Application of free rotational models of molecular reorientation to the explanation of high frequency effects in dielectric relaxation

摘要

Exact solutions obtained by Gross [J. Chem. Phys. 23, 1415 (1955)] and Sack [Proc. Phys. Soc. London, Sect. B 70, 402 (1957)] for the complex polarizability of assemblies of nonelectrically interacting rotators subjected to a variety of collisions and various approximations to that quantity, specifically the Rocard equation are reappraised in view of recent attempts to use a variety of forms of that equation for the interpretation of far infrared resonance absorption spectra. It is shown that for small values of the inertial parameter (heavy damping) the Rocard equation yields a really good approximation for the complex polarizability only for the small collision model considered by Gross and Sack. In the case of large inertial parameter values it is emphasized by means of plots of the complex polarizability that such an approximation always exhibits behavior characteristic of a sharply resonant system, i.e., a pronounced absorption peak well in excess of the Debye peak and a strongly negative real part, while the exact complex polarizability spectrum for the same parameter values merely displays inertia corrected Debye relaxation. Therefore, an explanation of the resonant term other than that based on a Rocard equation with a large inertial parameter must be sought as that equation strictly applies to inertia corrected Debye (heavily damped) relaxation only. The application of the itinerant oscillator model and the three variable Mori theory to the problem is discussed in view of this conclusion.