Alfrey

Alfrey, T., Jr., Mechanical Behavior of High Polymers, Interscience, New York, 1948. 

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 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 copolymerization. 

For the reaction of radical i with monomer j, Price and Alfrey assume that the cross-propagation rate constant can be written as... 

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. 

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

Alfrey-Price Q-e schei Alfven waves Algae... 

Acrylamide copolymerizes with many vinyl comonomers readily. The copolymerization parameters ia the Alfrey-Price scheme are Q = 0.23 and e = 0.54 (74). The effect of temperature on reactivity ratios is small (75). Solvents can produce apparent reactivity ratio differences ia copolymerizations of acrylamide with polar monomers (76). Copolymers obtained from acrylamide and weak acids such as acryUc acid have compositions that are sensitive to polymerization pH. Reactivity ratios for acrylamide and many comonomers can be found ia reference 77. Reactivity ratios of acrylamide with commercially important cationic monomers are given ia Table 3. 

For a growing radical chain that has monomer 1 at its radical end, its rate constant for combination with monomer 1 is designated and with monomer 2, Similady, for a chain with monomer 2 at its growing end, the rate constant for combination with monomer 2 is / 22 with monomer 1, The reactivity ratios may be calculated from Price-Alfrey and e values, which are given in Table 8 for the more important acryUc esters (87). The sequence distributions of numerous acryUc copolymers have been determined experimentally utilizing nmr techniques (88,89). Several review articles discuss copolymerization (84,85). 

The early kinetic models for copolymerization, Mayo s terminal mechanism (41) and Alfrey s penultimate model (42), did not adequately predict the behavior of SAN systems. Copolymerizations in DMF and toluene indicated that both penultimate and antepenultimate effects had to be considered (43,44). The resulting reactivity model is somewhat compHcated, since there are eight reactivity ratios to consider. 

Copolymers of VF and a wide variety of other monomers have been prepared (6,41—48). The high energy of the propagating vinyl fluoride 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 value of 0.010 0.005 and an e value of 0.8 0.2 have been determined (49). The low value of is consistent with titde resonance stability and the e value is suggestive of an electron-rich monomer. 

Alfrey and Price proposed a means of predicting monomer reactivity in copolymerization from two parameters, (a measure of resonance) and e (a measure of polar effects) (8). These parameters have been related to the reactivity ratios by equations 15—17. 

Terpolymerizations or ternary copolymerizations, as the names suggest, are polymerizations involving three monomers. Most industrial copolymerizations involve three or more monomers. The statistics of terpolymerization were worked out by Alfrey and Goldfinger in 1944.111 If we assume terminal model kinetics, ternary copolymerization involves nine distinct propagation reactions (Scheme 7.9). 

The method for the prediction of reactivity ratios in most widespread usage is the Q-e scheme.17 147 This scheme was devised in 1947 by Alfrey and Price148 who... 

Waters61 have measured relative rates of p-toluenesulfonyl radical addition to substituted styrenes, deducing from the value of p + = — 0.50 in the Hammett plot that the sulfonyl radical has an electrophilic character (equation 21). Further indications that sulfonyl radicals are strongly electrophilic have been obtained by Takahara and coworkers62, who measured relative reactivities for the addition reactions of benzenesulfonyl radicals to various vinyl monomers and plotted rate constants versus Hammett s Alfrey-Price s e values these relative rates are spread over a wide range, for example, acrylonitrile (0.006), methyl methacrylate (0.08), styrene (1.00) and a-methylstyrene (3.21). The relative rates for the addition reaction of p-methylstyrene to styrene towards methane- and p-substituted benzenesulfonyl radicals are almost the same in accord with their type structure discussed earlier in this chapter. 

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 ... 

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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