On refining the parameters of a Random Network Model for determining the effective thermal conductivity of particulate thermal interface materials

Predictive modeling using fundamental physical principles is critical to developing new Thermal Interface Materials (TIMs) since it can be used to quantify the effect of particle volume fraction and arrangements on the effective thermal conductivity. In our prior work, we described a Random Network Model (RNM) that can efficiently capture the near-percolation transport in these particle-filled systems, taking into account the inter-particle interactions and random size distributions. The accuracy of the RNM is dependent on the parameters inherent in analytical description of thermal transport between two spherical particles, and their numerical approximation into a network model. In the present study, based on a finite element analysis, the network model is improved by developing an approximation of the critical cylindrical region between two spherical particles over which energy is transported. Taking the finite element (FE) results (generated by COMSOL™) as a reference, this critical parameter demonstrated a much larger effect on the thermal conductance of a single cell than other parameters (thermal conductivity ratio of fillers and matrix, ratio of radii of two neighboring particles and distance between two neighboring particles). Thirty different microstructures were generated using COMSOL™ at volume fractions of 40%, 50%, 58% and 70% respectively. Comparing RNM results with FE results and experimental data, a linear relationship of the critical parameter and the volume fraction was found that provides a more accurate prediction of the effective thermal conductivity of the particulate thermal interface material for a given volume fraction.