Tunneling and percolation transport regimes in segregated composites

We consider the problem of electron transport in segregated conductor-insulator composites in which the conducting particles are connected to all others via tunneling conductances, thus forming a global tunneling-connected resistor network. Segregation is induced by the presence of large insulating particles, which forbid the much smaller conducting fillers from occupying uniformly the three-dimensional volume of the composite. By considering both colloidal-like and granular-like dispersions of the conducting phase, modeled respectively by dispersions in the continuum and in the lattice, we evaluate by Monte Carlo simulations the effect of segregation on the composite conductivity sigma, and show that an effective-medium theory applied to the tunneling network reproduces accurately the Monte Carlo results. The theory clarifies that the main effect of segregation in the continuum is that of reducing the mean interparticle distances, leading to a strong enhancement of the conductivity. In the lattice-segregation case the conductivity enhancement is instead given by the lowering of the percolation thresholds for first and beyond-first nearest neighbors. Our results generalize to segregated composites the tunneling-based description of both the percolation and hopping regimes introduced previously for homogeneous disordered systems.

Transport exponent in a three-dimensional continuum tunneling-percolation model

Claudio Grimaldi, Niklaus Johner, Peter Ryser

The tunneling-percolation mechanism of conduction in disordered conductor-insulator composites is studied for a realistic continuum model where conducting and impenetrable spherical particles are dispersed in a three-dimensional continuum insulating material. Conduction between particles is via tunneling processes and a maximum tunneling distance d is introduced. We determine the percolation critical concentration for several values of d. By doing so, we relax the restrictions applied in the previous studies of the problem, i.e., the considerations of the underlying lattice and the contribution of only the nearest neighbors. The tunneling-percolation transport is then analyzed by studying the conductance of the composite at and near the percolation threshold using a decimation procedure and a conjugate gradient algorithm. We show that at the critical concentration, and independently of the tunneling parameters, the critical transport exponent t reduces to the universal value t(0) similar or equal to 2, while moving away from the percolation threshold, the conductance exponent becomes larger than t(0), acquiring a strong concentration dependence. We interpret this feature as arising from the peculiar form of the distribution function for the local tunneling conductances. Consequently, apparent non-universality of transport appears when the conductance of the composite is fitted by forcing the exponent to be independent of the concentration. This leads us to believe that our tunneling-percolation theory is sufficient to explain the nonuniversal transport exponents observed in real disordered conductor- insulator compounds.

2008

Solution of the tunneling-percolation problem in the nanocomposite regime

Gianluca Ambrosetti, Claudio Grimaldi, Thomas Maeder, Peter Ryser

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 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.

2010

Electron tunneling in conductor-insulator composites with spherical fillers

Gianluca Ambrosetti, Claudio Grimaldi, Niklaus Johner, Thomas Maeder, Peter Ryser

We report on our Monte Carlo calculations of the conductivity of monosized and conducting spherical particles dispersed in a homogeneous matrix, with interparticle transport mechanism given by electron tunneling. We show that our numerical results can be reproduced by a simple formula based on a critical path analysis and ξ which gives also a practical way to estimate the characteristic tunneling length in real composites. We find that ξ is about 1 nm for several low structure carbon black polymer composites, in agreement with the expected order of magnitude.

2009