Signature of Low-Dimensional Diffusion in Complex Systems

We present a clear signature of the dimensionality of water diffusion in a powder sample of a synthetic hectorite (a model clay), by analyzing the corresponding neutron scattering functions. The data follow the theoretical predictions for a powder-averaged two-dimensional diffusion, with a two-dimensional diffusion coefficient of 0.75 x 10(-9) m2 s(-1). Neutron scattering data of bulk water are used as a reference, representing motion in three dimensions. The approach is based on analyzing the scattered intensity at zero energy transfers, along with the broadening of the scattering functions, collected at a wide range of energy resolutions. The mathematical relationship between these two quantities follows, for a given shape of the resolution function, a universal master curve, independent of the diffusion coefficient, but strongly dependent on the dimensionality of the motion, which can thus be determined with clarity.