Surface free energies liquids

The total free energy of the system is then made up of the molar free energy times the total number of moles of the liquid plus G, the surface free energy per unit area, times the total surface area. Thus... 

The surface free energy can be regarded as the work of bringing a molecule from the interior of a liquid to the surface, and that this work arises from the fact that, although a molecule experiences no net forces while in the interior of the bulk phase, these forces become unbalanced as it moves toward the surface. As discussed in connection with Eq. Ill-IS and also in the next sections, a knowledge of the potential function for the interaction between molecules allows a calculation of the total surface energy if this can be written as a function of temperature, the surface free energy is also calculable. 

A case can be made for the usefulness of surface tension as a concept even in the case of a normal liquid-vapor interface. A discussion of this appears in papers by Brown [33] and Gurney [34]. The informal practice of using surface tension and surface free energy interchangeably will be followed in this text. 

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 change in surface free energy, AG accompanying a small displacement of the liquid such that the change in area of solid covered,, is... 

The integral A/, while expressible in terms of surface free energy differences, is defined independently of such individual quantities. A contact angle situation may thus be viewed as a consequence of the ability of two states to coexist bulk liquid and thin film. 

Returning to more surface chemical considerations, most literature discussions that relate adhesion to work of adhesion or to contact angle deal with surface free energy quantities. It has been pointed out that structural distortions are generally present in adsorbed layers and must be present if bulk liquid adsorbate forms a finite contact angle with the substrate (see Ref. 115). Thus both the entropy and the energy of adsorption are important (relative to bulk liquid). The... 

The basic phenomenon involved is that particles of ore are carried upward and held in the froth by virtue of their being attached to an air bubble, as illustrated in the inset to Fig. XIII-4. Consider, for example, the gravity-free situation indicated in Fig. XIII-5 for the case of a spherical particle. The particle may be entirely in phase A or entirely in phase B. Alternatively, it may be located in the interface, in which case both 7sa nnd 7sb contribute to the total surface free energy of the system. Also, however, some liquid-liquid interface has been eliminated. It may be shown (see Problem XIII-12) that if there is a finite contact angle, 0sab> the stable position of the particle is at the interface, as shown in Fig. XIII-5Z>. Actual measured detachment forces are in the range of 5 to 20 dyn [60]. 

The cleaning process proceeds by one of three primary mechanisms solubilization, emulsification, and roll-up [229]. In solubilization the oily phase partitions into surfactant micelles that desorb from the solid surface and diffuse into the bulk. As mentioned above, there is a body of theoretical work on solubilization [146, 147] and numerous experimental studies by a variety of spectroscopic techniques [143-145,230]. Emulsification involves the formation and removal of an emulsion at the oil-water interface the removal step may involve hydrodynamic as well as surface chemical forces. Emulsion formation is covered in Chapter XIV. In roll-up the surfactant reduces the contact angle of the liquid soil or the surface free energy of a solid particle aiding its detachment and subsequent removal by hydrodynamic forces. Adam and Stevenson s beautiful photographs illustrate roll-up of lanoline on wood fibers [231]. In order to achieve roll-up, one requires the surface free energies for soil detachment illustrated in Fig. XIII-14 to obey... 

The simplest approach to understanding the reduced melting point in nanocrystals relies on a simple thennodynamic model which considers the volume and surface as separate components. Wliether solid or melted, a nanocrystal surface contains atoms which are not bound to interior atoms. This raises the net free energy of the system because of the positive surface free energy, but the energetic cost of the surface is higher for a solid cluster than for a liquid cluster. Thus the free-energy difference between the two phases of a nanocrystal becomes smaller as the cluster size... 

The effects of fluorination on solid-surface free energies parallel the liquid trends Perfluormated polymers have the lowest cntical surface tensions, which directly relate to their antistick properties [19], but substimtion of fluorine by hydrogen or by the more polarizable ehloiine atom markedly raises their surface free energy. 

When the sphere and plane are separated by a small distance D, as shown in Figure 4, then the force due to the Laplace pressure in the liquid bridge may be calculated by considering how the total surface free energy of the system changes with separation [1] ... 

However, on rigid substrates, the growth of dry zones is accompanied by a rim of excess liquid with width X (Fig. 10). As the dewetting proceeds, X increases. For short times and < K, the growth of dry patches is controlled only by surface tension forces and the dewetting speed is constant. A constant dewetting speed of 8 mm-s has been measured when a liquid film of tricresyl phosphate (TCP) dewets on Teflon PFA, a hard fluoropoly-mer of low surface free energy (p. = 250 MPa, 7 = 20 mJ-m ). 

For practical purposes, if the contact angle is greater than 90° the liquid is said not to wet the solid (if the liquid is water one speaks of a hydrophobic surface) in such a case drops of liquids tend to move about easily and not to enter capillary pores. If 8 = 0, (ideal perfect wettability) Eq. (A.4.3) no longer holds and a spreading coefficient, Sls(V). reflects the imbalance of surface free energies. 

IVa represents a physical bond resulting from highly localized intermolecular dispersion forces. It is equal to the sum of the surface free energies of the liquid, 7, and the solid, 72. loss the interfacial free energy, 7,2. It follows that Eq. (2.1) can be related to a model of a liquid drop on a solid shown in Fig. 2.2. Resolution of forces in the horizontal direction at the point A where the three phases are in contact yields Young s equation... 

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