Reaction Kinetics of a Long-Chain Molecule. II. Arends' Solution

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Abstract
In Part I [J. Chem. Phys. 37, 2584 (1962)] we considered the reaction kinetics of a long‐chain molecule, each segment of which carries a reactive group. The reactivity of each group depended upon whether zero, one, or two of its nearest neighbors had reacted. The average fractions of reacted groups and of unreacted with zero, one of two reacted neighbors were found as functions of time. Now we derive C. B. Arends' [J. Chem. Phys. 38, 322 (1963)] solution for the average fraction of sequences of unreacted groups of n for n=1, 2, ···. We start with the infinite set of differential equations for these average fractions derived by W. G. Lloyd and T. Alfrey, Jr. [J. Chem. Phys. 38, 318 (1963)]. We solve them by assuming a solution of the form derived by Arends. Thus we verify that Arends' solution satisfies the equations of Lloyd and Alfrey and we derive it more simply. In addition we show that the present results yield exactly those of Part I, thus verifying the hypothesis introduced in that work.

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