Magnetic nuclei in a magnetic field can adopt nuclear-spin states of different energy. As a system reaches equilibrium, the population differences between the different nuclear-spin states decays exponentially through relaxation. The intensity of a resonance signal in the NMR spectrum is related to the difference in population between the two energy levels of the different nuclear-spin states. This means that the rate at which this difference returns to equilibrium and relaxation has a profound effect on the sensitivity and resolution of an NMR spectrum. Longitudinal magnetisation, Mz, is restored to its equilibrium value Mzo by longitudinal relaxation, characterised by the longitudinal relaxation time T1. Transverse magnetisation, Mx and My, decays by transverse relaxation characterised by the transverse relaxation time T2. Nuclear-spin relaxation is mainly modulated via through-space interactions between different nuclear spins and via Brownian rotational tumbling as the orientation of the molecule varies relative to the applied magnetic field.
Slowly tumbling large molecules, such as proteins, undergo rapid transverse relaxation, which causes line broadening in the NMR spectrum. This imposes an upper limit on the size of molecules whose structures can be usefully interpreted by NMR. Small molecules tumble at high rates and have much slower relaxation rates, and therefore a sharper well-resolved NMR spectrum.
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