Probing the structure of porous media using NMR spin echoes

The NMR pulsed field gradient spin-echo (PFGSE) amplitude M(k,t) is a direct measure of the diffusion propagator of the molecules of a fluid diffusing in the pores of a porous medium. For small values of k = gamma g delta, where g is the gradient strength, delta is the duration of the gradient pulse, and gamma the gyromagnetic ratio, the PFGSE amplitude gives the diffusion coefficient D(t). The exact short-time diffusion coefficient, D(t)/D0 = 1-(4 square root of D0tS)/(9 Vp square root of pi)-D0tHS/(12Vp) + rho tS/6Vp, provides an important method for determining the surface to pore-volume ratio S/Vp. Here the mean surface curvature H = <1/R1 + 1/R2>. Combining early D(t) with the magnetization decay one obtains the surface relaxivity rho. The long-time effective diffusion constant derived from PFGSE gives information on the tortuosity of the connected space. The diffusion coefficient measured by PFGSE equals that derived from electrical conductivity only when rho = 0. Exact solutions with partially absorbing boundary conditions for a periodic structure are used to illustrate the influence of rho on the diffusion coefficient. M(k,t) can be well represented by a convolution of the structure factor of the connected pore space with an appropriate Gaussian propagator. This ansatz provides a model-independent way of obtaining the structure factor.