The surface energy of solids

The surface tension defined above was related to an interface that behaved mechanically as a membrane stretched uniformly and isotropically by a force which is the same at all points on the surface. A surface property defined this way is not always applicable to the surfaces of solids and the surface energy of planar surfaces is defined to take anisotropy into account. The surface energy is often in the literature interchanged with surface tension without further notice. Although this may be useful in practice, it is strictly not correct. 

The surface energy can be derived by an alternative treatment. Let us initially consider a large homogeneous crystal that contains N atoms and that has a planar 

To create a new surface we have to break bonds and remove the superfluous atoms. At equilibrium at constant pressure and temperature the work demanded to increase the surface area of a one-component system by an amount dAs is given as 

For an isotropic phase there are no differences between surface energy and surface tension. However, for crystals, which are anisotropic in nature, the relationship between these two quantities is significant and also theoretically challenging, see e.g. the recent review by Rusanov [2], 

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There are numerous techniques which provide information related to the surface energy of solids. A large array of high-vacuum, destructive and non-destructive techniques is available, and most of them yield information on the atomic and chemical composition of the surface and layers just beneath it. These are reviewed elsewhere [83,84] and are beyond the scope of the present chapter. From the standpoint of their effect on wettability and adhesion, the property of greatest importance appears to be the Lifshitz-van der Waals ( dispersion) surface energy, ys. This may be measured by the simple but elegant technique of... 

Measurement of the contact angle at a solid-liquid interface is a widely used method for the determination of the surface energy of solid polymers. Fowkes [1] first proposed that the surface energy of a pure phase, y y could be represented by the sum of the contribution from different types of force components, especially the dispersion and the polar components, such that ... 

The following Section II.2. is devoted to the attempts on calculating 7 from fundamental atomic and molecular constants. In Section II.3., semi-empirical expressions for the surface energy of solids are briefly reviewed. 

When an adsorbing surface is exposed to a gas or vapour adsorption will take place, being accompanied by the absorption or evolution of heat. Such thermal changes have already been noted in the extension and contraction of surface films of liquids. Although the direct determination of the surface energy of solid surfaces presents many experimental difficulties yet of its existence there is no doubt. On the adsorption of a gas or vapour a diminution in the free surface energy of the system likewise occurs. From the Gibbs-Helmholtz relationship dcr... 

Measurement of the surface energy of a liquid is relatively easy to both perform and understand. All methods are based on measuring the work required to create a new surface by transferring molecules from bulk liquid. However, what about the surface energy of a solid Clearly, for solids it is impractical to move molecules from bulk to the surface. There are basically two ways by which we can attempt to obtain the surface energy of solids ... 

The second approach to obtaining the surface energies of solids involves the study of wetting and non-wetting liquids on a smooth, clean solid substrate. Let us examine the situation for a non-wetting... 

Girifalco and co-workers (18), on the other hand, derived the following expression which can be used to estimate the surface energies of solids from the increasingly available heats of immersion ... 

This simple calculation demonstrates that the surface energies of solids can be much higher... 

The cohesive force between solid surfaces and the surface energy of solids." Ibid., 13 (7th Ser.) 853-862. 

In the example of Table 4.4, the surface energy of solid W in equilibrium with a saturated vapour of Cu is lower than °sv due to adsorption of Cu atoms on the W surface. This is generally characteristic of metallic A-B pairs having a low mutual miscibility (Eustathopoulos and Joud 1980). For this reason, results of sessile drop experiments for such systems cannot be interpreted by taking for the surface energy of the solid metal the value of equilibrium with its own vapour (see Sections 1.4.2 and 5.2). 

H. Jones, The surface energy of solid metals. Metal Sci. J., 5 15-18.L.Z. (1971) Mezey, and J. Giber, The surface free energies of solid chemical elements calculation from internal free enthalpies of atomization, Jpn. J. Appl Phys., 21(11) 1569-1571 (1982)... 

The surface energy of solid magnesia, MgO, at 1500 °C is 1.2 J m . Estimate the pressure differential between a spherical pit of diameter of 5 X 10 m and that over the surface of a flat plate of magnesia at this temperature. 

The surface energy of solid crystals is generally anisotropic, i.e. it depends on the crystallographic orientation of the strrface. In that case a generalisation of the Gibbs-Thomson eqrration (14) was given by... 

Missol, W. (1973) Calculation of the surface energy of solid metals from work fun(4ion values and electron configuration data. Phys. Status Solidi (b), 58, 767-773. 

The work of cohesion of a liquid Wc is defined as that which is required to create two new interfaces with a total interfacial tension of 2y. Under conditions of complete wetting, W. = 2y tTsv, which shows that the work of adhesion for completely wetting liquids is always larger than the work of cohesion. Adhesion problems generally require the consideration of aspects other than wetting alone. An important issue is to determine the surface energies of solids. The surface tensions of liquid-vapour and liquid-air interfaces can easily be determined from the pressure difference across... 

An Analytical Method for Determining the Surface Energy of Solid Polymers... 

Oji is the surface energy of solid-liquid interface is the bulk enthalpy of fusion... 

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