Theory of intramolecular spin relaxation by translational diffusion in locally ordered fluids

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Abstract
The theory of spin relaxation induced by translational diffusion of small molecules or ions in locally ordered fluids, developed in parts I and II of this series, is extended to cylindrical geometry as, for example, in polyelectrolyte solutions or in hexagonal lyotropic liquid crystals. The theory is based on the Smoluchowski diffusion equation with nonuniform potential of mean force and translational diffusivity and on the cylindrical cell model. Formally exact closed-form expressions are derived for the zero-frequency spectral density associated with radial diffusion, while a general numerical algorithm is described for computing the full frequency-dependent spectral density. Several useful approximations, such as the dynamic cell approximation, the steady state approximation and the surface diffusion approximation, are formulated and their accuracy quantitatively assessed. Calculations are reported for a mean-field interaction model based on the nonlinear Poisson-Boltzmann equation, with emphasis on applications of the theory to counterion spin relaxation in polyelectrolyte solutions.