-dianisylethylene ( — 1.96), again emphasizes the electron rich nature of the vinyl group in vinylferrocene. 

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

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 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 ... 

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 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. 

A useful scheme was proposed by Alfrey and Price (1947) to provide a quantitative description of the behavior of vinyl monomers in radical polymerization, in terms of two parameters for eac/t monomer rather than for a monomer pair. These parameters are denoted by Q and e and the method is known as the O - e scheme. An advantage of the method is that it allows calculation of monomer reactivity ratios ri and T2 from the same Q and e values of the monomers irrespective of which monomer pair is used. The scheme assumes that each radical or monomer can be classified according to its reactivity (or resonance effect) and its polarity so that the rate constant for a radical-monomer reaction, e.g., the reaction of Mi ° radical with M2 monomer, can be written as... 

An att pt to organize the vast amount of copolymerization data in a coherent manner was made by Alfrey and Price in terms of the Q and e" S(dieme. Q is a factor which can be correlated with the specific reactivity of a monomer as determined by resonance effects, and e is a measure of the electron-donating or electron-accepting nature of the radical formed. The relationships between the rate constants of the copolymerization propagation reactions and the Q and e values are given by ... 

From the theoretical analysis above it is clear that knowledge of the values of fi and T2 is necessary for a good assessment of the copolymerization. These values for ri and r2 have been given for some monomer combinations in Chapter 3. They can also be estimated theoretically by using the Q and e values according to Alfrey and Price (1) ... 

Following the Alfrey-Price scheme, the charge transfer complexes in the copolymerization reactions were characterized by their Q and e values. Using the known NVPI values Q — 0.07 and e = —0.15), " the estimated values for BVE-MA (C = 0.36 and e = 1.17) and a-methylstyrene-MA (Q = 0.10, e = 0.67) were determined. These results confirm the concept that the charge-transfer complexes should readily copolymerize with... 

Copolymers of VF and a wide variety of other monomers have been prepared (9,81,82,94-98). The high energy of the propagating VF radical strongly influences the course of these polymerizations. VF incorporates well with other monomers that do not produce stable free radicals, such as ethylene and vinyl acetate, but is sparingly incorporated with more stable radicals such as acrylonitrile [107-13-1] and vinyl chloride. An Alfrey-Price Q value of 0.010 0.005 and an e value of 0.8 0.2 have been determined (99). The low value of Q is consistent with little resonance stability and the e value is suggestive of an electron-rich monomer. 

The results of the Alfrey-Price Q-e parameters [76] (where Q and e take into account the stabilization by resonance and the polar effects of the monomer) are commonly used to predict the monomer reactivity ratios. The Alfrey-Price parameters are known for AN, MAN, MVCN, and MATRIF [68]. The calculated values of the reactivity ratios, and r2, and the product (rj x rj) are summarized in Table 20.2. 

The relation between monomer reactivity ratios and the Alfrey-Price Q-e parameters is explained in the introduction to the tables of monomer reactivity ratios and Q-e values, compiled by Robert Z. Greenley and published in the present volume (1,2). Although very widely used, the Q-e scheme is well known to have serious limitations (3), which have prompted several attempts to improve upon it. Qne such endeavour was the Patterns of Reactivity scheme, first described as long ago as 1959 (4-7), when the Q-e scheme was only about ten years old despite the indisputably more satisfaetory basis of this procedure, it did not achieve popularity but recent revisions have greatly improved both its accessibility and its accuracy (3,8,9). 

When r and ri should be calculated for high-pressure copolymerization, following Alfrey and Price, the pressure dependence of Q, e data must be taken into account. Some values of Q and e for high pressures are collected in Section G. The dependence of the e data of two monomers on pressure is given by the equation... 

Shen (118) suggested a formal analogy between the Hammett equation and the Price-Alfrey equation. Charton and Capato (119) have derived relationships between e and q values and the Hammett equation as follows. 

Values of e are correlated by the Op constants in accord with eq. (61) (119, 120). Kawabata, Tsuruta, and Furukawa (121) have proposed a revised form of the Price-Alfrey equation based on the definition e = 0 for styrene. On the basis of this redefinition, they have calculated a new set of Q values. These Q values are linear in the Hammett 0 constants. It is not clear from their paper whether this linear relationship is for substituents directly bonded to the carbon-carbon double bond or whether it is applicable only to Q values for substituted styrenes. Charton and Capato (119) were unable to obtain significant correlations between any a constants and the q values of Schwan and Price (117). Zutty and Burkhart (122) have proposed a redefinition of the Price-Alfrey equation based on ethylene as the reference system with Qo and e defined as 1 and 0, respectively. 

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