Frequency-dependent (ac) Conduction in Disordered Composites: a Percolative Study

TL;DR

This paper investigates the frequency-dependent ac conduction in disordered composite materials using a percolative resistor-tunneling network model, revealing power-law behavior near criticality and contrasting low-frequency responses.

Contribution

It introduces a correlated RC model for ac conduction in disordered systems and compares its predictions with effective medium approximation and traditional models.

Findings

Power-law exponent of 0.7 near percolation threshold

Low-frequency quadratic or linear dependence on frequency

Comparison of model predictions with experimental data

Abstract

In a recent paper [Phys. Rev. B{\bf57}, 3375 (1998)], we examined in detail the nonlinear (electrical) dc response of a random resistor cum tunneling bond network ($RRTN$, introduced by us elsewhere to explain nonlinear response of metal-insulator type mixtures). In this work which is a sequel to that paper, we consider the ac response of the $RRTN$-based correlated $RC$ ($CRC$) model. Numerical solutions of the Kirchoff's laws for the $CRC$ model give a power-law exponent (= 0.7 near $p = p_c$) of the modulus of the complex ac conductance at moderately low frequencies, in conformity with experiments on various types of disordered systems. But, at very low frequencies, it gives a simple quadratic or linear dependence on the frequency depending upon whether the system is percolating or not. We do also discuss the effective medium approximation ($EMA$) of our $CRC$ and the traditional random $RC$ network model, and discuss their comparative successes and shortcomings.