Piezoresistivity and conductance anisotropy of tunneling-percolating systems

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 lambda remains universal also when the conductive exponent is not, suggesting a purely geometric origin of 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 RuO2-glass systems which show nonuniversal transport properties and coexistence between tunneling and percolating behaviors.