André Micke

Modelling the complex problem of intracrystalline diffusion and first-order phenomena in microporous solid particles under constant-volume/variable-concentration conditions

Abstract Microporous solids with pore diameters comparable to effective molecular cross-sections are mainly used as both stereo-selective absorbents and shape-selective catalysts. Often complex phenomena govern the overall rate of processes of both physical adsorption and catalytic reaction. Transport and reaction rates are usually determined independently of each other. In contrast to this procedure, this paper describes a way to model such phenomena comprising internal diffusion in microporous particles coupled with any first-order rate process inherent both in the physical system, i.e. sorption system with nonlinear sorption isotherm and any particle size distribution, and the experimental apparatus characteristics. Modelling and complete solution of the models for both constant and variable boundary conditions were carried out by means of non-linear Volterra integral equations. It becomes possible to determine both the diffusion coefficients and rate constants of constituents of a complex process using only one experimental arrangement. The approach is incorporated into the software ZEUS (zeolite uptake simulator).

Theory of zero length column chromatography with the condition of a well-stirred sorbing zone

In this paper, a complete solution of the mathematical model of ZLC chromatography using a Volterra integral technique is described. The model includes the effects of isotherm non-linearity, extracolumn broadening and various types of intrinsic sorption kinetics. Another attribute of the model is that it describes exactly the initial stage of the ZLC chromatographic experiment. The above effects (influence of the diffusivity, of the carrier gas flow rate and of the isotherm non-linearity) on the shape of the system response is demonstrated. The effectiveness of the model is illustrated by experimental curve fitting.

Diffusion and Immobilization Mechanisms in Zeolites Studied by ZLC Chromatography

Zero Length Column chromatography was used to study mass transfer in zeolites involving coupled diffusion and immobilization mechanisms. A modeling based on Volterra integral equation technique was utilized to simulate sorption and desorption kinetic curves and compare results of the simulations with experimentally obtained curves. This approach was applied to analyze sorption kinetics in the model system: toluene/silicalite-1 (75°C–178°C). The system generally shows a non-Fickian behavior and can be described by diffusion coupled with immobilization.

Intracrystalline diffusion of benzene in microporous gallosilicate with MFI structure

Adsorption equilibrium and kinetic data have been measured for benzene on microporous gallosilicate with MFI structure (MFI-ZAG, zeolite analogous gallosilicate) over the temperature range 300–350 K. The sorption capacity is similar to that for Ga-free MFI systems. The sorption heat is found to be constant over the entire concentration range considered. Sorption kinetics were measured by a constant-volume–variable-pressure method and evaluated via the formalism of the Volterra integral equation technique (program package ZEUS). Intracrystalline diffusion was found to govern the rate of sorption uptake. Corresponding diffusivity data could be calculated as concentration and temperature dependences. The intracrystalline diffusivity can be described fully by the Barrer constant-jump-length model. The sorption data are compared with those for another MFI-ZAG sample synthesized under modified conditions.

Utilization of Zeolites for Processes of Gas Desulphurization

Present day utilization of zeolitic molecular sieves for sorptive processes of the removal of low-level sulphur compounds in gases from various origins is outlined. Fundamental research and developmental challenges that occur in this field of the practical utilization of zeolites, are characterized. Appropriate ways towards successful application of processes of selective sorption by means of zeolites are proposed.

Evaluation of diffusion coefficients for intracrystalline transport superimposed by first-order phenomena in molecular sieve crystals

Abstract First-order phenomena that may take place in molecular sieve structures besides intracrystalline diffusion shift the effective diffusivity. This shift depends on the ratio of rates of mobilizing and immobilizing the sorbate in the microporous structure. The corresponding uptake curves obtain an unusual but characteristic shape. The phenomenon is exemplified by the system p -xylene/microporous gallosilicate of MFI-type. For the quantification of the kinetic parameters [intracrystalline diffusivities, (im)-mobilization rates], the Volterra integral equation technique is used.

Sorption kinetics of benzene on a gallosilicate with MFI structure

Abstract Adsorption equilibrium and kinetic data were measured for benzene on microporous gallosilicate with MFI structure (MFI-ZAG, zeolite analogous gallosilicate). The equilibrium data were found to be in general agreement with those for benzene on Ga-free MFI structures. The non-equilibrium data, as measured at elevated temperature, obey an intracrystalline molecular transport mechanism which is described by Ficks second law. No additional transport mechanisms were found. The diffusivities show a weak concentration dependence at constant temperature. From their temperature dependences at constant loading, however, a concentration-dependent activation energy is derived. This behaviour is analogous to that of the adsorption heat.

Comparison of Macroscopic Transient Methods to Determine Transport Coefficients for Microporous Sorption Systems

Macroscopic transient methods are analysed with respect to their applicability to the investigation of molecular transport in microporous sorption systems. Various levels of sophistication of data evaluation for non-equilibrium sorption results obtained by means of batch methods are identified and characterized. Special attention is paid to the characterization of Fickian (intracrystalline) diffusion as well as to the identification and quantification of additional rate mechanisms that, in general, may simultaneously occur in molecular sieve systems. A state of the art determination of transport coefficients is exemplified for the system n-hexane/silicalite-I. Its uptake behaviour can be understood by superposition of processes of Fickian diffusion and intracrystalline molecular immobilization/mobilization.

Sorption Kinetics of Oxygen on CaA Type Molecular Sieve

Intracrystallme diffusivities for oxygen on CaA type zeolite crystals were determined at temperatures 77 K, 193 K and 293 K by a constant volume/variable pressure technique. The diffusivity data were found to be significantly higher than reported in literature hitherto. A concentration dependence of oxygen mobility exists where diffusivities decrease with increasing concentration.