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

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 polariza bility of assemblies of nonelectrically interacting rotators subjected to a variety of collisions and various approximations to that quantity, specifi cally 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 ine rtial parameter (heavy damping) the Rocard equation yields a really good ap proximation for the complex polarizability only for the small collision mod el considered by Gross and Sack. In the case of large inertial parameter va lues 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 D ebye peak and a strongly negative real part, while the exact complex polari zability spectrum for the same parameter values merely displays inertia cor rected Debye relaxation. Therefore, an explanation of the resonant term oth er than that based on a Rocard equation with a large inertial parameter mus t be sought as that equation strictly applies to inertia corrected Debye (h eavily damped) relaxation only. The application of the itinerant oscillator model and the three variable Mori theory to the problem is discussed in vi ew of this conclusion. (C) 1999 American Institute of Physics. [S0021-9606( 99)50410-8].