Investigating the Validity of the Knudsen Prescription for Diffusivities in a Mesoporous Covalent Organic Framework

Molecular dynamics (MD) simulations were performed to determine the self-diffusivity (D_i,self) and the Maxwell–Stefan diffusivity (Đ_i) of hydrogen, argon, carbon dioxide, methane, ethane, propane, n-butane, n-pentane, and n-hexane in BTP-COF, which is a covalent organic framework (COF) that has one-dimensional 3.4-nm-sized channels. The MD simulations show that the zero-loading diffusivity (Đ_i(0)) is consistently lower, by up to a factor of 10, than the Knudsen diffusivity (D_i,Kn) values. The ratio Đ_i(0)/D_i,Kn is found to correlate with the isosteric heat of adsorption, which, in turn, is a reflection of the binding energy for adsorption on the pore walls: the stronger the binding energy, the lower the ratio Đ_i(0)/D_i,Kn. The diffusion selectivity, which is defined by the ratio D_1,self/D_2,self for binary mixtures, was determined to be significantly different from the Knudsen selectivity (M₂/M₁)^1/2, where M_i is the molar mass of species i. For mixtures in which component 2 is more strongly adsorbed than component 1, the expression (D_1,self/D_2,self)/(M₂/M₁)^1/2 has values in the range of 1–10; the departures from the Knudsen selectivity increased with increasing differences in adsorption strengths of the constituent species. The results of this study have implications in the modeling of diffusion within mesoporous structures, such as MCM-41 and SBA-15.