Time‐dependent diffusion coefficient as a probe of geometry

作者：Pabitra N. Sen · 发表于：Concepts in Magnetic Resonance Part A · 年份：2004 · DOI：10.1002/cmr.a.20017 · 被引用次数：336 · 研究领域：NMR spectroscopy and applications、Advanced Neuroimaging Techniques and Applications、Hydrocarbon exploration and reservoir analysis

Abstract This is a tutorial describing how the time‐dependent diffusion coefficientD(t) of mobile molecules confined in pores or cells carries information about the confining geometry. At early times,D(t) =D0[1 − (4/9$\sqrt{\pi}$ )(S/Vp)$\sqrt{D_{0}t}$ ] gives, irrespective of details, the pore surface to volume ratio (S/Vp), which is a measure of microscopic length. HereD0is the bulk unrestricted diffusion coefficient. At long times,D(t) reaches a limiting valueD0/α at a rate that depends on macroscopic length scales characteristic of the medium. The geometrical parameter “tortuosity” α plays an important role in various transport processes in porous media, such as the electrical conductivity. Extensions of these concepts to permeable pore walls, fluid identification by combining diffusion with relaxation, restricted diffusion in inhomogeneous magnetic fields leading to edge enhancement, and fractal surfaces are briefly described. © 2004 Wiley Periodicals, Inc. Concepts Magn Reson Part A 23A: 1–21, 2004