Intracrystalline Diffusion Coefficient Research Articles

Modelling adsorption based on an isoreticular MOF‐series of IFPs—Part II: Dynamic adsorption in fixed beds

AbstractBased on experimental pure component data for the characterization of the isostructural imidazolate framework Potsdam (IFP) series reported in Part I, a model for the simulation of non‐isothermal dynamic adsorption of CO2/CH4‐mixtures in fixed‐bed columns is presented in this Part II. The robustness of the model is examined and validated, by comparison to experimental breakthrough data at different process conditions, such as varying concentration, temperature, and pressure. Thereby, different predictive methods for the estimation of adsorption equilibria of mixtures are compared (RAST, IAST, ML). The results show that ideal behaviour can be assumed with good accuracy for the system under consideration, except for IFP‐2, which shows significant deviations at increased pressures and temperatures. A detailed kinetic analysis reveals that mass transfer is significantly influenced by micropore diffusion. Thus, only for IFP‐1 the dynamic separation of CO2 and CH4 is equilibrium‐driven, while for the remaining IFPs the kinetic regime dominates the process, which in some cases increases the separation efficiency (IFP‐2 to ‐7) but can also inhibit it (IFP‐8). The determined intracrystalline diffusion coefficients show very good agreement with values for metal organic framework (MOF) compounds of similar structure reported in the literature.

Development and application of an exchange model for anisotropic water diffusion in the microporous MOF aluminum fumarate

Diffusion of water in aluminum fumarate was studied by means of pulsed field gradient (PFG) nuclear magnetic resonance (NMR). Due to water molecules exchanging between the intracrystalline anisotropic pore space and the isotropic intercrystalline void space the model of intracrystalline anisotropic diffusion fails to describe the experimental PFG NMR data at high observation times. Therefore, the two-site exchange model developed by Kärger is extended to the case of exchange between an anisotropic and an isotropic site. This extended exchange model is solved by numerical integration. It describes the experimental data very well and yields values for the intracrystalline diffusion coefficient and the mean residence times of the respective sites. Further PFG NMR studies were performed with coatings consisting of small aluminum fumarate crystals, which are used in adsorptive heat transformation applications. The diffusion coefficients of water in the small crystal coating are compared to the values expected from the extended two-site exchange model and from the model of long-range diffusion.

Adsorption equilibrium and kinetics of cesium onto insoluble Prussian blue synthesized by an immediate precipitation reaction between Fe3+ and [Fe(CN)6]4−

The adsorption equilibrium and kinetics of cesium ion (Cs+) onto insoluble Prussian blue (PB) prepared by an immediate precipitation reaction between Fe3+ and [Fe(CN)6]4− was investigated under initial Cs+ concentration of under 0.15 mmol/L. Synthesis conditions in this method were almost insensitive to the adsorption ability of insoluble PB, and this method provided one of the smallest PB crystallites among synthesis methods. Even when molar concentration of H3O+ was more than 200 times higher or molar concentration of K+ was more than 50,000 times higher than that of Cs+ in the aqueous solution, the equilibrium adsorption amount was reduced by only approximately one-half to two-third of that in the pure system; that is, the insoluble PB synthesized possessed a considerably high adsorption selectivity for Cs+. In contrast to the excellent adsorption ability under adsorption equilibrium, adsorption rate was quite slow. It took at least 2 weeks at 25 °C to completely attain the adsorption equilibrium, even though the primary particle size (crystallite size) and secondary particle size (aggregate size of the crystallites) were sufficiently small at approximately 14 nm and 53–106 μm, respectively. This slow adsorption is primarily due to the large resistance of intracrystalline diffusion; the intracrystalline diffusion coefficient was extremely small at less than 3.3 × 10−22 m2/s. We also found that increase in temperature could significantly decrease this diffusion resistance, resulting in much quicker elimination of Cs+ from the aqueous solution.

Nonuniform Chain-Length-Dependent Diffusion of Short 1-Alcohols in SAPO-34 in Liquid Phase

Liquid-phase diffusion of 1-alcohols in SAPO-34 was explored by batch experimentation. The uptake of pure and binary mixtures of 1-alcohols, dissolved in tert-butanol, was obtained for C1–C8 1-alcohols at temperatures between 25 and 80 °C, concentrations varying between 0.5 and 10 wt %, and crystal sizes between 7.5 and 20 μm. The experimental uptake data were fitted with an intracrystalline diffusion model and a linear driving force model. The intracrystalline diffusion coefficient showed a nonuniform stepwise decrease with chain length, ranging from 10–12 m2/s for methanol to 10–20 m2/s for 1-pentanol. No effect of the external concentration on the intracrystalline diffusion coefficient was observed. Variation of the crystal size showed that the intracrystalline diffusion is the rate-limiting step. On the basis of the Arrhenius equation, the activation energies of diffusion of ethanol, 1-propanol, and 1-butanol were determined, being, respectively, 27.8, 47.8, and 47.2 kJ/mol. Co-diffusion occurred in the uptake of binary mixtures of methanol/ethanol, methanol/1-propanol, and ethanol/1-propanol, where mutual effects could be noticed. From this experimental work, it could be concluded that the small dimensions of the SAPO-34 framework generate a very sterically hindered diffusion of 1-alcohols into the crystals, resulting in a chain-length-dependent behavior, interesting to obtain efficient kinetic-based separations.

Sub-millimeter Heterogeneity of Yttrium and Chromium during Growth of Semi-pelitic Garnet

X-ray maps of yttrium and chromium in two garnets from a semipelitic schist from central Nepal reveal parallel, spiraling bands of high and low concentration � 10^30 m wide. This zoning mimics similar concentration bands defined by foliation in the matrix outside the garnets. The garnets apparently incorporated the matrix zoning intact during growth at conditions up to lower amphibolite facies.These observations and interpretations indicate that Yand Cr concentrations remained heterogeneous at the scale of tens of micrometers during breakdown of matrix minerals and growth of garnet. This conclusion extends results of previous work, which showed that Y and Cr do not homogenize at the centimeter to millimeter scale during metamorphism to amphibolite facies. The width of the concentration bands in the garnets places a constraint on the maximum effective intracrystalline diffusion coefficient for both Y and Cr in garnet of about 10 ^21 cm 2 /s for peak metamorphic conditions of about 9 kbar at 5708C. Different concentrations of Yand Cr at different positions around the rim of each garnet indicate disequilibrium for these elements between garnet and matrix phases. The presence of an internal foliation defined by the Yand Cr concentration bands rules out pre-kinematic garnet growth. Most useful in conjunction with other indicators, zoning of these elements in garnet is thus a tool for deciphering the relative timing of deformation and garnet growth.

Exploring Crystal Morphology of Nanoporous Hosts from Time-Dependent Guest Profiles

The persistence of resistance: In the zeolite silicalite-1, the influence of transport barrier on the surface and between crystal segments, are negligibly small in comparison to the transport resistance of the intracrystalline pore system. Diffusion experiments are conducted with these zeolite crystals and intracrystalline diffusion coefficients of guest molecules determined.

PFG NMR investigation of hydrocarbon diffusion in large NaX zeolite crystals: Effect of internal field gradients on diffusion data

Self-diffusion coefficients for intracrystalline diffusion of hydrocarbon molecules adsorbed in large crystals of NaX zeolite have been measured by the pulsed field gradient (PFG) NMR technique, at ambient temperature and at different diffusion times (from 6 to 12 ms). Two NMR pulse sequences, stimulated and 13-interval bipolar spin echo, were used to examine the influence of internal field gradients on diffusion data. For both sequences the effective self-diffusion coefficient of the guest molecules was found to decrease with increasing observation times. The extrapolated intracrystalline diffusion coefficient is independent of the NMR sequence. In contrast, the estimated extent of molecular diffusion depends strongly on the pulse program. For the small molecules (butane to hexane), the domain size, R, of restricted diffusion obtained with the stimulated spin-echo sequence is smaller than the crystal dimension whereas R is always comparable to it when the 13-interval pulse sequence is used. This shows the effect of internal field gradients on the diffusion data leading to wrong values of R if the stimulated pulse sequence is used. The light hydrocarbons diffuse freely inside the zeolite particles whereas the crystal boundaries act as reflecting surfaces, as previously observed. On the other hand, even with the 13-interval pulse sequence, the smaller values of R obtained for large molecules as n-heptane and octane shows that their displacement is hindered by restrictions in the NaX macro-crystals.

Molecular simulation of adsorption and diffusion of chlorinated alkenes in ZSM-5 zeolites

In this work, adsorption and diffusion of trichloroethylene (TCE) and tetrachloroethylene (PCE) in ZSM-5-type zeolites were studied using molecular simulation methods. Grand canonical Monte Carlo technique was to calculate adsorption isotherms and heats of vaporization of TCE and PCE in zeolite. The results demonstrated that the Pnma-P2(1)2(1)2(1) symmetry transition of the zeolite framework has no significant effect on the TCE adsorption capacity of the silicalite, but it causes an increase of the PCE adsorption capacity. Simulations using a silicalite framework with Pnma symmetry showed that the adsorption capacity of the silicalite was limited to five molecules per unit cell. However, when a framework with P2(1)2(1)2(1) symmetry was used in the simulations, the capacity reached to eight molecules per unit cell, which is the actual adsorption capacity. To calculate intracrystalline diffusion coefficients of these compounds, molecular dynamics simulations were performed at different temperatures and loadings. The results show that the zeolite symmetry has a significant impact on diffusion coefficients of the sorbate molecules.

On the problem of field-gradient NMR measurements of intracrystalline diffusion in small crystallites—Water in NaA zeolites as an example

Necessary conditions for measuring intracrystalline diffusion in small crystal size systems via field-gradient NMR are discussed. As an illustrative case self-diffusion coefficients of water adsorbed in NaA zeolites (average crystal diameter about 1 μm) have been measured by 1H-NMR stimulated echoes in static magnetic field gradients of up to 180 T/m in the temperature range of 254–344 K. Obtaining intracrystalline diffusion coefficients necessitates a sufficiently high spatial resolution only provided by such large field gradients.

Combining macroscopic and microscopic diffusion studies in zeolites using NMR techniques

In this study the zero length column (ZLC) technique is extended to the case where the decay of the adsorbed phase concentration is observed directly by nuclear magnetic resonance (NMR). An adsorption-desorption apparatus compatible with a 400-MHz NMR spectrometer was developed. It operates with nitrogen or helium as the inert purge gas. The column of the adsorbent material is placed in the sensitive region of the superconducting magnet and the rf coil of the NMR spectrometer. The time scales of the adsorption and desorption processes depend on concentration, temperature and crystal shape and are found to be in the range of 1-10 min. From the desorption branch, the non-equilibrium ZLC-NMR measurements yield intracrystalline diffusion coefficients in the range of 10(-13) to 10(-11) m2/s for different alkanes in silicalite-1. These values are always found to be smaller than the values measured by pulsed field gradient NMR under equilibrium condition indicating that there must be additional transport resistance at the external surface of these silicalite-1 zeolite crystals.

Synthesis and characterization of the layered sodium silicate ilerite

A sodium ilerite, molar ratios 1Na 2O:8.2SiO 2:10.2H 2O, was obtained with a good crystalline structure and characterized by several NMR techniques in addition to X-ray diffraction (XRD). The X-ray pattern of the as-synthesized ilerite is in very good agreement with the structure proposed by Gies and coworkers. The narrow 29Si MAS NMR signals (FWHM=0.3 ppm) indicate a good short-range order of the framework. The proton dynamics influences several 29Si NMR parameters. The 16 ppm signal in the 1H MAS NMR spectra is explained by a proton in a bridging position in the short (2.3 Å) O4–O4 bonding. The quadrupole coupling constant C qcc=100 kHz with η=0.2 for the 16 ppm signal, which was obtained from the 2H MAS NMR spectra, confirms this explanation. 17O NMR shows also a separate signal for SiOH groups but cannot resolve the three expected lines for SiOSi. PFG NMR detects a small mobile portion of water in the ilerite, which is located probably on the external surface of the crystallites. An intracrystalline diffusion coefficient of the intercalated water molecules of the order of magnitude 10 −15 m 2 s −1 was obtained by NMR tracer exchange experiments.

Hydrocarbon Diffusion Measurements and Coke Distribution in Zeolite Pellets: A Study by 1H NMR Imaging and 129Xe NMR Spectroscopy

Diffusion of benzene in HZSM-5 zeolite in powder or pellet form and of 2,3-dimethylpentane (DMP) in HY zeolite pellets, more or less deactivated by formation of coke during n-heptane cracking, was studied by 1H NMR imaging and 129Xe NMR of adsorbed xenon used as a probe. The shape and the evolution of the signal intensity of the 1D profile, representing the proton distribution along the axis of the cylindrical tube containing the catalyst, make it possible to determine the intracrystalline molecular diffusion coefficient of benzene when this is adsorbed (≈10-14 m2 s-1). Comparison of the 129Xe NMR spectra, recorded during benzene adsorption, with those simulated assuming intracrystalline diffusion gives a similar value of the diffusion coefficient (≈10-15 m2 s-1). For DMP in HY coked pellets, the NMR profile shows a maximum, which moves during DMP adsorption. This was interpreted as the superposition of two competing processes: intercrystalline diffusion and intracrystalline diffusion of DMP from uncoked to highly coked zones of the crystallites. 1D and 2D images at equilibrium adsorption of the probe clearly confirm the heterogeneous distribution of the coke shown by 129Xe NMR spectroscopy.

Determination of the intracrystalline diffusion coefficients of alkanes in H-ZSM-5 zeolite by a transient technique using the temporal-analysis-of-products (TAP) reactor

A transient technique using the temporal analysis of products (TAP) reactor system was used to determine the intracrystalline diffusion coefficients of isobutane and 2-methylpentane in a H-ZSM-5 zeolite sample at temperatures between 423 and 598 K. A mathematical model was set up which describes the transport phenomena occurring in the transient experiment. The features of this model were then explored by model simulation. The method and the underlying model were successfully validated by fitting experimental data, deriving intracrystalline diffusion coefficients by parameter estimation, and comparing them with published values obtained by independent methods.

Estimation of the intracrystalline diffusion coefficient of the reactant during selective catalytic reduction of nitrogen oxide by propane on Co-ZSM-5

In order to estimate the effect of diffusion during the selective catalytic reduction of nitrogen oxides (NOx) using propane on Co-ion-exchanged ZSM-5, the catalytic activity was measured for the catalysts prepared from zeolites having different crystal sizes. The conversions of NOx and propane on a catalyst having a large crystal size (1.3 μm) were much less than those on a catalyst having a smaller crystal size (0.10 μm). Based on the experimental data and certain assumptions, the effective intracrystalline diffusion coefficient of NO during the reaction in the presence of water vapor at 673 K was estimated to be (6-9)× 10-15 m2/s.

Binary adsorption and desorption rates of propylene-propane mixtures on 13 X molecular sieves

The experimental adsorption and desorption rate data for pure propylene, pure propane, and propylene-propane mixtures on 13 X molecular sieves are presented for different temperatures and compositions; these rate data were efficiently determined using the differential sorption bed system described by Liapis et al. (Liapis et al. (1992) Rates and equilibria of adsorption and desorption of propane and propylene on 13 X molecular sieves determined experimentally using a differential sorption bed system. Sep. Technol. 2, 141–154). Propylene is the most preferentially adsorbed component, and the desorption rates of propylene and propane are slower than the adsorption rates. Mathematical models were constructed and solved, and it was found that the two-component model could provide a quantitative measure of the interactions between propylene and propane, and could describe the behavior of binary adsorption kinetics including the overshoot of the equilibrium loading by the less preferentially adsorbed propane. The theoretical results indicate that the desorption rates are not described by the same intracrystalline diffusion coefficients as the adsorption rates.

Diffusion anisotropy in molecular sieves: A Fourier transform PFG NMR study of methane in A1PO 4-5

By analyzing the shape of the 1H PFG NMR spin echo decay of methane in large crystals of AlPO 4-5, we demonstrate that diffusion of methane is unidirectional but not single file. The intracrystalline diffusion coefficient is 2.9 × 10 −9 m 2s −1. The same experiment, when performed on AlPO 4-5 crystals of much smaller size, results in an isotropic diffusivity that is higher by nearly three orders of magnitude. This crystal size artifact emphasizes the importance of using large zeolite crystals in NMR measurements to obtain intracrystalline diffusivities.

Molecular dynamics investigation of the diffusion of methane in a cubic symmetry zeolite of type ZK4

Extensive molecular dynamics simulations of methane diffusion in a cubic-type zeolite ZK4 have been performed by using a model including the vibrations of the silicate framework. In order to understand the role of the lattice dynamics in assisting the diffusive motion of the sorbed molecules we studied the same system also in the rigid framework approximation. Even more evidently than in the case of zeolite structures where the micropores are essentially cylindrical, the framework oscillations are confirmed to be an essential factor in determining the magnitude of the intracrystalline diffusion coefficient.

Frequency response for nonisothermal adsorption in biporous pellets

The frequency response for nonisothermal adsorption in a biporous pellet is analyzed theoretically, using a mathematical model which includes heat and mass transfer resistances in both micropores and macropores. It is confirmed that, when the heat effect is involved, the out-of-phase component may exhibit a bimodal form. Moreover, it is shown that when both macropore diffusion and micropore diffusion resistances are comparable, macropore diffusion behaves like a surface barrier and leads to an intersection of the in-phase and out-of-phase response functions. When either micropore diffusion or macropore diffusion alone is dominant, the frequency response is essentially the same and, therefore, provides no information concerning the nature of the controlling diffusional resistance. Experimental data for light linear paraffins-5A, reported by Yasuda (1991, J. phys. Chem. 95, 2486–2492), are reanalyzed by the present nonisothermal model. It turns out that the reported experimental response can be equally well represented by a nonisothermal model using several different combinations of mass transfer resistances. It, therefore, appears that the bimodal behavior of the experimental out-of-phase data is caused by the heat effect, thus contradicting the conclusion of Yasuda that there are two adspecies with different mobilities. With the reported data, it is, however, not possible to extract reliable values for the intracrystalline diffusion coefficient, and the nature of the controlling mass transfer resistances cannot be established with certainty.

Studies of molecular diffusion in porous crystals (zeolites)

The conventional way to study molecular diffusion in porous crystallites (zeolites) is to follow the rate of mass change of a sample after changing the pressure of the surrounding atmosphere, and it was one of the most important results of the application of NMR spectroscopy in interface science to show that intracrystalline molecular diffusion coefficients measured in this way were wrong up to five orders of magnitude. The NMR method applied in these measurements is the so-called pulsed field gradient (PFG NMR) technique. Its basic principles, the procedures of measurement and its limitations are discussed, and recent results are presented concerning the anisotropy of molecular diffusion in zeolites of non-cubic symmetry.

Intracrystalline diffusion in zeolites 9. Determination of intracrystalline diffusion coefficients from exothermic calorimetric curves

A method has been proposed for the determination of the intracrystalline diffusion coefficients for polar substances in zeolites from the exothermic calorimetric curves. If the differential heat of adsorption falls as the degree of filling increases, diffusion is an exothermic process and, therefore, the release of heat in a system with a steep adsorption isotherm (in the case of a measured addition) continues even though the adsorption process may have finished. The exothermic calorimetric curve for NH3 adsorption by the zeolite NU has been taken as an illustration.