Abstract
A statistical treatment is used to describe the dipole–dipole relaxation processes of spins S=1/2 diffusing on finite two-dimensional (2D) surfaces. This leads to a general expression for the dipolar correlation function G(τ) including pairwise autocorrelation and cross-correlation terms. We show that for a finite 2D planar surface, G(τ) decays faster than that for an infinite planar surface. For finite 2D planar surfaces, dipolar translational correlation times, τ̄c are expressed in terms of the diffusion coefficient, the distance of closest approach between spins, and the area of the surface. It is shown that there is rapid motional line shape narrowing for sufficiently small two-dimensional surfaces. The calculation of resonance line shapes for the infinite 2D surface is discussed, but remains an unsolved problem when the only relaxation processes are those that arise from intermolecular dipolar interactions.
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