Dynamic Statistical Mechanics Modeling of Percolation Networks in Conductive Polymer Composites for Smart Sensor Applications

Conductive polymer composites (CPCs) are widely used in flexible electronics due to their tunable electrical properties and mechanical deformability. However, accurately predicting the evolution of conductive networks, particularly under compressive strain, remains a significant challenge. In this study, we developed a statistical mechanics model and an extended dynamic statistical mechanics model to quantitatively describe percolation behavior in CPCs. The static model incorporates filler geometry, aspect ratio (AR), and surface-to-volume ratio, and was validated using Monte Carlo simulations. Results show that the percolation threshold for spherical fillers was 0.11965, while significantly lower values of 0.00669 and 0.00203 were observed for plate- and rod-shaped fillers, respectively, confirming the enhanced connectivity of anisotropic particles. To capture strain-dependent behavior, a dynamic model was constructed using a Smoluchowski-type gain-loss framework. This model separates conductive network formation (gain) from network disconnection (loss) caused by filler alignment and Poisson-induced expansion. At high Poisson's ratios (0.3 and 0.5), the model accurately predicted the reduction in connectivity, particularly for anisotropic fillers. Across all tested conditions, the model exhibited strong agreement with simulation data, with RMSE values ranging from 0.0004 to 0.0449. The results confirm that high AR fillers enhance conductivity under compression, while large Poisson's ratios suppress network formation. These findings provide a reliable, physically grounded modeling framework for designing strain-sensitive devices such as flexible pressure sensors.