Penultimate unit effect

It is usually assumed that propagation rate constants in homopolymerization ( p) arc independent of chain length and, for longer chains (length >20), there is experimental evidence to support this assumption.356 6 However, there is now a body of indirect evidence to suggest that the rate constants for the first few propagation steps p(l), kp(2), etc. can be substantially different from (overall) (refer Scheme 4.45). The effect can be seen as a special ease of a penultimate unit effect (Section 7.3,1.2). Evidence comes from a number of sources, for example ... 

For radicals 1, ktA/ktc shows a marked dependence on the bulk of the substituent (R2). While phenylethyl radicals (2) and cumyl radicals (5) afford predominantly combination, there are indications of a substantial penultimate unit effect. The radicals 6, with an a-neopentyl substituent, give predominantly disproportionation, Termination in AMS polymerization might therefore also give substantial... 

Problems arise with any of the abovementioned methods in the measurement of transfer constants for very active transfer agents. Bamford 8 proposed the technique of moderated copolymerization. In these experiments, the monomer of interest is copolymcrizcd with an excess of a moderating monomer that has a much lower (preferably negligible) transfer constant. The method has also been applied to evaluate penultimate unit effects on the transfer constant.28-j0... 

The general features of the penultimate model in what have become known as the explicit and implicit forms are described in Section 7.3.1.2.1. Evidence for remote unit effects coming from small molecule radical chemistry and experiments other than copolymerization is discussed in Section 7.3.1.2.2. In Sections 7.3.1.2.3 and 7.3.1.2.4 specific copolymerizations are discussed. Finally, in Section 7.3.1.2.5, we consider the origin of the penultimate unit effects. A general recommendation is that when trying to decide on the mechanism of a copolymerization, first consider the explicit penultimate model."... 

Experimental studies on models of the propagating radicals in S-AN copolymerization32,33 and a few other systems34 provide support for an explicit penultimate unit effect. Of particular interest is the data of Tirrcll and coworkers. They investigated the relative reactivity of S and AN towards various /-substituted propyl radicals (Scheme 7.3 and Table 7.2). They found that ... 

Further examples of significant penultimate unit effects come from studies of rate constants for addition of the first propagating species to monomer (Scheme 7.4). There, is a strong dependence on the particular initiating species. The data in Tabic 7.4 were provided in Fischer and Radom s review.35... 

It is known that the penultimate unit influences the conformation of both model radicals and propagating radicals.32 3 Since addition requires a particular geometric arrangement of the reactants, there are enthalpic barriers to overcome for addition to take place and also potentially significant effects on the entropy of activation. Comparisons of the rate constants and activation parameters for homopropagation with those for addition of simple model radicals to the same monomers also provide evidence for significant penultimate unit effects (Section 4.5.4). 

Penultimate unit effects are also important in both substitution40"41 and in addition-fragmentation chain transfer.42"44 Some examples are provided in Sections 6.2, 6.2.2.4, 6.2.3.4 and 9.5. 

Rased on the above data, it would seem unusual if reactivity of the propagating species in copolymerization were insensitive to the nature of the last added monomer units. However, while there are ample experimental data to suggest that copolymerizations should be subject to penultimate unit effects that affect the rate and/or copolymer composition, the origin and magnitude of the effect is not always easily predictable. 

Triad information is more powerful, but typically is subject to more experimental error and signal assignments are often ambiguous (Section 7.3.3.12). Triad data for the MMA-S system are consistent with the terminal model and support the view that any penultimate unit effects on specificity are small.Mv lS... 

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... 

Hcuts et a .,64 while not disputing that penultimate units might influence the activation energies, proposed on the basis of theoretical calculations that penultimate unit effects of the magnitude seen in Ihe S-AN and other systems (i.e. 2-5 fold) can also be explained by variations in the entropy of activation for the process. They also proposed that this effect would mainly influence rate rather than specificity. 

Perhaps because of this complexity, few studies on determining kld/ktt, in cross termination in copolymerization have been reported and most of the available data come from model studies, it is also usually assumed, without specific justification, that penultimate unit effects are unimportant in determining which reactions occur and that values of k klt for the homotermination reactions are similar to those in the corresponding homopolymerizations. 

S. Losio, P. Stagnaro, T. Motta, M.C. Sacchi, F. Piemontesi, and M. Gal-imberti, Penultimate-unit effect in ethene/4-methyl-l-pentene copolymerization for a sequential distribution of comonomers, Macromole-cules, 41 (4) 1104—1 111, 2008. 

Variants of the above have been used to explain unusual data where it was suspected that monomer units penultimate to the chain end (or even further back) were affecting the reaction rate constants (6). Such treatments suffer from a degree of arbitrariness in that the experimental data may not provide an adequate test of the kinetic model (3). In some cases, penultimate unit effect models have been used to interpret unusual data where one might expect depropagation to be important. 

Complications occur due to penultimate unit effects, complexation, the presence of hot radicals etc. See further text in Sect. 5.5, 5.6, and 5.8. 

Anomalies in the course of copolymerizations which have been ascribed to penultimate unit effects can alternatively be explained by the reversibility of one or several addition types. 

Living polymerizations continue to attract the attention of theorists studying transfer. Chinese authors have analyzed the penultimate unit effect on transfer to a monomer mathematically [53]. According to their conclusions, the penultimate effect is important when the activities of the growth centres on the polymer chain and on the monomer (after transfer) are widely different, otherwise it can be neglected. 

The simple copolymer model is a first-order Markov chain in which the probability of reaction of a given monomer and a macroradical depends only on the terminal unit in the radical. This involves consideration of four propagation rate constants in binary copolymerizations, Eqs. (7-2)-(7-4). The mechanism can be extended by including a penultimate unit effect in the macroradical. This involves eight rate constants. A third-order case includes antepenultimate units and 16 rate coefficients. A true test of this model is not provided by fitting experimental and predicted copolymer compositions, since a match must be obtained sooner or later if the number of data points is not saturated by the adjustable reactivity ratios. 

When the penultimate unit effect has to be taken into account the set of four equations in Scheme (2-50) has to be replaced by eight equations. For example, instead of the first equation from Scheme 2-50 two new equilibria must be considered ... 

In several sections of this volume the microstructure of homo- and copolymers is discussed. The microstructure of the products can be used as a diagnostic tool to get information as to the uniformity of polymers formed, reactivities of comonomers, etc. In the absence of penultimate unit effect and subsequent segmental redistribution the microstructure of the copolymer chain is defined by the reactivity ratios and comonomer feed. Thus, the dyad and triad content may be a test of the applicability of the simple four-parameter scheme. 

---