Tunneling-percolation behavior of polydisperse prolate and oblate ellipsoids

Kale, Sohan; Sabet, Fereshteh A.; Jasiuk, Iwona; Ostoja–Starzewski, Martin

doi:10.1063/1.4933100

Cited by 29 publications

(24 citation statements)

References 29 publications

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“…It treats two-body connectedness probabilities analogously to liquid state correlation functions and has been widely applied in the context of spherical and nonspherical particles and mixtures thereof [2,6,9,32,33]. In particular for slender rod-like particles, the agreement with results from Monte Carlo simulations is excellent [20,21,25,34,35].…”

Section: Connectedness Percolation Theorymentioning

confidence: 99%

Continuum percolation of polydisperse rods in quadrupole fields: Theory and simulations

Finner

Kotsev

Miller

et al. 2018

The Journal of Chemical Physics

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We investigate percolation in mixtures of nanorods in the presence of external fields that align or disalign the particles with the field axis. Such conditions are found in the formulation and processing of nanocomposites, where the field may be electric, magnetic, or due to elongational flow. Our focus is on the effect of length polydispersity, which-in the absence of a field-is known to produce a percolation threshold that scales with the inverse weight average of the particle length. Using a model of non-interacting spherocylinders in conjunction with connectedness percolation theory, we show that a quadrupolar field always increases the percolation threshold and that the universal scaling with the inverse weight average no longer holds if the field couples to the particle length. Instead, the percolation threshold becomes a function of higher moments of the length distribution, where the order of the relevant moments crucially depends on the strength and type of field applied. The theoretical predictions compare well with the results of our Monte Carlo simulations, which eliminate finite size effects by exploiting the fact that the universal scaling of the wrapping probability function holds even in anisotropic systems. Theory and simulation demonstrate that the percolation threshold of a polydisperse mixture can be lower than that of the individual components, confirming recent work based on a mapping onto a Bethe lattice as well as earlier computer simulations involving dipole fields. Our work shows how the formulation of nanocomposites may be used to compensate for the adverse effects of aligning fields that are inevitable under practical manufacturing conditions.

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Section: Connectedness Percolation Theorymentioning

confidence: 99%

Continuum percolation of polydisperse rods in quadrupole fields: Theory and simulations

Finner

Kotsev

Miller

et al. 2018

The Journal of Chemical Physics

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“…Next to the connectivity range, there are many factors that influence the formation of transient networks in nanoparticle dispersions. A vast body of literature has shown that the particle anisometry, [15][16][17][18][19] size polydispersity, [13][14][15][19][20][21][22][23][24][25][26] the presence of nonconducting particles, [15] inter-particle interactions [27][28][29] and external fields [18,30] can have tremendous effects on the percolation threshold, while the influences of flexibility and the precise particle shape seem to be rather subtle. [27,31,32] In this article we focus on the fact that many types of conductive nanoparticle, like carbon nanotubes or graphene, have a strongly anisotropic shape, which strongly affects their interactions and the way they react to external orienting fields.…”

Section: Introductionmentioning

confidence: 99%

Geometric percolation of hard nanorods: The interplay of spontaneous and externally induced uniaxial particle alignment

2020

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We present a numerical study on geometric percolation in liquid dispersions of hard slender colloidal particles subjected to an external orienting field. In the formulation and liquid-state processing of nanocomposite materials, the alignment of particles by external fields such as electric, magnetic or flow fields is practically inevitable, and often works against the emergence of large nanoparticle networks. Using continuum percolation theory in conjunction with Onsager theory, we investigate how the interplay between externally induced alignment and the spontaneous symmetry breaking of the uniaxial nematic phase affects cluster formation within nanoparticle dispersions. It is known that the enhancement of particle alignment by means of a density increase or an external field may result in the breakdown of an already percolating network. As a result, percolation can be limited to a small region of the phase diagram only. Here, we demonstrate that the existence and shape of such a "percolation island" in the phase diagram crucially depends on the connectivity length -a critical distance defining direct connections between neighbouring particles. Deformations of this percolation island can lead to peculiar re-entrance effects, in which a system-spanning network forms and breaks down multiple times with increasing particle density. arXiv:1910.00621v1 [cond-mat.soft]

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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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Tunneling-percolation behavior of polydisperse prolate and oblate ellipsoids

Cited by 29 publications

References 29 publications

Continuum percolation of polydisperse rods in quadrupole fields: Theory and simulations

Continuum percolation of polydisperse rods in quadrupole fields: Theory and simulations

Geometric percolation of hard nanorods: The interplay of spontaneous and externally induced uniaxial particle alignment

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

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