NMR relaxation and the orientational structure factor

A class of NMR relaxation mechanisms is considered which is characterized by molecular reorientations mediated by translational displacements. This particularly refers to systems in which molecules are confined to disordered structures determining the local preferential orientations of the incorporated molecules and providing translational degrees of freedom with a certain reduced dimensionality. Examples are solvent molecules adsorbed on surfaces of macromolecules, particle aggregates, or porous media. The orientation correlation function of molecules diffusing along such confining structures therefore does not only reflect the molecular dynamics but also the structural properties of the system. An orientational structure factor is introduced analogous to the structure factor of scattering theory. A number of typical model situations is treated. Experimental relaxation data of the hydration shells of lipid bilayers, proteins, and silica fine-particle aggregates are considered for comparison. The main measuring technique was field-cycling NMR relaxation spectroscopy permitting the record of frequency dependences over many decades. The data for hydrated proteins can perfectly be described by an equipartition of surface wave numbers in a certain range defined by the dimensions of the protein and, on the other hand, of the water molecules.