Theoretical Depolymerization Kinetics. II. The Effect of Molecular-Weight Distribution in Degrading Polymers Undergoing End-Group Initiation

Abstract

It is shown that the set of coupled rate equations describing the end‐group‐initiated degradation of a polymer containing various degrees of polymerization can be transformed into a set of coupled equations describing the rate of change of the moments of the molecular‐weight distribution. These moment equations can be used as the basis for approximate but systematic treatments of degradation in systems with arbitrary initial molecular‐weight distributions. In particular, in this paper it is shown that if the Schulz—Zimm distribution is assumed to be sufficiently general to represent the molecular‐weight distribution through the course of the degradation, the moment equations allow the problem to be reduced to three simultaneous differential equations. These equations have been solved by digital computer and the sample weight, number‐average molecular weight, and distribution‐width parameter tabulated as functions of time for a wide range of kinetic parameters and initial distributions.