Theory of spin relaxation by translational diffusion in two-dimensional systems

Abstract

Spin relaxation rates T−11 and T−12 are calculated for nuclear (or electron) spins diffusing on finite two-dimensional, planar, or spherical surfaces. The spin relaxation is assumed to be due to modulation of the intermolecular dipole–dipole interactions. It is shown that the mathematical divergences encountered in a number of previous theoretical treatments of this problem for infinite planar surfaces have no physical significance; these divergences are avoided by limiting the calculations to two-dimensional systems that are finite, but that are otherwise of arbitrarily large size. The theoretical relaxation rates T−11 and T−12 for finite, planar two-dimensional systems are found to have a number of unique properties that should facilitate the interpretation of magnetic resonance spectra of molecules physically adsorbed on solid surfaces. For example, the reduction in dimensionality of rapid diffusive motion yields relaxation rates typical of slow motion in three-dimensional systems. Under certain conditions the relaxation rate T−11 is strongly dependent on the size of the two-dimensional surface on which atoms or molecules diffuse. Moreover the shape of the surface (planar or spherical), which is of particular importance in the description of the two-dimensional dynamics, can profoundly alter the frequency and temperature dependences of the spin-relaxation rates. The theory appears to be directly applicable to recent experiments by J. Tabony [Prog. Nucl. Magn. Reson. Spectrosc. 14, 1 (1980)].