Dynamics of molecular liquids: A comparison of different theories with application to wave vector dependent dielectric relaxation and ion solvation

Abstract

Explicit expressions are given for the Fourier–Laplace transform of the van Hove function for fluids of particles interacting through orientation dependent pair potentials. The expressions are obtained from the Kerr approximation together with diffusion models for the self part of the van Hove function and apply at all frequencies and wavelengths. Both spherical (scalar diffusion constants) and nonspherical (tensorial diffusion constants) diffusors are considered and the theory is applied to k-dependent dielectric relaxation and ion solvation dynamics. The required equilibrium structure is obtained using the hypernetted chain (HNC) or reference hypernetted chain (RHNC) theories and Kerr/RHNC(HNC) results are given for fluids of dipolar hard spheres, dipolar hard ellipsoids, and water-like particles. Comparisons are made with earlier work based upon coupling equilibrium theories, such as the mean spherical approximation (MSA) for dipolar hard spheres with a dynamical equation of the Smoluchowski–Vlasov (SV) type. It is shown that for spherical diffusors with the self part of the van Hove function treated at the Fick–Debye level, the SV and Kerr equations are in fact equivalent. However, even for spherical diffusors, the results obtained can differ substantially depending upon the equilibrium theory and/or the molecular model employed. For nonspherical diffusors, the anisotropy of the rotational diffusion tensor can also be an important parameter influencing the k-dependent dielectric relaxation.