A study of random capacitor networks to assess the emergent properties of dielectric composites

This paper examines whether emergent behaviour is observed in dielectric composites, i.e. mixtures of two phases with zero conductivity and of permittivity ϵ₁ and ϵ₂. The model developed enabled the study of random capacitor networks which contain capacitors of two different magnitudes (C1 and C2), which represent the two individual dielectric phases of a composite. The effective capacitance of the network was examined as a function of the individual capacitor magnitudes and their volume fraction. The capacitor networks exhibit an emergent region where there is low variability between individual random networks of a particular composition. The logarithm of the network capacitance scaled linearly with the logarithm of the capacitance ratio (C1 and C2), indicating that under particular conditions a logarithmic mixing rule can be used to determine the properties of dielectric mixtures.