Revisiting spin-lattice relaxation time measurements for dilute spins in high-resolution solid-state NMR spectroscopy

Numerous nuclear magnetic resonance (NMR) measurements of spin-lattice relaxation times (T1S) for dilute spins such as (13)C have led to investigations of the motional dynamics of individual functional groups in solid materials. In this work, we revisit the Solomon equations and analyze how the heteronuclear cross relaxation between the dilute S (e.g. (13)C) and abundant I (e.g. (1)H) spins affects the measured T1S values in solid-state NMR in the absence of (1)H saturation during the recovery time. It is found theoretically that at the beginning of the S spin magnetization recovery, the existence of non-equilibrium I magnetization introduces the heteronuclear cross relaxation effect onto the recovery of the S spin magnetization and confirmed experimentally that such a heteronuclear cross relaxation effect results in the recovery overshoot phenomena for the dilute spins when T1S is on the same order of T1H, leading to inaccurate measurements of the T1S values. Even when T1S is ten times larger than T1H, the heteronuclear cross relaxation effect on the measured T1S values is still noticeable. Furthermore, this cross relaxation effect on recovery trajectory of the S spins can be manipulated and even suppressed by preparing the initial I and S magnetization, so as to obtain the accurate T1S values. A sample of natural abundance l-isoleucine powder has been used to demonstrate the T1S measurements and their corresponding measured T1C values under various experimental conditions.