Excluded volumes of anisotropic convex particles in heterogeneous media: Theoretical and numerical studies

Understanding the excluded volume of anisotropic particle is of great importance in the evaluation of continuum percolation and random packing behaviors of soft/hard particle systems in heterogeneous disordered media. In this work, we obtain the excluded volumes of several anisotropic convex particles including prolate spheroids, oblate spheroids, spherocylinders, and Platonic particles, using theoretical and numerical approaches. According to the second virial coefficient, we first present a theoretical scheme for determining the excluded volumes of anisotropic particles. Also, the mean tangent diameters of anisotropic convex particles are formulated by the quantitative stereology. Subsequently, Monte Carlo simulations are demonstrated to numerically evaluate the excluded volumes. The theoretical results of the dimensionless excluded volume are thereafter compared with that of the numerical results to verify the validity of the theoretical scheme. We further investigate the dependence of the dimensionless excluded volume on the geometric characteristics of anisotropic particles based on the proposed theoretical and numerical schemes. Results show that the dimensionless excluded volume mainly relies on the shape and surface information of anisotropic particles. The developed theoretical and numerical schemes can provide theoretical insights into the percolation threshold and packing density of soft/hard anisotropic particle systems in heterogeneous materials, physics, and chemistry fields. © 2016 Tech Science Press.