Dispersion and Absorption in Dielectrics I. Alternating Current Characteristics

TLDR

The empirical formula ε*−ε∞=(ε0−ε∞)/[1+(iωτ0)1−α] describes dielectric dispersion and absorption, with parameters ε0, ε∞, ω, τ0, and α (0–1), and predicts a circular‑arc locus in the complex plane, though its physical significance remains unclear. Assuming a distribution of relaxation times, the Fuoss–Kirkwood method yields the required distribution function to satisfy the empirical formula. A three‑element circuit model shows that the dispersion mechanism behaves as a complex impedance with a frequency‑independent phase angle, conserving energy such that the stored‑to‑dissipated energy ratio per cycle is constant across frequencies.

Abstract

The dispersion and absorption of a considerable number of liquid and dielectrics are represented by the empirical formula ε*−ε∞=(ε0−ε∞)/[1+(iωτ0)1−α]. In this equation, ε* is the complex dielectric constant, ε0 and ε∞ are the ``static'' and ``infinite frequency'' dielectric constants, ω=2π times the frequency, and τ0 is a generalized relaxation time. The parameter α can assume values between 0 and 1, the former value giving the result of Debye for polar dielectrics. The expression (1) requires that the locus of the dielectric constant in the complex plane be a circular arc with end points on the axis of reals and center below this axis. If a distribution of relaxation times is assumed to account for Eq. (1), it is possible to calculate the necessary distribution function by the method of Fuoss and Kirkwood. It is, however, difficult to understand the physical significance of this formal result. If a dielectric satisfying Eq. (1) is represented by a three-element electrical circuit, the mechanism responsible for the dispersion is equivalent to a complex impedance with a phase angle which is independent of the frequency. On this basis, the mechanism of interaction has the striking property that energy is conserved or ``stored'' in addition to being dissipated and that the ratio of the average energy stored to the energy dissipated per cycle is independent of the frequency.