Physical Review · 1963 · 581 citations · 14 references
Relaxation ProcessEngineeringSpin SystemsMagnetic ResonanceQuantum Spin IceSpin DynamicSpin PhenomenonMolecular DynamicsMagnetismMolecular KineticsBiophysicsPhysicsNuclear Magnetic RelaxationDipole-dipole InteractionsRotational Brownian MotionPhysical ChemistryQuantum MagnetismApplied PhysicsCondensed Matter PhysicsDynamic Nuclear PolarizationCorrelation FunctionsMedicine
Using a semiclassical density‑operator approach, the authors model spin‑rotational relaxation in spherical liquid molecules by treating molecular angular velocity classically with a Langevin‑type equation and assuming isotropic rotational Brownian motion, then compute exponentially decaying correlation functions of angular‑velocity components with a correlation time τ1 distinct from the dipole‑dipole τ2, which they use to evaluate tensor spin‑rotational interactions. The analysis shows that τ1 is much smaller than τ2, which explains the experimentally observed quenching of spin‑rotational relaxation in liquids, and that τ1 T increases with temperature, accounting for the temperature dependence of this relaxation effect.
The contribution of spin-rotational interactions to the nuclear magnetic relaxation of identical spin-\textonehalf{} nuclei at equivalent positions in spherical liquid molecules is calculated by use of the semiclassical form of the density-operator theory of relaxation, and the result is compared with the contributions of intra- and intermolecular dipole-dipole interactions. The angular velocity of a molecule is treated classically by assuming that it obeys an equation analogous to the Langevin equation that is postulated in treatments of translational Brownian motion. The change in orientation of a molecule is assumed to be due to isotropic rotational Brownian motion. By use of this model the correlation functions of components of the angular velocity of a molecule are calculated, and are found to have an exponentially decaying time dependence with a time constant (correlation time) ${\ensuremath{\tau}}_{1}$ that is quite different in its temperature dependence than the correlation time ${\ensuremath{\tau}}_{2}$ of the dipole-dipole interactions. In typical situations ${\ensuremath{\tau}}_{1}$ is much smaller than ${\ensuremath{\tau}}_{2}$. Use is made of this fact to evaluate the correlation functions of the functions of the orientation and angular velocity that occur in the tensor spin-rotational interactions. The result that ${\ensuremath{\tau}}_{1}\ensuremath{\ll}{\ensuremath{\tau}}_{2}$ explains the experimentally observed "quenching" of the relaxation effect of spin-rotational interactions in liquids, and the result that ${\ensuremath{\tau}}_{1}T$ increases as the temperature increases explains the experimentally observed temperature dependence of the relaxation effect of spin-rotational interactions in liquids.
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Infra-Red and Raman Spectra of Polyatomic Molecules
H. W. Thompson · Nature · 1946 · 1.3K citations · Full text