Onion-Like Progressive Tunneling Model for Predicting Electrical Conductivity in Carbon Black-Filled Natural Rubber Composites

Abstract

Conductive natural rubber composites (CNRs) filled with carbon black (CB) are widely explored for flexible sensing applications due to their tunable electrical properties. This study introduces a simulation framework integrating Monte Carlo methods with two representative volume element (RVE) models—uniform (Uni-RVE) and overlap face-centered cubic (OFCC-RVE)—to investigate the electrical conductivity and percolation behavior in CB-filled CNRs. An onion-like progressive tunneling effect is introduced to represent the distance-dependent conductivity more realistically. The OFCC-RVE model, incorporating particle agglomeration and variable tunneling distances, demonstrates strong agreement with experimental data. A power-law decay function is applied to capture conductance attenuation at different interparticle distances. The model achieves a mean absolute percentage error of 5.2% when compared with experimental measurements, highlighting its predictive accuracy and efficiency. This approach provides a computationally efficient and physically grounded framework for evaluating and optimizing the electrical performance of conductive rubber composites.