The temperature–frequency dependence of conductive random RC networks modelling heterogeneous/composite materials

Abstract

The purpose of this study was to investigate the temperature’s effect on the dielectric response of 2D random RC networks (RRCNs) modelling heterogeneous/composite materials. We presented a comparative analysis for the conductivity behaviour using the modified effective medium approximation (EMA) and Franck and Lobb (FL) algorithm. We showed that the Summerfield frequency, the characteristic frequency $\omega _{c}$ of the conductivity and the loss frequency $\omega _{\max }$, all followed an Arrhenius dependence; they could be used as scaling frequencies. Using the loss frequency $\omega _{\max }$ for different temperatures, we could represent each dielectric property in a master curve form. This latter exhibited a behaviour related to the time–temperature superposition principle (TTSP). We showed that the DC conductivity and $\omega _{\max }$ exhibited the Barton–Nakajima–Namikawa (BNN) relationship $\sigma '_{dc}=a\varDelta \varepsilon '\omega _{\max }$ for which $a\sim 1$ as found in the literature, where $\varDelta \varepsilon '$ is the dielectric loss strength. In addition, we showed that for capacitors’ proportion $p=0.40$, random RC networks preserved their universal power-law (UPL) behaviour when the temperature was considered with a slight difference in the exponent value differing from the capacitors proportion. We found that the normalized conductivity and complex permittivity both scaled as $\sigma '/\sigma _{dc}\propto (\omega /\omega _{\max })^{n}$ and $\varepsilon /\varepsilon _{s}\propto (\omega /\omega _{\max })^{n-1}$, respectively, reflecting the universal dielectric response (UDR).

Graphical abstract