Interface nonlinear kinetics

Linde, H., Schwartz, R, and Wilke, H., Dissipative structures and nonlinear kinetics of the Marangoni instability, in Dynamics and Instability of Fluid Interfaces, Sorensen, T.S. (ed.). Springer-Verlag, Berlin, 1979, p. 75. 

The properties of many industrial materials are determined by the local properties of interfaces. The kinetics of gas/solid heterogeneous processes may be determined by the electric field that is generated as a result of segregation. This effect has many applied aspects. Also, the properties of materials that exhibit nonlinear characteristics are determined by interface composition and stracture. 

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]. 

Clearly, then, the chemical and physical properties of liquid interfaces represent a significant interdisciplinary research area for a broad range of investigators, such as those who have contributed to this book. The chapters are organized into three parts. The first deals with the chemical and physical structure of oil-water interfaces and membrane surfaces. Eighteen chapters present discussion of interfacial potentials, ion solvation, electrostatic instabilities in double layers, theory of adsorption, nonlinear optics, interfacial kinetics, microstructure effects, ultramicroelectrode techniques, catalysis, and extraction. 

As this volume attests, a wide range of chemistry occurs at interfacial boundaries. Examples range from biological and medicinal interfacial problems, such as the chemistry of anesthesia, to solar energy conversion and electrode processes in batteries, to industrial-scale separations of metal ores across interfaces, to investigations into self-assembled monolayers and Langmuir-Blodgett films for nanoelectronics and nonlinear optical materials. These problems are based not only on structure and composition of the interface but also on kinetic processes that occur at interfaces. As such, there is considerable motivation to explore chemical dynamics at interfaces. 

The function f(it) can be given in a concrete expression as "S"-shape nonlinear function, schematically shown on the left in Figure 8A. For the convenience of analysis we take the approximation to express the "S"-shape characteristics with the combination of two straight lines as shown on the right in Figure 8A. The third term of Equation 2-2 means the increment of [D] with compression at the air/water interface. To simplify the analysis, we further assume kj k i. This assumption is consistent with the observed stability of the bilayers formed at the zero surface pressure point. The kinetics of [D] can be then expressed as... 

Recently we have found that sustained electrical oscillations are generated in a liquid membrane consisting of water/oil phase, where the aqueous phase contains surfactant and alcohol [3,10]. The difference between the concentrations in the aqueous and the oil phases forms the driving force of electrical oscillations. In the last section, we would like to describe this type of rhythmic oscillation from the point of view of the nonlinearity in the kinetics of transfer of lipid molecules through the oil/water interface. It is... 

Figure 26. Predictions of the Adler model shown in Figure 25 assuming interfacial electrochemical kinetics are fast, (a) Predicted steady-state profile of the oxygen vacancy concentration ( ) in the mixed conductor as a function of distance from the electrode/electrolyte interface, (b) Predicted impedance, (c) Measured impedance of Lao.6Cao.4Feo.8-Coo.203-(5 electrodes on SDC at 700 °C in air, fit to the model shown in b using nonlinear complex least squares. Data are from ref 171.

Two reasons are responsible, for the greater complexity of chemical reactions 1) atomic particles change their chemical identity during reaction and 2) rate laws are nonlinear in most cases. Can the kinetic concepts of fluids be used for the kinetics of chemical processes in solids Instead of dealing with the kinetic gas theory, we have to deal with point, defect thermodynamics and point defect motion. Transport theory has to be introduced in an analogous way as in fluid systems, but adapted to the restrictions of the crystalline state. The same is true for (homogeneous) chemical reactions in the solid state. Processes across interfaces are of great... 

To complete the set of kinetic equations we observe that ub = (A/ /Ac)b where Acb can be expressed in terms of <5 ,b. Finally, the requirement of mass conservation yields a further equation. Considering the inherent nonlinearities, this problem contains the possibility of oscillatory solutions as has been observed experimentally. Let us repeat the general conclusion. Reactions at moving boundaries are relaxation processes between regular and irregular SE s. Coupled with the transport in the untransformed and the transformed phases, the nonlinear problem may, in principle, lead to pulsating motions of the driven interfaces. 

Let us remember that Eqns. (12.22) and (12.23) have to be coupled to the diffusion equations in the a and 0 phases in order to complete the total set of kinetic equations for the phase transformation (Le., the advancement of the interface). This set is very complicated and nonlinear and may lead to non-monotonic behavior of vb and the chemical potentials of the components in space and time, as has been observed experimentally (Figs. 10-13 and 12-9). Coherency stresses and other complications such as plastic flow have been neglected in this discussion. 

One outstanding feature of the technique which deserves a particular emphasis is that mass transport properties coupled with interfacial kinetics can be analyzed without (or with a minimal) perturbation pf the interface potential, particularly for systems presenting locally high nonlinearities. 

In general, the functions Hi and Fjc are nonlinear. These norUinearities are usually due to the exponential activation of the electrochemical rate constants by the potential (see Section 5.5). In addition, even for time-invariant electrochemical systems, equations (14.2) can comprise either differential equations, when only kinetic equations are considered to be involved at the interface, or partial differential equations, when distributed processes occur in the bulk of the solution (such as may result from transport of the reacting species or a temperature gradient in the solution). 

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