A percolation-based model for the conductivity of nanofiber composites

Chatterjee, Avik P.

doi:10.1063/1.4840098

Cited by 18 publications

(15 citation statements)

References 30 publications

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“…When applied to dispersions of rods with inter-particle tunnelling, these results amount to predict that the critical tunnelling distance δ c depends upon the rod length distribution only through L w for a given volume fraction of the nanotubes 11,13,26 . The resulting bulk conductivity σ is thus expected to display a similar quasi-universal behaviour as a function of L w , implying that knowledge of the scaled variance of L, 〈 〉 〈 〉 − L L / 1 2 2 , is necessary in order to control σ.…”

mentioning

confidence: 96%

Role of the particle size polydispersity in the electrical conductivity of carbon nanotube-epoxy composites

Molaei

Grimaldi

Forró

et al. 2017

Sci Rep

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Carbon nanotubes (CTNs) with large aspect-ratios are extensively used to establish electrical connectedness in polymer melts at very low CNT loadings. However, the CNT size polydispersity and the quality of the dispersion are still not fully understood factors that can substantially alter the desired characteristics of CNT nanocomposites. Here we demonstrate that the electrical conductivity of polydisperse CNT-epoxy composites with purposely-tailored distributions of the nanotube length L is a quasiuniversal function of the first moment of L. This finding challenges the current understanding that the conductivity depends upon higher moments of the CNT length. We explain the observed quasiuniversality by a combined effect between the particle size polydispersity and clustering. This mechanism can be exploited to achieve controlled tuning of the electrical transport in general CNT nanocomposites.

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mentioning

confidence: 96%

Role of the particle size polydispersity in the electrical conductivity of carbon nanotube-epoxy composites

Molaei

Grimaldi

Forró

et al. 2017

Sci Rep

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“…Only a few, for instance, the McLachlan equation, can mathematically describe the conductivity over the whole range of possible filler fractions. Additionally, many modeling works have also been suggested to describe the conductivity properties, which have been summarized by Thomassin et al quite well. However, it must be noted that nonanalytical simulation methods, for instance, when Monte Carlo generated model composites are analyzed with either finite element modeling (FEM) or electrical network methods, can, to some extent, also be used to predict the conductivity both below and above the percolation threshold.…”

Section: Introductionmentioning

confidence: 99%

Novel Theoretical Self‐Consistent Mean‐Field Approach to Describe the Conductivity of Carbon Fiber–Filled Thermoplastics: PART II. Validation by Computer Simulation

Yang¹,

Schubert²,

Qu³

et al. 2018

Macro Theory & Simulations

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Conductive Polymer CompositesThe electrical conductivity of polymeric fiber composites is generally strongly dependent on the constituent conductivities, the fiber filler fraction, the fiber aspect ratio, and on the orientation of the fibers. Even though electrically conductive polymer composites are emerging materials of high scientific and commercial interest, accurate mathematical models for describing such materials are rare. A very promising mathematical model for predicting the electrical conductivity below the electrical percolation threshold, for both isotropic and anisotropic composites, is however recently published by Schubert. The shortcomings of that study are that the model includes so far only one predicted parameter and that it is not sufficiently validated. In the current study, finite element modeling is used to successfully validate the model of Schubert for isotropic fiber composites and to accurately determine the predicted parameter. These theoretical predictions are finally compared with experimental conductivity data for isotropic carbon fiber/poly(methyl methacrylate) (PMMA) composites with fiber filler fractions in the range 0-12 vol% and fiber aspect ratios from 5 to 30. The model forecasts, without any adjustable parameters, are satisfactory close to the experimental data.

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“…For a given arrangement of particles, calculation of the conductivity by way of the CPA proceeds through the following operational steps [21]: [20,23], and enables integrating ideas from percolation theory with estimates (such as that in equation (2)) for how the conductance between a pair of particles varies with their separation and relative angular displacement.…”

Section: Model and Theorymentioning

confidence: 99%

“…In order to establish that given choices for the aspect ratio, volume fraction, ODF, p, K, and     correspond to the threshold for connectedness percolation, we first evaluate the auxiliary variable x as the solution to [18,20]:…”

Section: Lattice-based Estimation For the Percolation Thresholdmentioning

confidence: 99%

“…The impact of deviations from a perfectly random particle arrangement, such as effects due to clustering, can be addressed through an extension of this approach [18] (albeit one that should be viewed as being strictly operational). A pathway has been explored recently [20] that combines this model with the Critical Path Approximation [21] ("CPA") to describe the variation in conductivity with particle volume fraction for an isotropic orientational distribution.…”

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confidence: 99%

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

Chatterjee¹,

Grimaldi²

2015

J. Phys.: Condens. Matter

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The Critical Path Approximation ("CPA") is integrated with a lattice-based approach to percolation to provide a model for conductivity in nanofibre-based composites. Our treatment incorporates a recent estimate for the anisotropy in tunnelingbased conductance as a function of the relative angle between the axes of elongated nanoparticles. The conductivity is examined as a function of the volume fraction, degree of clustering, and of the mean value and standard deviation of the orientational order parameter. Results from our calculations suggest that the conductivity can depend strongly upon the standard deviation in the orientational order parameter even when all the other variables (including the mean value of the order parameter S ) are held invariant.3

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A percolation-based model for the conductivity of nanofiber composites

Cited by 18 publications

References 30 publications

Role of the particle size polydispersity in the electrical conductivity of carbon nanotube-epoxy composites

Role of the particle size polydispersity in the electrical conductivity of carbon nanotube-epoxy composites

Novel Theoretical Self‐Consistent Mean‐Field Approach to Describe the Conductivity of Carbon Fiber–Filled Thermoplastics: PART II. Validation by Computer Simulation

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

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