Piezoresistivity and tunneling-percolation transport in apparently nonuniversal systems

Abstract

We formulate a generalized tunneling-percolation model that describes the electrical properties of conductorinsulator cellular disordered systems. This model predicts and explains the experimentally observed universal and nonuniversal behaviors of such properties and the crossover between them. Studying both the conductance and the corresponding piezoresistive response coefficient we show, by using effective-medium theories and Monte Carlo calculations, that the crossover of the conductivity-percolation exponent is reflected by a corresponding crossover in the behavior of the above coefficient, thus providing a more practical means to characterize the critical region of the system.

A model for the dependence of the electrical conductance with the applied stress in insulating-conducting composites

“…͑8͒ is a derivative expression while integrated relationships, like = o ͑p − p c ͒ t , are not longer valid in the considered range of conductance-strain far from the percolation threshold. Variations in t with have been experimentally presented by Johner et al, 17 although for relatively small values of ͉͑ ͉ ϳ 10 −4 ͒ and at the vicinity of the percolation threshold. Therefore, we present in this section the expressions of , ⌫ ʈ , and G in terms of t͑ ͒ and ͑p − p c ͒͑ ͒ without assuming any functional dependence of t͑ ͒ and ͑p − p c ͒͑ ͒ with , which must be valid in the whole range of possible strains.…”

“…It must be noted that changes of ͑p − p c ͒ with the applied stress must be taken into account because of the relatively large strains considered here, which represents a central difference with respect to Ref. 17 where very small strains were used and therefore the dependence of p − p c with was reasonably neglected. Hence, in terms of differential equations, the differential strain, d is the origin of the differential changes d and d͑p − p c ͒.…”

“…This picture, the coexistence of a lattice of sites together with a subnetwork of "tunneling bonds" seems to be at present the more developed description of the socalled tunneling-percolation model ͑TPM͒. 13,14,16,17,20,21,24,27 In practice, there is no simple manner to distinguish between direct contact and tunneling. Hence, both possibilities are kept, as already indicated by Kchit and Bossis.…”

“…These systems are usually considered as isotropic percolating networks where the dependence of transport properties, like the dc-electrical conductance, G, are expressed as functions of the percolation probability between neighboring particles. [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] Many experimental works have been reported concerning the effect of mechanical stress on G ͑Refs. 9, 19, and 28-39͒ and the ac-impedance of composites, [38][39][40][41][42] but the systematic theoretical investigation of the dependence of G with the external applied stress has been initiated in a few relevant works in recent years.…”

“…9, 19, and 28-39͒ and the ac-impedance of composites, [38][39][40][41][42] but the systematic theoretical investigation of the dependence of G with the external applied stress has been initiated in a few relevant works in recent years. [13][14][15][16][17]20,21,24 The main experimental features commonly observed in pressure sensors based on elastomer composites are high sensitivity at low applied stress, currently with exponential rise of G as function of the applied pressure, followed by saturation. 29,35,36,39 The aim of this work is to contribute to the discussion about the dependence of G with the external applied stress ͑and the resulting strain͒ by introducing a model which accounts for these features.…”