Percolation probability in a system of cylindrical particles.

A broad variety of materials, ranging from composites and heat transfer nano-fluids to electrochemical energy storage electrodes, widely employ cylindrical particles of various aspect ratios, such as carbon nanotubes. These particles are generally excellent conductors of heat and electricity and when dispersed in a continuous medium influence dramatically the transport properties of the heterogeneous material by forming a percolating network. Numerous theories exist to predict key parameters such as particle concentration at the percolation threshold and transport properties at concentrations beyond the threshold. The microstructure formed by connecting particles in the material is an important determinant toward such parameters but often requires complex numerical models to resolve. In this paper, we present an analytical, probabilistic model capturing the microstructure of a system of randomly positioned, soft-core, cylindrical particles with a finite aspect ratio, valid at arbitrary particle concentration. Our analytical framework allows for the calculation of the particle contact number distribution and percolation probability of the particle system. We show that our analytical model is more accurate than excluded volume theory for predicting the percolation threshold for spherocylinders of finite aspect ratios, and agrees well with the corresponding numerical results. Our theory describes the percolating network topology above the percolation threshold and can serve as the foundation for analytical composition-structure-property relationships for heterogeneous materials with conducting cylindrical particles.