Heterogeneous reactions, interfaces

The solvent used in catalytic hydrogenation is chosen for its ability to dissolve the alkene and is typically ethanol, hexane, or acetic acid. The metal catalysts are insoluble in these solvents (or, indeed, in any solvent). Two phases, the solution and the metal, aie present, and the reaction takes place at the interface between them. Reactions involving a substance in one phase with a different substance in a second phase aie called heterogeneous reactions. 

Our interest is in solution kinetics, so we will concern ourselves only with homogeneous reactions, which take place in a single phase. Heterogeneous reactions take place, at least in part, at interfaces between phases.) Further, we will mainly work with closed systems, those in which matter is neither gained nor lost during the period of observation. 

To describe hypergolic heating, Anderson and Brown (A10) proposed a theoretical model based upon spontaneous exothermic heterogeneous reactions between the reactive oxidizer and a condensed phase at the gas-solid interface. In these studies, the least complex case was considered, i.e., the one in which the solid phase is instantaneously exposed to a stagnant (nonflowing) gaseous oxidizer environment. This situation can be achieved experimentally provided the sample to be tested is suddenly injected into the desired environment in a manner designed to minimize gas flow. 

Fig. 20. Heterogeneous reactions occurring at oxidizer-particle-polymeric-binder interface (A6).

The role of mixing in heterogeneous reactions is obvious. In multiphase processes mixing imposed by a stirrer or an external pump is necessary to increase the interface through which reactants pass to meet their partner in the other phase and/or to intensify mass transfer between phases. Mixing can also play a significant role in the case of homogeneous reactions. Chemical reactions occur at the molecular level. Reactant molecules introduced into a reactor encounter the environment in the vicinity of the inlet. The composition of the mixture there is obviously... 

Similarly to charge-transfer processes at solid-electrolyte interfaces, the ET rate for heterogeneous reactions at ITIES is determined by the flux of reactants to the interface as well... 

Early studies of ET dynamics at externally biased interfaces were based on conventional cyclic voltammetry employing four-electrode potentiostats [62,67 70,79]. The formal pseudo-first-order electron-transfer rate constants [ket(cms )] were measured on the basis of the Nicholson method [99] and convolution potential sweep voltammetry [79,100] in the presence of an excess of one of the reactant species. The constant composition approximation allows expression of the ET rate constant with the same units as in heterogeneous reaction on solid electrodes. However, any comparison with the expression described in Section II.B requires the transformation to bimolecular units, i.e., M cms . Values of of the order of 1-2 x lO cms (0.05 to O.IM cms ) were reported for Fe(CN)g in the aqueous phase and the redox species Lu(PC)2, Sn(PC)2, TCNQ, and RuTPP(Py)2 in DCE [62,70]. Despite the fact that large potential perturbations across the interface introduce interferences in kinetic analysis [101], these early estimations allowed some preliminary comparisons to established ET models in heterogeneous media. 

As heterogeneous reactions at the interface electrode-electrolyte, electrochemical reactions are intrinsically more complex than typical (thermal) chemical transformations (Figure 1). We mostly neglect the exact structure of the interface in the following description. Transport of the educt... 

Electron movement across the electrode solution interface. The rate of electron transfer across the electrode solution interface is sometimes called k. This parameter can be thought of as a rate constant, although here it represents the rate of a heterogeneous reaction. Like a rate constant, its value is constant until variables are altered. The rate constants of chemical reactions, for example, increase exponentially with an increasing temperature T according to the Arrhenius equation. While the rate constant of electron transfer, ka, is also temperature-dependent, we usually perform the electrode reactions with the cell immersed in a thermostatted water bath. It is more important to appreciate that kei depends on the potential of the electrode, as follows ... 

In the above expression, ci k is the concentration of species i in phase k, and si kj is the stoichiometric coefficient of species i in phase k participating in heterogeneous reaction 1 (see eq 8). is the specific surface area (surface area per unit total volume) of the interface between phases k and p. ih.k- is the normal interfacial current transferred per unit interfacial area across the interface between the electronically conducting phase and phase k due to electron-transfer reaction h, and it is positive in the anodic direction. In the above expression, Faraday s law... 

The second type is simple phase transitions in which one phase transforms into another of identical composition, e.g., diamond graphite, quartz coe-site, and water ice. This type sounds simple, but it involves most steps of heterogeneous reactions, including nucleation, interface reaction, and coarsening. 

The mathematical difficulty increases from homogeneous reactions, to mass transfer, and to heterogeneous reactions. To quantify the kinetics of homogeneous reactions, ordinary differential equations must be solved. To quantify diffusion, the diffusion equation (a partial differential equation) must be solved. To quantify mass transport including both convection and diffusion, the combined equation of flow and diffusion (a more complicated partial differential equation than the simple diffusion equation) must be solved. To understand kinetics of heterogeneous reactions, the equations for mass or heat transfer must be solved under other constraints (such as interface equilibrium or reaction), often with very complicated boundary conditions because of many particles. 

In this chapter, the essential aspects of kinetics of heterogeneous reactions (nucleation, interface reaction, and mass/heat transfer) are first presented. Then one class of heterogeneous reactions, the dissolution and growth of crystals, bubbles, and droplets, is elaborated in great detail. Some other heterogeneous reactions are then discussed with examples. Many complex problems in heterogeneous reactions remain to be solved. 

If the interface reaction rate is extremely small so that mass/heat transfer is rapid enough to transport nutrients to the interface, then interface reaction rate (Equation 4-33) is the overall heterogeneous reaction rate (Figure 1-lla). If the interface reaction is relatively rapid and if the crystal composition is different from the melt composition, the heterogeneous reaction rate may be limited or slowed down by the mass transfer rate because nutrients must be transported to the interface and extra junk must be transported away from the interface (Figures 1-llb and 1-llc). If the crystal composition is the same as the melt composition, then mass transfer is not necessary. When interface reaction rate and mass transfer rate are comparable, both interface reaction and mass transfer would control the overall heterogeneous reaction (Figure 1-lld). 

Experimental investigations will continue to play a critical role in understanding heterogeneous reaction kinetics, such as mineral dissolution rates in silicate melts and in aqueous solutions, the melting rates at the interfaces of two... 

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