Diffusive Transport in Pores. Tortuosity and Molecular Interaction with the Pore Wall

Abstract

The self-diffusion of neat water, dimethyl sulfoxide (DMSO), octanol, and the molecular components in a water–DMSO solution was measured by 1H and 2H NMR diffusion experiments for those fluids imbibed into controlled pore glasses (CPG). Their highly interconnected structure is scaled by pore size and shows invariant pore topology independent of the size. The nominal pore diameter of the explored CPGs varied from 7.5 to 72.9 nm. Hence, the about micrometer mean-square diffusional displacement during the explored diffusion times was much larger than the individual pore size, and the experiment yielded the average diffusion coefficient. Great care was taken to establish the actual pore volumes of the CPGs. Transverse relaxation experiments processed by inverse Laplace transformation were performed to verify that the liquids explored filled exactly the available pore volume. Relative to the respective diffusion coefficients obtained in bulk phases, we observe a reduction in the diffusion coefficient that is independent of pore size for the larger pores and becomes stronger toward the smaller pores. Geometric tortuosity governs the behavior at larger pore sizes, while the interaction with pore walls becomes the dominant factor at our smallest pore diameter. Deviation from the trends predicted by the Renkin equation indicates that the interaction with the pore wall is not a just simple steric one but is in part dependent on the specific features of the molecules explored here.