Percolation threshold and excluded volume of overlapping spherotetrahedral particle systems: Shape evolution from tetrahedron to sphere

Understanding the excluded volume of particle is of great importance in the evaluation of continuum percolation and random packing behaviors of particle systems in disordered media. Particle shape plays a crucial role in determining its excluded volume and the percolation threshold of particle systems. Real particles in nature usually have rounded corners. In this work, the rounded corner effect on the excluded volumes of spherotetrahedral particles and the percolation thresholds of continuum percolation systems of randomly orientated congruent overlapping spherotetrahedral particles, is systematically investigated. We characterize the shape evolution of spherotetrahedron from an ideal tetrahedron (Tᵣᵣ = 0) to a perfect sphere (Tᵣᵣ = 1) via a rate of roundness Tᵣᵣ as its shape descriptor. The excluded volume of spherotetrahedron is theoretically formulated by the second virial coefficient and the geometrical properties of spherotetrahedron. In addition, the excluded volume is also simulated in order to verify the correctness of the theoretical model. On the other hand, the percolation threshold of congruent overlapping spherotetrahedron systems is analyzed by using a Monte Carlo finite-size scaling analysis. The critical volume fraction ϕc representing the percolation threshold as the particle shape evolution from Tᵣᵣ = 0 to Tᵣᵣ = 1 is determined with a high degree of accuracy. Moreover, a linear fitting function on Tᵣᵣ for the percolation threshold is proposed and shown to yield accurate predictions of ϕc. We find that ϕc is a universal monotonic increasing function of Tᵣᵣ, as well as the dimensionless excluded volume is a universal monotonic decreasing function of Tᵣᵣ. This work has practical applications in predicting effective transport and mechanical properties of disordered media.