Activation bulk diffusion through

The mechanism of surface diffusion has been much studied by Miyabe and Guiochon [116-122]. These authors showed that the activation energy of surface diffusion can be considered as the sum of two terms. The first one is the energy needed to make a hole in the mobile phase. It is independent of the adsorption energy of the solute considered but depends only on the nature of the mobile phase. The second contribution is the energy needed for the molecule of adsorbate to jump from the monolayer into this hole. This activation energy is proportional to the isosteric heat of adsorption. Experimental results confirmed that the values of the surface diffusion coefficients of several series of compounds are related to those of their bulk diffusivities through the equation ... 

In principle, different reference electrodes may be used if the cell is provided with a separate compartment and a Luggin capillary. But if the flow cell technique is to be applied, it is more convenient to avoid the use of capillaries where the solution cannot be easily exchanged. Active bulk components could diffuse through the capillary and give rise to erroneous responses. A small palladium gauze charged with hydrogen directly immersed in the solution can be used as the reference electrode (PdH ) [18]. 

Model calculations have demonstrated that active cells are surrounded by zones containing substrate concentrations lower than those of the bulk liquid [12-14], This concentration gradient results from the dynamic interplay between the rates of substrate uptake and diffusion through the diffusion layer surrounding the cell (see [15] for details). Boone et al. [13] developed a model using spherical coordinates that allows calculation of the diffusive substrate flux to a suspended spherical cell. In their model calculations, the cell surface concentration was set to arbitrary values between zero and about half of the bulk concentration. It... 

On the other hand, the work by Yan et al. and Jin et al. using silicon wafers and Ni as catalysts has suggested that bulk silicon would diffuse through the nanoparticles to produce SiNW. In this case, solid silicon in the wafer reacts with Ni catalysts to directly make SiNW. If this is true, it falls into the category of root growth. However, as we will illustrate below, the use of hydrogen in the presence of metal catalysts may activate a new reaction pathway that converts Si in the substrate into silane. As a result, the suggested solid-liquid-solid model may actually be the VLS model at work. 

Fig. 17. Scheme of the active oxygen migration through bulk diffusion in Bi2Mo,0 2/... 

The concept proposed by us is pictured simply in Fig. 23. The level of water represents the chemical potential of active oxygen involved in the oxidation of propylene, and the vessels connected on the tank are involved in two kinds of active sites that activate molecular oxygen to atomic species and oxidize propylene to acrolein. If active sites expressed by vessels are isolated from each other, each site must do everything by itself to convert propylene to acrolein. This situation is less convenient than the preparation of the active catalyst system. When active species of oxygen can migrate rapidly through the bulk diffusion of oxide ion as shown in Fig. 23, equal-... 

If the activity of the immobilised catalyst is sufficiently high, the reaction which it mediates occurs essentially at the interface between the catalyst and the substrate solution. In the case of the surface immobilised enzyme or a thin microbial film this will, of course, occur irrespective of the level of activity. Under these conditions the limiting process for transporting substrate from the bulk of the solution to the immobilised enzyme is molecular or convective diffusion through the layer of solution immediate to the carrier. Under steady-state conditions, the rate of reaction at the active sites is equal to the rate at which substrate arrives at the site. This... 

The immobilization of enzymes may introduce a new problem which is absent in free soluble enzymes. It is the mass-transfer resistance due to the large particle size of immobilized enzyme or due to the inclusion of enzymes in polymeric matrix. If we follow the hypothetical path of a substrate from the liquid to the reaction site in an immobilized enzyme, it can be divided into several steps (Figure 3.2) (1) transfer from the bulk liquid to a relatively unmixed liquid layer surrounding the immobilized enzyme (2) diffusion through the relatively unmixed liquid layer and (3) diffusion from the surface of the particle to the active site of the enzyme in an inert support. Steps... 

Figure 7 further shows that, as gaseous C02 moves up the absorber, phase equilibrium is achieved at the vapor-liquid interface. C02 then diffuses through the liquid film while reacting with the amines before it reaches the bulk liquid. Each reaction is constrained by chemical equilibrium but does not necessarily reach chemical equilibrium, depending primarily on the residence time (or liquid film thickness and liquid holdup for the bulk liquid) and temperature. Certainly kinetic rate expressions and the kinetic parameters need to be established for the kinetics-controlled reactions. While concentration-based kinetic rate expressions are often reported in the literature, activity-based kinetic rate expressions should be used in order to guarantee model consistency with the chemical equilibrium model for the aqueous phase solution chemistry. 

Washcoat thickness is analogous to particle size in that reactants must penetrate its pore structure and interact with the dispersed active sites. The products produced must diffuse through the structure and out into the bulk gas. This phenomenon differs from that involving a particle in that only the gas-solid washcoat surface is available since the other side is bonded to the wall of the monolith. 

The main reason a porous gas electrode is so active,7 therefore, is that it allows particularly large maximum diffusion currents by diffusion through (fairly) thin meniscus layers. But this thesis brings a corresponding antithesis because it implies that farther up the pore where there is no meniscus but bulk solution, the gaseous... 

Two effects cause the low production capacity of large-grained catalyst. First, large grain size retards transport of the ammonia formed inside the catalyst into the bulk gas stream. This is because the ammonia transport proceeds by slow diffusion through the pore system. The second effect is a consequence of the fact that a single catalyst grain in the oxide state reduces from the outside to the interior of the particle. The water vapor produced inside the catalyst by reduction comes into contact with already reduced catalyst on its way to the outer surface of the catalyst. This induces a severe recrystallization. As an example, if the particle size increases from about 1 to 8 mm, the inner surface decreases from 11 to 16 m2/g to 3 to 8 m2/g74. Therefore the choice of catalyst requires the optimization of 1) catalyst size versus catalyst activity, 2) catalyst size versus pressure drop across the converter and 3) the impact of 1 and 2 on... 

Figure 5. Schematic arrangement of the surface of a partly crystallized E-L TM amorphous alloy such as Pd-Zr. A matrix of zirconia consisting of the two polymorphs holds particles of the L transition metal (Pd) which are structured in a skin of solid solution with oxygen (white) and a nucleus of pure metal (black). The arrows indicate transport pathways for activated oxygen either through bulk diffusion or via the top surface. An intimate contact with a large metal-to-oxide interface volume with ill-defined defective crystal structures (shaded area) is essential for the good catalytic performance. The figure is compiled from the experimental data in the literature [26, 27].

The rate and selectivity of a surface-catalyzed reaction can be affected by the existence of concentration or temperature gradients in the quiescent layer of fluid which surrounds the catalyst particle or is contained within its pores upon whose surface much of the exposed active material is distributed. The reactants in the bulk phase reach the reactive sites by diffusion through these regions of the fluid, and they affect the kinetics when the rates of the surface-catalyzed reactions are fast relative to the rate of transport of reactants to the catalytic sites. In the hydrogenation of unsaturated liquids or compounds in solution, the agitation of the liquid-catalyst mixture must be adequate to assure that the solution remains saturated with hydrogen. 

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