Percolation in suspensions of polydisperse hard rods : quasi-universality and finite-size effects

We present a study of connectivity percolation in suspensions of hard spherocylinders by means of Monte Carlo simulation and connectedness percolation theory. We focus attention on polydispersity in the length, the diameter and the connectedness criterion, and invoke bimodal, Gaussian and Weibull distributions for these. The main finding from our simulations is that the percolation threshold shows quasi universal behaviour, i.e., to a good approximation it depends only on certain cumulants of the full size and connectivity distribution. Our connectedness percolation theory hinges on a Lee-Parsons type of closure recently put forward that improves upon the often-used second virial approximation [ArXiv e-prints, May 2015, 1505.07660]. The theory predicts exact universality. Theory and simulation agree quantitatively for aspect ratios in excess of 20, if we include the connectivity range in our definition of the aspect ratio of the particles. We further discuss the mechanism of cluster growth that, remarkably, differs between systems that are polydisperse in length and in width, and exhibits non-universal aspects.Comment: 7 figure

Computational Studies on the Effective Properties of Two-Phase Heterogeneous Media

The effective elastic modulus and conductivity of a two phase material system are investigated computationally using a Monte Carlo scheme. The continuum contains circular, spherical or ellipsoidal inclusions that are either uniformly or randomly embedded in the matrix. The computed results are compared to the applicable effective medium theories. It is found that the random distribution, permeability and particle aspect ratio have non-negligible effects on the effective material properties. For spherical inclusions, the effective medium approximations agree well with the simulation results in general, but the analytical predictions on void or non-spherical inclusions are much less reliable. It is found that the results for overlapping and nonoverlapping inclusions do not differ very much at the same volume fraction. The effect of the particle morphology is also investigated in the context of prolate and oblate ellipsoidal particles. The geometric percolation thresholds for circular, elliptical, square and triangular disks in the three-dimensional space are determined precisely by Monte Carlo simulations. These geometries represent oblate particles in the limit of zero thickness. The normalized percolation points, which are estimated by extrapolating the data to zero radius, are &eta c=0.9614 ± 0.0005, 0.8647 ± 0.0006 and 0.7295 ± 0.0006 for circles, squares and equilateral triangles, respectively. These results show that the noncircular shapes and corner angles in the disk geometry tend to increase the interparticle connectivity and therefore reduce the percolation point. For elliptical plate, the percolation threshold is found to decrease moderately when the aspect ratio &epsilon is between 1 and 1.5 but decrease rapidly for &epsilon greater than 1.5. For the binary dispersion of circular disks with two different radii, &eta c is consistently larger than that of equisized plates, with the maximum value located at around r_1/r_2 =0.5

Stress-dependent electrical transport and its universal scaling in granular materials

We experimentally and numerically examine stress-dependent electrical transport in granular materials to elucidate the origins of their universal dielectric response. The ac responses of granular systems under varied compressive loadings consistently exhibit a transition from a resistive plateau at low frequencies to a state of nearly constant loss at high frequencies. By using characteristic frequencies corresponding to the onset of conductance dispersion and measured direct-current resistance as scaling parameters to normalize the measured impedance, results of the spectra under different stress states collapse onto a single master curve, revealing well-defined stress-independent universality. In order to model this electrical transport, a contact network is constructed on the basis of prescribed packing structures, which is then used to establish a resistor-capacitor network by considering interactions between individual particles. In this model the frequency-dependent network response meaningfully reproduces the experimentally observed master curve exhibited by granular materials under various normal stress levels indicating this universal scaling behaviour is found to be governed by i) interfacial properties between grains and ii) the network configuration. The findings suggest the necessity of considering contact morphologies and packing structures in modelling electrical responses using network-based approaches.Comment: 12 pages, 4 figure

Dielectric mixtures -- electrical properties and modeling

In this paper, a review on dielectric mixtures and the importance of the numerical simulations of dielectric mixtures are presented. It stresses on the interfacial polarization observed in mixtures. It is shown that this polarization can yield different dielectric responses depending on the properties of the constituents and their concentrations. Open question on the subject are also introduced.Comment: 40 pages 12 figures, to be appear in IEEE Trans. on Dielectric

Composition and Manufacturing Effects on Electrical Properties of Li/FeS2 Thermal Battery Cathodes

Li/FeS2 thermal batteries provide a stable, robust, and reliable power source capable of long-term electrical energy storage without performance degradation. These systems rely on a eutectic salt that melts at elevated temperature, activating the cell. When the electrolyte melts, the cathode becomes a suspension, with cathode particles suspended in a molten salt. The suspension experiences mechanical deformation, or slumping.\u27 This slump changes the mechanical compression of the cell, as well as the tortuosity and electronic and ionic conductivity of the cell as the cathode mesostructure is reordered in response to the external compressive stress. The combined effect of deformation, component composition, and manufacturing conditions on electrical conductivity has not been studied, yet the cathode electrical properties are critically important to battery performance. This thesis presents simulation results from a computer model in combination with experiments to elucidate the effects of electrical conductivity in FeS2 cathode pellets when composition and manufacturing parameters are varied. Experiments applied impedance spectroscopy measurements of pressed-powder cathode pellets before and after slumping. Pellets were manufactured with variations in pellet density, FeS2 particle size distribution, and FeS2 content. The results showed that prior to slumping, the electrical conductivity increased with pellet density and FeS2 content. After slumping, pellets exhibited greater electrical conductivity, but the effects of processing parameters appear to have been erased, at least within the ranges tested. The conformal decomposition finite element method (CDFEM) was applied to surface-meshed geometric representations of cathode microstructures generated from microcomputed tomography reconstructions. Results from the SIERRA/Aria finite element code indicate that the selected processing and composition parameters do not provide a clear trend on the preslumped electrical conductivity, but density slightly affected the postslumped conductivity. These results indicate that the simulations lacked fidelity compared to experiments. However, the simulations combined with experimental data provide a fundamental look at the effects of processing and composition on thermal battery microstructure and electrical conductivity. The understanding of manufacturing effects on battery performance is not well developed, and this effort represents a step forward in correlated and predicting performance of cells based upon observed manufacturing trends.\u2

Stochastic Finite Element Modelling of Char Forming Filler Addition and Alignment – Effects on Heat Conduction into Polymer Condensed Phase

Micro- and nano-filler particles have been considered as char-forming flame retardants for polymers. It has been shown that suitable particles may operate in the condensed phase to prevent or delay the escape of fuel into the gas phase. Good flame retardancy performance may be achieved in composites with comparatively low filler loadings. However, many candidate filler materials, such as rod-like and plate-like carbon allotrope fillers with high aspect ratio, will effectively enhance the composite’s thermal conductivity, and hence, may greatly increase heat input into the condensed phase. Moreover, anisotropy in terms of thermal conductivity must be considered when rod-like and plate-like particles are aligned, for example as a result of manufacturing processes. The presented study investigates these effects, i.e., thermal conductivity enhancement due to filler addition and alignment, using a modeling framework based on Monte Carlo simulation that was developed for predicting effective composite properties considering filler-matrix and particle-to-particle interfacial effects. A stochastic finite element analysis was performed to model rod-shaped carbon particles embedded in a polymer matrix. The chosen analysis is demonstrated to be an effective means for elucidating the effect of filler addition and alignment on the heat conduction into polymer materials containing fillers as char-forming flame retardants