Time evolution to similarity solutions for polymer degradation

The theory of polymer decomposition is basic in understanding polymer and plastics stability durability, characterization, and recycling. Polymers degrade by chain scission occurring randomly along the chain, at the chain midpoint, at the chain end, or by a combination of random chain-scission and chain-end scission. Mathematical solutions for polymer degradation were previously constrained to particular stoichiometric kernels (usually random scission) and to specialized distributions (such as the exponential distribution). Because the first term in a Laguerre-polynomial expansion is the gamma distribution and the initial molecular-weight distributions (MWDs) of polymers can be represented as superposed gamma distributions, the mathematical solution is represented as the time evolution of generalized gamma distribution parameters. Such solutions show how the first three moments of the MWD evolve in time for each of the chain-scission models. The rate coefficient for random chain scission is assumed to depend on MW chi as chi(lambda), and the stoichiometric kernel is symmetric as in random or midpoint chain scission. Except when lambda = 0, the distribution evolves to a similarity solution with the MW and time appearing together in the dimensionless group, chi(lambda)/beta(t). The case of chain-end scission, however, has no similarity solution.