Discrete and continuous models for polymerization and depolymerization

A fundamental continuous model for the distribution kinetics of polymerization and its reverse, depolymerization, is shown to be consistent with the well-known discrete model. Solutions for discrete and continuous models are compared and shown to have identical expressions for molecular weight (MW) moments. Representing the continuous molecular-weight distribution (MWD) as a gamma distribution compares well with exact polymerization and depolymerization MWD solutions of the discrete model, except when the number of repeat units in the polymer is small. None of the solutions for chain end polymerization or depolymerization has the self-similar form, for which the MW and time would appear together in the same similarity variabl