Connection between the macroscopic electric and mechanical susceptibilities

Abstract

The following relationship is derived between the dielectric permittivity ε(ω) and the complex shear viscosity η(ω): [ε(ω)−ε∞]/(ε0−ε∞) = [1−i ωη(ω)K]−1. This equation is derived from both a generalization of Debye's treatment and from the Kubo formalism. The model consists of dipoles imbedded in rigid beads that are in turn imbedded in the viscous medium. A frequency dependent η(ω) implies nonexponential decay of the electric dipoles and results in skewed-arc behavior in the Cole-Cole plots except when η(ω) is represented by a single Maxwell element or by a single Viogt element. Consistency with the requirements of causality and reality is displayed. Experimental ε(ω) are predicted reasonably accurately by use of experimental η(ω) and the above equation.