Diffusion in Pore Networks: Effective Self-Diffusivity and the Concept of Tortuosity

Molecular transport in confined spaces plays a fundamental role in well-established and emerging technologies such as catalysis, gas separation, electrochemical energy storage, and nanofluidics. In all these applications, fluids penetrate the voids of porous materials often having a complex morphology. This demands a deep understanding of how structural variables such as pore size distribution and pore connectivity affect transport in order to design or optimize processes and devices. In previous work from this laboratory, the effect of these structural variables had been studied at infinite dilution. Here, we consider nonvanishing densities and investigate the influence of adsorbate density on the effective diffusivity and tortuosity. At finite densities the transport and self-diffusivity are not equivalent at the single pore level, leading to differing effective diffusion coefficients and tortuosities. The tortuosity has previously been shown to be governed not only by the pore network topology, but also by temperature and the gas species. Here, we show it to vary significantly with adsorbate density and the diffision mode (i.e., collective or self), which has important repercussions on modeling and interpretation of experimental data. While the effective self-diffusivity of supercritical gases is found to qualitatively behave similar to that estimated in single pores, subcritical fluids present widely different behavior, with a maximum at low adsorbate densities when the coexisting population of small and large mesopores is significant, consistent with experimental evidence. We discuss under what conditions a monotonically decreasing single-pore self-diffusivity can lead to the appearance of such maximum in a network.