Experimental determination of pore shape and size using q-space NMR microscopy in the long diffusion-time limit

The signal obtained with q-space NMR imaging applied to a confined liquid is directly related to the pore shape in the limit where all molecules have sampled the whole pore. We investigate the diffusion of water across a ∼50 μm thick film formed between planes of glass. The diffusion time t is changed almost three orders of magnitude. For short t, the root-mean-square displacement increases with a rate which is slightly less than for freely diffusing water. At t longer than 0.3 s, the displacement is constant at 24 μm which implies that the water is confined in the measuring direction defined by the applied gradient pulses. Perfectly smooth and aligned planes give rise to sharp diffraction-like features on the echo attenuation curve, i.e., NMR signal vs. the reciprocal space vector q. The experimental data with rather smooth local minima and maxima can be explained in terms of either surface roughness or a misalignment of the planes. We discuss the averaging effect of diffusion along a laterally inhomogeneous film and propose two model-free methods to determine the pore shape from the echo attenuation curve obtained in the long-t limit.