Price-Alfrey equation

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. 

The numbers in the brackets show the e values of Price-Alfrey equation. The donor strength decreases in the following order ... 

Explain the Q and e scheme and write the Price-Alfrey equation. 

Though molecular orbital calculations allow accurate predictions of reactivity ratios, many chemists rely upon the Price-Alfrey Q-e equations. These are based on (1) the polarity of the double bonds of the monomers or of the propagating chain ends, (2) mesomerism of the substituents with the double bonds or with the chain ends, and (3) the steric hindrance of the substituents. This relationship is expressed in the following equation ... 

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. 

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. 

Price i was the first to suggest that the factor of specificity in monomer addition is owing to electrostatic interaction of net charges on the monomer double bond and on the radical arising from polarization by the substituent. Alfrey and Price proposed that the rate constant be written, in analogy with Hammett s equation for the effects of nuclear substituents on the reactivity of aromatic compounds, as follows ... 

When the reactivity ratios ry can be expressed in terms of the parameters of the well-known Q-e scheme of Alfrey-Price [20,157], the condition (4.20) always holds [147, 150] and in the case of terpolymerization the general Eqs. (3.8) and (4.10) transform into the simplified equation [158]. It is rather curious that similar equations have been derived at the end of the 1940s [159] within the framework of the Alfrey-Price scheme, being investigated even for the general case of copolymerization of arbitrary number m of monomer types. 

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. 

In radical copolymerization the Alfrey-Price Q-e scheme has been proposed for systematizing a large amount of data and for correlating the reactivity of a monomer to its chemical structure. In this scheme the monomer reactivity ratios are given by the following equations ... 

Alfrey-price equation n. This copolymer equation enables you to predict the composition of the polymer as a function of the current ratio of monomers and the relative reactivities for monomers reacting with themselves or with the comonomer. 

Q-E scheme The Q-E scheme is used for quantitatively correlating relative monomer reactivities in co-polymerization reactions, introduced by Alfrey T, Price CC, J. Polymer Sci. 2, 101 (1947) for the purpose of defining an equation for each crosspropagation rate constant (ku or /c2i), in a co-polymerization reaction in terms of three constants characteristic of P is considered to be a function of the structures of the monomer P, Q, and e. 

Combining the two Alfrey-Price reactivity ratio equations [(22) and (23)] with Eq. (21) gives Eq. (24) as a full expression of this concept. 

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... 

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