On the role of inertial effects and dipole-dipole coupling in the theory of the Debye and far-infrared absorption of polar fluids III. The cosine potential itinerant oscillator model

Abstract

The polarizability and dynamic mobility for the itinerant oscillator model are calculated when the restriction to small oscillations is removed so that effects due to the cosine potential may be evaluated. The calculation is effected by expressing the Fokker-Planck equation for equal frictions per unit inertia in terms of sum and difference angular variables. The sum angle, Χ, yields the Fokker-Planck equation for a free rotator, the correlation functions of which are available in closed form. The difference angle, η, yields the Fokker-Planck equation for a rotator in a cosine potential. This equation is solved by the method of separation of the variables. The resulting set of differential-difference equations for the time responses is solved by using Reid’s numerical algorithm. The complex polarizability is then evaluated from the numerical results by assuming that the moment of inertia of the dipole is very much less than that of the cage in accordance with the basic concept of the model. Unlike the complex polarizability, the dynamic mobility may be evaluated from the numerical results without any assumption about the inertia ratios. The polarizabilities computed for the cosine potential are compared with the small oscillation polarizabilities for the same parameter values. It is found that the cosine potential gives rise to (i) substantial absorption at frequencies between the microwave and far-infrared (fir), bands (ii) an increase in the frequency of the maximum microwave absorption (iii) a decrease in the frequency of the maximum fir absorption (iv) a much more rapid fall-off of the fir absorption. If the barrier height parameter becomes large, the intermediate frequency absorption disappears and the effect of the cosine potential manifests itself as a shoulder on the fir absorption. An approximate formula for the polarizability in terms of the Fourier transform of the angular velocity correlation function is shown to be satisfactory for small oscillations only. The theoretical results are in qualitative agreement with experimental observations on methyl chloride.