Termination in dilute-solution free-radical polymerization: A composite model

Literature data are summarized for the chain-length-dependence of the termination rate coefficient in dilute solution free-radical polymerizations. In essence such experiments have yielded two prameter values: the rate coefficient for termination between monomeric free radicals, k(t)(1,1), and a power-law exponent e quantifying how k(t) values decrease with increasing cahin length. All indications are that the value e approximate to 0.16 in good solvent is accurate, however the values of k(t)(1,1) which have been deduced are considerably lower than well-established values for small molecule radicals. This seeming impasse is resolved by putting forward a 'composite' model of termination: it is proposed that the value e approximate to 0.16 holds only for long cahins, withe being higher for small chains - the value 0.5 is used in this paper, although it is not held to dogmatically. It is then investigated whether this model is consistent with experimental data. This is anon-trivial task because although the experiments themselves and thw ways in which they are analyzed are elegant and not too complicated, the underlying theory is sophisticated, as is outlined. Simulations of steady-state polymerization experiments are first of all carried out, and it is shown that the composite model of termination both recovers the e values which have been found and beautifully explains why these experiments considerably underestimate the true value of k(t)(1-1). Simulations of pulsed-laser polymerizations find the same, although not quite so strikingly. It is therefore concluded that our new termination model, which retains the virtue of simplicity and in which all parameter values are physically reasonable, is consistent with experimental data. Taking a wider view, it seems likely that the situation of the exponent e varying with chain length will not just be the case in dilute solution, but will be the norm for all conditions, which would give our model and our work a greater relevance.