Continuum Percolation in Anisotropic Rectangles: The Role of Excluded Area and Average Connectivity at the Threshold

Abstract

Percolation is a geometric phase transition in which formerly local clusters spontaneously form a system‐spanning cluster, also referred to as a percolating cluster, facilitating efficient charge transport in conductive materials. Here, a combinatorial approach is developed that integrates a theoretical framework with Monte Carlo simulations to investigate the percolation behavior of penetrable rectangles by systematically exploring the effects of aspect ratio and anisotropic orientation distributions. A theoretical model incorporating a modified expression for the average excluded area is proposed, with both the model and simulations providing rigorous validation and correcting the errors in the original work. With the aid of predictive modeling and simulations, the critical area fraction and bond number have been computed by considering the aspect ratio of rectangles with a specified degree of anisotropy. These results demonstrate that the bond number in isotropic networks remains within 3.6–4.5 across a wide aspect ratio range (1–1000), in strong agreement with established benchmarks reporting convergence to 3.6 for aspect ratios above 20. Using the predicted critical area fractions, the electrical conductivity trends of two‐dimensional (2D) conductive networks are modeled by fitting power‐law curves to the reported simulation and experimental results.