The nature of the chain-length dependence of the propagation rate coefficient and its effect on the kinetics of free-radical polymerization. 1. Small-molecule studies

In this paper we summarize and analyze the currently available small-molecule data, both experimental and theoretical, that is relevant to chain-length-dependent propagation in free-radical polymerization (FRP). We do this in order to appreciate the nature of chain-length-dependent propagation, because workers are becoming increasingly cognizant of its necessity in reaching a complete understanding of FRP kinetics. We show that studies of addition in small-molecule (model) systems support a chain-length dependence (at short chain lengths i) which is described by the following functional form, which therefore can be said to be physically realistic: , where the values of C₁ and i_1/2 are of the order of 10 and 1, respectively. These results are supported by transition state theory, which predicts a very similar behavior for the Arrhenius frequency factor. We illustrate that in systems with low number-average degree of polymerization (DP_n), this chain-length dependence can dramatically affect the observed (chain-length-averaged) propagation rate coefficient 〈k_p〉, which can be significantly higher than the long chain value, k_p. However, this effect is only observed if the activation energy for the first radical addition is similar to that for propagation. In the case that the former is significantly higher (e.g., when choosing a less than optimal initiator or in the case of retardative chain transfer), the chain-length-dependent propagation predicted by our model will not be observed, and in fact a significant lowering of 〈k_p〉 can in cases be expected up to relatively high DP_n.