EFFECT OF PARTICLE SHAPE AT FINITE CONCENTRATION ON ELASTIC-MODULI OF FILLED POLYMERS

This is a report on a theoretical study in which the approach of Eshelby, developed for dilute dispersions, is generalized to include the interaction of filler with filler. It is then utilized to determine the five elastic moduli of a filled polymer containing aligned ellipsoidal particles at finite concentrations phi . The anisotropic particle shape is characterized by an aspect ratio rho of an ellipsoid. The present theory compares well with available experiments in the literature. The experimentally verified Kerner equation for spherical particles and rule of mixtures for the longitudinal Young's modulus at rho yields infinity are special cases of the new results.