The quantitative approach to the composition heterogeneity of the products of reactions of polymers

The problem of describing the composition heterogeneity of the products of reactions of substituent groups on a polymer chain when there are interactions between neighboring groups is considered. A Monte Carlo simulation method and a modified first‐order Markovian approximation are proposed for obtaining composition distributions. The conditions of the mathematical experiment (the optimum length of the model chain and the size of the sample population) are found from a comparison of calculated parameters of the distribution of units with the exact values obtained by accurate analytical solution. These conditions depend upon the ratios k0:k1:k2 of rate constants for reaction of groups with neither, one, or both neighboring groups already reacted. The modified first‐order Markovian approximation gives results close to those of the Monte Carlo simulation for fairly long chains (100 units or more). Results are summarized graphically for calculations of the composition heterogeneity for various k0:k1:k2 ratios. As an example of the application of the suggested theoretical approaches the quaternization of poly‐4‐vinylpyridine with benzyl chloride is considered. The individual rate constants were found from experimental kinetic data. The functions of composition distribution calculated with these constants (k0 = 5.8 × 10−4 l mole−1 sec−1, k1 = k2 = 1.7 × 10−4 l mole−1 sec−1) were compared with experimental data obtained by gel permeation chromatography. Fairly good coincidence was found between experimental and calculated data. The satisfactory description of both reaction kinetics and composition heterogeneity by the same constants enables us to conclude that the neighboring group effect is dominant in this reaction.