Interface kinetics

Although the SOFC community has generally maintained an empirical approach to the three-phase boundary longer than the aqueous and polymer literature, the last 20 years have seen a similar transformation of our understanding of SOFC cathode kinetics. Few examples remain today of solid-state electrochemical reactions that are not known to be at least partially limited by solid-state or surface diffusion processes or chemical catalytic processes remote from the electrochemical—kinetic interface. 

Equation (4.119) reflects the dynamic situation at the interface. For higher order approximations we have to introduce kinetic interface models. This will be done for different phase boundaries in Chapter 10. At this point we introduce the most simple assumption the interface is a kinetic barrier which must be overcome by the individual ions through thermal activation. In such a model, the externally applied electric field increases the activation barrier in one direction and decreases it in the reverse direction. Letting a denote the asymmetry factor of the barrier, we can then formulate... 

In electrode kinetics, interface reactions have been extensively modeled by electrochemists [K.J. Vetter (1967)]. Adsorption, chemisorption, dissociation, electron transfer, and tunneling may all be rate determining steps. At crystal/crystal interfaces, one expects the kinetic parameters of these steps to depend on the energy levels of the electrons (Fig. 7-4) and the particular conformation of the interface, and thus on the crystal s relative orientation. It follows then that a polycrystalline, that is, a (structurally) inhomogeneous thin film, cannot be characterized by a single rate law. 

The width of the relaxation zone R, which is the thickness of the kinetic interface , may differ considerably from other lengths characterizing other properties of an interface (e.g., space charge width, elastic deformation width). 

The Dimensionless Relationship as Kinetic Interface Property Transfer Relationship... 

Figure 8 Adsorption kinetics (interface air-water) of cruciferin from rape-seed at various degrees of succinylation (pH 9.2, 1 = 0.15). 1, unmodified 2, 19% 3, 60% 4, 66% and 5, 84% succinylated. y = interfacial tension. (From Ref. 21.)...

Measuring the IPCE is also useful to determine the band gap. The band gap derived from IPCE may be higher than that obtained by optical spectroscopy techniques (see Chapter UV-Vis Spectroscopy ), since the onset of photocurrent may be limited by slow kinetics ( /interface) and/or electron transport ( /transport) This will have a minimum uncertainty of half of the wavelength step or bandpass (full-width at half maximum, or FWHM) used. Performing IPCE while applying a constant bias often increases the measured photocurrent, which could be due to either a shift of the Fermi level at the CE (not applicable in a three-electrode measurement) or due to increased carrier collection at the WE as a result of an increased depletion width. 

Mrol] Mrowec, S., Walec, T., Werber, T., The Kinetics of High-Tcmpcraturc Sulphurization of Iron-Chromium Alloys , Bull. Acad. Pol. Sci. Chim., 16(4), 221—I M (1968) (Experimental, Kinetics, Interface Phenomena, 8)... 

Sha2] Sharma, R.C., Purdy, G.R., Kirkaldy, J.S., Kinetics of the Pearlite Reaction in Fe-C-Cr , Metall. Trans. A, 10A(8), 1129-1139 (1979) (Phase Relations, Experimental, Calculation, Kinetics, Interface Phenomena, 32)... 

Hel] Heller, W., Brauner, J., Investigations on the Diffusion and Precipitation of Carbon in Ferritic Iron-Nickel Alloys by Measuring the Damping Capacity (in German), Arch. Eisenhuettenwes., 35(11), 1105-1110 (1964) (Experimental, Kinetics, Interface Phenomena, Phase Relations, 13)... 

In addition to extractive reaction, mass transfer is another important influence factor in the extraction process. When the mass transfer reached a stable state, the whole systems can keep a dynamic balance. The mass transfer happened between the aqueous phase and ILs, and the extraction kinetics interface of RE"" (n = 3 or 4) in ILs was shown in Fig. 5.6. Because the mass transfer rate also affects the extraction rate, the rate of RE " extraction is determined both by the chemical reaction rate and the mass transfer rate. Which one is more important in the two main factors is up to the experimental conditions. 

Pav] Pavlovsky, J., Diffirsion of Fe and Co in Co-Fe-B Amorphous Alloys , Metal. Mater., 32(2), 87-90 (1994), translated fiom Kovove Mater., 32(2), 126-131 (1994) (Kinetics, Interface Phenomena, Thermodyn., Experimental, 9)... 

Qualitative examples abound. Perfect crystals of sodium carbonate, sulfate, or phosphate may be kept for years without efflorescing, although if scratched, they begin to do so immediately. Too strongly heated or burned lime or plaster of Paris takes up the first traces of water only with difficulty. Reactions of this type tend to be autocat-alytic. The initial rate is slow, due to the absence of the necessary linear interface, but the rate accelerates as more and more product is formed. See Refs. 147-153 for other examples. Ruckenstein [154] has discussed a kinetic model based on nucleation theory. There is certainly evidence that patches of product may be present, as in the oxidation of Mo(lOO) surfaces [155], and that surface defects are important [156]. There may be catalysis thus reaction VII-27 is catalyzed by water vapor [157]. A topotactic reaction is one where the product or products retain the external crystalline shape of the reactant crystal [158]. More often, however, there is a complicated morphology with pitting, cracking, and pore formation, as with calcium carbonate [159]. 

M. Grunze and H. J. Kreuzer, eds.. Kinetics of Interface Reactions, Springer-Verlag, Berlin, 1987. 

Auerbaoh D J and Rettner C T 1987 Preoursor states, myth or reaiity a perspeotive from moieouiar beam studies Kinetics of Interface Reactions ed M Grunze and H J Kreuzer (Beriin Springer) p 125... 

We now consider how one extracts quantitative infonnation about die surface or interface adsorbate coverage from such SHG data. In many circumstances, it is possible to adopt a purely phenomenological approach one calibrates the nonlinear response as a fiinction of surface coverage in a preliminary set of experiments and then makes use of this calibration in subsequent investigations. Such an approach may, for example, be appropriate for studies of adsorption kinetics where the interest lies in die temporal evolution of the surface adsorbate density N. ... 

The applications of this simple measure of surface adsorbate coverage have been quite widespread and diverse. It has been possible, for example, to measure adsorption isothemis in many systems. From these measurements, one may obtain important infomiation such as the adsorption free energy, A G° = -RTln(K ) [21]. One can also monitor tire kinetics of adsorption and desorption to obtain rates. In conjunction with temperature-dependent data, one may frirther infer activation energies and pre-exponential factors [73, 74]. Knowledge of such kinetic parameters is useful for teclmological applications, such as semiconductor growth and synthesis of chemical compounds [75]. Second-order nonlinear optics may also play a role in the investigation of physical kinetics, such as the rates and mechanisms of transport processes across interfaces [76]. 

Since the electron density p(x) oc /(v)p, where /(v) is die electron wavefiinction, this implies that the electron wavefiinction varies in a similarly step-wise fashion at the interface. This indicates that d i //dx, where s indicates that the derivative is evaluated at the surface, becomes infinite. Since the electron kinetic... 

Electrode processes are a class of heterogeneous chemical reaction that involves the transfer of charge across the interface between a solid and an adjacent solution phase, either in equilibrium or under partial or total kinetic control. A simple type of electrode reaction involves electron transfer between an inert metal electrode and an ion or molecule in solution. Oxidation of an electroactive species corresponds to the transfer of electrons from the solution phase to the electrode (anodic), whereas electron transfer in the opposite direction results in the reduction of the species (cathodic). Electron transfer is only possible when the electroactive material is within molecular distances of the electrode surface thus for a simple electrode reaction involving solution species of the fonn... 

With SECM, almost any kind of electrochemical measurement may be carried out, whether voltaimnetric or potentiometric, and the addition of spatial resolution greatly increases the possibilities for the characterization of interfaces and kinetic measurements [, and 59]. It may be employed as an electrochemical tool... 

By virtue of their simple stnicture, some properties of continuum models can be solved analytically in a mean field approxunation. The phase behaviour interfacial properties and the wetting properties have been explored. The effect of fluctuations is hrvestigated in Monte Carlo simulations as well as non-equilibrium phenomena (e.g., phase separation kinetics). Extensions of this one-order-parameter model are described in the review by Gompper and Schick [76]. A very interesting feature of tiiese models is that effective quantities of the interface—like the interfacial tension and the bending moduli—can be expressed as a fiinctional of the order parameter profiles across an interface [78]. These quantities can then be used as input for an even more coarse-grained description. 

Hidalgo-Alvarez R, Martin A, Fernandez A, Bastes D, Martinez F and de las Nieves F J 1996 Electro kinetic properties, colloidal stability and aggregation kinetics of polymer colloids Adv. Colloid Interface Sc/. 67 1-118... 

Kinetic studies have benefited immensely from microcomputers. Whereas dedicated software is often necessary for interfacing to specific instmments, data analysis can be carried out using readily available software materials capable of producing high quaUty graphical output. Most recentiy, it has become common to measure concentrations in some way that produces digital data that is entered automatically into the computer (see Computer technology). 

Ceramic—metal interfaces are generally formed at high temperatures. Diffusion and chemical reaction kinetics are faster at elevated temperatures. Knowledge of the chemical reaction products and, if possible, their properties are needed. It is therefore imperative to understand the thermodynamics and kinetics of reactions such that processing can be controlled and optimum properties obtained. 

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