Surface tension Girifalco-Good equation

Calculate the solid surface tension for the copolymer using the Neumann equation, the Girifalco-Good equation ( = 1) and the Antonov mle ... 

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... 

A simple equation was developed by Girifalco and Good [16-18] to relate the interfacial tension of a solid-liquid interface where both surfaces are molecular to the surface tensions of the components. It contained a factor of the order of unity related to the molecular volumes of the components. It was generalized later by assuming that its general form is applicable to all types of interfaces and that the factor of order unity can be dropped out. In Equation 7.8, y12 is... 

This equation is somewhat similar to that of Girifalco and Good [11], except that these authors used a parameter in the last term (-2 NTy7 ) and did not distinguish between surface tensions resulting from various types of intermolecular forces. The values of were about 0.5 for water-hydrocarbon interfaces. The Berthelot relation in Equation 1 is not exact, as can be shown by the London pair potentials, but is seldom in error by more than 2%, and the geometric mean is applied to only the interacting contributions to the surface tension. 

The Good-Girifalco approach has been extended to the use of contact angles in the computation of surface tension values for solid-liquid interfaces. Considering a system where the fluid 2 is either vapor or air (in which case it can be ignored), and combining with Young s equation, one obtains the expression... 

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. 

Girifalco and Good [46] assumed the interaction between a solid and a liquid could be quantified by an interaction parameter ) times the geometric mean of the surface tension of the solid and the liquid resulting in Equation (3). 

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. 

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. 

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). 

Show that in the case of the Girifalco-Good theory the contact angle is related to the solid surface tension via the following equation ... 

The more important method presently available is the one based on the equation of Good and Girifalco (for recent reviews on these topics see references 15 and 16X which relates the interfacial tension between two condensed phases A and B to the surface tensions of A and B (A and B may be a solid polymer and a liquid) ... 

The method of equation of state is totally different from aU the surface tension component methods described in Sect. 7.2.2. The equation of state method assumes that the interfacial surface tension ysL depends on the surface tension of the liquid ytv and solid ysv only, i.e., ygL = /(/sv /lv)- Tho method was mainly developed in Neumann s laboratory [33-37]. Neumann et al. formulated three versions of the equation of state. The first version was based on Zisman s data comprising eight solid surfaces with low surface tensions [33,34]. According to Girifalco and Good [38], the liquid-solid interfacial surface tension between dissimilar molecules can be formulated as... 

By incorporating the definition of and Wq (see Contact angles and interfacial tension), Eqn. 1 can be rearranged to give the Good-Girifalco equation for interfacial tension Yi2 in terms of the Surface energy values yi and yi of the two phases... 

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