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Dispersion and Absorption in Dielectrics I


  Dispersion and Absorption in Dielectrics I. Alternating Current Characteristics
  Cole, Kenneth S.; Cole, Robert H.
  The Journal of Chemical Physics, Volume 9, Issue 4, p.341-351
  The dispersion and absorption of a considerable number of liquid anddielectrics are represented by the empirical formulaε*-ε∞=(ε0-ε∞)/[1+(iomegatau0)1-alpha].In this equation, ε* is the complex dielectricconstant, ε0 and ε∞ are the``static'' and ``infinite frequency'' dielectric constants,omega=2pi times the frequency, and tau0 is ageneralized relaxation time. The parameter alpha can assume valuesbetween 0 and 1, the former value giving the result of Debye for polardielectrics. The expression (1) requires that the locus of thedielectric constant in the complex plane be a circular arc with endpoints 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 themethod of Fuoss and Kirkwood. It is, however, difficult to understandthe physical significance of this formal result.
  If a dielectric satisfying Eq. (1) is represented by a three-elementelectrical circuit, the mechanism responsible for the dispersion isequivalent to a complex impedance with a phase angle which isindependent of the frequency. On this basis, the mechanism ofinteraction has the striking property that energy is conserved or``stored'' in addition to being dissipated and that the ratio of theaverage energy stored to the energy dissipated per cycle is independentof the frequency.