Solid surface tension 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-... 

The purpose of this chapter is to introduce the effect of surfaces and interfaces on the thermodynamics of materials. While interface is a general term used for solid-solid, solid-liquid, liquid-liquid, solid-gas and liquid-gas boundaries, surface is the term normally used for the two latter types of phase boundary. The thermodynamic theory of interfaces between isotropic phases were first formulated by Gibbs [1], The treatment of such systems is based on the definition of an isotropic surface tension, cr, which is an excess surface stress per unit surface area. The Gibbs surface model for fluid surfaces is presented in Section 6.1 along with the derivation of the equilibrium conditions for curved interfaces, the Laplace equation. 

A quantity that is closely related to surface tension is the contact angle. The contact angle 0 is defined as the angle (measured in the liquid) that is formed at the junction of three phases, for example, at the solid-liquid-gas junction as shown in Figure 6.2b. Although the surface tension is a property of the two phases that form the interface, 0 requires that three phases be specified for its characterization, as mentioned above. The above definition of contact angle is, however, highly simplified, and we take a more in-depth look at the concept later in this chapter. 

When describing liquid surfaces, the surface tension was of fundamental importance. If we try to extend the definition of surface tension to solids, a major problem arises [324], If the surface of a liquid increases, then the number of surface atoms increases in proportion. For a solid surface this plastic increase of the surface area is not the only possible process. Usually more important is an elastic increase of the surface area. If the solid surface is increased by mechanically stretching, the distance between neighboring surface atoms changes, while the number of surface atoms remains constant. The change in surface area is commonly described in terms of the surface strain. The total surface strain etot is given by the change in surface area divided by the whole surface area detot = dA/A. The surface strain may be divided into a plastic strain dep and an elastic strain dse so that dstot = dep + dee. 

Devaux2 made numerous experiments between 1903 and 1914. Using a light powder sprinkled on the surface, which is a convenient way of rendering the movements of the oil visible, he confirmed most of the results of Pockels and Rayleigh. He found that the oils spread to a definite maximum extension, which is of course the same as that at which the first fall in surface tension appears. Calculating the thickness of the films, he found it of the same order as the then approximately known dimensions of molecules.8 He was the first to notice that the films may be solid,... 

It is well known that the effect of surface tension is to minimize the area of a lie surface. From a thermodynamic standpoint, the notion of surface tension can als< applied to a solid surface, although its physical significance is more difficul explain. For our present purpose, we may adopt an analogous definition of surface tension of a clean solid adsorbent to that for a clean liquid surface. Thus,... 

The ACCA and APCA on an ideal solid surface are identical by definition, and are referred to as the "ideal contact angle (ICA)". As will be explained below, it is the value of the ICA that is required for the characterization of the wettability of a solid substrate in terms of its surface tension. Also, all predictions of wetting behavior start with the ICAas their basis. Therefore, even though ideal surfaces are rarely encountered in practice, the concept is of fundamental importance. 

Asphaltenes are dark brown to black friable solids that have no definite melting point, and when heated, usually intumesce, then decompose leaving a carbonaceous residue. They are obtained from petroleums and bitumens by addition of a nonpolar solvent (such as a hydrocarbon) with a surface tension lower than 25 dynes cm-1 at 25°C (such as liquefied petroleum gases, the low-boiling petroleum naphthas, petroleum ether, pentane, isopentane, and hexane) but are soluble in liquids having a surface tension above 25 dynes cm-1 (such as pyridine, carbon disulfide, carbon tetrachloride, and benzene) (6, 7). 

The total porosity of solids can be estimated by simple pycnometric methods using the differences in surface tension between gases and mercury. By definition, the porosity Pr(%) is given by ... 

This definition is based on different physical adsorption phenomena of gases in pores of different size. Adsorption interactions of adsorbates are stronger in micropores and modify the bulk properties (density, surface tension) of the adsorbed fluids. The maximum size of ultramicropores corresponds to the bilayer thickness of nitrogen molecules adsorbed on a solid surface (2 x 0.354 nm). 

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. 

It is possible to perform a physical analysis to predict either liquid lens or thick him formation, and the strength of adhesion between the two phases. In order to assess the adhesion strength, initially we need to formulate the work of cohesion and adhesion. In Section 2.1, we dehned the term cohesion to describe the physical interactions between the same types of molecule, so that it is a measure of how hard it is to pull a liquid (and solid) apart. In Section 3.5.3, we dehned, the work of cohesion, W), as the reversible work, per unit area, required to break a column of a liquid (or solid) into two parts, creating two new equilibrium surfaces, and separating them to inhnite distance. (In practice, a distance of a few micrometers is sufficient.) The work of cohesion required to separate liquid layers into two parts having unit area can obviously be expressed from the definition of surface tension as... 

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. 

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