Effective Conductivity of Percolation Media

Using Monte Carlo simulation, we studied the electrical conductivity of two-dimensional films. The films consisted of a poorly conductive host matrix and highly conductive rod-like fillers (rods). The rods were of various lengths fitting a log-normal distribution. They could be aligned along a direction. Special attention was paid to films having completely aligned rods. The impact of length dispersity and the extent of rod alignment on the insulator-to-conductor phase transition was studied. The greater the length dispersity the smaller the critical concentration. The anisotropy of the electrical conductivity was more pronounced in the vicinity of the phase transition. A finite size effect was found to be significant only in the vicinity of the phase transition.

show abstract

“…Step 2. Our method is based on the change of variables similar to that described in 39 . Note that the transformation…”

Section: Averaging Of the Electrical Conductivitymentioning

confidence: 99%

Simulation of the electrical conductivity of two-dimensional films with aligned rod-like conductive fillers: Effect of the filler length dispersity

Tarasevich

Vodolazskaya

Eserkepov

et al. 2018

Journal of Applied Physics

View full text Add to dashboard Cite

show abstract

“…Near the percolation threshold, the electrical anisotropy is greater. The evident anisotropy reflects the smearing of the percolation transition in the presence of an "external field" [38]. There are certain concentrations of defects where the sample is a good conductor along one direction and, at the same time, a bad conductor along the perpendicular direction.…”

mentioning

confidence: 99%

“…In the problem under consideration, the reciprocal electrical contrast h = σ l /σ k plays the role of the "external field", h ≪ 1. The external field smears the phase transition [38]. An infinitely large electrical contrast, when h = 0, corresponds to the absence of an external field.…”

mentioning

confidence: 99%

Influence of defects on the effective electrical conductivity of a monolayer produced by random sequential adsorption of linear k-mers onto a square lattice

Tarasevich

Laptev

Goltseva

et al. 2017

Physica A: Statistical Mechanics and its Applications

View full text Add to dashboard Cite

-The effect of defects on the behaviour of electrical conductivity, σ, in a monolayer produced by the random sequential adsorption of linear k-mers (particles occupying k adjacent sites) onto a square lattice is studied by means of a Monte Carlo simulation. The k-mers are deposited on the substrate until a jamming state is reached, i.e. a state where no one additional particle can be placed because the presented voids are too small or of inappropriate shapes. The presence of defects in the lattice (impurities) and of defects in the k-mers with concentrations of d l and d k , respectively, is assumed. The defects in the lattice are distributed randomly before deposition and these lattice sites are forbidden for the deposition of k-mers. The defects of the k-mers are distributed randomly on the deposited k-mers. The sites filled with k-mers have high electrical conductivity, σ k , whereas the empty sites, and the sites filled by either types of defect have a low electrical conductivity, σ l , i.e., a high-contrast, σ k /σ l ≫ 1, is assumed. We examined isotropic (both the possible x and y orientations of a particle are equiprobable) and anisotropic (all particles are aligned along one given direction, y) deposition. To calculate the effective electrical conductivity, the monolayer was presented as a random resistor network (RRN) and the FrankLobb algorithm was used. The effects of the concentrations of defects d l and d k on the electrical conductivity for the values of k = 2 n , where n = 1, 2, . . . , 5, were studied. Increase of both the d l and d k parameters values resulted in decreases in the value of σ and the suppression of percolation. Moreover, for anisotropic deposition the electrical conductivity along the y direction was noticeably larger than in the perpendicular direction, x. Phase diagrams in the (d l , d k )-plane for different values of k were obtained.

show abstract

Effective Conductivity of Percolation Media

Cited by 2 publications

References 45 publications

Simulation of the electrical conductivity of two-dimensional films with aligned rod-like conductive fillers: Effect of the filler length dispersity

Simulation of the electrical conductivity of two-dimensional films with aligned rod-like conductive fillers: Effect of the filler length dispersity

Influence of defects on the effective electrical conductivity of a monolayer produced by random sequential adsorption of linear k-mers onto a square lattice

Contact Info

Product

Resources

About