Diffusion Analysis in Pore Hierarchies by the Two-Region Model

Abstract

Mass transfer in hierarchically porous materials is a function of various parameters, notably including the diffusivities in the various pore spaces, their relative populations and the exchange rates. Their interplay is shown to be quantified in the two-region model of diffusion which in magnetic resonance imaging is in common use under the name Kärger equations. After manifold applications in NMR diffusometry with compartmented systems, the underlying formalism is now demonstrated to offer an excellent tool for assessing mass transfer in hierarchically porous materials. The potentials include a comprehensive description of mass transfer, in parallel with the specification of the various limiting cases and their reflection by experimental measurement. Information provided by application of microscopic techniques of measurement such as microimaging and pulsed field gradient NMR is shown to notably exceed the message of, e.g., macroscopic uptake measurement of diffusion in hierarchically porous media. This includes, in particular, experimental insight into the dominating mechanisms of mass transfer, which is crucial for the development of optimal strategies of performance enhancement for the technological exploitation of such materials. Depending on the microstructural and microdynamic situation, elucidated in such studies, very different and even mutually opposing strategies for performance enhancement are shown to result.