Tunneling conductivity in composites of attractive colloids

In conductor-insulator nanocomposites in which conducting fillers are dispersed in an insulating matrix, the electrical connectedness is established by inter-particle tunneling or hopping processes. These systems are intrinsically non-percolative and a coherent description of the functional dependence of the conductivity sigma on the filler properties, and in particular of the conductor-insulator transition, requires going beyond the usual continuum percolation approach by relaxing the constraint of a fixed connectivity distance. In this article, we consider dispersions of conducting spherical particles which are connected to all others by tunneling conductances and which are subjected to an effective attractive square-well potential. We show that the conductor-insulator transition at low contents phi of the conducting fillers does not determine the behavior of sigma at larger concentrations, in striking contrast to what is predicted by percolation theory. In particular, we find that at low phi the conductivity is governed almost entirely by the stickiness of the attraction, while at larger phi values sigma depends mainly on the depth of the potential well. As a consequence, by varying the range and depth of the potential while keeping the stickiness fixed, composites with similar conductor-insulator transitions may display conductivity variations of several orders of magnitude at intermediate and large phi values. By using a recently developed effective medium theory and the critical path approximation, we explain this behavior in terms of dominant tunneling processes which involve inter-particle distances spanning different regions of the square-well fluid structure as phi is varied. Our predictions could be tested in experiments by changing the potential profile with different depletants in polymer nanocomposites. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4705307]

Impact of tunneling anisotropy on the conductivity of nanorod dispersions

Claudio Grimaldi, Biagio Nigro

While the tunneling conductance between two spherical-like conducting particles depends on the relative interparticle distance, the wave function overlap between states of two rodlike particles, and so the tunneling conductance, depends also on the relative orientation of the rod axes. Modeling slender rodlike particles as cylindrical quantum wells of diameter D and length L >> D, we calculate the matrix element of the tunneling between two rods for arbitrary relative orientations of the rod axes. We show that tunneling between two parallel rods is about L/root D xi times larger than the tunneling matrix element for perpendicular rods, where xi is the tunneling decay length. By considering the full dependence of the tunneling conductance on the angle between rod axes, we calculate within an effective medium theory the conductivity of dispersions of rods with different degrees of alignment. We find that for isotropically oriented rods, the effect of orientation in the tunneling processes is marginal for all rod concentrations. On the contrary, for systems of strongly aligned rods, the enhanced tunneling between nearly parallel rods increases significantly the system conductivity in a relatively large concentration range. Next, we consider systems in which short-range attraction between rods is added, as in dispersions of rods with depletion interaction. We find that the strongly anisotropic attraction promotes enhanced tunneling between neighboring parallel rods, increasing the effective medium conductivity by several orders of magnitude compared to the case in which the angular dependence of tunneling is ignored, even for relatively weak attractions.

American Physical Society2014

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

Tunneling and percolation transport regimes in segregated composites

Claudio Grimaldi, Biagio Nigro, Peter Ryser

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.

2012