Surface energy solid-vapor

The interface between a solid and its vapor (or an inert gas) is discussed in this chapter from an essentially phenomenological point of view. We are interested in surface energies and free energies and in how they may be measured or estimated theoretically. The study of solid surfaces at the molecular level, through the methods of spectroscopy and diffraction, is taken up in Chapter VIII. 

Metals A and B form an alloy or solid solution. To take a hypothetical case, suppose that the structure is simple cubic, so that each interior atom has six nearest neighbors and each surface atom has five. A particular alloy has a bulk mole fraction XA = 0.50, the side of the unit cell is 4.0 A, and the energies of vaporization Ea and Eb are 30 and 35 kcal/mol for the respective pure metals. The A—A bond energy is aa and the B—B bond energy is bb assume that ab = j( aa + bb)- Calculate the surface energy as a function of surface composition. What should the surface composition be at 0 K In what direction should it change on heaf)pg, and why ... 

The specialty class of polyols includes poly(butadiene) and polycarbonate polyols. The poly(butadiene) polyols most commonly used in urethane adhesives have functionalities from 1.8 to 2.3 and contain the three isomers (x, y and z) shown in Table 2. Newer variants of poly(butadiene) polyols include a 90% 1,2 product, as well as hydrogenated versions, which produce a saturated hydrocarbon chain [28]. Poly(butadiene) polyols have an all-hydrocarbon backbone, producing a relatively low surface energy material, outstanding moisture resistance, and low vapor transmission values. Aromatic polycarbonate polyols are solids at room temperature. Aliphatic polycarbonate polyols are viscous liquids and are used to obtain adhesion to polar substrates, yet these polyols have better hydrolysis properties than do most polyesters. 

Eleat transfer occurs not only within the solid surface, droplet and vapor phases, but also at the liquid-solid and solid-vapor interface. Thus, the energy-balance equations for all phases and interfaces are solved to determine the heat-transfer rate and evaporation rate. 

Specific surface energy or surface tension of a solid Specific free energy of an interface between UC and U vapor Specific energy or tension of a liquid-solid interface Surface tension of a solid in a foreign vapor Surface tension of a grain boundary... 

It should be noted that, in the above equations, the effects of adsorption of vapor or gas on the solid surfaces are completely neglected. The amount of adsorption can be quite large, and may approach or exceed the point of monolayer formation at saturation. The spreading pressure, n, which is the amount of the reduction in surface energy on the solid surface due to the adsorption of vapor in equilibrium, is given by (Adamson, 1982)... 

The three interfacial surface energies, as shown at the three-phase junction in Figure 2.29, can be used to perform a simple force balance. The liquid-solid interfacial energy plus the component of the liquid-vapor interfacial energy that lies in the same direction must exactly balance the solid-vapor interfacial energy at equilibrium ... 

Fig. 14. Schematic illustration of a drop ofliquid spreading in contact with a solid surface, showing the relations between the relevant parameters the contact angle, 0 the solid/vapor interfacial free energy, Ysv the liquid/vapor interfacial free energy, yLV and the solid/liquid interfacial free energy, ySL. Young s equation describes the relationship between these parameters for a stationary drop at thermodynamic equilibrium [175]...

The very fact that the vapor phase of many substances can condense to form a liquid is a consequence of the existence of attractive van der Waals forces between atoms or molecules. An attractive intermolecular force is not needed for a gas to condense into a solid solidification can occur purely as a result of excluded-volume interactions among the molecules at sufficiently large densities. The pressure in a fluid, the cohesion between materials, and the existence of surface energy or surface tension all result, partially or wholly, from van der Waals forces. 

Values of surface energy measured by this technique were found to be 1.140 J/m2 for Ag at 903 °C, 1400J/m2 for Au at 1204 °C, and 1.650 J/m2 for Cu at 1000 °C. The solid-vapor surface energy is relatively independent of the temperature, but the surface energy of a solid-vapor interface depends on its crystallographic orientation, so these measured values must reflect an average value for many orientations. 

The basic theorem of adsorption may be stated as follows Adsorption on a solid by a vapor continues as long as the process can occur with a decrease in the surface energy—free energy—of the solid surface. If tr denotes this decrease in free energy per unit area, we have symbolically... 

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