Penultimate unit

We have tacitly assumed that the rate constants depend only on the last unit of the chain. In such a situation, the copolymerization is called a Markov copolymerization of first order. The special case (i), r r- = 1, is a Markov copolymerization of order zero. If reactivity also depends on the penultimate unit of the chain, the polymerization is a Markov copolymerization of second order. 

Rea.CtlVltyRa.tlO Scheme. The composition of a copolymer at any point in time depends on the relative rates that each monomer can add to a chain end. If it is assumed that the chemical reactivity of a propagating chain depends only on the terminal unit and is not affected by any penultimate units, then four possible propagation steps in the copolymerisation of two monomers, and M2, with two growing chain ends, M and M2, can be written as follows ... 

Methyl-2-furaldehyde gave a similar overall behaviour, but a penultimate effect was observed in its copolymerization with isopropenylbenzene whereby two molecules of the aldehyde could add together if the penultimate unit in the growing chain was from the olefin. This was borne out by the copolymers composition and spectra. The values of the reactivity ratios showed this interesting behaviour rx = 1.0 0.1, r2 = 0.0 0.1. An apparent paradox occurred the aldehyde, which could not homo-polymerize, had equal probability of homo- and copolymerization and the olefin, which homopolymerized readily, could only alternate. The structure arising from this situation was close to a regular sequence of the type ... 

If the reaction center adopts a preferred configuration with respect to the configuration of the penultimate unit in the chain (Scheme 4.1 km kr) then Bernoullian statistics apply. The stereochemistry of the chain is characterized by the single parameter, P m) or P r) [= 1 The -ad concentrations can be... 

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."... 

The influence of penultimate units on the kinetics of copolymerization and the composition of copolymers was first considered in a formal way by Merz et al and Ham.8 They consider eight propagation reactions (Scheme 7.2). 

In small molecule chemistry it is well established that p- and more remote substituents (Figure 7.2) can have a substantial influence on radical conformation, formation and reactivity. Thus, it should be anticipated that the nature of the penultimate unit of the propagating chain could significantly modify its reactivity towards monomers and other species. However, the magnitude of the effect w ill be dependent on the exact nature of the remote substituent and the reactants. It is... 

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). 

There is also clear evidence that penultimate group effects are important in determining the stereochemistry of addition in many homopolymerizations and copolymerizations. This is made evident from the fact that most homopolymers have tacticity (i.e. P(/ i)f0.5, Section 4.2). Indeed, for some homopolyinerizations there is evidence that the configuration of the pcnpcnultimatc unit may also influence the stereochemistry of addition/9 If penpen- and penultimate units... 

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. 

More complex models for diffusion-controlled termination in copolymerization have appeared.1 tM7j Russo and Munari171 still assumed a terminal model for propagation but introduced a penultimate model to describe termination. There are ten termination reactions to consider (Scheme 7.1 1). The model was based on the hypothesis that the type of penultimate unit defined the segmental motion of the chain ends and their rate of diffusion. 

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. 

Such an exchange reaction occurs when the monomers attack the penultimate unit of the chain end, which is possible only for the case of cyclic propagating species. 

The lack of solvent separated pairs raises the question whether some alternative mode of solvation should be considered. The ester group of the penultimate unit of the polymer, or the one preceeding it, could act as a solvating agent. The idea of intramolecular solvation was proposed by several workers in the field 37) and it is supported by the results of nmr studies of polymethyl methacrylate formed under various experimental conditions 38). Hypothetical structures such as those depicted below were proposed 39 h... 

The effect of penultimate units on the rate constants of anionic propagation is observed also in other systems. For example, the addition of styrene to the lithium salt of 1-phenyl-n-hexyl anion is 4 times faster than to polystyryl lithium 51). Similarly, the addition of monomer to the lithium salt of 1,1-diphenyl-n-hexyl lithium is faster than the addition to 1,1,3-triphenyl-n-octyl lithium or 2-poly-sty ry 1-1,1-diphenyl ethyl lithium, the latter two salts having comparable reactivities52 . See also Ref.53)... 

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