Theory of spin relaxation by diffusion on curved surfaces

A comprehensive theoretical analysis is presented which accounts for nuclear spin relaxation due to molecular surface diffusion on spheroidal aggregates undergoing restricted rotational diffusion in a uniaxial potential of mean torque. The model is formulated primarily with surfactant systems in mind, and should provide a realistic description of spin relaxation in nematic and smectic liquid crystals as well as in isotropic micellar solutions. Two efficient numerical schemes are developed to compute the joint time correlation functions and spectral density functions. In addition, a variety of useful analytical results are derived for special cases. Numerical calculations suggest that nuclear spin relaxation may be a unique method for monitoring small deviations from spherical aggregate shape.