Dispersion and Absorption in Dielectrics I. Alternating Current Characteristics

The dispersion and absorption of a considerable number of liquid and dielectrics are represented by the empirical formula $${\epsilon }^{*}{\mathrm{-\epsilon }}_{\infty }{\mathrm{=(\epsilon }}_0{\mathrm{-\epsilon }}_{\infty }{\text{)/[1+(iωτ}}_0{)}^{\text{1−α}}\mathrm{].}$$ 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.