Surface free energy, definition

A solid, by definition, is a portion of matter that is rigid and resists stress. Although the surface of a solid must, in principle, be characterized by surface free energy, it is evident that the usual methods of capillarity are not very useful since they depend on measurements of equilibrium surface properties given by Laplace s equation (Eq. II-7). Since a solid deforms in an elastic manner, its shape will be determined more by its past history than by surface tension forces. 

In Chapter III, surface free energy and surface stress were treated as equivalent, and both were discussed in terms of the energy to form unit additional surface. It is now desirable to consider an independent, more mechanical definition of surface stress. If a surface is cut by a plane normal to it, then, in order that the atoms on either side of the cut remain in equilibrium, it will be necessary to apply some external force to them. The total such force per unit length is the surface stress, and half the sum of the two surface stresses along mutually perpendicular cuts is equal to the surface tension. (Similarly, one-third of the sum of the three principal stresses in the body of a liquid is equal to its hydrostatic pressure.) In the case of a liquid or isotropic solid the two surface stresses are equal, but for a nonisotropic solid or crystal, this will not be true. In such a case the partial surface stresses or stretching tensions may be denoted as Ti and T2-... 

By definition, Wad is the sum of surface free energies of a liquid (Fiv) and a solid in vacuum (F8) minus the interfacial free energy (Fsl) according to Dupre s equation ... 

The balance of forces between surface tensions at the contact line results either in the Neumann triangle for a liquid/liquid/liquid or liquid/liquid/gas system or in the Young-Dupre equation on a liquid/liquid/solid or a liquid/gas/solid system (Fig. 1). While the Neumann triangle represents a true balance of forces, the Young-Dupre equation is little more than a definition of the (o As ctbs) term, a difference between the respective solid/fluid surface free energies and not truly solid/fluid interfacial tensions. 

Second, in thermodynamics it is more common to define surface tension in terms of work or the amount of energy needed to increase the surface with one unit area (i.e., the energy needed to bring a certain amount of molecules from the bulk to the surface). In this context the surface tension has a character of a surface free energy per unit area. The latter definition is in fact equivalent to the unit force per unit length (i.e. Nmjvr = NIm). The energy interpretation is by many researchers in thermodynamics considered the more fundamental one, and thus this interpretation is usually adopted for theoretical derivations. The surface tension is then defined as [1] [166] ... 

Using the Gibbs model, it is possible to obtain a definition of the surface or interfacial tension y. The surface free energy dG comprises three components (i) an entropy term S dT (ii) an interfacial energy term Ady, and (iii) a composition term S d/t (where W is the number of moles of component i with chemical potential nf. The Gibbs-Duhem equation is,... 

The quantity dy/dT, describing the change in the surface free energy with the increase in adsorption, is, by definition, equal to the chemical potential, p, and hence... 

In this introduction it may be useful to give a brief definition of surface tension and surface free energy. The dimension of the surface tension is related to unit length. Lenard s classical experiment (1924) is one of the best demonstrations of the surface force of a liquid acting on an extended wire in contact with a liquid surface. By carefully lifting the wire from the level of the surface, a force can be measured for as long as the pendent lamella remains in contact with the liquid bulk. The force measured in this way, divided by the length of the wire, leads to a well-... 

In contrast to the definition of the surface tension of a liquid by the acting force along a unit length, the surface free energy is defined by the reversible work necessary to extend the surface area by a square unit, e.g. 1 cm. The basic form of this definition is given by... 

There remains the question of the physical-i.e., operational [9] -definition of the terms. It appears to the writers that the derivation as a force balance is merely intuitional, and, as a consequence, it leaves the quantities and yg o undefined operationally. Thus, if these be viewed as forces parallel to the solid surface, one must ask with what property of the solid they are to be identified. Unlike the case with liquids, there is for solids a surface or stretching tension (the work per unit stretching of the surface [20, 25, 28]), in general nonisotropic. If this is what is involved, liquid drops on a crystalline surface of low symmetry should not be circular in cross section this is apparently contrary to observation. From the thermodynamic derivation, however, we see that one is dealing with the work of exchanging one type of solid interface for another, and that surface free energies, not stretching tensions, are the proper quantities. 

Subtracting Eq. (7) from Eq. (5), we obtain dF = d(YA)+d nfVi j Integrating this equation and dividing by the area A, an important definition of the system s specific surface free energy, results ... 

The scaled surface area and its variation with d> are of crucial importance in the definition and evaluation of the osmotic pressure , H, of a foam or emulsion. We introduced the concept in Ref 37, where it was referred to as the compressive pressure , P. It has turned out to be an extremely finitful concept (22,27,38). The term osmotic was chosen, with some hesitation, because of the operational similarity with the more familiar usage in solutions. In foams and emulsions, the role of the solute molecules is played by the drops or bubbles that of the solvent by the continuous phase, although it must be remembered that the nature of the interaetions is entirely different. Thus, the osmotic pressure is denned as the pressure that needs to be applied to a semipermeable, freely movable membrane, separating a fluid/fluid dispersion from its continuous phase, to prevent the latter from entering the former and to reduce thereby the augmented surface free energy (Fig. 4). The membrane is permeable to all the components of the continuous phase but not to the drops or bubbles. As we wish to postpone diseussion of compressibility effects in foams until latter, we assume that the total volume (and therefore the volume of the dispersed phase) is held constant. 

A crystal is surrounded at equilibrii n by flat, atomically smooth, low-index faces or, in Frank s classification, by singular faces. These faces in equilibrium forms are defined by the Gibbs definition of the equilibrium form requiring a minimum of the surface free energy of the crystal at constant volume (see Section 5.1). 

The equilibrium form of a crystal is defined as that possessing the minimal total surface free energy, d> = X Sispecific surface energies and the surface areas of the respective crystallographic faces. This definition goes back to Gibbs and Curie. 

In this chapter, the fundamental concepts of colloid science have been introduced. The definition of colloidal particles, those with sizes (in all directions) ranging from 1 nm to 10 pm, has been presented, and their relevance in soil science is stated. The importance of surface properties was remarked, introducing several definitions. The specific surface area is the area per unit mass the surface tension (or surface free energy) is defined as the Gibbs free energy per unit area. The surface excess of a given species is the amount (in moles per unit area) which is accumulated... 

Interfadal tension between two fluid phases is a definite and accurately measurable property depending on the properties of both phases. Also, the contact angle, depending now on the properties of the three phases, is an accurately measurable property. Experimental approaches are described, e.g., in Refs. 8,60, and 63 and in Ref. 62, where especially detailed discussion of the Wilhehny technique is presented. Theories such as harmonic mean theory, geometric mean theory, and acid base theory (reviewed, e.g., in Refs. 8, 20, and 64) allow calculation of the soHd surface energy (because it is difficult to directly measure) from the contact angle measurements with selected test liquids with known surface tension values. These theories require introduction of polar and dispersive components of the surface free energy. 

FIGURE 1.2 The thermodynamic definition of the surface free energy according to Gibbs. 

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