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

Comment on “Direct Determination of NMR Correlation Times from Spin−Lattice and Spin−Spin Relaxation Times”

“…5 The usefulness and limitations of this method are outlined elsewhere. 3,4,6 It has recently been brought to our attention that there are a number of NMR spectrometers operating at 5.87 and 8.45 T. This report extends our previous analysis to these magnetic field strengths (5.87 and 8.45 T). As a result of this and earlier reports, this technique is now available to a wide range of NMR spectrometers operating at field strengths between 4.7 and 14.1 T.…”

Effect of Water on Deep Eutectic Solvent/β-Cyclodextrin Systems

“…Generally speaking, small molecules have short rotational correlation times (fast rotation), whereas large molecules or aggregates have long rotational correlation times (slow rotation). The equations relating τ c to the longitudinal and transverse heteronuclear and homonuclear relaxation rates are well established, , and the theoretical treatment is described for the interested reader in the SI. To get a general idea, Figure displays the behavior of T 1 and T 2 for an aliphatic CH carbon at a magnetic field of 11.7 T. At very short correlation times (fast motion regime) the values of T 1 and T 2 are equal.…”

Nuclear Spin Relaxation and Molecular Interactions of a Novel Triazolium-Based Ionic Liquid

“…Isotropic carbons with hydrogen covalently bound, due to the very high magnetic moment of protons, are relaxed primarily by the dipolar relaxation mechanism in the absence of paramagnetic relaxants. R 1 is strongly influenced by dipole moments, bond distances, and molecular motion. , Plotting the natural log of R 1 against the inverse of temperature (from the Arrhenius Equation, eq , where m and b are constants, and R is a rate constant) gives an indication of the temperature-dependency of relaxation kinetics . A strong linear correlation in the Arrhenius plot is evidence of a single rate-limited thermally activated process. ln ( R ) = m T + b …”