Inertial Effects and Dielectric Relaxation

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Abstract
The study of dielectric relaxation in compressed gases requires an extension of existing theory. As the gas pressure is lowered below several hundred atmospheres, the inertial response of the dipoles gives rise to large deviations from the Debye equations. The absorption and dispersion depend on collision time and frequency of applied field in a manner which is sensitive to the molecular constants and to the state of dynamical order of the compressed gas. These phenomena are investigated by studying the response to an alternating electric field of a dilute solution of dipolar molecules in a nonpolar compressed gas. The dipoles are described by a classical distribution function which is a function of angular velocity, orientation, and time. We assume that the duration of collision may be neglected compared to the time between collisions, the period of the applied field, and the mean thermal period. The distribution function satisfies a kinetic equation; the effects of collisions are described by a collision kernel. One kernel yields a soft impact theory which is a generalization of Debye's Brownian motion treatment to include inertial effects. The complex polarization is given in the form of a convergent infinite continued fraction. Other models studied involve strong collisions and partial specular reflection. A common feature of all models is that the Debye relaxation shape is found at high pressures. Inertial corrections are important in the region between one and a few hundred atmospheres; the corrections depend on the model. Another common feature is the way in which the discrete rotational lines are linked with the Debye spectrum. The collision frequency 1/τ increases with increasing gas pressure; at low pressures it is proportional to the width of a rotation line. At high pressures when the Debye shape is found, the relaxation time t* is given by t* = 1/τ(I/kT). Here I is the moment of inertia of the dipole, k is Boltzmann's constant, and T is the temperature of the reservoir. Thus the relaxation time varies inversely with time between collisions. The physical reason is that collisions hinder the drift motion of the dipoles which is the cause of the relaxation of the polarization. At lower pressures the main contribution to the polarization arises from dipoles rotating with an angular frequency close to that of the applied field. This is related to the known result that the main contribution to the static polarization is from librating dipoles.