Diffusion Controlled Interfacial Reaction

In a multiphase stratified flow, the interfaces between immiscible fluids have several characteristics. Firstly, the specific interfacial area can be very large just as droplet-based flow. It can for example be about 10,000 m in a microchannel compared with only 100 m for conventional reactors used in chemical processes. Secondly, the mass transfer coefficient can be very high because of the small transfer distance and high specific interfacial area. It is more than 100 times larger than that achieved in typical industrial gas-liquid reactors. Thirdly, the interfaces of a stratified microchannel flow can be treated as nano-spaces. Simulation results show that the width of the interfaces of a stratified flow is in nanometers, and that diffusion-based mixing occurs at the interface. The interface width can be experimentally adjusted by adding surfactants. Finally, reactants only contact and react with each other at the interface. Therefore, the interfaces supply us with mediums to study interfacial phenomena, diffusion-controlled interfacial reactions and extraction. 

Kinetics of chemical reactions at liquid interfaces has often proven difficult to study because they include processes that occur on a variety of time scales [1]. The reactions depend on diffusion of reactants to the interface prior to reaction and diffusion of products away from the interface after the reaction. As a result, relatively little information about the interface dependent kinetic step can be gleaned because this step is usually faster than diffusion. This often leads to diffusion controlled interfacial rates. While often not the rate-determining step in interfacial chemical reactions, the dynamics at the interface still play an important and interesting role in interfacial chemical processes. Chemists interested in interfacial kinetics have devised a variety of complex reaction vessels to eliminate diffusion effects systematically and access the interfacial kinetics. However, deconvolution of two slow bulk diffusion processes to access the desired the fast interfacial kinetics, especially ultrafast processes, is generally not an effective way to measure the fast interfacial dynamics. Thus, methodology to probe the interface specifically has been developed. 

Manufacture and Processing. Mononitrotoluenes are produced by the nitration of toluene in a manner similar to that described for nitrobenzene. The presence of the methyl group on the aromatic ring faciUtates the nitration of toluene, as compared to that of benzene, and increases the ease of oxidation which results in undesirable by-products. Thus the nitration of toluene generally is carried out at lower temperatures than the nitration of benzene to minimize oxidative side reactions. Because toluene nitrates at a faster rate than benzene, the milder conditions also reduce the formation of dinitrotoluenes. Toluene is less soluble than benzene in the acid phase, thus vigorous agitation of the reaction mixture is necessary to maximize the interfacial area of the two phases and the mass transfer of the reactants. The rate of a typical industrial nitration can be modeled in terms of a fast reaction taking place in a zone in the aqueous phase adjacent to the interface where the reaction is diffusion controlled. 

All these results are consistent with the hypothesis that aryl cations react in aqueous media at diffusion-controlled rates with all nucleophiles that are available in the immediate neighbourhood of the diazonium ion. On this basis Romsted and coworkers (Chaudhuri et al., 1993a, 1993b) used dediazoniation reactions as probes of the interfacial composition of association colloids. These authors determined product yields from dediazoniation of two arenediazonium tetrafluoroborates containing ft-hexadecyl residues (8.15 and 8.16) and the corresponding diazonium salts with methyl groups instead of Ci6H33 chains. ... 

The retarding influence of the product barrier in many solid—solid interactions is a rate-controlling factor that is not usually apparent in the decompositions of single solids. However, even where diffusion control operates, this is often in addition to, and in conjunction with, geometric factors (i.e. changes in reaction interfacial area with a) and kinetic equations based on contributions from both sources are discussed in Chap. 3, Sect. 3.3. As in the decompositions of single solids, reaction rate coefficients (and the shapes of a—time curves) for solid + solid reactions are sensitive to sizes, shapes and, here, also on the relative dispositions of the components of the reactant mixture. Inevitably as the number of different crystalline components present initially is increased, the number of variables requiring specification to define the reactant completely rises the parameters concerned are mentioned in Table 17. 

Many of the electrochemical techniques described in this book fulfill all of these criteria. By using an external potential to drive a charge transfer process (electron or ion transfer), mass transport (typically by diffusion) is well-defined and calculable, and the current provides a direct measurement of the interfacial reaction rate [8]. However, there is a whole class of spontaneous reactions, which do not involve net interfacial charge transfer, where these criteria are more difficult to implement. For this type of process, hydro-dynamic techniques become important, where mass transport is controlled by convection as well as diffusion. 

As reversible ion transfer reactions are diffusion controlled, the mass transport to the interface is given by Fick s second law, which may be directly integrated with the Nernst equation as a boundary condition (see, for instance. Ref. 230 232). A solution for the interfacial concentrations may be obtained, and the maximum forward peak may then be expressed as a function of the interfacial area A, of the potential scan rate v, of the bulk concentration of the ion under study Cj and of its diffusion coefficient D". This leads to the Randles Sevcik equation [233] ... 

When the rate constants are large numbers (fast reactions), both the numerators and the denominators of Eq. (5.94) can be divided by k-. Since kjk. = A da and ( i) can be neglected relative to the other terms in the sum (A da A + A -I- A ), an equation identical with Eq. (5.73) is obtained for which only diffusion controls the partition rate. At the other extreme, when interfacial film diffusion is very fast, and the reactions are very slow, we can set 1 > QcA + k-i A ) and the rate equation becomes equal to... 

It is shown elsewhere (Section 7.9.2) that an approximate numerical formula for this limiting diffusion current iL is iL = 0.02 nc, where n is the number of electrons used in one step of the overall reaction in the electrode and c is the concentration of the reactant in moles liter-1. Hence, at 0.01 M, and n = 2, say, iL = 0.4 mA cm-2—a current density less than may be desirable for many purposes. The problem is how to increase this diffusion-controlled limiting current density and obtain data on the interfacial reaction free of interference by transport at increasingly high current densities. 

The value of t is important for a reason connected with the equation 5( = (nDt). As long as the time t in this equation is small, the limiting diffusion current, iL, will be large (for iL = DzFci/(nDt)U2 and hence diffusion control will be negligible [(1 /i) = 1 /ip) + (1 /iL)] and the region C-D of the transient will represent the interfacial electrode reaction. (However, t must be greater than x to reach the steady state.)... 

Quasi-reversible Less used The interfacial overpotential is < RT/F and the reaction is controlled both by diffusion and interfacial processes... 

The primary effect of micelles on light-induced electron transfer involves the intervention of an interfacial region which can significantly influence the radical ion association and dissociation equilibria by a combination of electrostatic and hydro-phobic interactions. Diffusive encounters of reaction partners are controlled within a micelle by the diffusion of one reactant to the highly polar surface, by collision of two reactants confined within the hydrophobic region in the interior of the micelle, and by the reaction of two reactants whose motions are confined to diffusion along the micellar surface. 

An alternative approach is to make the simplification that the rate of chemical reaction is fast compared to the rate of diffusion that is, the membrane diffusion is rate controlling. This approximation is a good one for most coupled transport processes and can be easily verified by showing that flux is inversely proportional to membrane thickness. If interfacial reaction rates were rate controlling, the flux would be constant and independent of membrane thickness. Making the assumption that chemical equilibrium is reached at the membrane interfaces allows the coupled transport process to be modeled easily [9], The process is... 

When an ionic single crystal is immersed in solution, the surrounding solution becomes saturated with respect to the substrate ions, so, initially the system is at equilibrium and there is no net dissolution or growth. With the UME positioned close to the substrate, the tip potential is stepped from a value where no electrochemical reactions occur to one where the electrolysis of one type of the lattice ion occurs at a diffusion controlled rate. This process creates a local undersaturation at the crystal-solution interface, perturbs the interfacial equilibrium, and provides the driving force for the dissolution reaction. The perturbation mode can be employed to initiate, and quantitatively monitor, dissolution reactions, providing unequivocal information on the kinetics and mechanism of the process. 

In practice, the amount of solid molecules on the surface being exposed to the solution is difficult or even impossible to quantify. Instead, the solid surface area to solution volume ratio is often used to quantify the amount of solid reactant. Therefore, experimentally determined second-order rate constants for interfacial reactions have the unit m s h As the true surface area of the solid is very difficult to determine, the BET (Brunauer-Emmett-Teller) surface area is fte-quentiy used. The maximum diffusion-controlled rate constant for a particle suspension containing pm-sized particles is ca 10 m s and for mm-sized particle suspensions the corresponding value is I0 m s h Unfortunately, the discrepancy between the true surface area and the BET surface area and the non-spherical geometry of the solid particles makes it impossible to exactly determine the theoretical diffusion-controlled rate constant. 

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