Internal interfacial energy

A is the surface area of the boundary layer. From Eq.(5.2) the expression of the internal interfacial energy Ua becomes ... 

The atoms and molecules at the interface between a Hquid (or soHd) and a vacuum are attracted more strongly toward the interior than toward the vacuum. The material parameter used to characterize this imbalance is the interfacial energy density y, usually called surface tension. It is highest for metals (<1 J/m ) (1 J/m = N/m), moderate for metal oxides (<0.1 J/m ), and lowest for hydrocarbons and fluorocarbons (0.02 J /m minimum) (4). The International Standards Organization describes weU-estabHshed methods for determining surface tension, eg, ISO 304 for Hquids containing surfactants and ISO 6889 for two-Hquid systems containing surfactants. 

Analysis is simplified if 7 is isotropic—i.e., independent of geometrical attributes such as interfacial inclination n and, for internal interfaces in crystalline materials, the crystallographic misorientation across the interface. All interfacial energy reduction then results from a reduction of interfacial area through interface motion. The rate of interfacial area reduction per volume transferred across the interface is the local geometric mean curvature. Thus, local driving forces derived from variations in mean curvature allow tractable models for the capillarity-induced morphological evolution of isotropic interfaces. 

Until now we have considered the total energy quantities of the system. Now we turn to the interfacial excess quantities. We start with the internal interfacial or internal surface energy... 

Surface stress — The surface area A of a solid electrode can be varied in two ways In a plastic deformation, such as cleavage, the number of surface atoms is changed, while in an elastic deformation, such as stretching, the number of surface atoms is constant. Therefore, the differential dUs of the internal surface energy, at constant entropy and composition, is given by dUs = ydAp + A m g m denm, where y is the interfacial tension, dAp is the change in area due to a plastic deformation, gnm is the surface stress, and enm the surface strain caused by an elastic deformation. Surface stress and strain are tensors, and the indices denote the directions of space. From this follows the generalized Lippmann equation for a solid electrode ... 

Moganite is a silica polymorph similar to, but distinct from, quartz. Its structure is related to that of quartz by twinning at the unit cell scale (and accompanying structural distortions) and its enthalpy is 3.4+0.7 kJ/mol higher than that of quartz (Petrovic et al. 1996). If one considers this twining as creating internal interfaces at the unit cell scale, then this relatively small enthalpy difference is consistent with a small interfacial energy. However one should stress that there are no broken bonds at such interfaces. 

Unlike equations (3) and (4), equation (5) is not in divergence form. To alleviate this difficulty we consider the specific total energy E = e(V, ) + ( ) the specific kinetic, internal, and interfacial energy. Now compute the time rate of chanffeof E- +, 2 V, .dT,rpdu,2d Vdu,... 

Emulsification is essential for the development of aU types of skin- and hair-care preparations and a variety of makeup products. Emulsions are fine dispersions of one liquid or semisolid in a second liquid (the continuous phase) with which the first substance is not miscible. Generally, one of the phases is water and the other phase is an oily substance oU-in-water emulsions are identified as o/w water-in-oil emulsions as w/o. When oil and water are mixed by shaking or stirring in the absence of a surface-active agent, the two phases separate rapidly to minimize the interfacial energy. Maintenance of the dispersion of small droplets of the internal phase, a requirement for emulsification, is practical only by including at least one surface-active emulsifier in the oil-and-water blend. 

These results give access to the interfacial tension as a thermodynamic excess quantity of the force-free plane D-face. Note that the interfacial tension and the absolute adsorptions of aU components contribute to the interfacial energy, both the specific excess internal energy and the specific excess Helmholtz firee energy. At a first glance, this statement is very natural, indeed. In the literature, however, interfacial tension and interfacial energy are very often considered as synonyms. Clearly, this is wrong. 

When associated with the first term gives rise to the internal and Madelung energies, while the second term represents the covalent energy. We will use the summation made in (1.4.64) when discussing interfacial energies in Chapter 5. 

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