Radical reactivity ratio

TABLE 6-2 Monomer Reactivity Ratios RADICAL COPOLYMERIZATION 491 in Radical Copolymerization ... 

The parameters rj and T2 are the vehicles by which the nature of the reactants enter the copolymer composition equation. We shall call these radical reactivity ratios, although similarly defined ratios also describe copolymerizations that involve ionic intermediates. There are several important things to note about radical reactivity ratios ... 

The reciprocal of a radical reactivity ratio is sometimes used to quantitatively express the reactivity of monomer M2 by comparing its rate of addition to radical Mi - relative to the rate of Mi adding to Mi-. 

Any discussion based on reactivity ratios is kinetic in origin and therefore reflects the mechanism or, more specifically, the transition state of a reaction The transition state for the addition of a vinyl monomer to a growing radical involves the formation of a partial bond between the two species, with a corre sponding reduction of the double-bond character of the vinyl group in the monomer ... 

Chain-Growth Associative Thickeners. Preparation of hydrophobically modified, water-soluble polymer in aqueous media by a chain-growth mechanism presents a unique challenge in that the hydrophobically modified monomers are surface active and form micelles (50). Although the initiation and propagation occurs primarily in the aqueous phase, when the propagating radical enters the micelle the hydrophobically modified monomers then polymerize in blocks. In addition, the hydrophobically modified monomer possesses a different reactivity ratio (42) than the unmodified monomer, and the composition of the polymer chain therefore varies considerably with conversion (57). The most extensively studied monomer of this class has been acrylamide, but there have been others such as the modification of PVAlc. Pyridine (58) was one of the first chain-growth polymers to be hydrophobically modified. This modification is a post-polymerization alkylation reaction and produces a random distribution of hydrophobic units. 

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). 

An example of a commercial semibatch polymerization process is the early Union Carbide process for Dynel, one of the first flame-retardant modacryhc fibers (23,24). Dynel, a staple fiber that was wet spun from acetone, was introduced in 1951. The polymer is made up of 40% acrylonitrile and 60% vinyl chloride. The reactivity ratios for this monomer pair are 3.7 and 0.074 for acrylonitrile and vinyl chloride in solution at 60°C. Thus acrylonitrile is much more reactive than vinyl chloride in this copolymerization. In addition, vinyl chloride is a strong chain-transfer agent. To make the Dynel composition of 60% vinyl chloride, the monomer composition must be maintained at 82% vinyl chloride. Since acrylonitrile is consumed much more rapidly than vinyl chloride, if no control is exercised over the monomer composition, the acrylonitrile content of the monomer decreases to approximately 1% after only 25% conversion. The low acrylonitrile content of the monomer required for this process introduces yet another problem. That is, with an acrylonitrile weight fraction of only 0.18 in the unreacted monomer mixture, the low concentration of acrylonitrile becomes a rate-limiting reaction step. Therefore, the overall rate of chain growth is low and under normal conditions, with chain transfer and radical recombination, the molecular weight of the polymer is very low. 

Table 5. Free-Radical Copolymerization Reactivity Ratios,...

GopolymeriZation. The importance of VDC as a monomer results from its abiHty to copolymerize with other vinyl monomers. Its Rvalue equals 0.22 and its e value equals 0.36. It most easily copolymerizes with acrylates, but it also reacts, more slowly, with other monomers, eg, styrene, that form highly resonance-stabiHzed radicals. Reactivity ratios (r and r, with various monomers are Hsted in Table 2. Many other copolymers have been prepared from monomers for which the reactivity ratios are not known. The commercially important copolymers include those with vinyl chloride (VC),... 

Although reactivity ratios indicate that VP is the more reactive monomer, reaction conditions such as solvent polarity, initiator type, percent conversion, and molecular weight of the growing radical can alter these ratios (138). Therefore, depending on polymerization conditions, copolymers produced by one manufacturer may not be identical to those of another, especially if the end use appHcation of the resin is sensitive to monomer sequence distribution and MWD. 

Chain-Growth Gopolymerization Theory. The theory of chain-growth (eg, radical, anionic, etc) copolymerisation has received more attention than that of step-growth or other copolymerisations. In the case of chain-growth copolymerisation, growing polymer chains must choose between more than one monomer. Such a choice or relative reactivity has been quantitatively treated by the reactivity ratio (6,7) and the Q-e schemes (8). 

Table 2 shows characteristic reactivity ratios for selected free-radical, ionic, and coordination copolymerizations. The reactivity ratios predict only tendencies some copolymerization, and hence some modification of physical properties, can occur even if and/or T2 are somewhat unfavorable. For example, despite their dissimilar reactivity ratios, ethylene and propylene can be copolymerized to a useful elastomeric product by adjusting the monomer feed or by usiag a catalyst that iacreases the reactivity of propylene relative to ethylene. 

In contrast to ionic chain polymerizations, free radical polymerizations offer a facile route to copolymers ([9] p. 459). The ability of monomers to undergo copolymerization is described by the reactivity ratios, which have been tabulated for many monomer systems for a tabulation of reactivity ratios, see Section 11/154 in Brandrup and Immergut [14]. These tabulations must be used with care, however, as reactivity ratios are not always calculated in an optimum manner [15]. Systems in which one reactivity ratio is much greater than one (1) and the other is much less than one indicate poor copolymerization. Such systems form a mixture of homopolymers rather than a copolymer. Uncontrolled phase separation may take place, and mechanical properties can suffer. An important ramification of the ease of forming copolymers will be discussed in Section 3.1. 

Similar anomalies have been encountered by several workers in the bulk and solution polymerization of this monomer induced by classical free-radical initiators84-86) also, particularly low rates of conversion were observed. The most thorough kinetic study was carried out by Aso and Tanaka86) who again found normal results and a value of k jkt much lower than that for styrene. Copolymerization studies of 2-vinylfuran (Mj) have given the following values of the reactivity ratios ... 

Reactivity ratios for the copolymerization of AN with 7 in methanol at 60 °C, proved to be equal to rx AN= 3,6 0,2 and r%n = 0 0,06, i.e., AN is a much more active component in this binary system. The low reactivity of the vinyl double bond in 7 is explained by the specific effect of the sulfonyl group on its polarity26. In addition to that, the radical formed from 7 does not seem to be stabilized by the sulfonyl group and readily takes part in the chain transfer reaction and chain termination. As a result of this, the rate of copolymerization reaction and the molecular mass of the copolymers decrease with increasing content of 7 in the initial mixture. 

The rates of addition to the unsubstituted terminus of monosubstituted and 1,1-disubstiluted olefins (this includes most polymerizable monomers) are thought to be determined largely by polar Factors.2 16 Polymer chemists were amongst the first to realize that polar factors were an important influence in determining the rate of addition. Such factors can account for the well-known tendency for monomer alternation in many radical copolymerizations and provide the basis for the Q-e, the Patterns of Reactivity, and many other schemes for estimating monomer reactivity ratios (Section 7.3.4). 

Certain monomers may act as inhibitors in some circumstances. Reactivity ratios for VAc-S copolymerization (r< 0.02, rVu -2.3) and rates of cross propagation are such that small amounts of S are an effective inhibitor of VAc polymerization. The propagating chain with a terminal VAc is very active towards S and adds even when S is present in small amounts. The propagating radical with S adds to VAc only slowly. Other vinyl aromatics also inhibit VAc polymerization.174... 

Fukuda et al.lj were the first to recognize that a further two radical reactivity ratios were required to completely define the polymerization kinetics. 

Further evidence that penultimate unit effects are small in the MMA-S system comes from comparing the reactivities of small model radicals with the reactivity ratios (Section 7.3.1.2.2 and Table 7.4). 

If it is assumed that penultimate unit effects on the reaction entropy are insignificant, the terms in eqs. 18 and 19 corresponding to the stabilization energy of the reactant propagating radical will cancel and rVli=ryly There should be no explicit penultimate unit effect on copolymer composition. On the other hand, the radical reactivity ratio j (eq. 20) compares two different propagating radicals so... 

One final point should be made. The observation of significant solvent effects on kp in homopolymerization and on reactivity ratios in copolymerization (Section 8.3.1) calls into question the methods for reactivity ratio measurement which rely on evaluation of the polymer composition for various monomer feed ratios (Section 7.3.2). If solvent effects arc significant, it would seem to follow that reactivity ratios in bulk copolymerization should be a function of the feed composition.138 Moreover, since the reaction medium alters with conversion, the reactivity ratios may also vary with conversion. Thus the two most common sources of data used in reactivity ratio determination (i.e. low conversion composition measurements and composition conversion measurements) are potentially flawed. A corollary of this statement also provides one explanation for any failure of reactivity ratios to predict copolymer composition at high conversion. The effect of solvents on radical copolymerization remains an area in need of further research. 

There have, however, been attempts to correlate Q-e values and hence reactivity ratios to, for example, c NMR chemical shifts 50 or the results of MO calculations 51153 and to provide a better theoretical basis for the parameters. Most recently, Zhan and Dixon153 applied density functional theory to demonstrate that Q values could be correlated to calculated values of the relative free energy for the radical monomer reaction (PA + Mn — PA ). The e values were correlated to values of the electronegativities of monomer and radical. 

The thiol shows a preference to react w ith propagating radicals with a tenninal S unit (Scheme 7.21). This selectivity is due both to chemospecificity in the reaction with thiol and to the relative concentrations of the various propagating species (determined by the reactivity ratios). 

The effects of solvent on radical copolymerization are mentioned in a number of reviews.69 72 97,98 For copolymerizations involving monomers that arc ionizablc or form hydrogen bonds (AM, MAM, HEA, HEMA, MAA, etc.) solvent effects on reactivity ratios can be dramatic. Some data for MAA-MMA copolymerization are shown in Table 8.4.w... 

For copolymerizations between non protie monomers solvent effects are less marked. Indeed, early work concluded that the reactivity ratios in copolymerizations involving only non-protic monomers (eg. S, MMA, AN, VAe, etc.) should show no solvent dependence.100101 More recent studies on these and other systems (e.g. AN-S,102-105 E-VAc,106 MAN-S,107 MMA-S,10s "° MMA-VAc1" ) indicate small yet significant solvent effects (some recent data for AN-S copolymerization are shown in Table 8.5). However, the origin of the solvent effect in these cases is not clear. There have been various attempts to rationalize solvent effects on copolymerization by establishing correlations between radical reactivity and various solvent and monomer properties.71,72 97 99 None has been entirely successful. 

Studies on the reactions of small model radicals with monomers provide indirect support but do not prove the bootstrap effect.111 Krstina et ahL i showed that the reactivities of MMA and MAN model radicals towards MMA, S and VAc were independent of solvent. However, small but significant solvent effects on reactivity ratios are reported for MMA/VAc111 and MMA S 7 copolymerizations. For the model systems, where there is no polymer coil to solvate, there should be no bootstrap effect and reactivities are determined by the global monomer ratio [Ma0]/[Mb0].1j1... 

Although, there are reports on differences in reactivity ratios observed for conventional radical eopolymeri/.ation v.y living radical copolymeri/.alion (ATRP"75 276 546 >l8 or RAK D48), most research suggests that reactivity ratios are identical31 8 549 and any discrepancies in composition should be attributed to other factors. 

In comparing observed reactivity ratios between various polymerization systems, it is important to take into account the possible effect of molecular weight on copolymer composition.3475 19 In conventional radical eopolymeri/.ation, the specificity shown in the initiation and termination steps can have a significant effect on the composition of low molecular weight copolymers (usually <10 units). These effects are discussed in Section 7.4.5. In a living polymerization molecular weights are low at low conversion and increase with conversion. In these... 

One might also anticipate that the influence of bootstrap effects (Section 8.3.1.2) would be quite different in living and non-living processes. 68 A comprehensive study of reactivity ratios in living and conventional radical polymerization may provide a test of the various hypotheses for the origin of this effect. 

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