Verification of the Maxwell–Stefan theory for tracer diffusion in zeolites

Abstract

Using the Maxwell–Stefan theory for diffusion we derive a simple formula to relate the tracer (i.e. self) diffusivity D ∗ and Maxwell–Stefan (MS), or jump, diffusivity D – . The presence of the interchange coefficient D – ij in the MS formulation causes the self diffusivity to be lower than the jump diffusivity. Assuming the interchange coefficient to be given by D – / F we derive: D ∗= D – 1+Fθ where F is a factor to take account of topology effects within the zeolite matrix. The validity of the MS formulation is established by performing kinetic Monte Carlo simulations for diffusion of methane, perfluoromethane, 2-methylhexane and iso-butane in silicalite. Furthermore, it is shown that the exchange coefficient D – ij is a quantification of correlation effects during the hopping of molecules. For iso-butane, the isotherm inflection leads to a sharp inflection in the diffusion behaviour. The influence of molecular repulsive forces on the loading dependence of the jump and self-diffusivities is also discussed with the aid of published Molecular Dynamics simulations for methane.