On the rheological modeling of filled polymers with particle-matrix interactions

Abstract

In this paper constitutive equations are developed for the rheological description of highly filled polymers in which particle-matrix interactions are more significant than interparticle interactions. At any point in the deformation history the polymer chains are classified as either “free” or “trapped” (to the particles), the total stress being assumed to be the sum of the stresses in these two types of chains. When a load is applied to this system, it is hypothesized that a fraction of the trapped chains becomes free, and that simultaneously some free chains become trapped, with a balance between the two described by a deformation rate dependent kinetic equation. The rheological behavior of the free chains is described by stable nonlinear viscoelastic constitutive equations for unfilled polymers. For the trapped chains similar equations are used, but with the relaxation time in the evolution equation scaled by a scalar “mobility” function of the degree of chain debonding from the particles. All the basic features of highly filled systems such as anisotropic yield stresses, thixotropy, and frozen memory during relaxation can be described by this scheme without using any yield criterion. Preliminary comparisons are made with experimental data in simple shear and simple elongation.