Rotational motion in molecular liquids

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Abstract
This paper is concerned with rotational motion and the coupling between rotational and translational motion in molecular fluids. The van Hove angular space–time correlation function is expanded in a basis set of rotational invariants and some properties of the expansion are discussed. General expressions for collective reorientational time correlation functions and relaxation times are given in terms of the expansion coefficients. It is shown that this expansion allows the Kerr and Vineyard approximations which relate the distinct and self parts of the van Hove function to be cast in tractable form and Fourier–Laplace space solutions can be obtained for all frequencies and wave vectors. General solutions are given as well as explicit results for the simpler but important k=0 case. The dielectric relaxation of polar–nonpolarizable molecules is discussed and both infinite samples and the reaction field boundary conditions sometimes employed in the computer simulation of polar fluids are considered. It is shown that in the Kerr theory the frequency dependent dielectric constant ε(ω) is correctly independent of the boundary conditions applied. This is not true of the Vineyard approximation. Applying the Kerr theory and using a result for the self part of the van Hove function recently given by Caillol, we investigate the dielectric relaxation of both spherical and nonspherical diffusors. The nonspherical model is that of Berne and Pecora and couples the rotational and translational diffusion. It is found that within the Kerr approximation spherical diffusors behave as Debye dielectrics at all frequencies. However, in the nonspherical case ε(ω) can deviate substantially from the Debye result and we conclude that for highly anisotropic diffusors the coupling between rotational and translational motion can significantly contribute to the observed dielectric relaxation.