Modulus evaluation of particulate composites using generalized viscosity model for solutions with suspended particles

Abstract

AbstractThe theoretical relationship between the shear modulus of a particulate reinforced composite and the viscosity of a solution with suspended particles was first proposed by Goodier. Since that time several partially successful attempts have been made in the literature to derive equations to describe the available relative shear modulus–particulate concentration data. Recently a new generalized suspension viscosity equation appeared in the literature which for the first time addresses the detailed effects of particle size, particle size distribution, and packing fraction. This new viscosity equation was applied to available modulus literature on particulate composites in this study. Four significant particulate composite modulus derivations in the literature were all shown in this study to yield the same theoretical “intrinsic modulus” of a particulate composite. The generalized viscosity–modulus equation yielded an excellent fit of the shear modulus–particulate concentration data of both Smallwood and Nielsen using a variable intrinsic modulus. Some fillers predicted the Einstein limiting value of the intrinsic modulus while other fillers yielded intrinsic modulus values that were either larger or smaller than this value. The intrinsic modulus for carbon black in rubber was much larger than Einstein's predicted value. However, intrinsic modulus values smaller than Einstein's prediction were obtained at temperatures below the glass transition temperature of the matrix. Unfortunately, the previously obtained direct relationship between the particle interaction coefficient and particulate size for suspension viscosities with a constant intrinsic viscosity was not obtaind for shear modulus—particulate concentration data using a variable intrinsic modulus. © 1994 John Wiley & Sons, Inc.