Reactions of adjacent substituents on polymer chains: Combinatorial consequences of the mechanism

Abstract

This paper deals with a statistical problem arising from the pairwise reaction of immediately adjacent substituents along the backbone of a linear polymer chain. The possibility arises that a given substituent becomes unavailable for reaction as a result of the reaction of its nearest neighbors on either side. Previous treatments of this problem have not explicitly taken the consequences of the reaction mechanism into account. In this paper, it is shown that the expected number of unreacted substituents remaining after exhaustive pairwise reaction is a function of the reaction mechanism. For example, in the case of the chain model adopted here, which corresponds to a perfectly regular head-to-tail vinyl halide (-CH₂-CHX-), we show that the fraction of halide atoms remaining after exhaustive removal is equal to 0.1233. The result is compared with results obtained from previous work.