Dynamics of Molecular Weight Distributions for Polymer Scission

The dynamics of molecular weight distributions (MWDs) for polymer degradation is of interest to various applications. The time evolutions of MWDs can be determined by solving the governing population balance equations, which are generally solved by moment techniques wherein the initial distribution is represented by a gamma distribution. The evolution of MWD is determined by the time dependence of the gamma distribution parameters. The population balance equations (PBEs) can also be solved numerically by converting them to partial differential equations (PDEs). The degradation rate coefficient in the PBE depends on the molecular weight x as $(x - x_o)^{\lambda}$ or as a quadratic polynomial in x. The solutions obtained with the moment technique, which are inaccurate for certain cases, are compared with the solutions determined by solving the PDEs. The utility of the numerical scheme is also discussed for cases where the initial distribution cannot be represented satisfactorily by a gamma distribution