Two-Dimensional (2D) NMR Methods

4 Relaxation in NMR SpectroscopyMatthias Ernst

Physical Chemistry, ETH Zürich, Vladimir-Prelog-Weg 2, Zürich 8093, Switzerland

4.1 Introduction

Relaxation in magnetic resonance describes the process of a spin system returning to the thermal-equilibrium state. In order to observe such a phenomenon, we have to generate a non-equilibrium state in the first place. In NMR, we can do this using radio-frequency (RF) pulses that manipulate the state of the spin system by rotations [1–3]. Combined with free-evolution periods, such experiments allow us to generate a large number of different non-equilibrium states and observe their return toward the thermal equilibrium. The complex path to thermal equilibrium involves coherent evolution of the density operator and incoherent auto- and cross-relaxation processes that lead to decay and transfer of coherences and populations. The versatility of Fourier-transform NMR allows us to measure the time evolution of different coherence and populations, thus allowing the detailed characterization of different relaxation processes as the density operator returns to the thermal-equilibrium state.

Phenomenologically, the relaxation process can be described by local fields at the location of the spin that fluctuate as a function of time on different time scales. Such fluctuating local fields can be generated by anisotropic interaction (dipolar coupling, chemical-shielding anisotropy [CSA], quadrupolar interaction for nuclei and g-tensor anisotropy, ...