Measuring Patterson functions of inhomogeneous liquids using the nuclear dipolar field

The long-range nuclear dipolar interactions in liquids are not averaged out by molecular motion and give rise to the dipolar field. In nuclear magnetic resonance experiments, this field can be used to probe the structure of heterogeneous samples. In this contribution, we demonstrate theoretically and experimentally how the signal generated by the dipolar field can provide structural information without the use of any model structure. In the limit where the dipolar field weakly perturbs the evolution of the magnetization, and where the molecular motion is not significantly restricted by the structure, the autocorrelation function, or Patterson function, of the spin density can be obtained. The signal generated by the dipolar field is measured as a function of the spatial modulation imposed on the magnetization and an integral transform of the signal amplitude yields the Patterson function. If the structure is anisotropic, a three-dimensional data set has to be acquired and Fourier transformed, If the sample is isotropic, modulation of the magnetization along single direction is sufficient and the Patterson function can be calculated from a Hankel transform of the signal amplitude. (C) 1997 American Institute of Physics.