Statistical Treatments of Rubber Structure

Chemical reactions are random in nature and can therefore be subjected to mathematical analyses based on probability theory. This is a particularly necessary approach to polymer structure in which the effect of chance inherent in the reactions is preserved in physical form and therefore much attention has been given to deductions from such treatments. It is the purpose of this paper to review the results of those investigations which have particular application to rubbery high polymers. Some emphasis will be given to the authors' view that experimental testing of the derived expressions is still far from being satisfactory and that the subject in spite of the effort expended is still only at its beginning. Consideration of details of polymer structure is not merely an academic exercise. The properties of raw rubbers are highly dependent on polymer chain length and for many important ones such as viscosity, either in solution or in the melt, the dependence is not simply linear. Unless linear dependence on the number of molecules and their size does apply, an average value of molecular weight is insufficient to characterize a rubber sample in respect of the property considered and further knowledge of the distribution of molecular weights among the rubber molecules is required. The properties of rubbers are also markedly influenced by the occurrence of branching in the polymer chains; the insolubility and elasticity conferred by vulcanization are the results of the formation of complex branched structures which have been the subjects for statistical treatments.