### Abstract

A Monte Carlo model with equipotential approximation and tunneling resistance is developed to predict the percolation threshold and electrical conductivity of carbon nanotube (CNT) polymer nanocomposites. We first establish a random CNT network, and then calculate their intrinsic and contact conductance. To provide a pathway for the current to flow from CNT to polymer, a thin coated surface (CS) is introduced. The CNTs, CS, and the two electrodes then constitute the three major components of the conduction process. To solve this problem, we develop the method of equipotential approximation to determine the electrical potentials of CNTs and CS, and further determine their coefficient matrix by the walk-on-spheres method. In this way the electrical properties of CNT nanocomposites, both before and after percolation, are predicted. It is demonstrated that the developed theory compares well with three sets of experimental data for the electrical conductivity and several sets of data for the percolation threshold. The effects of barrier heights, polymer conductivity, aspect ratio, diameter (and chirality) of CNTs are also investigated. This equipotential approximation possesses the distinct features that it can break through the limits of ellipsoidal fillers and properly estimate the electrical conductivity with any shape, orientation and distribution of fillers.

Original language | English (US) |
---|---|

Pages (from-to) | 125-138 |

Number of pages | 14 |

Journal | Carbon |

Volume | 146 |

DOIs | |

State | Published - May 1 2019 |

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### All Science Journal Classification (ASJC) codes

- Chemistry(all)
- Materials Science(all)

### Cite this

*Carbon*,

*146*, 125-138. https://doi.org/10.1016/j.carbon.2019.01.098

}

*Carbon*, vol. 146, pp. 125-138. https://doi.org/10.1016/j.carbon.2019.01.098

**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.

Research output: Contribution to journal › Article

TY - JOUR

T1 - A Monte Carlo model with equipotential approximation and tunneling resistance for the electrical conductivity of carbon nanotube polymer composites

AU - Fang, Chao

AU - Zhang, Juanjuan

AU - Chen, Xiqu

AU - Weng, George

PY - 2019/5/1

Y1 - 2019/5/1

N2 - A Monte Carlo model with equipotential approximation and tunneling resistance is developed to predict the percolation threshold and electrical conductivity of carbon nanotube (CNT) polymer nanocomposites. We first establish a random CNT network, and then calculate their intrinsic and contact conductance. To provide a pathway for the current to flow from CNT to polymer, a thin coated surface (CS) is introduced. The CNTs, CS, and the two electrodes then constitute the three major components of the conduction process. To solve this problem, we develop the method of equipotential approximation to determine the electrical potentials of CNTs and CS, and further determine their coefficient matrix by the walk-on-spheres method. In this way the electrical properties of CNT nanocomposites, both before and after percolation, are predicted. It is demonstrated that the developed theory compares well with three sets of experimental data for the electrical conductivity and several sets of data for the percolation threshold. The effects of barrier heights, polymer conductivity, aspect ratio, diameter (and chirality) of CNTs are also investigated. This equipotential approximation possesses the distinct features that it can break through the limits of ellipsoidal fillers and properly estimate the electrical conductivity with any shape, orientation and distribution of fillers.

AB - A Monte Carlo model with equipotential approximation and tunneling resistance is developed to predict the percolation threshold and electrical conductivity of carbon nanotube (CNT) polymer nanocomposites. We first establish a random CNT network, and then calculate their intrinsic and contact conductance. To provide a pathway for the current to flow from CNT to polymer, a thin coated surface (CS) is introduced. The CNTs, CS, and the two electrodes then constitute the three major components of the conduction process. To solve this problem, we develop the method of equipotential approximation to determine the electrical potentials of CNTs and CS, and further determine their coefficient matrix by the walk-on-spheres method. In this way the electrical properties of CNT nanocomposites, both before and after percolation, are predicted. It is demonstrated that the developed theory compares well with three sets of experimental data for the electrical conductivity and several sets of data for the percolation threshold. The effects of barrier heights, polymer conductivity, aspect ratio, diameter (and chirality) of CNTs are also investigated. This equipotential approximation possesses the distinct features that it can break through the limits of ellipsoidal fillers and properly estimate the electrical conductivity with any shape, orientation and distribution of fillers.

UR - http://www.scopus.com/inward/record.url?scp=85061587826&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85061587826&partnerID=8YFLogxK

U2 - 10.1016/j.carbon.2019.01.098

DO - 10.1016/j.carbon.2019.01.098

M3 - Article

VL - 146

SP - 125

EP - 138

JO - Carbon

JF - Carbon

SN - 0008-6223

ER -