A Monte Carlo model with equipotential approximation and tunneling resistance for the electrical conductivity of carbon nanotube polymer composites

Fang, Chao; Zhang, Juanjuan; Chen, Xiqu; Weng, George J.

doi:10.1016/j.carbon.2019.01.098

Cited by 57 publications

(23 citation statements)

References 70 publications

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“…When no percolation path was formed, with the GNP concentration increasing, the increase of U z = d resulted in the increase of the total current, which caused the increase of conductivity by about one order of magnitude. This phenomenon was similar to that of the CNT composite, and the difference was that the conductivity of the CNT composite increased by about two or three orders of magnitude at this stage [ 32 ]. It can be seen that due to the differences in the shapes of the GNP and the CNT, the contribution of the GNP to conductivity was weaker than that of the CNT before the formation of the percolation path.…”

Section: Resultsmentioning

confidence: 66%

“…With the further addition of GNPs, the number of percolation paths increased, and there may have been a shorter percolation path that brought about a further increase of the tunneling current and the conductivity. Similarly, above the percolation threshold, the increment of the conductivity of the GNP composite was smaller than that of the CNT composite [ 32 ], which might be attributable to the geometric properties of GNPs and CNTs.…”

Section: Resultsmentioning

confidence: 99%

“…It is clear that the conductivity of a composite is determined by contact conductance after the percolation threshold. In addition, barrier height does not change the percolation threshold of GNP composites, but for CNT composites, the percolation threshold slightly increases with increases of barrier height [ 32 ]. The reason for this phenomenon is that the gap between fillers in a CNT network has a certain randomness.…”

Section: Resultsmentioning

confidence: 99%

“…We built a mathematical model to describe the shape of a GNP, as shown in Equation (1):

where g and ρ are point sets in three-dimensional space and a given positive number, respectively. If g is a set of isolated points, then f that satisfies Equation (1) is a set of spheres with radius ρ ; if g is a set of line segments with length L , then f comprises CNTs with radius ρ and length L + 2 ρ [ 32 ]; similarly, if g is a set of round faces with diameter of D ’, then f comprises a GNP with diameter of D = D ’ + 2 ρ and a thickness of 2 ρ .…”

Section: Monte Carlo Methods For Graphene Nanoplatelet Polymer Compmentioning

confidence: 99%

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Calculating the Electrical Conductivity of Graphene Nanoplatelet Polymer Composites by a Monte Carlo Method

et al. 2020

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Electrical conductivity is one of several outstanding features of graphene–polymer nanocomposites, but calculations of this property require the intricate features of the underlying conduction processes to be accounted for. To this end, a novel Monte Carlo method was developed. We first established a randomly distributed graphene nanoplatelet (GNP) network. Then, based on the tunneling effect, the contact conductance between the GNPs was calculated. Coated surfaces (CSs) were next set up to calculate the current flow from the GNPs to the polymer. Using the equipotential approximation, the potentials of the GNPs and CSs met Kirchhoff’s current law, and, based on Laplace equation, the potential of the CSs was obtained from the potential of the GNP by the walk-on-spheres (WoS) method. As such, the potentials of all GNPs were obtained, and the electrical conductivity of the GNP polymer composites was calculated. The barrier heights, polymer conductivity, diameter and thickness of the GNP determining the electrical conductivity of composites were studied in this model. The calculated conductivity and percolation threshold were shown to agree with experimental data.

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Section: Resultsmentioning

confidence: 66%

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

“…We built a mathematical model to describe the shape of a GNP, as shown in Equation (1):

Section: Monte Carlo Methods For Graphene Nanoplatelet Polymer Compmentioning

confidence: 99%

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Calculating the Electrical Conductivity of Graphene Nanoplatelet Polymer Composites by a Monte Carlo Method

et al. 2020

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“…The macroscopic properties of the randomly organized media has attracted research interest for many decades. Nowadays, the the critical study points are the determination of the properties of composites filled with the carbonaceous fillers, like carbon nanotubes (CNT) [1][2][3][4], or graphene nanoplatelets (GNP) [5][6][7][8]. All these objects have high aspect ratios, and there is an interest to develop anisotropic composites using the partially oriented fillers [9][10][11].…”

Section: Introductionmentioning

confidence: 99%

Percolation and Transport Properties in The Mechanically Deformed Composites Filled with Carbon Nanotubes

et al. 2020

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The conductivity and percolation concentration of the composite material filled with randomly distributed carbon nanotubes were simulated as a function of the mechanical deformation. Nanotubes were modelled as the hard-core ellipsoids of revolution with high aspect ratio. The evident anisotropy was observed in the percolation threshold and conductivity. The minimal mean values of the percolation of 4.6 vol. % and maximal conductivity of 0.74 S/m were found for the isotropic composite. Being slightly aligned, the composite demonstrates lower percolation concentration and conductivity along the orientation of the nanotubes compared to the perpendicular arrangement.

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Improving Properties of Poly(vinylidene fluoride) by Adding Expanded Graphite without Surface Modification via Water‐Assisted Mixing Extrusion

Tong

Chen

et al. 2020

Macro Materials & Eng

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Expanded graphite (EG) is introduced into poly(vinylidene fluoride) (PVDF) by melt mixing extrusion with water injection. The results demonstrate that the unfunctionalized EG in composite prepared with water injection exbibits better dispersion than that in the one prepared without water injection due to the promoting role of water during extrusion. Thus, the PVDF/EG composite with loading of 4 wt% prepared by water‐assisted mixing extrusion (WAME) exhibits electrical conductivity of about three orders of magnitude higher than the neat PVDF and one order of magnitude higher than the one prepared without water injection. Comparing to the neat PVDF, the thermal conductivity of the composites prepared with and without water injection is increased by 101.5% and 75.0%, respectively. The introduced EG leads to increased Young’s modulus and tensile strength especially for the composite prepared by WAME. The present work indicates that WAME can promote the dispersion of EG in PVDF matrix without any extra functionalization.

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A Monte Carlo model with equipotential approximation and tunneling resistance for the electrical conductivity of carbon nanotube polymer composites

Cited by 57 publications

References 70 publications

Calculating the Electrical Conductivity of Graphene Nanoplatelet Polymer Composites by a Monte Carlo Method

Calculating the Electrical Conductivity of Graphene Nanoplatelet Polymer Composites by a Monte Carlo Method

Percolation and Transport Properties in The Mechanically Deformed Composites Filled with Carbon Nanotubes

Improving Properties of Poly(vinylidene fluoride) by Adding Expanded Graphite without Surface Modification via Water‐Assisted Mixing Extrusion

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