Influence of cross-relaxation on NMR spin-lattice relaxation times

Abstract

When intramolecular dipole-dipole interaction is a significant nuclear magnetic resonance spin-lattice relaxation mechanism, the recovery of the longitudinal magnetization after a perturbation no longer follows a simple exponential curve described by a single time constant T 1. This cross-relaxation effect is analyzed for the case of a nonselective 180° pulse applied to a system of two spin 1 2 nuclei (I and S), in terms of two “external” relaxation parameters, T XI and T xs, and the dipolar relaxation time T 1D. If the experimental relaxation data are plotted on a semilogarithmic graph, the deviations from linearity due to cross-relaxation may not be large enough to be detected in the presence of statistical errors on the measurements, but the derived slope can, nevertheless, show a significant error. In general for weakly coupled systems these errors are found to be quite small; they vanish for the I signals of a heteronuclear system where the S nucleus is strongly irradiated or where T XI or T XS is much shorter than T 1D. Experimental results for the heteronuclear 13CH spin system in formic acid and the homonuclear HH spin system in cytidine indicate errors of the order of 10 %. Cross-relaxation effects can be much more serious in strongly-coupled spin systems with appreciable asymmetry in the external relaxation ( T XI ≠ T XS). The lines of an AB quartet follow four separate recovery curves showing marked deviations from pure exponentials, particularly for the weak outer lines. This is illustrated with experimental results for the ring protons of tyrosine.