Theory of absorption in solid dielectrics

Most solid dielectrics are imperfect in the sense that when a constant d-c. voltage is suddenly applied, a displacement of electricity first takes place almost instantly to a certain value, and then continues to increase asymptotically towards an ultimate magnitude. Accordingly, an initial electric charge and a greater final charge may be distinguished, with the corresponding values of initial and final permittivities. The purpose of the present investigation is to establish certain general properties of the function which expresses the increase in the initial electric displacement with the time. The initial and the final leakage conductivities of the material are also taken into consideration. An assumption is made that the law of relaxation of electric displacement in the individual particles of the dielectric is a simple exponential function of time, but that the exponent varies from particle to particle. In some “non-viscous” particles the final displacement takes place instantly, in some others it occurs infinitely slowly, while for a great majority of the particles the relaxation proceeds at various finite rates. A “distribution function” for the numbers of different particles is introduced and the general conditions which this function must satisfy are established. The results are then applied to a particular form of distribution function which has a large enough number of parameters for representing experimental data on a given dielectric with sufficient accuracy. Integrations are carried out for the cases of direct and sinusoidal applied voltages. With direct voltage, expressions are deduced for the permittivity and conductivity as functions of time. Since experimental curves of these two quantities can be obtained, a comparison with the theoretical formulas will permit a determination of the numerical values of the parameters in the assumed distribution function. With alternating voltages, the apparent permittivity and the - pparent conductivity are expressed as functions of the frequency. Since experimental values of these quantities may be computed from measurements of capacitance and dielectric loss, another possibility is thus afforded for checking an assumed distribution function. The ultimate aim of the theory (as now developed and as may be improved in the future) is to make it possible to correlate and to mutually check a vast amount of experimental data on absorption and on dielectric loss, and to enable one to predict these quantities within the range of voltages and frequencies for which no test figures are available.