Prediction of Bound-Rubber Modulus by Clausius—Mossotti Approximation

Abstract

Abstract The Clausius—Mossotti approximation has been used to determine the modulus of bound rubber attached to carbon black in a gum-rubber/carbon-black compound. The effective hydrodynamic concentration of the carbon-black/bound-rubber structure was first determined based on the assumption of spherical filler particles with a uniform layer of bound rubber on the surface. The true carbon-black concentration was then subtracted from this concentration, and a three component modeling scheme was used. The three components were considered to be bound-rubber, carbon black, and gum-rubber matrix. The Clausius—Mossotti approximation was used to determine the bound-rubber modulus that would give the same compound modulus based on equivalent hydrodynamic volume. Results indicate that bound-rubber concentration decreases with increasing strain. At zero strain, the bound-rubber concentration is approximately equal to the carbon-black concentration. Modulus values of bound rubber were found to be 3 to 4 times greater than gum-modulus values at very low strains. The relatively greater magnitude of bound-rubber modulus decreased with increasing strain until the filler effect appears to be almost purely hydrodynamic. The electromagnetic theory-based Clausius—Mossotti model was found to predict bound-rubber moduli that were in agreement with a mechanical model, the Kerner model.