Implicit penultimate unit effect

The majority of copolymerization systems studied so far can by represented well by the implicit penultimate unit effect (IPUE) model, where the two radical reactivity ratios, Si = kau/km and S2 - ki22/ 222. are introduced as additional parameters, to account for the influence of the penultimate unit on homopropagation. Within the IPUE model, no penultimate unit effect is considered for the reactivity ratios r = r2i and r2i = rx2- Despite the remarkable... 

IPUE implicit penultimate unit effect (model for copolymerisation)... 

While copolymer composition is well-described by the terminal model, the copolymer-averaged propagation rate coefficient (kp. Equation 3.45) for many common systems [10, 26, 27] is not. The measured kp values can be higher or lower than the terminal model predictions, with the deviation substantial in some cases. The implicit penultimate unit effect model, which accounts for the influence of the penultimate monomer-unit of the growing polymer radical on the propagation kinetics [26, 27], provides a good representation of this behavior ... 

Thus the adjusted monomer reactivity ratios of the penultimate model are replaced simply by their corresponding terminal model values. However, since the penultimate imit effect can remain in the radical reactivity ratios (ie, through values of Si 1), equation 4 does not collapse to its equivalent terminal model form (ie, kii kiii). Since the composition and triad/pentad fraction equations contain only n terms, they collapse to the corresponding terminal model equations. However, since it contains both ft and ku terms, the propagation rate equation, though simpler than that of the explicit penultimate model, continues to differ from that of the terminal model. There is thus an implicit penultimate unit effect— that is, a penultimate unit effect on the propagation rate but not the composition or sequence distribution. 

The implicit penultimate unit effect model, which accounts for the influence of the penultimate monomer unit of the growing polymer radical on the propagation kinetics [51], provides a good representation of this behavior [Eqs. (52)]. 

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."... 

However, recent experimental and theoretical work has shown that the assumptions of the implicit penultimate model are unlikely to be applicable to the majority of copol5mierization systems. We have recently published a review of this evidence (37,42), which draws on direct experimental and theoretical measures of reactivity ratios, model testing in a range of copolymerization systems, and other tests of the mechanism of the propagation step via, for example, the examination of solvent effects on reactivity ratios. These studies provide strong evidence for penultimate imit effects but, in all cases where penultimate unit effects have been measured directly, effects on radical selectivity have been shown to be significant. In other words all available evidence contradicts the assumption of the implicit penultimate model that the penultimate unit affects reactivity but not selectivity. 

In addition, steric penultimate imit effects should also lead to explicit (rather than implicit) penultimate imit effects, as they would obviously he sensitive to the steric properties of the monomer with which they were reacting. Recently, experimental evidence for significant entropic penultimate unit effects has been pubhshed (44), confirming predictions made in an earlier theoretical study (45). These studies further confirm that, if there are penultimate imit effects in fi ee-radical copolsrmerization, then they are most likely to be explicit effects. 

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