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

Reference:

Richardson, P., Almond, D. P. and Bowen, C. R., 2009. A study of random capacitor networks to assess the emergent properties of dielectric composites. Ferroelectrics, 391 (1), pp. 158-167.

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Official URL:

http://dx.doi.org/10.1080/00150190903004767

Abstract

This paper examines whether emergent behaviour is observed in dielectric composites, i.e. mixtures of two phases with zero conductivity and of permittivity 1 and 2. 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.

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