Modeling electrical conductivity of polymeric nanocomposites: A review

This review critically evaluates computational frameworks for predicting the electrical conductivity (EC) of polymer nanocomposites, categorizing existing approaches into four groups: atomistic, empirical, continuum, and multi-scale modeling. These methodologies are systematically compared with respect to their treatment of filler morphology, orientation, dispersion, aspect ratio, waviness, agglomeration, interphase characteristics, computational cost, scalability, physical fidelity, and predictive capability. Atomistic and empirical approaches provide valuable insights into nanoscale mechanisms and conductivity trends, whereas continuum and multi-scale models offer greater applicability to engineering-scale systems. The analysis indicates that multi-scale approaches possess the greatest potential for predictive conductivity modeling; however, current implementations remain only partially coupled across length scales. A comprehensive gap analysis identifies three major barriers to improved predictive accuracy: uncertainty in electron tunneling physics, inadequate representation of conductive network topology, and insufficient characterization of the interphase region. In addition, the absence of standardized experimental benchmark datasets limits objective validation and comparison of existing models. Future developments should focus on rigorous nano-to-macro scale coupling, stochastic representation of microstructural variability, uncertainty quantification, integration of experimentally characterized three-dimensional microstructures, and physics-informed machine learning to achieve more reliable and transferable conductivity predictions.