Accurate RTOP Estimation from PFG-NMR Signal

The return to the origin probability (RTOP) for diffusing molecules is a valuable indicator of porous media microstructure [1-2]. For example, in isolated pores with nonrelaxing walls, the pore volume is related to the RTOP at long diffusion times. Similarly, in disordered media, the temporal scaling of the RTOP is necessary in the estimation of the fractal dimension of the medium [3]. However, the RTOP is related to the pulsed field gradient (PFG) NMR signal via an integration over the entire q-space. The unavailibility of data at large wavevectors is a serious problem particularly in restricted domains where the NMR signal does not attenuate significantly even at relatively large wavenumbers. In principle, the extrapolation of the signal values can be performed by model fitting to data. However, very different signal profiles are possible depending on the particular specimen under examination whose structure is not known a priori. Another alternative is the cumulant expansion, which may fail to converge to the true signal attenuation. Fig. 1a shows the failure of both the cumulant expansion and sometimes used biexponential fitting in describing the theoretical signal attenuation from rectangular pores at long diffusion times.