Diffusion of Alkane Mixtures in Zeolites:  Validating the Maxwell−Stefan Formulation Using MD Simulations

Molecular dynamics (MD) simulations have been carried out for pure components, binary, ternary, and quaternary mixtures containing methane, ethane, propane, and n-butane in FAU zeolite at 300 K for a range of molecular loadings ϑ, approaching saturation limits. The n-dimensional matrix of Maxwell−Stefan (M−S) diffusivities [Δ], defined by (N) = −ρ[Δ][Γ](∇ϑ), was determined along with the self-diffusivities, D_i,self. Additionally, configurational-bias Monte Carlo (CBMC) simulations were carried out to obtain the pure component sorption isotherms and the saturation capacities ϑ_i,sat. From the information on Δ_ij, D_i,self, and ϑ_i,sat, the various M−S diffusivities were determined:  (1) component Đ_i, reflecting the interactions of the species i with the zeolite, self-exchange Đ_ii, and (2) binary exchange Đ_ij. The obtained data underline the major advantage of the M−S formulation that at a given occupancy, θ = ϑ_i/ϑ_i,sat within the zeolite, the Đ_i has nearly the same value for species i whether this species is present on its own or in a mixture with other species. The same advantage holds, too, for the self-exchange Đ_ii; the value at a given occupancy, θ, is the same whether determined from pure component, binary, or ternary mixture data. For all binary and ternary mixtures studied, it was verified that the binary exchange coefficient Đ_ij can be interpolated from the corresponding values of the self-exchange parameters Đ_ii and Đ_jj using a generalization of the interpolation formula developed earlier (Skoulidas et al., Langmuir, 2003, 19, 7977). We also demonstrate that if the occupancy dependence of the pure component parameters Đ_i and Đ_ii are modeled properly, this information is sufficient to provide very good estimates of the matrix [Δ] for mixtures with 2, 3, or 4 components over the entire range of loadings. Simulations of mixture diffusion of alkanes in MFI and LTA confirm that the above-mentioned advantages of the M−S formulation also hold for these zeolite topologies.