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In conductor-insulator composites in which the conducting particles are dispersed in an insulating continuous matrix the electrical connectedness is established by interparticle quantum tunneling. A recent formulation of the transport problem in this kind of composites treats each conducting particle as electrically connected to all others via tunneling conductances to form a global tunneling network. Here, we extend this approach to nonhomogeneous composites with a segregated distribution of the conducting phase. We consider a model of segregation in which large random insulating spherical inclusions forbid small conducting particles to occupy homogeneously the volume of the composite, and allow tunneling between all pairs of the conducting objects. By solving numerically the corresponding tunneling resistor network, we show that the composite conductivity is enhanced by segregation and that it may remain relatively large also for very small values of the conducting filler concentration. We interpret this behavior by a segregation-induced reduction of the interparticle distances, which is confirmed by a critical path approximation applied to the segregated network. Furthermore, we identify an approximate but accurate scaling relation permitting to express the conductivity of a segregated systems in terms of the interparticle distances of a corresponding homogeneous system, and which provides an explicit formula for the conductivity which we apply to experimental data on segregated RuO2-cermet composites., Comment: 10 pages, 9 figures

We noted that the tunneling-percolation framework is quite well understood at the extreme cases of percolation-like and hopping-like behaviors but that the intermediate regime has not been previously discussed, in spite of its relevance to the intensively studied electrical properties of nanocomposites. Following that we study here the conductivity of dispersions of particle fillers inside an insulating matrix by taking into account explicitly the filler particle shapes and the inter-particle electron tunneling process. We show that the main features of the filler dependencies of the nanocomposite conductivity can be reproduced without introducing any \textit{a priori} imposed cut-off in the inter-particle conductances, as usually done in the percolation-like interpretation of these systems. Furthermore, we demonstrate that our numerical results are fully reproduced by the critical path method, which is generalized here in order to include the particle filler shapes. By exploiting this method, we provide simple analytical formulas for the composite conductivity valid for many regimes of interest. The validity of our formulation is assessed by reinterpreting existing experimental results on nanotube, nanofiber, nanosheet and nanosphere composites and by extracting the characteristic tunneling decay length, which is found to be within the expected range of its values. These results are concluded then to be not only useful for the understanding of the intermediate regime but also for tailoring the electrical properties of nanocomposites., Comment: 13 pages with 8 figures + 10 pages with 9 figures of supplementary material (Appendix B)

We report on a model of polymer nanocomposites with fibrous fillers which explicitly considers the microscopic filler features and replicates the composites as random distributions of particles interconnected via electron tunneling. By exploiting the critical path method, we are able to obtain simple formulas, applicable to most nanotube and nanofiber composites, which allow to infer the overall composite conductivity starting from few parameters like filler volume fraction, size, and aspect-ratio. The validity of our formulation is assessed by reinterpreting existing experimental results and by extracting the characteristic tunneling length, which is mostly found within its expected value range. These results can be used practically to tailor the electrical properties of nanocomposites., Comment: 4.4 pages, 3 figures, corrected typos and references updated

We evaluate the percolation threshold values for a realistic model of continuum segregated systems, where random spherical inclusions forbid the percolating objects, modellized by hard-core spherical particles surrounded by penetrable shells, to occupy large regions inside the composite. We find that the percolation threshold is generally a non-monotonous function of segregation, and that an optimal (i. e., minimum) critical concentration exists well before maximum segregation is reached. We interpret this feature as originating from a competition between reduced available volume effects and enhanced concentrations needed to ensure percolation in the highly segregated regime. The relevance with existing segregated materials is discussed., Comment: 5 pages, 4 figures

A vast class of disordered conducting-insulating compounds close to the percolation threshold is characterized by nonuniversal values of transport critical exponent t, in disagreement with the standard theory of percolation which predicts t = 2.0 for all three dimensional systems. Various models have been proposed in order to explain the origin of such universality breakdown. Among them, the tunneling-percolation model calls into play tunneling processes between conducting particles which, under some general circumstances, could lead to transport exponents dependent of the mean tunneling distance a. The validity of such theory could be tested by changing the parameter a by means of an applied mechanical strain. We have applied this idea to universal and nonuniversal RuO2-glass composites. We show that when t > 2 the measured piezoresistive response \Gamma, i. e., the relative change of resistivity under applied strain, diverges logarithmically at the percolation threshold, while for t = 2, \Gamma does not show an appreciable dependence upon the RuO2 volume fraction. These results are consistent with a mean tunneling dependence of the nonuniversal transport exponent as predicted by the tunneling-percolation model. The experimental results are compared with analytical and numerical calculations on a random-resistor network model of tunneling-percolation., Comment: 13 pages, 12 figures

We propose a model of transport in thick-film resistors which naturally explains the observed nonuniversal values of the conductance exponent t extracted in the vicinity of the percolation transition. Essential ingredients of the model are the segregated microstructure typical of thick-film resistors and tunneling between the conducting grains. Nonuniversality sets in as consequence of wide distribution of interparticle tunneling distances., Comment: 3 pages, 1 figure

We propose a theory of the origin of transport nonuniversality in disordered insulating-conducting compounds based on the interplay between microstructure and tunneling processes between metallic grains dispersed in the insulating host. We show that if the metallic phase is arranged in quasi-one dimensional chains of conducting grains, then the distribution function of the chain conductivities g has a power-law divergence for g -> 0 leading to nonuniversal values of the transport critical exponent t. We evaluate the critical exponent t by Monte Carlo calculations on a cubic lattice and show that our model can describe universal as well nonuniversal behavior of transport depending on the value of few microstructural parameters. Such segregated tunneling-percolation model can describe the microstructure of a quite vast class of materials known as thick-film resistors which display universal or nonuniversal values of t depending on the composition., Comment: 8 pages, 5 figures (Phys. Rev. B - 1 August 2003)(fig1 replaced)

We re-analyse earlier measurements of resistance R and piezoresistance K in RuO2-based thick-film resistors. The percolating nature of transport in these systems is well accounted by values of the transport exponent t larger than its universal value t=2.0. Furthermore, we show that the RuO2 volume fraction dependence of the piezoresistance data fit well with a logarithmically divergence at the percolation thresold. We argue that the universality breakdown and divergent piezoresistive response could be understood in the framework of a tunneling-percolating model proposed a few years ago to apply in carbon-black--polymer composites. We propose a new tunneling-percolating theory based on the segregated microstructure common to many thick-film resistors, and show that this model can in principle describe the observed universality breakdown and the divergent piezoresistance., Comment: 15 pages, 7 figures, (iopams.sty, stestack.sty)

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 discuss our results in relation to the nature of transport for a variety of materials such as carbon-black--polymer composites and RuO_2-glass systems which show nonuniversal transport properties and coexistence between tunneling and percolating behaviors., Comment: 6 pages, 3 figures, Added discussion on experiments