Theory of dielectric relaxation

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Abstract
A theory of dielectric relaxation is presented which relates the frequency-dependent dielectric constant to a truly single-particle correlation function. For a sample of suitable geometry, linear response theory is used to relate the polarization to a many-particle correlation function. This correlation function is shown to have the same form as, and to be related to, a true single-particle correlation function; this relationship, proved in limited form elsewhere but generalized here, is the principal result of this work. This contrasts with the usual method of obtaining ‘ small ’ macroscopic correlation functions by reducing the sample dimension until it contains but a single particle, assuming all along that macroscopic dielectric theory is applicable. We are thus able to devise a relationship between the single-particle relaxation time and the observed many-particle relaxation time which will enable the dielectric relaxation data to be compared with reorientational relaxation times obtained in other experiments, such as light-scattering and magnetic resonance. The form of the single-particle correlation function appropriate for the study of dipolar liquids is then considered in a systematic study based on a theory due to Mori. It is shown, by comparison with the experimental results, that slowly varying torques acting on the molecule play an important role, as was first suggested by Zwanzig.