A calculation of the complex dielectric constant of a polar liquid by the librating molecule method

The dielectric constant of polar liquids is calculated by assuming a model of the molecule which describes its interaction with the electric field and by introducing means of calculating certain averages demanded by the statistical mechanical theory. In this paper we make a calculation for the time-dependent case which parallels the approach of Onsager. The model is introduced at the beginning, and the average torque on a molecule due to the local field is found by solving quasistatically the problem of a polarizable dipole performing small librations in a cavity in a continuum having a complex dielectric constant. The result of the calculation predicts a non-exponential decay of the macroscopic polarization. The results are compared with the treatment of similar type by Scaife, and with treatments by means of the Kubo theory of non-equilibrium statistical mechanics. These latter allow the introduction of the model at a late stage in the calculation, as in the theories of Kirkwood, Frohlich and Buckingham on the static case. Such a treatment, as carried out by Glarum, and a modification of it by the authors are considered. It is found that the results of the present paper show a certain agreement with the results of Scaife and with the authors' modification of the treatment of Glarum.