Uncertainty quantification of percolating electrical conductance for wavy carbon nanotube-filled polymer nanocomposites using Bayesian inference

Abstract

This research focuses on the uncertainty quantification of electrical percolation behavior in wavy carbon nanotube (CNT)-filled polymer nanocomposites with a three-dimensional representative volume element accounting for both tunneling resistance (quantum carrier tunneling) and stochasticity in CNT waviness. The developed percolation model is validated with existing experimental data, and model parameters for electrical conductance converge to the optimal value with Markov Chain Monte Carlo (MCMC) based on Bayesian inference. The predicted 95% confidence interval of electrical conductance indicates a different trend between two-and three-parameters of the electrical conductance model. The main trend of correlation between the percolation threshold (φc) and a parameter of the phase transition (critical exponent, t) indicates a statistically linear relationship via evaluation of the Pearson correlation coefficient. Moreover, the correlation between intrinsic conductance of CNTs (σo) and t also strongly affect the magnitude and slope of electrical conductance in uncertainty quantification. This work can contribute to a robust and reliable design of the PNC considering the physical uncertainty satisfying the target electrical performance through controlling φc, σo, and t.