Electrical Conductivity Analysis for Networks of Conducting Rods Using a Block Matrix Approach: A Case Study under Junction Resistance Dominant Assumption

In recent years, numerous studies have reported that high aspect-ratio and rod-shaped nanoparticles, including carbon nanotubes and metallic nanowires, are promising materials for the next-generation flexible and stretchable transparent conductive films. The functionality of the films is determined by their optoelectric performance, which is significantly affected by the microstructure inside the coated films. In this study, we derive closed-form equations for the electrical conductivity analysis of networks of conducting rods based on the block matrix, Kirchhoff's laws, and junction resistance dominant assumption (JRDA) model. This simple model is used to reveal a linear algebraic structure underneath the proposed block matrix approach. The block matrix approach under JRDA allows mapping among the key parameters of the rod network system, for example, junction resistance, network structure, and conductivity. Based on numerical experiments, we report a range of parameters for a valid JRDA model. Finally, we apply the model to as-coated silver nanowire networks to demonstrate the extraction of information directly from the micrographs of the networks.