Tunneling-percolation Model Research Articles

Tunneling-percolation model of multicomponent nanocomposites

Using a mixture of different types of fillers has been experimentally shown to improve the electrical conductivity of polymer nanocomposites beyond the weighted average due to synergistic effects. In this study, we develop a critical path analysis-based tunneling-percolation model for multicomponent systems of nanocomposites with ellipsoidal fillers. The nature of the interaction between different filler components is controlled by a key modeling parameter capturing the tunneling interactions between fillers. This generalization allows us to examine scenarios where the nature of a given type of filler can be varied continuously from an insulating-type to a conductive-type. The percolation behavior of two-component systems with a combination of prolate, oblate, and spherical fillers is investigated using Monte Carlo simulations for different relative volume fractions and nature of interactions while keeping the total volume fraction fixed. The simulation results are shown to be in semi-quantitative agreement with predictions made by the second-virial-approximation-based theories. Our results suggest that for multicomponent systems with well-dispersed fillers, the synergistic effects are linked directly with the nature of interactions between different filler types. Moreover, addition of prolate fillers to oblate or spherical fillers should generally improve the electrical conductivity of multicomponent nanocomposites.

Effect of filler alignment on percolation in polymer nanocomposites using tunneling-percolation model

In this study, we examine the effect of filler alignment on percolation behavior of polymer nanocomposites using Monte Carlo simulations of monodisperse prolate and oblate hard-core soft-shell ellipsoids representing carbon nanotubes and graphene nanoplatelets, respectively. The percolation threshold is observed to increase with increasing extent of alignment as expected. For a highly aligned system of rod-like fillers, the simulation results are shown to be in good agreement with the second virial approximation based predictions. However, for a highly aligned system of disk-like fillers, the second virial approximation based results are observed to significantly deviate from the simulations, even for higher aspect ratios. The effect of filler alignment on anisotropy in percolation behavior is also studied by predicting the percolation threshold along different directions. The anisotropy in percolation threshold is found to vanish even for highly aligned systems of fillers with increasing system size.

Photo-thermal electrical resistance response of polyisoprene/nanographite composites

Laser induced photo-thermal resistance response (PTRR) of polyisoprene/nanographite (PN) composites was studied. An inverse character of photoresistance in comparison to semiconductor-like materials was observed: electrical resistance of the PN composite increases when the intensity of the laser radiation is increased. The observed response can be explained by the photo-thermal effect: if the temperature of the PN composite rises because of optical radiation absorption then the electrical resistance increases due to positive temperature coefficient of the composite. Theoretical explanation of the positive temperature coefficient effect in PN composites based on tunneling-percolation model is given.

Tunneling-percolation behavior of polydisperse prolate and oblate ellipsoids

We report Monte Carlo simulations of systems of polydisperse prolate and oblate ellipsoids using the critical path based tunneling-percolation model. For polydisperse prolate ellipsoids, the critical percolation volume fraction ϕc is shown to have a quasi-universal dependence on weight-averaged aspect ratio. For polydisperse oblate ellipsoids, ϕc is shown to have a quasi-universal dependence on the apparent aspect ratio, which is a function of up to fourth moment of the size distribution, as given by the generalized connectedness percolation theory. The functions are observed to approach the theoretical predictions for higher volume fractions and higher aspect ratios. The model predictions are compared with experimental data available on polydisperse multi-walled nanotubes (prolate ellipsoids) and graphene nanoplatelets (oblate ellipsoids) to estimate the tunneling lengthscale which is found to be well within the expected range.

Rheological and Electrical Properties of CB/HDPE Composites

The rheological and electrical properties of composites formed by filling high density polyethylene (HDPE) with carbon black (CB) were characterized. Nonuniversal electrical behavior was observed with critical exponent t of 2.9 for the composites. The phenomenon was interpreted in terms with tunneling-percolation model. The effects of shearing frequency and particle concentration on the rheological behavior of the composites were investigated. A second plateau of storage modulus and strong shear thinning behavior were observed at low frequencies induced by aggregation of fillers. And the rheological percolation threshold is found to coincide well with the electrical one.

Tuning the Sensitivity of a Metal-Based Piezoresistive Sensor Using Electromigration

We report a simple method to enhance the piezoresistive sensitivity of a gold film by more than 30 times and demonstrate it using a microcantilever resonator. Our method depends on controlled electromigration that we use to tune the resistance and sensitivity of the piezoresistive sensor. We attribute the enhancement in strain sensitivity to the creation of an inhomogeneous conduction medium at a predefined location by directed and controlled electromigration. We understand this phenomenon with tunneling-percolation model, which was originally hypothesized to explain nonuniversal percolation behavior of composite materials.

Diffusion, Swelling and Electrical Properties of Polyisoprene/Multiwall Carbon Nanotube Composites in Organic Solvent Vapours

Polyisoprene/nanostructured carbon composites have been fabricated utilizing multiwall carbon nanotubes and carbon black nanoparticles as electrically conductive filler materials. Simultaneous measurements of (1) absorbed mass of organic solvent vapours (OSV), (2) swelling predicted elongation of sample and (3) electrical resistance changes versus the time of the presence of polyisoprene/multiwall carbon nanotube composites (PCNTC) in the OSV ambience were carried out by an in-house computerized setup. Non-Fickian anomalous diffusion has been found for all PCNTC samples as well as for reference samples of polyisoprene/high structure carbon black composites (PCBC). Obtained results indicate that the filler material content can play a substantial role in vapour diffusion into the composite. An advanced tunneling-percolation model was developed and used for describing of the OSV sensing effect in PCNTC and PCBC.

A computational study of tunneling-percolation electrical transport in graphene-based nanocomposites

Using a tunneling-percolation model and Monte Carlo simulations, we study the resistivity of graphene-based nanocomposites as a function of both graphene sheet and device parameters. We observe an inverse power law dependence of resistivity on device dimensions and volume fraction near the percolation threshold, and find that high aspect ratio graphene sheets result in a much lower resistivity, particularly at low sheet densities. Furthermore, we find that graphene sheet area affects nanocomposite resistivity more strongly than sheet density does. These results impart important fundamental insights for future experimental investigations and applications of graphene-based conductive nanocomposites.

TUNNELING PERCOLATION MODEL OF THE ELECTRICAL CONDUCTIVITY OF PARTICULATE NANOCOMPOSITES

The nanocomposites consisting of conducting nanoparticles and insulating matrix are studied. A tunneling percolation model is developed for their peculiar conduction behavior based on the equivalent-particle concept. It provides a clear microstructure-property correlation by combining many-particle statistics, effective-medium theory, and classical percolation theory. Its availability is assessed by available experimental data.

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

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 ${t}_{0}\ensuremath{\simeq}2$, 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 nonuniversality 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.

Percolation transition and hydrostatic piezoresistance for carbon black filled poly(methylvinylsilioxane) vulcanizates

The percolation transition and the hydrostatic piezoresistance for carbon black (CB) filled poly(methylvinylsilioxane) vulcanizates were studied as a function of CB volume fraction. A revised tunneling-percolation model based on the method of “subcritical networks” was proposed, which can not only account for the apparent nonuniversal percolation, but also figure out the contribution of changing tunneling current to the hydrostatic piezoresistance. Although there is a general tendency that the relative contribution of tunneling current increases with increasing filler concentration, it is always the variation of effective filler volume fraction which dominates the hydrostatic piezoresistance for the present system, due to the rather limited mobility of the mediating polymer layer between neighboring CB aggregates. The pressure and concentration dependences of the hydrostatic piezoresistance were interpreted in terms of the connectivity and/or the fractal nature of the percolation network. The concentration dependence of hydrostatic piezoresistance could even be associated with the strength of filler–matrix interaction. The baseline drift and poor reproducibility of hydrostatic piezoresistance were ascribed to the residual compressive strain of the rubber matrix, which could not be completely eliminated but could be deducted from the piezoresistance by a novel resistance baseline removal method.

Piezoresistivity and tunneling-percolation transport in apparently nonuniversal systems

We formulate a generalized tunneling-percolation model that describes the electrical properties of conductor-insulator 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.

Spatially inhomogeneous transport in phase-separated polycrystalline manganites

Based on intrinsic phase separation between ferromagnetic metallic domains and paramagnetic insulating domains, and extrinsic band-bending effects at the grain boundaries, a tunneling percolation model is established for the magnetotransport in phase-separated polycrystalline manganites. Within this model, the competition between intrinsic colossal magnetoresistance and extrinsic tunneling magnetoresistance in these materials is mapped onto a multicomponent bond-disordered random resistor network, where the fraction of each kind of bond is determined self-consistently. For the existence of a distribution of intergranular distance and the exponential dependence of tunneling resistance on the intergranular distance, the network exhibits strong disorder dependence of low-field magnetoresistance and is expected to yield a nonuniversal behavior of electrical transport in some particular cases, which are also magnetic field dependent. Further numerical simulations on the temperature dependence of resistance and magnetoresistance give a reasonable explanation of the dependence of magnetotransport on the intergranular connectivity and the grain size. All of these results agree will with experimental observation.

Tunneling-percolation origin of nonuniversality: Theory and experiments

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.

Segregated tunneling-percolation model for transport nonuniversality

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.

Piezoresistivity and conductance anisotropy of tunneling-percolating systems

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 $\ensuremath{\lambda}$ remains universal also when the conductive exponent is not, suggesting a purely geometric origin of $\ensuremath{\lambda}.$ We obtain these results by an exact solution of the piezoresistive problem on a Bethe lattice and by Monte Carlo calculations and finite-size scaling analysis on square lattices. We discuss our results in relation to the nature of transport for a variety of materials such as carbon-black--polymer composites and ${\mathrm{RuO}}_{2}$-glass systems which show nonuniversal transport properties and coexistence between tunneling and percolating behaviors.