Nuclear Spin Relaxation in Ellipsoids Undergoing Rotational Brownian Motion

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Abstract
The nuclear spin relaxation times T1 and T2 have been calculated for two identical nuclei of spin I = ½ fixed in an ellipsoid undergoing rotational Brownian motion. The ellipsoid is subject to small random changes in orientation in which the rotation probabilities about its three major axes are different. This anisotropic motion yields five nuclear correlation times; isotropic motion yields only one correlation time. The results are applicable provided that the static dipolar coupling is effectively averaged to small values by the rotational motion. For nonviscous liquids, T1 = T2. When the rotation probabilities about two axes are equal, the relaxation‐time expressions simplify a great deal, but they retain the essential relaxation features of anisotropic rotational motion; the number of nuclear correlation times is reduced to three; the relaxation times for rapid motion have been calculated as a function of the ratio of the two rotation probabilities for this case. The relaxation rates in ellipsoids of revolution obeying the Stokes approximation for motion in a continuous medium have been compared to those for spheres having the same volume. The rates for very nonspherical particles are large compared to those for the spheres. An example of internal motion of the internuclear vector within the ellipsoid is calculated.