Spin dynamics and thermodynamics in solid-state NMR cross polarization

Abstract

We investigate spin thermodynamic processes taking place during Hartmann–Hahn cross-polarization experiments in solids, in which spin polarization is transferred between two nuclear spin species by the application of two strong rf fields. As is well known, optimum cross polarization is achieved for a particular ratio of the two rf field strengths called the Hartmann–Hahn condition; we find experimentally that this condition provides the optimum transfer not only on kinetic grounds, as is usually supposed, but also for thermodynamic reasons. By measurement of the evolution of the spin observables in a ferrocene single crystal we demonstrate the existence of a quasi-equilibrium state with nonuniform spin temperature and less than maximum entropy. A modified spin thermodynamic theory is developed whose main features are the important role of the dipolar energy for the quasi-equilibrium state and the existence of constants of the motion other than the total energy. A new cross-polarization experiment is suggested which is shown to provide efficient cross polarization even for mismatched Hartmann–Hahn conditions.