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 Theta, approaching saturation limits. The n-dimensional matrix of Maxwell-Stefan (M-S) diffusivities Delta, defined by (N) = -rhoDeltaGamma(nabla Theta), 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 Theta(i)(,sat). From the information on Delta(ij), D(i)(,self), and Theta(i)(,sat), the various M-S diffusivities were determined: (1) component D(i), reflecting the interactions of the species i with the zeolite, self-exchange D(ii), and (2) binary exchange D(ij). The obtained data underline the major advantage of the M-S formulation that at a given occupancy, theta = Sigma(N)(n)(i=l)Theta(j)/Theta(j)(,sat) within the zeolite, the D(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 D(ii); the value at a given occupancy, theta, 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 D(ij) can be interpolated from the corresponding values of the self-exchange parameters D(ii) and D(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 D(i) and D(ii) are modeled properly, this information is sufficient to provide very good estimates of the matrix Delta 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.