A model for a polar dielectric liquid exhibiting Cole-Davidson behavior

Although many dielectric liquids do exhibit Debye behavior, or a close approximation to it, others exhibit behavior for which the plot of ε" against ε\´ as the frequency is varied is not a semicircle, but one of several possible other shapes. These shapes can be predicted by the adoption of the postulate that the liquid exhibits more than one discrete relaxation time, or a smooth distribution of relaxation times. One such shape is the Cole-Davidson plot, which tends towards a semicircle as the frequency is reduced towards zero, and to a straight line of positive slope as the frequency becomes indefinitely high. Although this behavior can be predicted by the postulate of a distribution of relaxation times, leading to a modified form of the Debye equation, the replacement of the geometrical description by an algebraic description of the behavior does not explain the basic physical reason giving rise to it. There are reasons for believing that under ordinary laboratory experimental conditions the average vibrational angle of the dipoles is very small, less than say ten microdegrees. This is not enough to cause the field, and so the torque, experienced by the dipoles to vary significantly on account of the variation in the direction of their dipole moments caused by this vibrational motion. However, statistically there will be some dipoles which experience a greater angular movement, and the torque they experience may vary significantly because of the change in the angle between their dipole moment and the applied field. An earlier theoretical analysis of the consequences of such large Angular dipole displacements when a dc field is applied to a polar dielectric liquid indicated that under certain idealized conditions, the build-up of polarization with time, although quasi-exponential, deviates somewhat from true exponential behaviour, especially at very short times. This indicates that when an ac field is applied, deviations from ideal Debye behavior, might be expected, particularly at high frequencies. This possibility is considered in the present paper, and it is shown that a skewed arc can be predicted on the basis of the dynamics of the polar molecules of the dielectric.