Ising Model for Conductive Percolation in Electrically Conductive Adhesives by Considering Random Arrangement of Conducting Particles

Abstract

Problem statement: Thermodynamically, particles in composites will arrange in a way such that the Helmholtz free energy is minimized. However, even a single structure has the lowest free energy, it should not ignore the probability of other structures having larger energies to occur, although at small chances. Approach: All possible arrangements of particles in the composites, therefore, must be taken into account in the theory or simulation development. Results: The composite energy depends on the interaction between components in the composites. To consider the effect of interactions on energy, in this study we used a simple Ising model incorporated with the Bragg-Williams approximation. We used the model to predict the average packing fraction and the percolation threshold in composites as well as other quantities related to percolation phenomenon. Conclusion/Recommendations: We found several predictions that have not been reported by previous authors. This model can be important in the understanding conductivity development in electrically conductive adhesive composites.