Combined surface exchange/diffusion

The different elementary steps involved in a combined surface exchange/ diffusion process can be summarized as follows for <7e ffy -... 

At one extreme diffusivity may be so low that chemical reaction takes place only at suface active sites. In that case p is equal to the fraction of active sites on the surface of the catalyst. Such a polymer-supported phase transfer catalyst would have extremely low activity. At the other extreme when diffusion is much faster than chemical reaction p = 1. In that case the observed reaction rate equals the intrinsic reaction rate. Between the extremes a combination of intraparticle diffusion rates and intrinsic rates controls the observed reaction rates as shown in Fig. 2, which profiles the reactant concentration as a function of distance from the center of a spherical catalyst particle located at the right axis, When both diffusion and intrinsic reactivity control overall reaction rates, there is a gradient of reactant concentration from CAS at the surface, to a lower concentration at the center of the particle. The reactant is consumed as it diffuses into the particle. With diffusional limitations the active sites nearest the surface have the highest turnover numbers. The overall process of simultaneous diffusion and chemical reaction in a spherical particle has been described mathematically for the cases of ion exchange catalysis,63 65) and catalysis by enzymes immobilized in gels 66-67). Many experimental parameters influence the balance between intraparticle diffusional and intrinsic reactivity control of reaction rates with polymer-supported phase transfer catalysts, as shown in Fig. 1. 

Besides interacting with suspended particles, a chemical also undergoes direct exchange at the sediment surface by diffusion and advection into the hyporheic zone. Furthermore, resuspension followed by exchange between water and particles also adds to the sediment-water interaction. These processes have been extensively discussed in Chapter 23, especially in Box 23.2. There we concluded that the effect from the different mechanisms can be combined into a flux of the form (see Eq. 23-25) ... 

As an alternative to DET, small, artificial substrate/co-substrate electroactive molecules (mediators) can be used to shuttle electrons between the enzyme and the electrode (Figure 5.3b). This involves a process in which the enzyme takes part in the first redox reaction with the substrate and is re-oxidized or reduced by the mediator which in turn is regenerated, through a combination of physical diffusion and self-exchange, at the electrode surface. The mediator circulates continuously between the enzyme and the electrode, cycled between its oxidized and reduced forms, producing current. This process is known as mediated electron transfer (MET). 

Again, for the purpose of this chapter, this step is deflned as any process which is unaffected by the agitation conditions, e.g. the surface integration step in crystallization and the combined in-pore diffusion and chemical reaction at the surface associated with such particles as ion-exchange resins and catalysts. Figure 17.2 shows diagrammatically this idealized two-step mechanism. 

Let us consider a perovskite membrane covered by a film of metal nanoparticles (e.g., Ni). In such a situation, the different elementary steps involved in a combined H2 splitting over Ni, surface exchange at the feed/perovskite and perme-ate/perovskite membrane sides, and diffusion process within the perovskite membrane can be summarized as follows for Ue ... 

Extension of the equilibrium model to column or field conditions requires coupling the ion-exchange equations with the transport equations for the 5 aqueous species (Eq. 1). To accomplish this coupling, we have adopted the split-operator approach (e.g., Miller and Rabideau, 1993), which provides considerable flexibility in adjusting the sorption submodel. In addition to the above conceptual model, we are pursuing more complex formulations that couple cation exchange with pore diffusion, surface diffusion, or combined pore/surface diffusion (e.g., Robinson et al., 1994 DePaoli and Perona, 1996 Ma et al., 1996). However, the currently available data are inadequate to parameterize such models, and the need for a kinetic formulation for the low-flow conditions expected for sorbing barriers has not been established. These issues will be addressed in a future publication. 

Even where ion exchange is not affected by the above factors, the Nernst-Planck equations are not very useful for diffusion phenomena in the film. After all, the Nernst film is somewhat enigmatic and there is a combination of diffusive and convective mass transfer that changes from the bulk solution to the particle surface. Nernst (1904) originally defined the outer limit of film only as the point where the concentration profile, if linearly extrapolated from the particle surface, reaches the concentration level of the bulk solution. 

From the NMR tracer desorption and self-diffusion data (second and third lines of Table I), one obtains the relation Timm > TmlL. In the example given, intercrystalline molecular exchange is limited, therefore, by transport resistances at the surface of the individual crystals. Combined NMR and high-resolution electron microscopy studies 54) suggest that such surface barriers are caused by a layer of reduced permeability rather than by a mere deposit of impenetrable material on the crystal surface, although that must not be the case in general. 

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