Understanding the anomalous frequency responses of composite materials using very large random resistor-capacitor networks
1 LEPM, Faculté de Physique, USTO-MB, BP 1505 El M'Naouer, 31000 Oran, Algeria
2 Department of Architecture and Civil Engineering, University of Bath, Bath, BA2 7AY, UK
3 Department of Mechanical Engineering, University of Bath, Bath, BA2 7AY, UK
4 Department of Mathematical Sciences, University of Bath, Bath, BA2 7AY, UK
Received: 16 July 2016
Received in final form: 6 November 2016
Published online: 8 March 2017
In this paper large resistor-capacitor (RC) networks that consist of randomly distributed conductive and capacitive elements which are much larger than those previously explored are studied using an efficient algorithm. We investigate the emergent power-law scaling of the conductance and the percolation and saturation limits of the networks at the high and low frequency bounds in order to compare with a modification of the classical Effective Medium Approximation (EMA) that enables its extension to finite network sizes. It is shown that the new formula provides a simple analytical description of the network response that accurately predicts the effects of finite network size and composition and it agrees well with the new numerical calculations on large networks and is a significant improvement on earlier EMA formulae. Avenues for future improvement and explanation of the formula are highlighted. Finally, the statistical variation of network conductivity with network size is observed and explained. This work provides a deeper insight into the response of large resistor-capacitor networks to understand the AC electrical properties, size effects, composition effects and statistical variation of properties of a range of heterogeneous materials and composite systems.
Key words: Solid State and Materials
© The Author(s) 2017. This article is published with open access at Springerlink.com
Open Access This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.