Investigating the validity of the Bosanquet formula for estimation of diffusivities in mesopores

Abstract

Molecular Dynamics (MD) simulations were performed to determine the self-diffusivity, D_i,self, of H₂, CO₂, Ar, Kr, CH₄, C₂H₆, C₃H₈, and nC₄H₁₀ for a variety of pore concentrations within one-dimensional mesopores of 2 nm, 3 nm, 3.4 nm, 4 nm, 5.8 nm, 7.6 nm and 10 nm sizes. The MD simulated values of D_i,self are compared with estimations of the commonly used Bosanquet formula 1/D_i,self=1/D_i,Kn+1/D_ii,fl, that combines molecule-wall and molecule-molecule interactions:, where D_i,Kn is the Knudsen diffusivity, and D_ii,fl is the self-diffusivity of species i in the fluid phase at the same molar concentration, ci, as within the mesopores. For components with poor adsorption strength, such as H₂, the MD simulated Di,self values are in good agreement with the estimations using the Bosanquet formula for the whole range of pore concentrations. For components with strong adsorption at the pore walls, the MD simulated values are significantly lower than the Bosanquet estimations when molecule-wall interactions are dominant. These deviations are traceable to the failure of the Knudsen prescription of diffuse reflectance on molecule-wall collisions, because adsorption at the pore walls introduces a bias in the molecular hops. For any given molecule, the Bosanquet estimations tend to be increasingly accurate when the pore diameters are increased.