Non-symmetrical dielectric relaxation behaviour arising from a simple empirical decay function

TLDR

An empirical dielectric decay function γ(t)=exp[–(t/τ0)^β] can be analytically transformed to a frequency‑dependent complex dielectric constant when β=0.5. The study proposes that this representation could generally describe α relaxations in other polymers. The Hamon approximation, with a minor correction, accurately models the function for β=0.5 when log(ωτ0) > –0.5, but fails at lower frequencies. The resulting dielectric constant and loss curves are non‑symmetrical about the logarithm of the frequency of maximum loss, lie between Cole‑Cole and Davidson‑Cole forms, and the empirical model agrees well with experimental α‑relaxation data for polyethyl acrylate after a short extrapolation.

Abstract

The empirical dielectric decay function γ(t)= exp –(t/τ0)β may be transformed analytically to give the frequency dependent complex dielectric constant if β is chosen to be 0.50. The resulting dielectric constant and dielectric loss curves are non-symmetrical about the logarithm of the frequency of maximum loss, and are intermediate between the Cole-Cole and Davidson-Cole empirical relations. Using a short extrapolation procedure, good agreement is obtained between the empirical representation and the experimental curves for the α relaxation in polyethyl acrylate. It is suggested that the present representation would have a general application to the α relaxations in other polymers. The Hamon approximation, with a small applied correction, is valid for the present function with β= 0.50 in the range log(ωτ0) > –0.5, but cannot be used at lower frequencies.