Direct Determination of Quadrupolar and Dipolar NMR Correlation Times from Spin–Lattice and Spin–Spin Relaxation Rates

Abstract

Recent developments in the mathematical solution of nuclear magnetic resonance (NMR) relaxation equations describing rotational motion allow investigators to determine correlation times, τ, on the nanosecond time scale. NMR rotational correlation equations for quadrupolar and dipolar relaxation can be solved for nuclei in moderately viscous media using R2/R1 ratios. In the case of quadrupolar nuclei, the R2/R1 ratios can be used to solve the rotational correlation equations directly. For dipolar nuclei including 1H, 13C, 15N, 19F, 31P, and 113Cd, it is necessary to solve the rotational correlation time equations at each magnetic field strength using iterative methods. The resulting solutions are fitted to pairs of polynomials (R2/R1=1.1–20 and 20–1200) at individual magnetic field strengths (4.7, 6.35, 7.05, 9.4, 11.75, and 14.1 T). The investigator determines the R2/R1 ratio at a specific magnetic field and uses the appropriate polynomial to determine the rotational correlation time. Correlation times are used to study molecular interactions where dipolar relaxtion occurs and to determine quadrupole coupling constants, χ, where quadrupole relaxation is the predominant mechanism. 1H-NMR diffusion constants can be compared with NMR correlation times to provide data about the transport properties of the system being studied. ©1999 John Wiley & Sons, Inc. Concepts Magn Reson 11: 51–60, 1999