Surface tension Girifalco-Good-Fowkes equation

EXAMPLE 6.5 Estimation of Interfacial Tensions Using the Girifalco-Good-Fowkes Equation. The following are the interfacial tensions for the various two-phase surfaces formed by n-octane (O), water (W), and mercury (Hg) for n-octane-water, y = 50.8 mJ m 2 for n-octane-mercury, y = 375 mJ m 2 and for water-mercury, y = 426 mJ m 2. Assuming that only London forces operate between molecules of the hydrocarbon, use Equation (100) to estimate y d for water and mercury. Do the values thus obtained make sense Take y values from Table 6.1 for the interfaces with air of these liquids. 

The same logic that we used to obtain the Girifalco-Good-Fowkes equation in Section 6.10 suggests that the dispersion component of the surface tension yd may be better to use than 7 itself when additional interactions besides London forces operate between the molecules. Also, it has been suggested that intermolecular spacing should be explicitly considered within the bulk phases, especially when the interaction at d = d0 is evaluated. The Hamaker approach, after all, treats matter as continuous, and at small separations the graininess of matter can make a difference in the attraction. The latter has been incorporated into one model, which results in the expression... 

Laplace equation A thermodynamic derivation Determining surface tension from the Kelvin equation Heat of immersion from surface tension and contact angle Surface tension and the height of a meniscus at a wall Interfacial tensions from the Girifalco-Good-Fowkes equation... 

Equation (7.29) is known as the Girifalco-Good-Fowkes-Young equation. By using this relationship, the dispersion components of the solid or liquid surface tension could be evaluated. 

From a practical applications point of view, both the critical surface tension approach and the use of contact angles with the Good-Girifalco-Fowkes equation represent handy tools for the characterization of the wettability, and therefore something of the chemical nature, of solid surfaces. The choice of technique is basically one of preference and convenience. 

Table 5.3 lists a few approximate values of O for liquid/water interfaces, as obtained by applying Equation 5.30 to experimental values for the interfacial and surface tensions. Alternatively, O may be evaluated theoretically. It is noted that Fowkes equation for the interfacial tension, Equation 5.24, is a special case of Girifalco and Good s approximation, namely, for the condition that the attraction within and between the phases across the interface is governed by dispersion forces. 

Many theories for estimating the interfacial tensions have been presented in Sections 3.5.1-3.5.3. The equations for the surface and interfacial tensions as well as for the work of adhesion are summarized in Table 3.6. Notice that the work of adhesion corresponds to the cross term of the interfacial tension expression (under the square roots), which reflects different contributions of intermolecular forces, according to the various theories (either the total surface tensions in Girifalco—Good and Neumann, only those contributions due to dispersion forces in Fowkes, due to both dispersion and specific forces in Owens-Wendt, separately dispersion, polar and hydrogen bonding ones in Hansen/Beerbower, or the van der Waals and as5mimetric acid/base effects in van Oss et ai). 

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