Quadrupolar solid-state NMR and repetitive experiments: Some aspects in the Liouville space. Application to spins I=1

Abstract

The aim of this work is to generalize the Ernst-Anderson model developed to account of the steady-state regime of isolated spins I=1/2 subject to a train of strictly identical pulse sequences separated by free evolution periods of same duration. We generalize this model to the general case of spins I≥1 and general pulse sequence within the framework of the Liouville space. In particular, it is proved that under reasonable assumptions, a well defined steady-state regime is reached which is independent of the initial conditions. The general formal expressions obeyed by the steady-state density operator are given as a function of pulse propagators and relaxation operator for single and two-pulse sequences. In solid-state NMR where recycle time can be made, at the same time, much longer than typical coherence relaxation times and smaller than typical population relaxation times, further simplification leads to more tractable formula. As an example, the formalism is applied to I=1 spins with hard and soft single pulse sequence, or to the solid echo sequence. In particular, we were able to generalize the Ernst-Anderson formula to spins I=1. The pertinence of the theory is verified by comparing the theoretical and numerical simulations outputs to ²H single crystal experiments performed on nonadecane/urea C₁₉D₄₀/urea-H₄ compound.

Keywords: Deuterium; Liouville space; Progressive saturation; Quadrupolar NMR; Solid-state NMR; Spin I=1.