Tunneling conductivity in anisotropic nanofiber composites: a percolation-based model

Chatterjee, Avik P.; Grimaldi, Claudio

doi:10.1088/0953-8984/27/14/145302

Cited by 11 publications

(11 citation statements)

References 36 publications

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“…The percolation threshold is isotropic, see also [13,14], which we here link to the uniqueness of the percolating cluster. There have already been numerous studies of anisotropic continuum percolation, some using analytic calculations [e. g., [15][16][17] others are based on Monte Carlo simulations [e. g., 13,18] or experiments [e. g., 19]. There are also detailed studies of anisotropic lattice percolation [20][21][22].…”

mentioning

confidence: 99%

Anisotropy in finite continuum percolation: threshold estimation by Minkowski functionals

Klatt¹,

Schröder‐Turk²,

Mecke³

2017

J. Stat. Mech.

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Abstract. We examine the interplay between anisotropy and percolation, i. e., the spontaneous formation of a system spanning cluster in an anisotropic model. We simulate an extension of a benchmark model of continuum percolation, the Boolean model, which is formed by overlapping grains. Here we introduce an orientation bias of the grains that controls the degree of anisotropy of the generated patterns. We analyze in the Euclidean plane the percolation thresholds above which percolating clusters in x-and in y-direction emerge. Only in finite systems, distinct differences between effective percolation thresholds for different directions appear. If extrapolated to infinite system sizes, these differences vanish independent of the details of the model. In the infinite system, the uniqueness of the percolating cluster guarantees a unique percolation threshold. While percolation is isotropic even for anisotropic processes, the value of the percolation threshold depends on the model parameters, which we explore by simulating a score of models with varying degree of anisotropy. To which precision can we predict the percolation threshold without simulations? We discuss analytic formulas for approximations (based on the excluded area or the Euler characteristic) and compare them to our simulation results. Empirical parameters from similar systems allow for accurate predictions of the percolation thresholds (with deviations of < 5% in our examples), but even without any empirical parameters, the explicit approximations from integral geometry provide, at least for the systems studied here, lower bounds that capture well the qualitative dependence of the percolation threshold on the system parameters (with deviations of 5%-30%). As an outlook, we suggest further candidates for explicit and geometric approximations based on second moments of the so-called Minkowski functionals.

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mentioning

confidence: 99%

Anisotropy in finite continuum percolation: threshold estimation by Minkowski functionals

Klatt¹,

Schröder‐Turk²,

Mecke³

2017

J. Stat. Mech.

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“…Due to the different simulating and hardware configuration of the workstations, the specific simulation strategy should be determined also according to the actual situation. For simulation experiments where the accuracy requirements are not very high, following simulation conditions are also worth recommending due to low computational cost: Length of the fibers as variable and radius fixed as constant Box size = 450 um Periodic boundary conditions…”

Section: Resultsmentioning

confidence: 99%

A Study of Finite Size Effects and Periodic Boundary Conditions to Simulations of a Novel Theoretical Self‐Consistent Mean‐Field Approach

Yang

Nilsson

Schubert

2019

Macro Theory & Simulations

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In a previous work, a very promising mathematical model for predicting the electrical conductivity below the electrical percolation threshold, for both isotropic and anisotropic composites, was published by Schubert. In this work, periodic boundary condition of the simulation is utilized. The results are also compared to the previous work and other theoretical models. The truncated fibers due to finite size of the simulation volume are considered as two individual pieces so that the real aspect ratios will also be taken into consideration. A comparison is made between two groups, in which the length and the radius of the carbon fibers are changed, respectively, under certain aspect ratios. With three different sizes of the simulation volumes, the influence on the results due to the finite size effect is calculated.

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“…In order to draw a comparison with the results that are obtained according to Eq. 2, we will adopt a simplified form of the anisotropic tunneling conductance, which is obtained with the underlying assumption that the centres of mass of two connected rods are close to their line of shortest distance [63]:…”

Section: Models and Simulationsmentioning

confidence: 99%

Simulation study of the electrical tunneling network conductivity of suspensions of hard spherocylinders

et al. 2018

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Using Monte Carlo simulations, we investigate the electrical conductivity of networks of hard rods with aspect ratios 10 and 20 as a function of the volume fraction for two tunneling conductance models. For a simple, orientationally independent tunneling model, we observe non-monotonic behaviour of the bulk conductivity as a function of volume fraction at the isotropic-nematic transition. However, this effect is lost if one allows for anisotropic tunneling. The relative conductivity enhancement increases exponentially with volume fraction in the nematic phase. Moreover, we observe that the orientational ordering of the rods in the nematic phase induces an anisotropy in the conductivity, i.e. enhanced values in the direction of the nematic director field. We also compute the mesh number of the Kirchhoff network, which turns out to be a simple alternative to the computationally expensive conductivity of large systems in order to get a qualitative estimate.

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Tunneling conductivity in anisotropic nanofiber composites: a percolation-based model

Cited by 11 publications

References 36 publications

Anisotropy in finite continuum percolation: threshold estimation by Minkowski functionals

Anisotropy in finite continuum percolation: threshold estimation by Minkowski functionals

A Study of Finite Size Effects and Periodic Boundary Conditions to Simulations of a Novel Theoretical Self‐Consistent Mean‐Field Approach

Simulation study of the electrical tunneling network conductivity of suspensions of hard spherocylinders

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