Spin locking and spin-lattice relaxation in a liquid entrapped in nanosized cavities

We study the dynamics of the nuclear spins in a liquid entrapped in nanosized cavities. This spin system is like a solid system where all the spins are coupled equally with the same interaction constant. It is shown that, under the high temperature approximation, the system is described by the two-temperature quasi-equilibrium density matrix. We find that the mixing rate W and the local dipolar field ω_loc depend on the cavity size V, shape F, and cavity orientation. For a large number of spins N the rate W decreases as the inverse square root of the number of spins, and is proportional to the concentration of the molecules, C. The spin-lattice relaxation rates, 1/T_1ρ and 1/T_1d, are proportional to C²/N. An NMR study of the dynamics of a spin system allows extraction of the cavity size and shape, its orientation relative to the magnetic field, and the molecular concentration.