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

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 $$\omega _{c}$$ ω c of the conductivity and the loss frequency $$\omega _{\max }$$ ω max , all followed an Arrhenius dependence; they could be used as scaling frequencies. Using the loss frequency $$\omega _{\max }$$ ω 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 $$\omega _{\max }$$ ω max exhibited the Barton–Nakajima–Namikawa (BNN) relationship $$\sigma '_{dc}=a\varDelta \varepsilon '\omega _{\max }$$ σ dc ′ = a Δ ε ′ ω max for which $$a\sim 1$$ a ∼ 1 as found in the literature, where $$\varDelta \varepsilon '$$ Δ ε ′ is the dielectric loss strength. In addition, we showed that for capacitors’ proportion $$p=0.40$$ 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 $$\sigma '/\sigma _{dc}\propto (\omega /\omega _{\max })^{n}$$ σ ′ / σ dc ∝ ( ω / ω max ) n and $$\varepsilon /\varepsilon _{s}\propto (\omega /\omega _{\max })^{n-1}$$ ε / ε s ∝ ( ω / ω max ) n - 1 , respectively, reflecting the universal dielectric response (UDR). Graphical abstract