Micropore transport diffusivities

For the detailed study of reaction-transport interactions in the porous catalytic layer, the spatially 3D model computer-reconstructed washcoat section can be employed (Koci et al., 2006, 2007a). The structure of porous catalyst support is controlled in the course of washcoat preparation on two levels (i) the level of macropores, influenced by mixing of wet supporting material particles with different sizes followed by specific thermal treatment and (ii) the level of meso-/ micropores, determined by the internal nanostructure of the used materials (e.g. alumina, zeolites) and sizes of noble metal crystallites. Information about the porous structure (pore size distribution, typical sizes of particles, etc.) on the micro- and nanoscale levels can be obtained from scanning electron microscopy (SEM), transmission electron microscopy ( ), or other high-resolution imaging techniques in combination with mercury porosimetry and BET adsorption isotherm data. This information can be used in computer reconstruction of porous catalytic medium. In the reconstructed catalyst, transport (diffusion, permeation, heat conduction) and combined reaction-transport processes can be simulated on detailed level (Kosek et al., 2005). 

Considering only micropore transport with constant parameters, the single component uptake by pore diffusion in RS-10, following a step change in gas concentration, is given by... 

Fig. 1-1. Transport processes in solid-liquid soil reactions—Nonactivated processes 1. Transport in the soil solution, 2. Transport across a liquid film at the solid-liquid interface, 3. Transport in a liquid-filled micropore. Activated processes 4. Diffusion of a sorbate at the surface of the solid, 5, Diffusion of a sorbate occluded in a micropore, 6. Diffusion in the bulk of the solid.

Macropore and film diffusion are relatively well understood and are therefore not discussed in any detail in this voliune. In contrast, despite intensive study over the last 30 years, our imderstanding of micropore diffusion is still far from complete. At the micropore scale diffusive transport is largely controlled by steric interactions which are dominated by repulsive forces. The relative diameter of the micropore and the diffusing molecifie is clearly a critical variable. For small spherical or spheroidal molecules there is a clear... 

The diffusivity (D) defined in this way is not necessarily independent of concentration. It should be noted that for diffusion in a binary fluid phase the flux (/) is defined relative to the plane of no net volumetric flow and the coefficient D is called the mutual diffusivity. The same expression can be used to characterize migration within a porous (or microporous) sohd, but in that case the flux is defined relative to the fixed frame of reference provided by the pore walls. The diffusivity is then more correctly termed the transport diffusivity. Note that the existence of a gradient of concentration (or chemical potential) is implicit in this definition. 

To establish the relationship between self- and transport diffusion it is necessary first to consider diffusion in a binary adsorbed phase within a micropore. This can be conveniently modeled using the generalized Maxwell-Stefan approach [45,46], in which the driving force is assumed to be the gradient of chemical potential with transport resistance arising from the combined effects of molecular friction with the pore walls and collisions between the diffusing molecules. Starting from the basic form of the Maxwell-Stefan equation ... 

Abstract Infrared spectroscopic methodsfor the measurement of adsorption and adsorption kinetics of some aromatics (benzene, ethylbenzene, p-xylene), pyridine, and paraffins in solid microporous materials such as zeolites (MOR, ZSM-5, silicalite-1) are described as well as the evaluation of the spectroscopically obtained data. The adsorption isotherms are of the Langmuir-Freundlich type. Isosteric heats of adsorption, transport diffusivities, and activation energies of diffusion as deduced from the spectroscopic measurements are compared with literature data as far as available, and they are found to be in reasonable agreement with results provided by independent techniques. Special attention is paid to sorption and sorption kinetics of binary mixtures, especially the problems of co- and counter-diffusion. ... 

Fundamentals of sorption and sorption kinetics by zeohtes are described and analyzed in the first Chapter which was written by D. M. Ruthven. It includes the treatment of the sorption equilibrium in microporous sohds as described by basic laws as well as the discussion of appropriate models such as the Ideal Langmuir Model for mono- and multi-component systems, the Dual-Site Langmuir Model, the Unilan and Toth Model, and the Simphfied Statistical Model. Similarly, the Gibbs Adsorption Isotherm, the Dubinin-Polanyi Theory, and the Ideal Adsorbed Solution Theory are discussed. With respect to sorption kinetics, the cases of self-diffusion and transport diffusion are discriminated, their relationship is analyzed and, in this context, the Maxwell-Stefan Model discussed. Finally, basic aspects of measurements of micropore diffusion both under equilibrium and non-equilibrium conditions are elucidated. The important role of micropore diffusion in separation and catalytic processes is illustrated. 

The major contributor to the MTZ, especially in vapor- ffiase adsorption, is diffusion resistance. " Ad-soiptive diffusion is the sum of sevei different mechuisms. There is bulk diffusion through the film around the adsoibent particle. Then the molecules most overcome the macropoie difiiision resistance that is usually characterized as Maxwell diffusion. In fliose pores that have dimensions on the ordo of molecular dimensions, the transport is by Knudsen diffusion. In these micropores, the diffusion can also occur by sorfece diffusion. Typically, the entire process is characterized by a single overall diffusion coefficient. 

For several reasons the reliable measurement of micropore-diffusion has proved to be far more difficult than expected. A wide range of different experimental techniques have been applied (see Table 3). We now know that when the diameter of the diffusing molecule is even slightly smaller than the pore diameter, diffusion within an ideal micropore is surprisingly fast and difficult to measure by macroscopic methods since the size of available zeolite crystals is limited. Such fast processes can, however, be measured relatively easily by PFG NMR and QENS. As the molecular diameter of the sorbate approaches (or even exceeds) the minimum diameter of the pore the diffusional activation energy increases and the diffusivity drops by orders of magnitude. Slow transport-diffusion (for example ethane, propane, etc. in CHA or Zeolite A - see Fig. 7) is easily measured macroscopically but inaccessible to microscopic techniques. The range of systems and experimental conditions where reliable measurements can be made by both macroscopic and microscopic methods is therefore quite restricted. 

The typical gas transport mechanisms in porous membranes are molecular diffusion and viscous flow, capillary condensation, Knudsen diffusion, surface diffusion, and configurational or micropore-activated diffusion. The contributions of these different mechanisms depend on the properties of both the membrane and the gas under the operating temperature and pressure. Figure 2.3 illustrates schematically the gas transport mechanisms in a single membrane pore. 

Gas-Phase Transport in Catalyst, Microporous, and Diffusion Layers The role of the different porous media in the fuel cell (catalyst layer, microporous layer, and diffusion media) in liquid transport can be grasped by understanding capillary flow behavior in mixed wettability porous media. The role of these porous media in controlling gas -phase flow can be simply understood through gas-phase transport relationships. Recall from Chapter 5 that the diffusivity in porous media must be modified to account for the tortuosity and porosity of the porous media ... 

In principle, the separation properties of a multilayer porous ceramic membrane, such as permselectivity, should be dependent only on the pore size distribution of the top separation layer. However, they can be compromised if resistances in the intermediate layers and the macroporous support become significant. For transport through macro- and meso-pores, molecular diffusion, Knudsen diffusion and viscous flow all contribute to the total transport, while the activated surface flow of the adsorbed phase will affect microporous transport. Therefore, any theoretical models used in analysing the transport data of gases through a porous ceramic membrane with a distributed pore size must take the following contributions into consideration (1) viscous flow, (2) Knudsen flow, (3) surface flow and (4) molecular sieving... 

The tme driving force for any diffusive transport process is the gradient of chemical potential rather than the gradient of concentration. This distinction is not important in dilute systems where thermodynamically ideal behavior is approached. However, it becomes important at higher concentration levels and in micropore and surface diffusion. To a first approximation the expression for the diffusive flux may be written... 

For a macroporous sorbent the situation is slightly more complex. A differential balance on a shell element, assuming diffusivity transport through the macropores with rapid adsorption at the surface (or in the micropores), yields... 

Although microporous membranes are a topic of research interest, all current commercial gas separations are based on the fourth type of mechanism shown in Figure 36, namely diffusion through dense polymer films. Gas transport through dense polymer membranes is governed by equation 8 where is the flux of component /,andare the partial pressure of the component i on either side of the membrane, /is the membrane thickness, and is a constant called the membrane permeability, which is a measure of the membrane s ability to permeate gas. The ability of a membrane to separate two gases, i and is the ratio of their permeabilities,a, called the membrane selectivity (eq. 9). 

Other microporous materials have been synthesized using the porogen polyethylene glycol in polyethylene oxide-urethane gels [27]. Micropores were formed in the gel, and it was found that the diffusion of larger species, vitamin B12, was enhanced relatively more than that of a smaller species, proxyphylline. This result is in qualitative agreement with that found for electrophoretic transport by RiU et al. [322] discussed earher, where the mobility of larger species was preferentially enhanced in the templated media. 

The in vitro system we have been using to study the transepithelial transport is cultured Madin-Darby canine kidney (MDCK) epithelial cells (11). When cultured on microporous polycarbonate filters (Transwell, Costar, Cambridge, MA), MDCK cells will develop into monolayers mimicking the mucosal epithelium (11). When these cells reach confluence, tight junctions will be established between the cells, and free diffusion of solutes across the cell monolayer will be markedly inhibited. Tight junction formation can be monitored by measuring the transepithelial electrical resistance (TEER) across the cell monolayers. In Figure 1, MDCK cells were seeded at 2 X 104 cells per well in Transwells (0.4 p pore size) as described previously. TEER and 14C-sucrose transport were measured daily. To determine 14C-sucrose... 

Figure 4.1 shows a schematic of a typical polymer electrolyte membrane fuel cell (PEMFC). A typical membrane electrode assembly (MEA) consists of a proton exchange membrane that is in contact with a cathode catalyst layer (CL) on one side and an anode CL on the other side they are sandwiched together between two diffusion layers (DLs). These layers are usually treated (coated) with a hydrophobic agent such as polytetrafluoroethylene (PTFE) in order to improve the water removal within the DL and the fuel cell. It is also common to have a catalyst-backing layer or microporous layer (MPL) between the CL and DL. Usually, bipolar plates with flow field (FF) channels are located on each side of the MFA in order to transport reactants to the... 

In this chapter, diffusion layers will be considered as fhe porous media that help the transport of fhe reactant fluids and producfs from one surface to another. In addition, the MPL will be defined as fhe additional layer or layers (made ouf of carbon black and water-repellenf particles) located between the CL and the DL. It is important to note that although "microporous layer" and "diffusion layer" are the common names for these components, as well as the ones used in this chapter, a number of different names can be found in the literature. 

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