Connectivity percolation in suspensions of hard platelets

Mathew, Maneesh; Schilling, Tanja; Oettel, Martin

doi:10.1103/physreve.85.061407

Cited by 55 publications

(57 citation statements)

References 36 publications

(78 reference statements)

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“…In terms of exploring the effect of filler overlapping and agglomerations, Xia et al [19] proposed a computational methodology under which it was possible to predict the percolation threshold for identical ellipses with the overlapping effect for a 2D structure, while Vovchenko et al [20] predicted the percolation threshold of composites filled with intersecting circular discs in a 3D structure. Besides, the conventional Monte Carlo approaches to predict the percolation threshold for materials reinforced with 2D particles, Mathew et al [21] conducted a Monte Carlo study on the percolation of hard platelets in a 3D continuum system considering the rate of order in the microstructure, proving its effect on the percolation threshold with the employment of isotropic-nematic (IN) transition.…”

Section: Electrical Simulation Modelsmentioning

confidence: 99%

“…4 Schematic presentation of the unit cell geometrical parameters conductivity in respect of volume fraction is modelled, while in the probability function of percolation the inflection point is calculated to be the percolation threshold in accordance to the suggested procedure described in Ref. [21].…”

Section: Representative Volume Element (Rve)mentioning

confidence: 99%

“…7, for k = 5 the sample characteristics have converged to a steady state, indicating this size as appropriate for our study. The percolation probability, in accordance to the procedure suggested by the [21], is fitted by the function (14) and the inflection point of this function is considered to be the percolation threshold. In Fig.…”

Section: Rve Analysismentioning

confidence: 99%

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Predictive Model of Graphene Based Polymer Nanocomposites: Electrical Performance

2016

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In this computational work, a new simulation tool on the graphene/polymer nanocomposites electrical response is developed based on the finite element method (FEM). This approach is built on the multi-scale multi-physics format, consisting of a unit cell and a representative volume element (RVE). The FE methodology is proven to be a reliable and flexible tool on the simulation of the electrical response without inducing the complexity of raw programming codes, while it is able to model any geometry, thus the response of any component. This characteristic is supported by its ability in preliminary stage to predict accurately the percolation threshold of experimental material structures and its sensitivity on the effect of different manufacturing methodologies. Especially, the percolation threshold of two material structures of the same constituents (PVDF/Graphene) prepared with different methods was predicted highlighting the effect of the material preparation on the filler distribution, percolation probability and percolation threshold. The assumption of the random filler distribution was proven to be efficient on modelling material structures obtained by solution methods, while the through-the -thickness normal particle distribution was more appropriate for nanocomposites constructed by film hot-pressing. Moreover, the parametrical analysis examine the effect of each parameter on the variables of the percolation law. These graphs could be used as a preliminary design tool for more effective material system manufacturing.

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Section: Electrical Simulation Modelsmentioning

confidence: 99%

Section: Representative Volume Element (Rve)mentioning

confidence: 99%

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Predictive Model of Graphene Based Polymer Nanocomposites: Electrical Performance

2016

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“…In general, the percolation threshold is a nonuniversal quantity, as it depends on the connectivity properties of the specific system under consideration [3]. For example, in continuum percolation systems, where objects occupy positions in a continuous space, the threshold depends on the shape of the objects [4][5][6][7][8], on their interactions [9][10][11], as well as on the connectedness criteria [12,13].…”

Section: Introductionmentioning

confidence: 99%

Continuum percolation of polydisperse hyperspheres in infinite dimensions

Grimaldi

2015

Phys. Rev. E

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We analyze the critical connectivity of systems of penetrable d-dimensional spheres having size distributions in terms of weighed random geometrical graphs, in which vertex coordinates correspond to random positions of the sphere centers and edges are formed between any two overlapping spheres. Edge weights naturally arise from the different radii of two overlapping spheres. For the case in which the spheres have bounded size distributions, we show that clusters of connected spheres are tree-like for d → ∞ and they contain no closed loops. In this case we find that the mean cluster size diverges at the percolation threshold density ηc → 2 −d , independently of the particular size distribution. We also show that the mean number of overlaps for a particle at criticality zc is smaller than unity, while zc → 1 only for spheres with fixed radii. We explain these features by showing that in the large dimensionality limit the critical connectivity is dominated by the spheres with the largest size. Assuming that closed loops can be neglected also for unbounded radii distributions, we find that the asymptotic critical threshold for systems of spheres with radii following a lognormal distribution is no longer universal, and that it can be smaller than 2 −d for d → ∞.

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“…By a suitable definition of entanglement, we associate entangled clusters in the suspension and explore their percolation properties [25]. Connectivity properties have been studied a lot recently by using concepts of percolation theory, in particular in suspensions of rod-like particles with sticky interactions [26][27][28][29][30][31][32][33], but have never systematically been applied to entangled particles. Depending on the opening angle and the particle concentration, we find a percolation transition for the cluster of entangled particles and identify the percolation threshold.…”

Section: Introductionmentioning

confidence: 99%

Colloidal suspensions of C-particles: Entanglement, percolation and microrheology

Hoell

Löwen

2016

The Journal of Chemical Physics

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We explore structural and dynamical behavior of concentrated colloidal suspensions made up by C-shape particles using Brownian dynamics computer simulations and theory. In particular, we focus on the entanglement process between nearby particles for almost closed C-shapes with a small opening angle. Depending on the opening angle and the particle concentration, there is a percolation transition for the cluster of entangled particles which shows the classical scaling characteristics. In a broad density range below the percolation threshold, we find a stretched exponential function for the dynamical decorrelation of the entanglement process. Finally, we study a set-up typical in microrheology by dragging a single tagged particle with constant speed through the suspension. We measure the cluster connected to and dragged with this tagged particle. In agreement with a phenomenological theory, the size of the dragged cluster depends on the dragging direction and increases markedly with the dragging speed.

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Connectivity percolation in suspensions of hard platelets

Cited by 55 publications

References 36 publications

Predictive Model of Graphene Based Polymer Nanocomposites: Electrical Performance

Predictive Model of Graphene Based Polymer Nanocomposites: Electrical Performance

Continuum percolation of polydisperse hyperspheres in infinite dimensions

Colloidal suspensions of C-particles: Entanglement, percolation and microrheology

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