Abstract

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.
LanguageEnglish
Article number39
JournalEuropean Physical Journal B
Volume90
Issue number3
DOIs
StatusPublished - 8 Mar 2017

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resistors
Resistors
frequency response
Frequency response
capacitors
Capacitors
Composition effects
composite materials
Scaling laws
Composite materials
Large scale systems
Electric properties
Chemical analysis
approximation
scaling laws
alternating current
electrical properties
low frequencies
saturation
conductivity

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Understanding the anomalous frequency responses of composite materials using very large random resistor-capacitor networks. / Aouaichia, Mustapha; McCullen, Nicholas; Bowen, Christopher; Almond, Darryl; Budd, Christopher; Bouamrane, R.

In: European Physical Journal B, Vol. 90, No. 3, 39, 08.03.2017.

Research output: Contribution to journalArticle

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