A generalized Knudsen theory for gas transport in disordered porous materials

Gas transport through nanoporous materials is central to membrane separations, catalysis, and energy technologies. Predicting permeability in these materials is crucial for performance evaluation and material design, but their complex porous network poses significant challenges. Here, we develop a generalized theoretical framework for Knudsen flow in random porous materials. We further derive a concise permeability equation dependent solely on two measurable structural parameters: mean pore size and porosity. Monte Carlo simulations across 5000 random porous networks with porosities ranging from 0 to 0.8 validate the theory with R² = 0.985. Non-equilibrium molecular dynamics simulations confirm the applicability of the theory to porous membrane materials, including polymers of intrinsic microporosity, polyamide, and zeolitic imidazolate frameworks. By accounting for molecular size effects, we extend the framework to predict gas selectivity in materials with sub-nanometer pores, showing good agreement with experimental data for weakly adsorbing gases. This work extends Knudsen theory to random porous networks and molecular-sized pores, providing a practical and accessible tool for predicting gas permeability and selectivity in nanoporous materials.