Dipole-dipole interactions in liquids entrapped in confined space

Abstract

At consideration of the spin dynamics of nuclei in liquids or gases the dipole-dipole interaction Hamiltonian is divided into an intramolecular interaction part describing the interaction between spins inside a molecule and the part related to the intermolecular interaction of spins of different molecules. For liquid entrapped in nanopores it is shown that due to restricted motion of molecules the intramolecular interactions are not averaged to zero and contribute in NMR signals for nanopores with the characteristic size of the order of the molecule hydrodynamic radius. The intermolecular interactions are essential for the pore characteristic size up to hundreds nm.It is shown that the transverse relaxation time, line width, and intensity of NMR signal for cylindrical and ellipsoidal pores should possess the same angular dependence and differ by form-factors for nanopores. Their dependences on the pore volume and form are analyzed. Although nanopores contain large number of spins, ~106, the line width is estimated as 300 Hz, that significantly differs from one for bulk water (~1 Hz).Assuming the Gaussian distribution of nanopore orientations, we calculated the anisotropy of the transverse relaxation rate for a collagen fiber sample possessing three histological zones with different degrees of fibers ordering. Good agreement with the published experimental data is obtained by adjustment of few parameters - the standard deviation, averaged fiber direction, and weight factors which characterize the ordering of fibrils, their orientations in each zone, and the relative dimensions of these zones.