Peter Struve

Sorption kinetics of n-hexane on MgA zeolites of different crystal sizes. Study of the rate-limiting transport mechanism

Starting from the necessity for more substantial evidence with regard to the occurrence of intracrystalline diffusion as the rate-limiting transport mechanism in sorption processes on zeolites, the variation of zeolite crystal size is regarded as a criterion and used in the case of the sorption system n-hexane/MgA zeolite.The experimental study has been carried out by using a constant volume variable pressure system. The uptake curves have been analysed by solution of the appropriate diffusion equation on the assumption that the uptake rate obtained is limited by intracrystalline diffusion. An additional analysis was done considering the sorption process as being limited by surmounting a transport resistance in the surface region of zeolite crystals.The experimental parameters covered the following ranges: temperature: 373–623 K, pressure: ≈ 4 × 10–3–265 Pa, amount sorbed: ≈ 2 × 10–4–3 × 10–1 mmol g–1, crystal size (mean edge length of cubic crystals): 0.7–43 µm.Over the whole of the ranges of amount sorbed and crystal size the apparent diffusion coefficient is independent of amount sorbed at constant temperature. At each temperature an unambiguous dependence of the apparent diffusion coefficient on zeolite crystal size has been found.Taking into account the analysis of sorption kinetics by a surface barrier model, the shape of uptake curves, the values of the apparent energy of activation and the peculiarities of crystal habit of several sample sizes the following conclusions concerning the rate-limiting transport mechanisms can be drawn: (i) In the crystal size region 0.7–13 µm a surface barrier is possible (for several crystal samples a surface barrier dependent on the crystal size is probable at lower temperatures). (ii) In the case of zeolite crystals with the sizes 33–43 µm the uptake process seems to be limited by intracrystalline diffusion.The energy of activation assumes values of ≳ 50 kJ mol–1 and ≈ 42 kJ mol–1 for the cases (i) and (ii), respectively.

Intracrystalline diffusion of benzene in NaX zeolite studied by sorption kinetics

Sorption uptake measurements have been used to measure the intracrystalline diffusivities of benzene in NaX zeolite within wide ranges of sorbate concentration at different temperatures. Their success is due to a significant decrease in the response time of the uptake equipment (< ca. 0.1 s) compared with current methods, this being obtained by application of a recently developed method of data evaluation that accounts for external effects (via a theory of statistical moments) and by using relatively large zeolite crystals (ca. 120 µm). The coincidence of corrected sorption diffusion data with n.m.r. self-diffusivities indicates that the sorption technique gives reliable information on intracrystalline molecular mobility, even for hydro-carbons in large-port microporous sorbents.

Influence of hydrothermal pretreatment on zeolitic diffusivity detected by comparative sorption kinetics and small-angle X-ray scattering investigations

Uptake data for ethane and n-decane on normally as well as hydrothermally pretreated zeolites NaCa-A and NaMg-A, respectively, are discussed as being limited by a crystal interface transport resistance. Small-angle X-ray scattering properties of these samples indicate that due to hydrothermal pretreatment, structure regions are built up whose elctronic density is different from that of zeolite. Comparing the results obtained with both techniques with earlier described n.m.r. self-diffusion behaviour of ethane on the same NaCa-A zeolites, the conclusion is drawn that heterogeneity regions detected should be localized at the zeolitic interface and strengthen its transport resistance.

Experimental evidence of the influence of sorption-heat release processes on the sorption kinetics of benzene in NaX zeolite crystals

Under constant-volume–variable-pressure conditions the sorption uptake of benzene by NaX zeolite crystals has been investigated with respect to the influence of external thermal conditions on the uptake rate. The information obtained permits quantitative conclusions concerning the influence of the sorption heat generated on the uptake rate, i.e. the decrease in apparent diffusivities calculated under the erroneous presumption of the isothermicity of the sorption process considered. A corresponding tentative mechanism which takes into account the generation of thermal interface barriers is proposed. Furthermore, there are experimental conditions for which the uptake of benzene by NaX zeolite crystals should be considered as an isothermic process. Within that parameter region agreement was obtained between the sorption diffusion data (corrected by the Darken equation) and the n.m.r. self-diffusivities, as reported earlier.

Analytical solution of simultaneous mass and heat transfer in zeolite crystals under constant-volume/variable-pressure conditions

The analytical solution for uptake curves of a single-component sorption under constant-volume/variable-pressure conditions has been derived, subject to certain simplifying assumptions. Rate mechanisms considered are intracrystalline diffusion and sorption-heat dissipation from the surface of the zeolite crystals to the surroundings.

A model for the mass-transfer resistance at the surface of zeolite crystals

A microdynamic model is proposed to describe the mass-transfer resistance localized at the surface of zeolite crystals. In addition to the intracrystalline diffusional resistance, this resistance occurs owing to the repulsion and attraction interaction between sorbing molecular species and the crystal surface. Especially for small crystals the surface resistance can exceed the intracrystalline diffusional resistance by several orders of magnitude. In particular, the model explains the non-linear behaviour of Arrhenius plots of uptake data exemplified for the sorption of n-hexane on NaMgA zeolite crystals.

Sorption kinetics of neopentane on NaX zeolites of different crystal sizes

By means of a constant-volume–variable-pressure method, the sorption kinetics of neopentane on two NaX zeolites with different crystal sizes (17.7 and 120 µm, respectively) have been investigated at 187 K. Whereas the kinetics on the larger crystals are mostly controlled by intracrystalline diffusion under the experimental conditions used, neopentane uptake on smaller crystals should be limited by intercrystalline transport. In both cases heat-transfer effects are superimposed upon the measured mass transport.

Application of the volterra integral equation to the mathematical modelling of adsorption kinetics under constant-volume/variable-concentration conditions

Mathematical solutions of adsorption kinetics on porous solids are usually developed for constant or variable concentration conditions. From both a theoretical and practical point of view the comparison of the kinetic parameters (e.g. intracrystalline diffusion coefficients of microporous adsorption systems) obtained from the various methods is valuable. This paper presents a solution which provides a numerical calculation of the kinetic curves at variable boundary conditions, e.g. constant-volume/variable-concentration, based on the appropriate analytical solution of Ficks diffusion law at constant boundary conditions, e.g. constant concentration.

Intercrystalline molecular transport in zeolites studied by uptake experiments and by nuclear magnetic resonance pulsed field gradient techniques

A comparison of n.m.r. self-diffusion and uptake measurements was performed with the systems cyclohexane (n-hexane)+NaX-zeolite. For intracrystalline adsorption kinetics a significant difference in the values of the corresponding rate constants was found. Intercrystalline self-diffusion coefficients and corresponding uptake coefficients, however, were found to be in good agreement. In accordance with this result, in both n.m.r. and uptake experiments the variation of pressure of compaction, sorbate concentration and temperature led to the same changes in the effective coefficients of intercystalline transport.

Intracrystalline Diffusion of Benzene in Ga-Silicate

Abstract The sorption kinetics of benzene in large Ga-MFI crystals was investigated under constant volume- variable pressure conditions. A complete analysis of the uptake curves has been performed using solution of a nonlinear Volterra equation which describes the interaction of uptake process with the apparatus. Within the time scale of uptake measurements (10 3 -10 4 s) the uptake curves were found to be consistent with the solution of the second Ficks law. Corrected diffusion coefficients were found to be essentially independent of loading within the loading range investigated and in contrast to the system benzene-HNaZSM-5 [1,2] their temperature dependence is much stronger.