Influence of carbon nanotubes parameters, boundary conditions, and scaling of the represetative volume on percolation and electric permeability of a nanocomposite

TL;DR

This study develops a digital twin model for the electrical conductivity of MWCNT/polymer nanocomposites, emphasizing the importance of boundary conditions, RVE size, and CNT geometry parameters for accurate percolation and conductivity predictions.

Contribution

It introduces a comprehensive modeling approach that highlights the critical role of boundary conditions, RVE size, and CNT geometry in accurately predicting nanocomposite electrical properties.

Findings

Periodic boundary conditions are essential for correct conductivity calculation.

Optimal RVE size depends on CNT volume fraction and dimensions.

CNT torsion significantly affects conductivity modeling accuracy.

Abstract

The paper aims at the development of a digital twin modelling the electrical conductivity of multi-wall carbon nanotube (MWCNT)/polymer nanocomposite. A comparative analysis is conducted for various formulations of boundary conditions in the representative volume element (RVE) with uniform and isotropic distribution of CNTs. Three types of boundary conditions studied: uniform boundary potentials for an RVE, uniform boundary potentials for a chain of two RVEs, and periodic boundary potentials. It is demonstrated that to calculate the electrical conductivity of the material correctly, the implementation of periodic boundary conditions for the RVE is required; on the contrary, the use of uniform boundary potentials leads to significant overestimation in conductance. The sensitivity of average conductivity to the RVE size is determined for different volume fractions (Vf) of CNTs. For example, the 5 micrometer size of the RVE is found to be optimal for 1% Vf of CNTs with 50 nm diameter and 5 micrometer average length. Beside the RVE size, we verify how model output changes in response to tuning parameters of the CNT geometry, such as curvature and torsion (twist). We find the presence of the second parameter, torsion, to be imperative for correct conductivity modelling since usage of the curvature alone leads to unavoidable dependence on segment size during CNT discretization. In literature, the influence of intrinsic MWCNT resistivity is often discarded as negligible due to ballistic transport of electrons. To verify this assumption, we check the sensitivity of results to finite resistivity of CNTs. Percolation threshold and the critical index are calculated for different sets of model parameters. The model finite-size effect on the percolation threshold is investigated.