Diffusion-limited surface reaction

Chemical/Physical. Matheson and Tratnyek (1994) studied the reaction of fine-grained iron metal in an anaerobic aqueous solution (15 °C) containing chloroform (107 pM). Initially, chloroform underwent rapid dehydrochlorination forming methylene chloride and chloride ions. As the concentration of methylene chloride increased, the rate of reaction appeared to decrease. After 140 h, no additional products were identified. The authors reported that reductive dehalogenation of chloroform and other chlorinated hydrocarbons used in this study appears to take place in conjunction with the oxidative dissolution or corrosion of the iron metal through a diffusion-limited surface reaction. 

Figure 6.2.2.1 Size of cellular adhesion area at various distances between the eiectrode tip and the substrate surface during the electrochemical treatment, (a) Phase contrast micrograph of HeLa cells cultured for 24 h on the BSA-coated glass substrate, which was pretreated by a Br - oxidation pulse of 30 sec at the tip-surface distance indicated in the micrograph, (b) Plots of the radius of the cell adhesion area versus the distance of electrode tip-substrate surface for the electrolysis periods of 10 sec (4) and 30 sec (O). Error bars for the plots were calculated from the standard deviation of at least four cellular patterns. Solid curves were calculated assuming a diffusion-limited surface reaction. [Reproduced with permission from H. Kaji, K. Tsukidate, T. Matsue, M. Nishizawa, J. Am. Chem. Soc. 126, 15026 (2004). Copyright 2004, American Chemical Society] (for colour version see colour section at the end of the book).

Overcoming Reaction-Diffusion Limitation Surface Catalysed Hygiene... 

Figure 3.3. Schematic representation of the adsorption, surface diffusion, and surface reaction steps identified by surface-science experiments on model supported-palladium catalysts [28]. Important conclusions from this work include the preferential dissociation of NO at the edges and defects of the Pd particles, the limited mobility of the resulting Nads and Oads species at low temperatures, and the enhancement in NO dissociation promoted by strongly-bonded nitrogen atoms in the vicinity of edge and defect sites at high adsorbate coverages. (Figure provided by Professor Libuda and reproduced with permission from the American Chemical Society, Copyright 2004).

Conde-Gallardo, A., Guerrero, M., Fragoso, R. and Castillo, N. (2006). Gas-phase diffusion and surface reaction as limiting mechanisms in the aerosol-assisted chemical vapor deposition of Ti02 films from titanium diisopropoxide. J. Mater. Res. 21(12), 3205-3209. 

Rates of chemical reactions always have a bearing on ignition, extinction, and flammability limits. There are many situations in which analyses of these phenomena reasonably may employ one-step, Arrhenius approximations to the rates. This fact enables common theories to be developed on the basis of energy considerations, which serve to correlate a number of different observed characteristics of ignition, quenching, and flammability limits. We shall focus our attention here on results explained by energy-conservation requirements and heat losses. In so doing, we exclude the consideration of special effects associated with finer details of chemical kinetics, such as radical diffusion or surface reactions. 

We see that at small particle sizes internal diffusion is no longer the sir step and that the surface reaction sequence of adsorption, surface reaction, a desorption Steps 3. 4, and 5) limit the overall rate of reaction. Consider nc one more point about internal diffusion and surface reaction. These steps through 6) are not at all affected by flow conditions external to the pellet. 

Overview In many industrial reactions, the overall rate of reaction is limited by the rate of mass transfer of reactants between the bulk fluid and the catalytic surface. By mas,s transfer, we mean any proces.s in which diffusion plays a role. In the rate laws and catalytic reaction steps described in Chapter 10 (diffusion, adsorption, surface reaction, desorption, and diffusion), we neglected the diffusion steps by saying we were operating under conditions where these steps are fast when compared to the other steps and thus could be neglected. We now examine the assumption that diffusion can be neglected. In this chapter we consider the external resistance to diffusion, and in the next chapter we consider internal resistance to diffusion. 

However, for mixed oxygen ion-electron conducting materials the surface processes can become rate limiting for oxygen transport through the membrane rather than bulk diffusion. Under surface reaction we understand the... 

The reactions of deposition or crystal growth are surface reactions. The reactants are adsorbed, more or less mobile molecules, e.g., A and in the fictitious reaction A -h B 0. These adsorbates form the substrate surface and growth is the annihilation reaction between the adsorbed reactants. The reaction rate r is expressed as usual (Chapter 6) in the reactant concentrations as r = k[ A][ B]. This can be done if the surface (the reaction space) can be considered to be a well-stirred reactor. In other words, the mobilities of A and B are high compared to the rate of the growth reaction. If that is no longer true and there is diffusion limitation the reaction can still be fitted to the above rate equation except that the reaction rate coefficient k is replaced by kit in which h — i —jS (with S being the spectral dimension). A characteristic value for his for the case of a reaction on a percolation cluster with a spectral dimension of... 

Figure 11.8 Simplified schematic to illustrate possible sources of fluctuations in corrosion current, /(-orr or corrosion potential measured at a distant reference electrode, for general corrosion with a diffusion-limited cathodic reaction such as oxygen reduction. Fluctuations leading to fluctuations in can be in (1), the transport rate of the cathodic reagent, leading to changes in diffusion-limited current (2) and (3), the relative areas of the anodic and cathodic processes, caused for example by detachment of surface scales or by changes in the electrode kinetics of these processes caused for example by the addition of corrosion inhibitors or change in surface concentration of such inhibitors (4), in the solution resistance between cathodic and anodic areas, if these are spatially separated, caused for example by fluctuations in local electrolyte composition itself linked to the occurrence of the corrosion reaction.

Figure 28. pH profile 1pm above the surface of the electrode calculated considering an oxygen diffusion limited cathodic reaction on the IM The hydrolysis reaction is considered to take place at the A1 matrix. Axisymet-rical FEM simulation (see Fig. 23). 

Catalyst Effectiveness. Even at steady-state, isothermal conditions, consideration must be given to the possible loss in catalyst activity resulting from gradients. The loss is usually calculated based on the effectiveness factor, which is the diffusion-limited reaction rate within catalyst pores divided by the reaction rate at catalyst surface conditions (50). The effectiveness factor E, in turn, is related to the Thiele modulus,

first-order rate constant, a the internal surface area, and the effective diffusivity. It is desirable for E to be as close as possible to its maximum value of unity. Various formulas have been developed for E, which are particularly usehil for analyzing reactors that are potentially subject to thermal instabilities, such as hot spots and temperature mnaways (1,48,51). 

The effectiveness of a porous catalyst T] is defined as the actual diffusion-limited reaction rate divided by the reaction rate that could have been achieved if all the internal surface had been at bulk concentration conditions. 

Very recently, considerable effort has been devoted to the simulation of the oscillatory behavior which has been observed experimentally in various surface reactions. So far, the most studied reaction is the catalytic oxidation of carbon monoxide, where it is well known that oscillations are coupled to reversible reconstructions of the surface via structure-sensitive sticking coefficients of the reactants. A careful evaluation of the simulation results is necessary in order to ensure that oscillations remain in the thermodynamic limit. The roles of surface diffusion of the reactants versus direct adsorption from the gas phase, at the onset of selforganization and synchronized behavior, is a topic which merits further investigation. 

Olefins are hydrogenated very easily, unless highly hindered, over a variety of catalysts. With active catalysts, the reaction is apt to be diffusion limited, since hydrogen can be consumed faster than it can be supplied to the catalyst surface. Most problems connected with olefin hydrogenation involve some aspect of regio- or stereoselectivity. Often the course of reduction is influenced greatly by the catalyst, by reaction variables, and by hydrogen availability at the catalyst surface. 

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