Q-e scheme, Alfrey-Price

All the mentioned types of the nontrivial dynamic behavior are excluded for the systems where the reactivity ratios ry can be described by the expressions of the well-known Alfrey-Price Q-e scheme [20], and as a result they are to follow the simplified terminal model (see Sect. 4.6). In these systems, due to the relations Bj(X)/Bj(x) = ajj/ajj which holds for all i and j, the functions 7e,-(2) according to relations (4.10) are the ratios of the homogeneous polynomials of degree 2. Besides, for the calculations of the coefficients ak of Eq. (5.11) one can use the simple formulae presented in terms of determinants Dj and D [6, p. 265]. The theoretical analysis [202] leads to the conclusion that in such systems even the limited cycles are not possible and all azeotropes are certainly unstable. Hence any trajectory H(p) and X(p) when p -> 1 inevitably approaches the SP corresponding to the homopolymer the number of which can be from 1 to m. The set of systems obtained due to the classification within the framework of the simplified model essentially impoverishes in comparison with the general case of the terminal copolymerization model since some types of systems cannot be principally realized under the restrictions which the Q-e scheme puts on the reactivity ratios r. ... 

Until the appearance of the Alfrey-Price Q — e scheme, it has been necessary to refer relative monomer reactivity ratios to the particular two-... 

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 ... 

These parameters also have been useful through the Alfrey-Price Q e scheme (33) for assessing the merit of new monomers in multicomponent macromolecular compositions. From the data just cited for ionogenic monomers and from the strength of associations that affect significant viscosity increases cited in Chapters 18 and 21-27 for hydrophobic monomers, it... 

The copolymerization reactivity ratios of 3 with other monomers correspond to a g = 0.82 and an c = 0.44 in the Alfrey-Price Q-e scheme, where Q describes the general monomer reactivity and e takes account of polar factors influencing copolymeri-... 

For conventional free-radical copolymerizations, polar effects of growing polymer radicals on the approaching monomer is expressed by the Alfrey-Price Q — e scheme, where the copolymerization tendency, i.e., product of monomer reactivity ratios, may be expressed, Eq. (20), in terms of e values. 

The first is answered by introducing relative reactivities. The second is approached by the Alfrey-Price Q-e scheme. To express the relationship of polymer composition to the monomer composition from which it is being formed, we go back to the kinetic scheme of Section 4.4. If we can assume that we achieve a steady-state population of chain radicals that grow to high molecular weight, the material balances for various species are few and simple for a binary system. 

Table 7.2. Correlation parameters for the reactivity of monomers towards radical polymerization in terms of the Alfrey Price (Q, e), Bamford -Jenkins (a, P), and Ito hfetsuda (AT, P) schemes...

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). 

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. 

The Q-e scheme neglects steric factors, but it is a useful guide when data for r and Y2 are not available. Following is an approach that relates the reactivity ratios to the Alfrey-Price e values ... 

Various attempts have been made to place the radical-monomer reaction on a quantitative basis in terms of correlating structure with reactivity. Success in this area would give a better understanding of copolymerization behavior and allow the prediction of the monomer reactivity ratios for comonomer pairs that have not yet been copolymerized. A useful correlation is the Q-e scheme of Alfrey and Price [1947], who proposed that the rate constant for a radical-monomer reaction, for example, for the reaction of Mp radical with M2 monomer, be written as... 

Considering now reactions (5 a) and (5 b) (p. 176), it was found that the addition of monomers to macroradicals produced by chain transfer depends directly on the reactivity and polarity of both the radical and the monomer (203) and that the Q—e scheme of Alfrey and Price can be applied to these graft copolymerizations by chain transfer (227). In this way some unsuccessful attempts for grafting were interpreted, e. g. vinyl acetate on polystyrene and methyl methacrylate on polyvinyl acetate and polyvinyl chloride. 

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. 

The violation of the condition (4.20) for the particular system means that the latter can not be described by the Q-e scheme. However, in addition to this scheme, there are known some others, also applied for the description of the reactivity of the polymer radical in propagation reactions [160], One such scheme proposed by Bamford [161, 162] was successfully used by Jenkins [163] for an interpretation of the experimental values [150] of parameter H for a number of ternary systems. For many of these the values of H are noticeably different from unity, as it has to be according to the predictions of the Alfrey-Price scheme, but are in satisfactory agreement with the values calculated through the Bamford scheme [163, 160],... 

All the above factors controlling monomer and radical reactivities contribute to the rate of polymerization, but in a manner which makes it difficult to distinguish the magnitude of each effect. Attempts to correlate copolymerization tendencies based on these factors are thus mainly of a semiempirical nature and can, at best, be treated as useful approximations rather than rigorous relations. However, a generally useful scheme was proposed by Alfrey and Price [23] to provide a quantitative description of the behavior of diferent monomers in radical polymerization, with the aid of two parameters, for each monomer rather than for a monomer pair. These parameters are denoted by Q and e and the method has been called the Q — e scheme. It allows calculation of monomer reactivity ratios r and T2 from properties of monomers irrespective of which 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... 

Taking into account polarity, steric factors, and resonance stabilization, T. Alfrey and C. C. Price (7) developed a Q-e scheme and predicted monomer reactivity. The effect of polarity on vinyl monomer copolymerization was recognized by F. R. Mayo and coworkers (8), who distinguished between monomers of average activity and those acting as electron donors or acceptors. By combining these theories with experimental data, calculation of product probabilities of various monomer combinations and determination of monomer reactivity parameters were possible. 

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

In many cases, all that is required in the first instance is a feeling for the type of copolymerization behaviour to be expected. If values of r and r for a particular copolymerization are not available, then the simple Q-e scheme developed by Alfrey and Price [12] is useful for estimating their values. The basis of the scheme is that the rate coefficient, fcpm, for reaction of a polymeric radical, p, with a monomer, m, is given by... 

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. 

Note 2. The Q-e scheme is known also as the Alfrey-Price scheme. 

Thus to each monomer corresponds a Q value and an e value from which ri and V2 values can be calculated for a couple of comonomers. One must stress the fact that the Alfrey-Price relation does not take into account steric effects and that the Q-e scheme does not apply to 1,2-disubstituted ethylenic monomers presenting a relatively low ceiling temperature. 

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. 

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 ... 

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

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... 

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