A transient-state theory of dielectric relaxation and some empirical laws

Recently there have been renewed interests in the fundamental theory of transient dielectric responses. It centers on the physical interpretation of the Curie-von Schweidler law for the depolarization current in a dielectric after a constant field is abruptly removed or applied [1]: J(t) = kt⁻ⁿ (ο < n < 1)(1) and on the asympototic frequency_dependence of the dielectric susceptibility, χ ∼ ω, which is derivable from some empirical formulas, in particular, the Cole-Davidson dispersion law [2]; χ(ω) = go/(1−iωτo)^α (0 < α < 1) (2) Even though the above behaviors deviate considerably from Debye's theory of dielectric relaxation, which predicts an expoential decay law for the current, the explanation has always been based on Debye's theory by assuming that a dielectric may contain a distribution of relaxation times (DRT). After an extensive search of dielectric data, Jonscher, Ngai, and White reported that there are some universal dielectric characteristics among a wide range of materials, and that these behaviors are direct results of this universality [3-5]. They also proposed that this universality is the result of some many-body interactions in condensed matter and may be related to the low energy excitation of correlated states. In a recent article Calderwood pointed out the following difficulties in this universality theory [6]: (1) If t⁻ⁿ decay is to be taken strictly as Jonscher has proposed, the decay curve will allow one to determine the past history of the dielectrics. (2) As the t⁻ⁿ decay law is not invariant under the displacement t + t+to, it is possible to excite a polarization current in each of two identical samples, one after another, such that the polarization will be equal at some later time but continue to evolve along two distinct curves, which implies that the polarization alone is not enough to specify the state of the dielectric. Since these difficulties would not exist in an exponential decay law, the DRT explanation was preferred and the t⁻ⁿ decay law should be taken only as an approximation.