Surface energy, of a liquid

Ramsay-Shields equation An equation relating the molecular surface energy of a liquid with its temperature... 

Interatomic potential Total surface energy of a liquid, a solid Height of a ridge point Displacement of neighboring atoms... 

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 ... 

This formula can be used to calculate the surface energy of a liquid when both the intermolecular potential and the distribution function are known. Thus, the distribution function of liquid argon obtained by Eisenstein and Gingrich10 and the known intermolecular potential give Ucaic = 27 erg/cm2, while the observed value, that is, the value obtained from the observed values of surface tension by Eq. 11.12, is U0bs = 35 erg/cm2. For mercury the distribution functions obtained by Boyd and Wake-ham5 and the interatomic potential obtained by Hildebrand, Wakeham, and Boyd16 can be used. The calculated value is Ucaie = 490 erg/cm2, which can be compared with the observed value Uohs = 500 erg/cm2. 

The same idea will be adopted to discuss the zero-point energy concerning the surface energy of a liquid. The decrease in zero-point energy of a molecule when it emerges from the interior to the surface of a liquid is thus... 

Once the dispersion component of surface energy of a liquid is known, the polar component can be obtained from the surface tension using Eqn. 10. The approach based on Eqns. 9 and 10 can then be used to estimate surface energies of solids, particularly polymers, very much in the same way as Ys values are obtained from Eqn. 8. Here, yi2 is eliminated between Eqn. 10 and the Young equation, giving... 

Behind this lies the Fowkes theory, in accordance with which the total surface free energy is due to the action of dispersion and polar forces. The contribution of the latter in the free energy can be distinguished. It can be seen that the free surface energy of a liquid is given by... 

The surface energy of a liquid or solid arises from the unsatisfied bonds of the surface atoms. Since these atoms are more strongly bound by internal forces, work (surface free... 

The uncertainties in choice of potential function and in how to approximate the surface distortion contribution combine to make the calculated surface energies of ionic crystals rather uncertain. Some results are given in Table VII-2, but comparison between the various references cited will yield major discrepancies. Experimental verification is difficult (see Section VII-5). Qualitatively, one expects the surface energy of a solid to be distinctly higher than the surface tension of the liquid and, for example, the value of 212 ergs/cm for (100)... 

First, we recall the expression for the free energy of a liquid layer of finite thickness / formed on a flat surface... 

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 ... 

In many cases the potential P(z) is small compared with the surface energy of the liquid and the droplet shape is very close to a spherical cap. If the height e and the radius of curvature R at the top of the droplets can be measured, an effective contact angle can be defined through the expression ... 

Table 10.48 Surface tension of a range of liquids and surface energies of a range of textile fibres [502]...

Free surface energy is the minimum work required to create an interface. The surface tension of a liquid is the free surface energy per unit of area in the bond between the liquid and the air. Thus, the minimum work required to create an interface is ... 

The surface energy of a cluster is 75, where 7 is the surface energy per unit area. For a liquid metal 7 is identical to the surface tension. The ... 

The problem has been treated theoretically by the use of the Gibbs adsorption isotherm, which has been used with success in treating the interfaces between liquids and gases (30). One of the most easily measurable properties of a liquid is its surface tension, and changes in this quantity can be determined with great accuracy. The surface tension of a liquid is numerically equal to its surface energy, as also are changes in these quantities. 

Thus, Ss is the surface entropy per square centimeter of surface. This shows that, to change the surface area of a liquid (or solid, as described in later text), there exists a surface energy (y surface tension) that needs to be considered. 

As an example, one may proceed with this theory and estimate the surface tension of a liquid with data on its heat of evaporation. The number of near neighbors of a surface molecule will be about half (6 = 12/2) than those in the bulk phase (12 neighbors). It is now possible to estimate the ratio of the attractive energies in the bulk and surface phases per molecule. We have the following data for a liquid such as CC14 ... 

A critical examination of the total surface energies of various liquids has been made by Langmuir and Harkins. It is found that the surface energies of the aliphatic hydrocarbons are mainly independent of the length of the hydrocarbon chain, whilst the surface... 

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