Analytical descriptions of (multiple-contact) cross-polarization dynamics and spin-lattice relaxation in solid alanine

Abstract

In this work, several exact and approximate analytical solutions to the quantum master equation are derived using both classical and non-classical coupling models to describe the kinetics of Hartmann-Hahn cross-polarization (HHCP) and multiple-contact CP (MCCP). Moreover, the analytical solution originally obtained by Naito and McDowell [J. Chem. Phys. 84 (1986) 4181.] is shown to be incorrect and the different regimes of spin diffusion and T1ρ relaxation are characterized by the amplitude of the second stage of the HHCP dynamics and the HHCP/MCCP crossing time. The analysis of the 1H–13C HHCP and MCCP dynamics together with (Lee-Goldburg) 1H T1ρ relaxation experimental data provides a consistent picture of spin dynamics in solid alanine and explains the apparent discrepancies previously observed between T1ρ and T1 relaxation measurements. The CH and CH3 protons relax as expected via spin diffusion towards the NH3 protons but the assumption of common proton spin temperature, in which the bottleneck of relaxation is at the NH3 sites, generally valid for T1 relaxation breaks down for T1ρ relaxation. A diffusion-limited situation in which nuclear Zeeman energy is transferred to the lattice faster than can be supplied by spin diffusion is observed instead.

Keywords

• Solid-state NMR
• Cross-polarization
• Magic-angle spinning
• Spin diffusion
• Spin-lattice relaxation