Nuclear spin–lattice relaxation in periodically irradiated systems

Abstract

A master equation for nuclear magnetic relaxation under conditions of periodic and cyclic rf irradiation is derived based on the stochastic Liouville equation. Conditions for the validity of the equation, involving both use of the motional narrowing approximation and the Magnus expansion, are discussed with particular attention given to the simultaneous presence of fluctuating and nonfluctuating interactions. The expressions derived are applied to several irradiation schemes: the Carr–Purcell sequence, where the echo decay time under translational diffusion is calculated; the cw and pulsed versions of spin locking in solids, with special emphasis on the origin and role of spin diffusion and on the exact relationship between the second moment and the prefactor in the T1ρ expression; and, finally, the four- and eight-pulse sequences used for suppression of homonuclear dipolar interactions, where it is shown that the x, y, and z axes of the interaction frame are ’’principal axes’’ of relaxation. Physical interpretation of the calculated results is presented. The relaxation times of cyclohexane under the eight-pulse cycle are experimentally determined and shown to confirm the theory.