Dynamic effects of pair correlation functions on spin relaxation by translational diffusion in liquids

Abstract

It is shown how the equilibrium pair correlation function between spin-bearing molecules in liquids may be incorporated as an effective force in the relative diffusion expressions, and how one may solve for the resulting time correlation functions and spectral densities needed for studies of spin relaxation by translational diffusion. The use of finite difference methods permits the solution no matter how complex the form of the pair correlation function (pcf) utilized. In particular, a Percus–Yevick pcf as well as one corrected from computer dynamics, both for hard spheres, are utilized. Good agreement with the experiments of Harmon and Muller on dipolar relaxation in liquid ethane is obtained from this analysis. Effects of ionic interactions in electrolyte solutions upon dipolar relaxation are also obtained in terms of Debye–Hückel theory for the pcf. Analytic solutions are given which are appropriate for the proper boundary-value problem for the relative diffusion of molecules (i.e., a distance of minimum approach) that has usually been neglected in the spin relaxation theories. Other molecular dynamics aspects of spin relaxation by translational diffusion in liquids are briefly discussed.