Diffusion of fluids in porous solids probed by pulsed field gradient spin echo NMR

Abstract

The response to the pulsed field gradient spin echo (PGSE) NMR experiment is described for fluid diffusing in pore networks. The behaviour is discussed in terms of the field gradient wavevector, q (=γδg/2π) and the diffusion time Δ. An analytical theory is outlined and compared with computer simulations for a regular lattice of pores. Theoretical results are also presented for a pore glass. In both cases effects of the confining structure are predicted to become of increasing importance as qb increases, where b is the pore separation. When qb is an integer, maxima occur in the spin echo amplitude as a function of q, analogous with diffraction from the pore network structure. For a regular lattice structure it is shown that when qb is an integer the PGSE response as a function of Δ has the appearance of completely bounded diffusion. The conditions on q and Δ required to measure the structure averaged diffusion coefficient, D eff, are deduced. Experimental results are shown for the diffusion of water contained in the spaces between loosely packed polystyrene spheres. These show the characteristics predicted by the pore glass theory.