Time‐dependent diffusion coefficient as a probe of geometry

This is a tutorial describing how the time‐dependent diffusion coefficient D ( t ) of mobile molecules confined in pores or cells carries information about the confining geometry. At early times, D ( t ) = D 0 [1 − (4/9 √π )( S / V p ) √D₀t ] gives, irrespective of details, the pore surface to volume ratio ( S / V p ), which is a measure of microscopic length. Here D 0 is the bulk unrestricted diffusion coefficient. At long times, D ( t ) reaches a limiting value D 0 /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.