Continuous and discontinuous models for transport phenomena in polymers



A model for transport phenomena in polymers accompanied by morphological changes is presented that includes the essential features of a variety of seemingly disparate models available in the literature. The latter are classified as special cases of the model considered, and according to whether discontinuities of the morphology are or are not explicitly described. An ordering analysis is presented that indicates under which conditions one or more of the terms appearing in the differential equations can be neglected. A special subcase, termed surface crystallization, is shown to emerge in a well-defined asymptotic sense from the general model, and is also shown to yield predictions which are closely analogous to those of a model of Astarita and Sarti that has been very successful in correlating experimental data of the type called case II transport. The advantage of the surface crystallization model is that it is not an ad hoc model. The models considered result in hyperbolic differential equations, as is often the case when relaxation phenomena are taken into account. A procedure for numerically solving hyperbolic equations with great ease is presented.