Determination of transport coefficients in microporous solids

Macroscopic transient methods are reviewed with respect to their applicability to the investigation of molecular transport in microporous sorption systems. Various levels of sophistication of data evaluation for nonequilibrium sorption results obtained by means of batch methods are identified and characterised. Special attention is paid to the characterisation ofFickian (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-art determination of transport coefficients is exemplified for the systems benzene/microporous gallosilicate of MFI-type, n-hexane/silicalite-I and p-ethyltoluene/ZSM-5. Their sorption rate behaviour can be understood either byFickian diffusion or byFickian diffusion and intracrystalline molecular immobilisation/mobilisation and surface barrier penetration, respectively. To analyse complex sorption rate patterns in microporous systems, the method oftotal curve fitting with full parameter region consideration becomes mandatory.     

Controlled gas adsorption properties of various pillared clays

Microporous pillared clays (PILC) were prepared by the intercalation of montmorillonite with particles of titania (Ti-PILC), zirconia (Zr-PILC), alumina (Al-PILC), iron oxide (Fe-PILC) and mixed lanthania/alumina (LaAl-PILC). Nitrogen adsorption isotherms (77 K) and XRD data provided information on the porosity, surface area, micropore volume and interlayer distance of these samples. The surface area varied between 198 and 266 m²/g for Ti- and Fe-PILC, respectively. The titania pillared clay had also the highest micropore volume (0.142 cc/g) and interlayer spacing (16–20 Å), compared to the Zr-PILC, which had the smallest spacing between the layers (max, 4 Å). Despite this fact, Zr-PILC always showed a high adsorption capacity for gases such as N₂, O₂, Ar or CO₂, due to its high adsorption field in the very small micropores.From gas adsorption experiments on these various PILCs, it became clear that their adsorption properties depend on the pillars in three ways: (i) the pillar height, (ii) the distribution of the pillars between the clay layers and (iii) the nature of the pillaring species.The incorporation of other elements in the pillars leads to specific adsorption sites in the pores. This was demonstrated by the preparation of mixed Fe/Cr and Fe/Zr pillared clays. Compared to the parent Fe-PILC, the incorporation of chromium and zirconium in the iron oxide pillars had a positive influence on the adsorption capacity. Also the modification of a PILC with cations increases both capacity and selectivity for gases. This was confirmed by the increased adsorption of N₂, O₂ and CO₂ at 273 K on a Sr²⁺ exchanged Al-PILC.     

Diffusion in Surface Modified ZSM-5 Studied Using the ZLC Method

Deposition of silane on a zeolite's external surface is a well established method of increasing its shape selective properties by modifying diffusion resistances. In this work the intracrystalline diffusivity of cyclohexane in both a parent and silanized ZSM-5 samples were measured using the zero length column technique. It was found that the apparent intracrystalline diffusivity did indeed decrease in the modified samples. Models based on a surface barrier approach to describe pore mouth narrowing and an increase in intracrystalline tortuosity as a result of pore blockage were used to interpret the experimental data. It is found that the data correspond most consistently with the model describing pore blockage.     

Analysis of Diffusion in Hollow Geometries

The diffusion in hollow particles of solid adsorbent materials was analyzed based on analytical solutions to the basic diffusion equation. Three geometric shapes (plane sheet, cylinder, and sphere) of sorbent material were considered for two kinds of boundary conditions. The equations for determining the equivalent sizes compared to their corresponding solid particles were obtained directly from the theoretical expressions of sorption uptake curves. Among the three hollow particles of impermeable inner surface, the sphere gives the highest gain in effective diffusion rate compared to the corresponding solid particle. For permeable inner surface, at lower hollow volume fractions, the plane sheet shows the highest gain, while at higher hollow volume fractions, the sphere shows the highest gain in effective diffusion rate.     

Adsorption and Diffusion Behavior of Ethane and Ethylene in Sol-Gel Derived Microporous Silica

High surface area silica (500 m²/g) was synthesized by the sol-gel method from tetraethyl orthosilicate. The total porosity of the sample was 37% and most of the pores were well below 2 nm in size. The adsorption characteristics of ethylene and ethane in the silica were measured from 300–350 K by gravimetry, and Langmuir adsorption constants and enthalpies and entropies of adsorption were determined. Quasielastic neutron scattering was used to determine the translation and rotational diffusivities of both adsorbates from 200–270 K. Based on the adsorption and translational diffusion characteristics of ethylene and ethane, separation factors of 1.1–2 for olefin to paraffin are predicted.     

Effective intraparticle diffusion coefficients of CoCl2 in mesoporous functionalized silica adsorbents

The scope of this work is to determine the effective intraparticle diffusion coefficient of CoCl₂ over mesoporous functionalized silica. Silica is selected as a carrier of the functionalized groups for its rigid structure which excludes troublesome swelling, often found in polymeric adsorbents. 2-(2-pyridyl)ethyl-functionalized silica is selected as a promising affinity adsorbent for the reversible adsorption of CoCl₂. The adsorption kinetics is investigated with the Zero Length Column (ZLC) method. Initially, experiments were performed at different flow rates to eliminate the effect of external mass transfer. The effect of pore size (60 Å and 90 Å), particle size (40?10^?6 m–1000?10^?6 m) and initial CoCl₂ concentration (1 mol/m³–2.0 mol/m³) on the mass transfer was investigated. A model was developed to determine the pore diffusion coefficient of CoCl₂ by fitting the experimental data to the model. The pore diffusion coefficients determined for two different pore sizes of silica are D _p (60 Å) =1.95?10^?10 [m²/s] and D _p (90 Å) =5.8?10^?10 [m²/s]. The particle size and the initial CoCl₂ concentration do not have an influence on the value of diffusion coefficient. However, particle size has an influence on the diffusion time constant. In comparison with polymer adsorbents, silica based adsorbents have higher values of diffusion coefficients, as well as a more uniform and stable pore structure.     

Critical Role of Dynamic Flexibility in Ge‐Containing Zeolites: Impact on Diffusion

Incorporation of germanium in zeolites is well known to confer static flexibility to their framework, by stabilizing the formation of small rings. In this work, we show that the flexibility associated to Ge atoms in zeolites goes beyond this static effect, manifesting also a clear dynamic nature, in the sense that it leads to enhanced molecular diffusion. Our study combines experimental and theoretical methods providing evidence for this effect, which has not been described previously, as well as a rationalization for it, based on atomistic grounds. We have used both pure‐silica and silico‐germanate ITQ‐29 (LTA topology) zeolites as a case study. Based on our simulations, we identify the flexibility associated to the pore breathing‐like behavior induced by the Ge atoms, as the key factor leading to the enhanced diffusion observed experimentally in Ge‐containing zeolites.     

Measurement of Diffusion in Zeolites—A Never Ending Challenge?

A review is given on the main problems associated with the determination and interpretation of molecular diffusion in zeolites. It is shown that the diffusivities may most decisively depend on the relevant space and time scales of observation, as well as on the physical state under which the measurements are carried out. Special emphasis is given to the microscopic techniques and their most recent evidence on the existence of transport resistances distributed over the intracrystalline space.     

Diffusion in glassy polymers: A model using a homogenization method and the effective medium theory

Glassy polymers are considered as inhomogeneous with regions in which the gas sorption follows Henry's law and others where it follows Langmuir's law. It is assumed that the linear dimensions of these regions are small compared with the macroscopic length of interest but large compared with the mean free path of the penetrant gas molecules. Applying an homogenization method it is shown that the average flux is directly proportional to the concentration gradient in the polymer. This relationship can be expressed in terms of an effective diffusion coefficient D_eff, which depends on the details of the microstructure. D_eff is evaluated in the framework of the effective medium theory and compared with experimental data for diffusion of five vapors in ethylcellulose.     

恒电位阶跃法研究贮氢合金MlNi_(3.75)Co_(0.65)Mn_(0.4)Al_(0.2)中氢的扩散行为

本文用恒电位阶跃法研究了不同放电深度 (DOD)和不同温度下贮氢合金MlNi3.75Co0 .6 5Mn0 .4 Al0 .2 中氢的扩散行为 .结果表明 :室温下该合金中氢的扩散系数随DOD的增大而增大 ,在5 0 %DOD的该合金中 ,氢的扩散系数随温度的升高而增大 ,扩散活化能为 19.87kJ/mol     

Sorption Kinetics and Intracrystalline Diffusion of Methanol in Ferrierite: An Example of Disguised Kinetics

Sorption kinetics of methanol in large crystals of ferrierite have been studied in detail by interference microscopy (IFM) and infra-red microscopy (IRM). The IFM measurements yield the transient concentration profiles, thus providing a direct measurement of both the surface resistance to mass transfer and the internal diffusion resistance. It is shown that, for this system, the uptake rate is controlled by the combined effects of surface resistance and diffusion through the 8-ring channels (in the y-direction). Transport through the 10-ring channels (in the z-direction) appears to be blocked by surface resistance. Although the overall uptake curves conform well to the “root t law” the diffusivity values derived from the uptake curves vary widely depending on the assumed direction of diffusion. Even if the correct direction of diffusion is assumed, the diffusivity values derived from the uptake curves are seriously in error as a result of the intrusion of surface resistance. The existence of transport resistances at the crystal surface is clearly apparent from the transient concentration profiles but is not obvious from the uptake curves.     

电极扩散层组分分析取样技术的研究

以直径小于１００微米的毛细管作取样管,以负压和虹吸为动力将电极扩散层内的溶深吸取出来,采用电位法离线检测,通过测量电极扩散层内的Ｃｕ＾２＋浓度,对各种取样方式进行了实验评价。获得阴极扩散层Ｃｕ＾２＋浓度较本体溶液低３０％,阳极扩散层内Ｃｕ＾２＋浓度较本体溶液高１６０％的结果,证明了方法的可行性,为毛细管电泳分析及其它分析方法测量扩散层内各物质浓度及形态建立了基础。     

气相扩散法生长溶菌酶晶体的动态光散射研究

首次采用动态光散射研究了气相扩散法生长溶菌酶晶体.实验中采用了两种溶解溶菌酶的方法,所得实验结果是有区别的.这种区别表明了NaCl对溶菌酶分子间相互作用产生十分重要的影响.实验结果表明,晶体生长过程中,溶液中溶菌酶始终保持单分子与两分子聚集体的状态,这种状态是生长晶体的基础.     

测氢扩散系数的电化学交流法研究

应用电化学交流法测定氢在纯铁中的扩散系数 .证明对电解氢在试样中的非稳态扩散 ,按菲克第二定律所设定的边界条件符合实际扩散行为 ,并论证了该方法的可行性     

Analysis of Dual Diffusion and Non-linear Adsorption Isotherm with a Time Lag Method

This paper presents an application of the time lag method in the analysis of an adsorption system, where dual diffusion mechanism is assumed to exist and the equilibrium relationship between the fluid and adsorbed phases is non-linear. The derived time lag is expressed in terms of system parameters and operating conditions in the form of a quadrature. The feature of this solution is that the relative contribution of the pore and surface diffusions is a strong function of upstream pressure when the time lag experiment is operated over the non-linear range of the adsorption isotherm. It is this nice feature that we take advantage of to determine the pore and surface diffusivities without resorting to isolation of the pore diffusion by using non-adsorbing gas as a reference, as usually done in many other work. This advantage is not manifested in linear systems where the relative contribution of the pore and surface diffusions is a constant, rendering the delineation of these two processes impossible. Effects of various parameters on the utility of this time lag method are discussed in this paper, and application of the method is demonstrated with experimental data of sulfur dioxide adsorption onto Carbolac carbon (Proc. Roy. Soc., A271, 1–18, 1963).     

Understanding the Role of Internal Diffusion Barriers in Pt/Beta Zeolite Catalyzed Isomerization of n‐Heptane

Applications of zeolites in catalysis are plagued by strong diffusion resistance, which results from limitations to molecular transport in micropores, across external crystal surfaces, but also across internal interfaces. The first type of diffusion resistance is well understood, the second is receiving increasing attention, while the diffusion barriers at internal interfaces remain largely unclear. We take Pt/Beta catalyzed isomerization of n‐heptane as the model system to explore the role of internal diffusion barriers in zeolite catalysis. The two as‐synthesized Pt/Beta catalysts have an identical Pt loading, similar Beta particle size and acidity, but different internal structures. A Pt/Beta crystal with no observable internal interfaces can be 180 % higher in activity and 22 % higher in selectivity than its counterpart with numerous internal interfaces. This can only be attributed to the strong transport barriers across internal interfaces, as supported by directly comparing the apparent diffusivities of the two Beta samples.     

Diffusion of Paraffins in Dealuminated Y Mesoporous Molecular Sieve

Mesoporous materials have been intensely studied recently, mainly as possible component for FCC (Fluid Catalytic Cracking) catalysts due to their large surface area and accessibility to large hydrocarbon molecules. It is thus of interest for the oil industry to understand the diffusion behavior of some standard molecules in these materials. Y Zeolites, usually employed in fluid catalytic cracking, can be modified by removal of aluminum atoms from the zeolitic framework to present a greater mesoporous contribution. Dealumination of Y zeolite framework is also known to improve the stability of the catalyst thus making it more suitable for the FCC operation. This study presents diffusion measurements performed with the ZLC (Zero-Length Column) method, developed in the late eighties by Eic and Ruthven (1988a, b). The ZLC method has been largely used for a number of systems, either in gas or in liquid phases. We have now applied the ZLC method for gas phase diffusion measurements of linear paraffins (C₇–C₁₀) in dealuminated Y zeolite (USY). Experimental data were obtained at different temperatures (150 to 240°C) and flow rates (40 to 120 ml/min) and correlated through a transient Fickian diffusion model.     

Direct Spectrochemical Analysis of Solids: A Method for Characterization of Sediments

Techniques for the direct analysis of powdered samples provide an advantageous alternative to methods using wet digestion in sample preparation. The direct spectrochemical methods based on electrothermal vaporization (ETV-ICP-OES, solid-ETV-AAS, etc.) show a great similarity to the classical method of dc arc excitation, used in spectrography. Owing to this, the classical dc arc spectrographical method was used in parallel with ETV methods in the direct solid sampling analysis of river and basin sediments. The calibration procedure is the major difficulty of all techniques applied to direct solid sample analysis because of a lack of suitable reference materials. Consequently, it was necessary to verify the application of model calibration samples, preferentially using the simple dc arc OES system and both spectrographic and spectrometric evaluation. The performance parameters of the methods mentioned are compared with those published for the ETV-ICP-OES and SS-ETV-AAS methods.     

Time-dependent Diffusion Coefficient and Conventional Diffusion Constant of Nanoparticles in Polymer Melts by Mode-coupling Theory (cited: 2)

Time-dependent diffusion coefficient and conventional diffusion constant are calculated and analyzed to study diffusion of nanoparticles in polymer melts. A generalized Langevin equa-tion is adopted to describe the diffusion dynamics. Mode-coupling theory is employed to calculate the memory kernel of friction. For simplicity, only microscopic terms arising from binary collision and coupling to the solvent density fluctuation are included in the formalism. The equilibrium structural information functions of the polymer nanocomposites required by mode-coupling theory are calculated on the basis of polymer reference interaction site modelwith Percus-Yevick closure. The effect of nanoparticle size and that of the polymer size are clarified explicitly. The structural functions, the friction kernel, as well as the diffusion coefficient show a rich variety with varying nanoparticle radius and polymer chain length. We find that for small nanoparticles or short chain polymers, the characteristic short time non-Markov diffusion dynamics becomes more prominent, and the diffusion coefficient takes longer time to approach asymptotically the conventional diffusion constant. This constant due to the microscopic contributions will decrease with the increase of nanoparticle size, while increase with polymer size. Furthermore, our result of diffusion constant from mode-coupling theory is compared with the value predicted from the Stokes-Einstein relation. It shows that the microscopic contributions to the diffusion constant are dominant for small nanoparticles or long chain polymers. Inversely, when nanonparticle is big, or polymer chain is short, the hydrodynamic contribution might play a significant role.     

Determination of The Oxygen Chemical Diffusion Coefficient in Perovskites by a Thermogravimetric Method

A thermogravimetric method has been used for the determination of the oxygen chemical diffusion coefficients in La_1–xSr_xMnO_3+δ; x=0; 0.05; 0.10; 0.15 (LSM). A temperature range of 700–1000°C was studied. The chemical diffusion coefficient varies between 1.6⋅10^–13 and 1.8⋅10^–10cm²s^–1 for the samples in the temperature range studied. The activation energy for oxygen chemical diffusion was determined to be 190–280 kJ mol^–1 for the LSM samples. The magnitude of the chemical diffusion coefficients of the LSM samples does not depend on the strontium site occupation factor. This revised version was published online in July 2006 with corrections to the Cover Date.