Gibbs free energy tension

By simple thermodynamic arguments Brown14 has shown that, consistent with the accuracy of this second-order approximation, one may obtain from the form of Eq. (87) the form of the excess Gibbs free energy of mixing (AG ), the enthalpy of mixing of a molten salt (AHm), and the deviation of the surface tension from linearity ... 

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)... 

In Chapter 4.2 we introduced the interfacial (surface) tension (equivalent to surface or interfacial energy) as the minimum work required to create a differential increment in surface area. The interfacial energy, equally applicable to solids and liquids, was referred to as the interfacial Gibbs free energy (at constant temperature, pressure and composition) (n refers to the composition other than the surfactant under consideration). 

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 ... 

With this interpretation of the surface tension in mind we immediately realize that 7 has to be positive. Otherwise the Gibbs free energy of interaction would be repulsive and all molecules would immediately evaporate into the gas phase. 

This, however, is not the whole energy difference. In addition, the drop has a surface tension which has to be considered. The total change in the Gibbs free energy is... 

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. 

The surface tension is the increase in the Gibbs free energy per increase in surface area at constant T, P, and JV. ... 

For a pure liquid the Gibbs dividing plane is conveniently positioned so that the surface excess is zero. Then the surface tension is equal to the surface free energy and the interfacial Gibbs free energy f[Pg.40]

To consider the elastic increase of the surface area the surface stress T is introduced. The change in the Gibbs free energy per unit area is given by the reversible work required to expand the surface against the surface tension 7 and the surface stress T... 

Here, R is the radius of the droplets and 7 is the liquid-liquid interfacial tension (see Section 13.5 and Table 13.2). The amount of AGem is equal to the Gibbs free energy gained upon demulsification. 

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... 

Thus surface or interfacial tension can also reflect the change in Gibbs free energy per area, consistent with the idea that area expansion requires energy. 

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... 

T absolute temperature R molar ideal gas constant Cp mean molar heat capacity area of surface or interface T thickness of interfacial layer Q heat (extensive) q heat per mole of adsorbate U internal energy H enthalpy S entropy G Gibbs free energy y surface tension... 

The surface tension y is the reversible work (i.e., the reversible increase in the Gibbs free energy G) as a result of the creation of a unit surface area, at constant temperature, pressure and composition [1-4]. The increase in G upon the creation of new surface area is caused by the imbalance of the molecular forces acting on the molecules at the surface, compared with the forces acting on molecules in the interior (bulk) of a liquid or a solid. The surface tension is the key physical property of the surface of a material. It is expressed in units of energy/area, such as J/m2 which is identical to 1000 dyn/cm. Dyn/cm are quoted more often than J/m2. 

Equation (593) is called Shuttleworth s equation and shows how we can calculate the surface stress. In theory, if we want to calculate the Gibbs free energy per unit area from surface tension and surface stress we may write... 

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