Mathematical modeling of chain-end scission using continuous distribution kinetics

Mathematical models that use continuous distributions to represent reacting polymer populations have been highly successful, and the method of moments is often used as a convenient means for obtaining solutions for the properties of the polymer population over time. However, there has been some controversy regarding the application of the method of moments for polymer degradation by chain-end scission. Here, we provide a rigorous treatment of chain-end scission using a continuous distribution for the polymer population and show that the method of moments has shortcomings for general use. As an alternative to the method of moments, we propose a solution method in which the continuous distribution is mapped to a set of discretized points, and the time-evolution of the distribution is obtained at the grid points. The results using this method are shown to agree well with the solution to the discrete model. The method is particularly well-suited for solving problems involving broadly distributed populations that are often found in nature.