Some “Reflections” on the Effects of Finite Gradient Pulse Lengths in PGSE NMR Experiments in Restricted Systems

Abstract

AbstractIt is generally difficult to analytically derive models describing the echo attenuation in pulsed gradient spin‐echo (PGSE) experiments for even the simplest porous systems that are commonly studied—especially when the gradient pulse (δ) is of finite length compared to the timescale of the diffusion measurement (Δ). Consequently, various levels of approximation are used to evaluate PGSE experiments. In the present paper, a conceptual view ofq‐space is given and two of the most common approximations, the short gradient pulse (SGP) and Gaussian phase distribution (GPD) approximations, are compared in detail with a recent matrix method, which provides “analytically” exact results giving a visual representation of the limitations of these approximations. The simulations are performed for diffusion between a pair of reflecting planes separated by a distancea.A modification that is sometimes applied to the short gradient pulse approximation in attempting to extend it to finite gradient pulses is also compared. The simulations reveal that, except when the experimental conditions closely match the requirements of the SGP and GPD simulations, the matrix method must be used in order to correctly interpret the data.