On the origin of transport non-universality and piezoresistivity in segregated conductor-insulator composites and application to thick-film resistors

In this thesis we address the description of electrical transport properties of disordered conductor-insulator composites, mostly by numerical Monte Carlo simulations and analytical study of realistic tunnelling-percolation models. Such composites are basically constituted by conducting particles dispersed in an insulating matrix and present a conductor-insulator phase transition, with critical exponent t, as the volume concentration of the conducting phase x is decreased towards a critical concentration xc. Percolation theory shows that close to this phase transition the conductivity Σ of the composite follows a simple power-law Σ = Σ0(x - xc)t        (1) with a universal transport exponent t = t0 ≃ 2, independent of the detailed characteristics of the system. Two representative examples of such composite materials are conducting polymers, used for example for anti-static purposes, electromagnetic interference shielding or current-limiting switches and thick-film resistors (TFRs) used as resistors in electronic applications where high thermal, chemical, mechanical and aging stability are needed and as sensing elements for force and pressure sensors. This work focuses mostly on TFRs, composed of a glassy phase embedding small conducting grains, which are, from our point of view, ideal model systems. They present a complex microstructure, due to segregation of the conducting phase in the spaces left over in between the large glassy regions, unusually large piezoresitive responses and are an important class among the composite materials presenting universality-breakdown of the critical transport exponent, showing values of t > t0, and as large as 10. Experimentally, non-universal transport exponents have been repeatedly observed, but we lack a theory accounting satisfactorily for this phenomenon. A better understanding of this transport non-universality is the main issue addressed in this thesis. We formulate a lattice and a continuum model, aimed at describing the transport properties of disordered conductor-insulator composites, presenting or not a segregated microstructure. Our main assumptions are that the transport properties, close to the phase transition, are governed by the formation of a percolating cluster of conducting particles and that the electrical transport between the conducting particles is mainly governed by simple tunnelling. We also introduce segregation in the continuum model, which is the main interaction between the conducting and insulating phases considered in this work. In this framework, we present a complete study of segregation and its influence on the critical concentration xc. We show how the relative size of the conducting and insulating particles changes the effectiveness of segregation. Moreover we show that the critical concentration xc is not a monotonically decreasing function of segregation, but presents a minimum, well before maximal segregation is reached, which is a result of broad technological interest. Now, the main outcome of this work is a new interpretation of the experimentally observed non-universality of the direct current transport exponent. We show that realistic tunnelling-percolation models, although not presenting true non-universality of transport, lead to a transport exponent t strongly depending on the concentration of the conducting phase x, so that the conductivity does, indeed, not follow a simple power-law. As t is experimentally extracted by fitting the concentration dependence of the conductivity with the simple power law of equation 1, apparent non-universal transport exponents will be obtained. This is what we call apparent non-universality, which might be experimentally very difficult to distinguish from true non-universality. We propose an analytical formula, containing only few parameters of our model, replacing the power-law of equation (1), which fits very nicely some experimental measurements of the conductivity of conductor-insulator composites. Our models also account for the large increase of the piezoresistivity experimentally observed in conductor-insulator composites close to the percolation threshold. But contrary to classical tunnelling-percolation predictions, we show that more realistic models lead to a saturation of the piezoresistivity close enough to the percolation threshold. This feature has not been observed yet, but would be a direct confirmation of the scenario proposed in this work for the appearance of transport non-universality.

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