Geometrical percolation threshold of congruent cuboidlike particles in overlapping particle systems

With the advances in artificial particle synthesis, it is possible to create particles with unique shapes. Particle shape becomes a feasible parameter for tuning the percolation behavior. How to accurately predict the percolation threshold by particle characteristics for arbitrary particles has aroused great interest. Towards this end, a versatile family of cuboidlike particles and a numerical contact detection algorithm for these particles are presented here. Then, combining with percolation theory, the continuum percolation of randomly distributed overlapping cuboidlike particles is studied. The global percolation threshold ϕ_c of overlapping particles with broad ranges of the shape parameter m in [1.0 ,+∞ ) and aspect ratio a /b in [0.1, 10.0] is computed via a finite-size scaling technique. Using the generalized excluded-volume approximation, an analytical formula is proposed to quantify the dependence of ϕ_c on the parameters m and a /b , and its reliability is verified. The results reveal that the percolation threshold ϕ_c of overlapping cuboidlike particles is heavily dependent on the shapes of particles, and much more sensitive to a /b than m . As the cuboidlike particles become spherical (i.e., m =1.0 and a /b =1.0 ), the maximum threshold ϕ_{c ,max} can be obtained.