A Phenomenological Theory of Dielectric Response

The phenomenological theory of the electret effect, as developed by Wiseman and Feaster and extended by Perlman and Meunier, is cast into a form which allows a unified treatment of a variety of experiments. Introducing Mikusinski operators, a superposition principle expresses the electric displacement operator as εE+P_b with $$P_b\mathrm{(t)=}{\displaystyle {\int }_{\mathrm{-\infty }}^0}\mathrm{\chi (t-T)E(T)dT,}$$ and ε=ε₀+χ_i+χ, where the operator χ characterizes the slow polarization response and the constant χ_i gives the fast response. Then, the field E within a dielectric of conductivity c is related to the electrode current density J by the operator equation E=Z(J—J̄), where Z=1/(c+sε) determines the impedance operator and the operator ${\mathrm{J̄=\{dP}}_b{\mathrm{/dt\}-\epsilon }}_i\text{E(−0)}$ gives the effects of fields applied before t=0. Applications include a derivation of interesting relations discovered by Gross, an evaluation of the accuracy of the quasiequilibrium approximation used by Perlman and Meunier, and the construction of an equivalent circuit.