Deviations from the ideal single-file behavior in actual systems, such as zeolitic host-guest systems with a one-dimensional channel structure, may occur if (i) there is a possibility of mutual passages of the diffusants and (ii) the influence of the file boundary on the movement of the diffusants cannot be neglected. The conditions under which such deviations may become relevant are investigated both by analytical methods and molecular dynamics simulations. The consequences of these deviations for experimental studies of singlefile diffusion are discussed.

We have used quasielastic neutron scattering to derive the self-and transport diffusion coefficients of hydrogen molecules adsorbed in NaX zeolite. For H 2 , incoherent scattering is dominant so that self-diffusion is measured. For D 2 , the coherent and incoherent contributions are of the same order of magnitude so that both collective and individual motions can be characterized. At low D 2 concentration, the self-and transport diffusivities have similar values. For higher loadings, the transport diffusivity increases rapidly and exceeds the self-diffusivity. Only close to the saturation of the zeolite does the transport diffusivity start to decrease. To our knowledge this is the first time that transport and selfdiffusion coefficients have been measured simultaneously for an adsorbed molecule. In contrast to numerous examples where discrepancies have been stated, these results are in agreement with each other. [S0031-9007(99)09209-1] PACS numbers: 68.35.Fx, 61.12.ExAs crystalline "sponges" with pores of molecular dimension, zeolites have become popular as environmentally friendly key materials for numerous industrial applications, including adsorption, catalysis, and ion exchange. In many cases, their efficiency is controlled by intracrystalline diffusion [1,2]. However, there is a remarkable mystery about its rate: The diffusivities measured at equilibrium are often found to be much larger than under nonequilibrium conditions [3,4], though standard theory would allow only the reverse situation [1,5]. Over many years, it has been a matter of controversy whether this discrepancy is but an artifact generated by the different temporal and spatial scales of observation of the experimental techniques. Applying quasielastic neutron scattering to the diffusion of hydrogen molecules in zeolite NaX, for the first time this source of discrepancy could be excluded.Diffusivities which are measured under the influence of concentration gradients, i.e., under nonequilibrium conditions, are generally referred to as transport diffusivities, D t . They are determined by macroscopic methods like gravimetry, volumetry, chromatography, or frequency response techniques. By contrast, self-diffusivities D s are measured under equilibrium conditions by microscopic techniques, viz. quasielastic neutron scattering (QENS) and pulsed-field gradient (PFG) NMR, which cover molecular displacements over nanometers and micrometers, respectively. Good agreement has been observed in recent years between the results obtained from the two microscopic techniques and from equilibrium molecular dynamics (EMD) simulations (e.g., Refs. [6,7]).For comparison with the self-diffusivities, the transport diffusivities are often represented in terms of the so-called corrected diffusivity, D 0 , which is defined by the relation,where c denotes the adsorbate concentration in equilibrium with the pressure p. The term ͑d lnp͞d lnc͒ is the thermodynamic factor. Adsorption by zeolites is generally described by a Langmuir-type isotherm so that the thermodynamic fact...

The first comparison is made of molecular dynamics (MD) simulation and experimental self-diffusivities for a binary mixture adsorbed inside a zeolite. MD results for methane/tetrafluoromethane mixtures in silicalite agree well with self-diffusion coefficients from pulsed field gradient NMR. At constant total loading, the diffusivities of both components decrease as the fraction of the larger, less-mobile CF4 in the system is increased. Singlet and pair distribution functions were also calculated. The simulations predict preferential adsorption of CF4 in the straight channels and methane in the zigzag channels.

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Translational diffusion of molecules in one-dimensional channel systems has been measured by quasi-elastic neutron scattering. The scattering function for a single-file diffusion model has been derived in order to differentiate this transport model from normal 1D diffusion. In the AlPO 4 -5 structure, ordinary 1D diffusion is observed for methane and ethane, whatever the loading, which indicates that the molecules are able to pass each other. The diffusion coefficients for both molecules are on the order of 10 -9 m 2 s -1 . On the other hand, a quite different regime is obtained by varying cyclopropane concentration in the same structure. At low loading, normal 1D diffusion is observed because the molecules can be considered as isolated, but at higher concentration cyclopropane is found to follow single-file diffusion. However, the mobility is too small to be determined. In the less open channel system of ZSM-48, ordinary 1D diffusion is found for small methane concentration, the diffusion coefficient being 2.5 × 10 -9 m 2 s -1 , at 155 K. At medium loading, single-file diffusion is observed with a mobility factor of 2 × 10 -12 m 2 s -1/2 . This is the first time that this technique has provided experimental evidence of single-file diffusion in zeolites.

The diffusion of a mixture of methane and xenon in the zeolite silicalite is studied by use of molecular dynamics (MD) simulations and pulsed field gradient (PFG) nuclear magnetic resonance (NMR). For a fixed total number of guest molecules, the ratio of xenon to methane is varied in order to examine the special properties of diffusion in a mixture. High xenon concentrations were found to slow the methane diffusivity in the mixture, while the diffusion of xenon is nearly unaffected by high methane concentrations. The reason for the dominance of xenon is the larger local heat of adsorption of xenon and the larger mass of xenon compared to methane in combination with channel size and topology in silicalite. Simulated and experimental data are in very good agreement with each other. Diffusion anisotropy as resulting from the MD simulations is discussed in terms of the correlation rule for diffusion in the interconnected pore system of ZSM-5 (Ka ¨rger,

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