Effective conductivity in a lattice model for binary disordered media with complex distributions of grain sizes

Abstract

PACS : 05.90.+m, 72.80.Ng, 72.80.Tm Using numerical simulations and analytical approximations we study a modified version of the twodimensional lattice model [R. Piasecki, phys. stat. sol. (b) 209, 403 (1998)] for random pH:(1 − p)L systems consisting of grains of high (low) conductivity for the H-(L-)phase, respectively. The modification reduces a spectrum of model bond conductivities to the two pure ones and the mixed one. The latter value explicitly depends on the average concentration γ(p) of the H-component per model cell. The effective conductivity as a function of content p of the H-phase in such systems can be modelled making use of three model parameters that are sensitive to both grain size distributions, GSD(H) and GSD(L). However, to incorporate into the model information directly connected with a given GSD, a computer simulation of the geometrical arrangement of grains is necessary. By controlling the polydispersity in grain sizes and their relative area frequencies, the effective conductivity could be raised or decreased and correlated with γ(p). When the phases are interchanged, a hysteresis-loop like behaviour of the effective conductivity, characteristic of dual media, is found. We also show that the topological non-equivalence of system's microstructure accompanies some GSDs, and it can be detected by the entropic measure of spatial inhomogeneity of model cells.

Experimental and Monte Carlo simulation studies on percolation behaviour of a shape memory polyurethane carbon black nanocomposite

“…Thus, attributed to the formation of a connected network of conductive inclusions within the insulating polymer matrix, conductivity of polymer nanocomposites follows a percolation-like behavior. [8][9][10][11][12][13].…”

“…For CB loading below the percolation threshold, conductivity between the particles occurs by means of hopping and tunnelling mechanisms. Studies by Piasecki 2003, Song 2016 and Kremer et al 1988 [10-12] explains interfacial polarisation effect, quantum tunnelling and interparticle interaction as reasons for conduction in nanocomposites depending on the filler content. For very low filler contents, on applying an external voltage to the material can cause an accumulation of charges at the interface between filler and matrix.…”

“…However, when applied voltage increases, more electrons hit the barrier leading to penetration of the barrier causing conduction based on quantum mechanical consideration [2]. As the volume fraction of the particles in the matrix increases, the interparticle distance reduces leading to large number of conductive networks [6,19,20,8,10,21]. Hence it can be understood that a combination of both electron hopping at nanosclae and conductive network formation at microscale have contribution for electrical conductivity.…”

A versatile entropic measure of grey level inhomogeneity

“…The morphological features of complex materials are vital for modelling and predicting their macroscopic properties, for instance, effective conductivity [1][2][3][4]. For binary micrographs of such materials, the quantitative characterization of the spatial distribution of pixels, in some cases allows correlate their properties and internal structure attributes.…”