Intracrystalline Diffusion Processes Research Articles

Equilibrium isotherms and transport diffusivities for CO2 and CO2/N2 mixtures in silicalite measured by Infra-Red Micro-imaging

Large crystals of silicalite (0.1–1 mm) were synthesized and used to study the kinetics and equilibrium of CO2 adsorption (at room temperature), both as a pure component and as a binary mixture with nitrogen, using Infra-Red Microscopy (IRM) coupled with Fourier Transform Infra-Red Spectroscopy (FTIR). The use of such large crystals permits the measurement of fast intra-crystalline diffusion processes, beyond the range normally accessible by macroscopic techniques. As expected the effect of N2 on the CO2 equilibrium was minimal but the effect on the intra-crystalline diffusivity was significant. Diffusivities (at 300 K) range from 4 × 10−8 to 4 × 10−9 m2 s−1 for CO2, decreasing with increasing total concentrations of CO2 and N2 in the adsorbed phase.

Restricted self-diffusion of adsorbed water in MIL-100(Al)

An extended two-site exchange model is presented, which is used to evaluate pulsed field gradient (PFG) nuclear magnetic resonance (NMR) measurements of water in the nanoporous metal-organic framework MIL-100(Al). Here the water molecules exchange between the inter- and the intracrystalline space during the observation time, but are also restricted in their movement by the crystal surface. The evaluation of temperature and loading dependent PFG NMR data yields information about the intracrystalline diffusion process, the radius of the restricting geometry and the time constants of the exchange process. The intracrystalline mean residence time is found to decrease with increasing temperature, which allows an estimate of the heat of adsorption under the equilibrium conditions of the NMR measurements.

Modeling hydrogen diffusion in hybrid activated carbon-MIL-101(Cr) considering temperature variations and surface loading changes

MIL-101(Cr) and activated carbon (AC) doped MIL-101(Cr) materials were synthesized under mild conditions, avoiding the use of hydrofluoric acid, and characterized by X-Ray Diffraction (XRD), Scanning Electron Microscopy (SEM) and physisorption. It was shown that the AC doping induced enhancements of the specific surface area and increase in the pore volume of the adsorbent. Hydrogen adsorption isotherms and kinetics were measured at 77 K up to 50 bar by using a volumetric method. A hydrogen uptake of 9.3 wt.% was measured for the hybrid material, which was significantly higher than that for pristine MIL-101(Cr) which reached an uptake of 6.2 wt.% under the same conditions of temperature and pressure. Effective diffusion coefficients were besides attempted to be extracted from experimental kinetic curves, by using the Linear Driving Force (LDF) model in a first approach. However, this model failed to describe correctly the experimental kinetic data as it does not explicitly consider the external mass transfer resistance, neither the temperature nor the surface loading effects on the intra-crystalline diffusion process. To overcome these limitations, a more detailed model was proposed, based on the evaluation of both an external mass transfer coefficient and of an internal surface diffusivity in the adsorbed phase that accounts for the effects of temperature and adsorbent surface coverage. This model was proved to predict well the hydrogen adsorption rates in both the MOF and hybrid AC-MOF material at 77 K, in the pressure range up to 20 bar.

Diffusion of aromatic hydrocarbons in silicalite/HZSM-5

Diffusion of benzene and the xylene isomers in silicalite/HZSM-5 has been studied by a wide range of different experimental techniques. The available data are reviewed in an attempt to draw general conclusions concerning the intracrystalline diffusion process. The results for benzene are remarkably consistent, and the conformity between transport and tracer diffusion and between single crystal membrane and ZLC and frequency response data suggests that diffusion is essentially isotropic with no significant difference between the self and “corrected” transport diffusivity. The situation is more complex for p-xylene which shows clear evidence of non-isotropic behavior and a significant difference between tracer and transport diffusivities.

Effectiveness factor for zeolite catalysed isomerization reactions

We analyze the influence of diffusion on the reversible isomerization reaction A 1↔A 2, occurring within a zeolite catalyst, of spherical, cylindrical, and slab geometries. The intra-crystalline diffusion process is described by the Maxwell–Stefan (M–S) equations. Two different guest–host confinement scenarios are examined. For strongly confined guest molecules, the M–S diffusivities Đ i decrease with loading inside the zeolite. For weakly confined guest molecules, the M–S diffusivities Đ i are independent of the loading. The correlation effects, typical of zeolite diffusion, are described by introducing an exchange coefficient Đ 12 in the M–S diffusion formulation. For facile exchange, D ̵ 12→∞ , correlation effects are washed out. For finite exchange, a logarithmic interpolation formula is used to calculate Đ 12 from the two pure component M–S diffusivities Đ i . Analytic expressions for the effectiveness factor are derived for a variety of confinement and exchange scenarios. In the development of the analytic solution we assume Langmuirian behavior of the pure components and that the mixture sorption loadings can be calculated from the multicomponent Langmuir isotherm. By means of a variety of numerical examples, we stress the various characteristic features of intra-crystalline diffusion influences in zeolite catalysis. The effectiveness factor is found to a strong function of (a) molecular loadings and mixture composition, (b) ratio of diffusivities of the participating species, and (c) the reaction equilibrium constant. Only for the case of low loadings of weakly confined guest molecules and vanishing correlation effects, is the classical formula for the effectiveness factor valid.

Scales of disequilibrium and rates of equilibration during metamorphism

Mounting evidence suggests that partial disequilibrium-meaning disequilibrium for some elements, but not for others-may be a common but rarely detected phenomenon during metamorphic mineral growth, even in ordinary prograde reactions that progress to completion. Detailed examination of compositional variations in garnet crystals over a range of metamorphic grade suggests distinctly different scales of equilibration for common elements, with strong temperature dependence. Under lower greenschist-facies conditions, Fe and Mg may equilibrate at hand-sample scale, whereas Mn and Ca may not equilibrate even at millimeter-scale. Although Mn may achieve hand-samplescale equilibration under upper greenschist-facies conditions, Ca and many trivalent cations (e.g., REEs) may not do so until temperatures exceed those of the middle amphibolite facies. Even in the lower granulite facies, some elements (e.g., Y, Yb) show indications of disequilibrium at sub-centimeter- scales during garnet growth. Analysis and numerical modeling of undisputed disequilibrium textures demonstrate that the most common impediment to equilibration during metamorphism is the sluggishness of intergranular diffusion, the same mechanism known to govern porphyroblast crystallization in many metamorphic environments. Despite this importance to petrology, few quantitative determinations exist of intergranular diffusion rates under metamorphic conditions. Using numerical simulations of coupled intergranular and intracrystalline diffusion processes in coronal textures around partially resorbed garnet crystals from the Llano Uplift, U.S.A., a very precise and relatively accurate estimate is obtained for the rate of intergranular diffusion of Al in fluid-undersaturated systems. This result and an earlier estimate for fluid-saturated systems provide bracketing values for Al diffusivity during metamorphism.

Sorption and diffusion of light hydrocarbons on NaY zeolites

This paper reports on the adsorption isotherms that were determined on zeolite Na-Y at 298, 313, and 333 K for propane and propylene and at 298 K for butane, trans-butene, 1-butene, and cis-butene. The pressure of the experiments ranged from 5 {times} 10{sup {minus}2} to 30 kPa. The weight of adsorbed hydrocarbons was determined by a gravimetric method with a vacuum microbalance. The Henry constants were evaluated from the equilibrium measurements in the low-concentration range, and their sequence propane {lt} butane {lt} trans-butene {lt} propylene {lt} 1-butene {lt} cis-butene, was discussed in terms of the different adsorbate-adsorbent interactions. Equilibrium data, over the whole pressure range, were correlated by using the simplified model by Ruthven, based on statistical thermodynamics, and the appropriate parameters are reported. For C4 hydrocarbons, the intracrystalline diffusion process was also investigated and the Darken equation was used to correlate the uptake curves at the higher pressures. The diffusion coefficients were found in the order butane {gt} trans-butene {gt} 1-butene {gt} cis-butene and were compared to the available values in literature.

Zeolitic diffusivities of hydrocarbons by the frequency response method

In order to prove the efficiency of the new frequency response method by actual data, it is applied to propane and ethane over Linde 5A systems, in which considerable discrepancies remain unresolved between the diffusivities determined by the sorption and nuclear magnetic resonance (NMR) methods. The frequency response measurements of the systems reveal that both systems are composed of two types of intracrystalline diffusion processes whose Fickian diffusivities differ from each other four orders of magnitude; the large diffusivity agrees with that obtained from NMR experiments, whereas the small diffusivity corresponds to none of the diffusivities by standard methods. Based on the present results, a model of the zeolitic diffusion which contains two kinds of admolecules, tightly and loosely bound within the cages, is proposed. The frequency response method would be effective therefore to clarify the whole aspect of the kinetic phenomena which seems available to characterize zeolite catalysts.