Dielectric friction and polar molecule rotational relaxation

Abstract

Using the Onsager cavity model the frequency dependent torque due to the long range dipole–dipole interaction is derived for an electric dipole rotating in a polar liquid. This generalizes to all orders the result first order in the angular velocity derived by Fatuzzo and Mason and by Nee and Zwanzig. For a constant angular velocity the dielectric frictional torque on a rotor is shown to depend upon the complex permittivity only at the frequency of rotation and has no zero frequency contribution as given by the first order theory. The effect of dielectric friction upon the rotational Einstein relation and the second fluctuation–dissipation theorem is derived. Unlike the first order theory and consistent with the suggestion of Hubbard and Wolynes this theory invalidates the rotational Einstein relation when long range dipolar coupling effects are included in the theory of rotational relaxation. The first order theory is valid only for high angular frequencies above (2kT/I⊥)1/2. The formulation presented in this report is most conveniently applicable when significant inertial effects are present. In a sample calculation for highly compressed polar gases it is shown that dielectric friction produces a contribution to the angular momentum relaxation time second order in the gas density. This contribution is significant for rapidly rotating polar molecules of small moment of inertia at number densities above 2×1021 cm−3.