Dependence of the conductivity of two-dimensional site percolation network on the length-ratio of conducting paths to all bonds: the viewpoint of effective path theory

Abstract Previous studies have found that the network conductivity of 2-dimensional disordered nanowire networks (DNNs) scaled linearly with the length-ratio of conducting-paths to all nanowires. To show the universality of this rule, the conducting behavior of a 2-dimensional site percolation problem is studied in this article with the assistance of a Monte Carlo based numerical simulation. It is observed that, as the existence probability of site increases in the 2-dimensional site percolated network, more conducting-paths are formed, and the network becomes more conductive. After correlating the site-percolated lattice to DNNs, the normalized network conductivity is observed to scale linearly with the length-ratio of conducting-paths to all bonds, which could be well described by the linear formula using a slope of 2 and an incept of 0.5. As a result, the length-ratio of conducting-paths could again serve as a basic topological parameter in describing the conducting behavior of 2-dimensional site percolation networks. Such universality enables the definition of an ‘effective path theory’, in which the normalized network conductivity scales linearly with the length-ratio of conducting-paths to all bonds.