Piezoresistivity and conductance anisotropy of tunneling-percolating systems

Abstract

Percolating networks based on interparticle tunneling conduction are shown to yield a logarithmic divergent piezoresistive response close to the critical point as long as the electrical conductivity becomes nonuniversal. At the same time, the piezoresistivity or, equivalently, the conductivity anisotropy exponent $\ensuremath{\lambda}$ remains universal also when the conductive exponent is not, suggesting a purely geometric origin of $\ensuremath{\lambda}.$ We obtain these results by an exact solution of the piezoresistive problem on a Bethe lattice and by Monte Carlo calculations and finite-size scaling analysis on square lattices. We discuss our results in relation to the nature of transport for a variety of materials such as carbon-black--polymer composites and ${\mathrm{RuO}}_{2}$-glass systems which show nonuniversal transport properties and coexistence between tunneling and percolating behaviors.