Convection and diffusion of polymer network strands

A review of several important constitutive equations is herein conducted with an eye towards determining those most suitable for use in modelling polymer melt processing. General principles are invoked for a priori screening of the equations without needing detailed comparison of the model predictions with experimental data. These principles, which are derived from continuum mechanics, thermodynamics and molecular kinetic theory, and dela with convection and diffusion of entangled polymer strands during flow, are: (1) During sudden deformations, the stress is a unique function of the total strain. (2) The second law of thermodynamics holds for all deformations. (3) The constitutive equation can be derived from a plausible molecular model which describes the convection and diffusion. (4) The model parameters can be determined by a reasonable number of rheometric experiments. Based on these principles, it is concluded that separable free energy models are the most promising. These are either BKZ integral models with a kernel factorable into a time-dependent and a strain-dependent part. or sets of Maxwell-type differential equations that employ a generalized convected derivative, and that are linear in stress in the absence of flow.