Review of the percolation threshold for spherocylinder-based systems in a continuum model

Abstract

This study presents a comprehensive review and comparative analysis of various methods for determining the percolation threshold in systems of spherocylinders—a critical parameter in the design of advanced composite materials. We evaluated a range of approaches, including analytical models based on excluded volume theory (soft- and hard-core), computational Monte Carlo simulations, and established experimental techniques. A central focus was reconciling the discrepancies between theoretical models, which often assume infinite aspect ratios, and experimental results from fillers with finite aspect ratios. Our analysis reveals that while traditional analytical bounds and hard-core models exhibit limited predictive accuracy, computational soft-core simulations for finite-sized fillers provide robust predictions that align well with experimental data. Moreover, empirical approximations fitted to numerical results demonstrate strong agreement across all aspect ratio regimes. The primary contribution of this work is a novel interpolation formula that unifies the distinct asymptotic behaviours observed at very low and very high aspect ratios. This formula shows excellent agreement with extensive simulation data and serves as a highly accurate, unified predictive tool. By clarifying the strengths and weaknesses of existing methods, this investigation provides a reliable framework for accurately predicting the percolation threshold in spherocylinder-based systems.