Factors Influencing Percolation Threshold

Abstract

Percolation theory is described as the study of connectivity through random networks. This mathematical theory is used to understand various systems, including disease spread, natural systems, and electrical connectivity. It studies how links between adjacent components are able to form a continuous path throughout the entire system once a critical concentration of components and driving force is reached — the percolation threshold. If this threshold is not met, the connectivity throughout the system will not be continuous, remaining as small, isolated clusters. Different systems show different connectivity vs concentration curve shapes such as linear, nonlinear, and exponential, as seen in many percolation graphs. This difference is seen across various materials and mediums in the electrical field, because particle shape, size distribution, and how components are arranged changes how easily a continuous conductive path can form. Additionally, when examining multiple percolation threshold results, the reported values vary widely across different studies. This paper aims to better understand why the percolation behavior of carbon nanotube composites vary by analyzing their conductivity patterns and percolation thresholds to understand how matrix properties, filler geometry and experimental set up determine conductivity behavior and why the percolation threshold differs from paper to paper.