Interfaces Gibbs free energy

As in the qualitative discussion above, let 7 be the Gibbs free energy per unit area of the interface between the crystal and the surrounding hquid. This is undoubtedly different for the edges of the plate than for its faces, but we... 

Ebox = total calculated energy inside the box drawn around the interface. This should be the Gibbs free energy. An approximation to it would be the internal energy atT=OK. 

In order to evaluate which of these scenarios leads to the most stable interfacial structure, we have to analyze the relation between the chemical potentials of both reservoirs and the overall energy. Therefore, we begin with the Gibbs free energy of the interface. 

The term G T, a,, A/, ) is the Gibbs free energy of the full electrochemical system x < x < X2 in Fig. 5.4). It includes the electrode surface, which is influenced by possible reconstructions, adsorption, and charging, and the part of the electrolyte that deviates from the uniform ion distribution of the bulk electrolyte. The importance of these requirements becomes evident if we consider the theoretical modeling. If the interface model is chosen too small, then the excess charges on the electrode are not fuUy considered and/or, within the interface only part of the total potential drop is included, resulting in an electrostatic potential value at X = X2 that differs from the requited bulk electrolyte value < s-However, if we constrain such a model to reproduce the electrostatic potential... 

This expression has the advantages that the electrode potential only appears in the last term and that the Gibbs free energy G depends only on the temperamre and quantities related to the electrode, allowing one to neglect the electrolyte part of the interface. 

Molecules in the surface or interfacial region are subject to attractive forces from adjacent molecules, which result in an attraction into the bulk phase. The attraction tends to reduce the number of molecules in the surface region (increase in inter-molecular distance). Hence work must be done to bring molecules from the interior to the interface. The minimum work required to create a differential increment in surface dA is ydA, where A is the interfacial area and y is the surface tension or interfacial tension. One also refers to y as the interfacial Gibbs free energy for the condition of constant temperature, T, pression, P, and composition (n = number of moles)... 

The most important property of a liquid-gas interface is its surface energy. Surface tension arises at the boundary because of the grossly unequal attractive forces of the liquid subphase for molecules at its surface relative to their attraction by the molecules of the gas phase. These forces tend to pull the surface molecules into the interior of the liquid phase and, as a consequence, cause liquids to minimize their surface area. If equilibrium thermodynamics apply, the surface tension 7 is the partial derivative of the Helmholtz free energy of the system with respect to the area of the interface—when all other conditions are held constant. For a phase surface, the corresponding relation of 7 to Gibbs free energy G and surface area A is shown in eq. [ 1 ]. 

The partial derivative of the Gibbs free energy per unit area at constant temperature and pressure is defined as the interfacial coefficient of the free energy or the interfacial tension (y), a key concept in surface and interface science ... 

The change of the molar Gibbs free energy inside the vapor due to curving the interface is therefore... 

In this chapter we introduce a more useful equation for the surface tension. This we do in two steps. First, we seek an equation for the change in the Gibbs free energy. The Gibbs free energy G is usually more important than F because its natural variables, T and P, are constant in most applications. Second, we have just learned that, for curved surfaces, the surface tension is not uniquely defined and depends on where precisely we choose to position the interface. Therefore we concentrate on planar surfaces from now on. 

Lippmanns classical derivation was simpler. He treated the mercury-electrolyte interface as a capacitor. The capacitance is assumed to increase with the surface area A much like a plate capacitor. One plate is the metal, the other the layer of counterions in the electrolyte. The potential difference between the two plates is U. A change in the Gibbs free energy of the system is equal to the reversible work upon a change of the surface A or of the charge Q ... 

The cosine cannot exceed one. Then we might ask What happens, if 7s — 7sl — 7l > 0 or 7S - 7Si is higher than 7// Does this not violate Young s equation No, it does not because in thermodynamic equilibrium 7s — Ysl — 1l can never become positive. This is easy to see. If we could create a situation with 7s > 7SL + 7l, then the Gibbs free energy of the system could decrease by forming a continuous liquid film on the solid surface. Vapor would condense onto the solid until such a film is formed and the free solid surface would be replaced to a solid-liquid interface plus a liquid surface. 

To derive Eq. (7.13) we consider the change of Gibbs free energy upon an infinitesimal rise of the liquid dh. This is simple because the shape of the liquid-vapor interface does not change. The change in Gibbs free energy is ... 

Dirt particles spontaneously leave a solid surface if it is energetically favorable to replace the dirt-solid interface (SD) by two interfaces the dirt-aqueous solution interface (DW) and the solid-aqueous solution interface (SW). Here, the solid is a textile fibre or any other material, which we want to clean (Fig. 7.22). The change in the Gibbs free energy... 

Surfactants form semiflexible elastic films at interfaces. In general, the Gibbs free energy of a surfactant film depends on its curvature. Here we are not talking about the indirect effect of the Laplace pressure but a real mechanical effect. In fact, the interfacial tension of most microemulsions is very small so that the Laplace pressure is low. Since the curvature plays such an important role, it is useful to introduce two parameters, the principal curvatures... 

The thermodynamic treatment of an interface generally considers a system composed of the interface (y) and two adjacent homogeneous phases (a and / ). The extensive properties of the systems must be ascribed to these three regions, for example, the Gibbs free energy G and the number of moles of a species in the system fulfill... 

The most stable compound of a multiphase binary system is often assumed to be the first to occur and grow at the A-B interface. The change, ArG , of the isobaric-isothermal potential (Gibbs free energy) in the reaction of formation of any compound from the elements under given conditions is usually considered to be a measure of its thermodynamic stability. The more negative the value of AfG°, the more stable the compound is. 

B. S. Hemingway, Gibbs free energies of formation for bayerite, nordstrandite, Al(OH)2+, and Al(OH)2 aluminum mobility, and formation of bauxites and laterites, Adv. Phys. Geochem. 2 285(1982). The mechanistic basis of the GLO Step Rule is discussed in Chap. 6 of W. Stumm, Chemistry of the Solid-Water Interface, Wiley, New York, 1992. See also Chap. 5 in W. Stumm and J. J. Morgan, op. cit.12... 

In order to set the stage for this review of the polymer dynamics on monolayers at interfaces with emphasis on A/W, we need to lay out its static properties first. Surface tension a represents a fundamental property of a liquid surface. The change in Gibbs free energy dG for a multi-component system including the surface contribution is written as... 

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