Good-Girifalco-Fowkes equation

B. Semiempirical Models The Girifalco-Good-Fowkes-Young Equation... 

In this version the relationship is called the Girifalco-Good-Fowkes equation. (We use a similar approach again in Chapter 10, e.g., see Equations (10.77) and (10.78), to determine the Hamaker constant for the van der Waals interaction forces.) Although we use y and yd interchangeably, it is important to recognize that yd values are determined by a particular strategy as illustrated in Example 6.5. 

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. 

Finally, we turn our attention to the third contribution to van der Waals attraction, London (or dispersion) forces between a pair of induced dipoles. It will be noted that (at least) one permanent dipole is needed for the preceding sources of attraction to be operative. No such restriction is present for the London component. Therefore this latter quantity is present between molecules of all substances, whether or not they have a permanent dipole. These are the same forces that we considered in Chapter 6 when we discussed the Girifalco-Good-Fowkes equation. 

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... 

In this table, is calculated from the Girifalco-Good-Fowkes-Young equation [20] using -hexadecane as the sole contact angle test liquid ... 

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. 

What is the Girifalco-Good equation What is the Fowkes approximation to the Girifalco-Good equation ... 

The model of Girifalco, Good, and Fowkes has been extended to other interactions. For example, if we assume that the surface energies are the sum of van der Waals (dispersive) and polar interactions, one often uses the equation [272]... 

Notice that, unlike the Girifalco-Good equation, the cross term includes a contribution only from the dispersion forces. Thus, the Fowkes equation is based on the fundamental assumption that the crossinteraction term across the interface (work of adhesion) is due to dispersion forces alone. 

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). 

While most (if not all) textbooks on colloids and interfaces limit their discussion about interfacial theories to Girifalco-Good and Fowkes/Owens-Wendt, the discussion is hardly complete without presenting the two most modem, possibly most widely used and certainly most controversial, theories, the acid-base theory of Carel van Oss, Manoj Chaudhury and Robert Good (from now on called here van Oss-Good) and the equation of state approach of A. Wilhelm Neumann. These theories, already presented in Chapter 3 (Equations 3.18 and 3.25 and 3.26), have resulted to extensive discussions — not the least between their developers, often with rather direct and not always entirely poUtc statements about the capabilities and limitations. Numerous articles have been published about these two theories both by their developers and by others. Thus, the pertinent hterature is enormous but we attempt a short review here. 

Using appropriate data from Table II-9, calculate the water-mercury interfacial tension using the simple Girifalco and Good equation and then using Fowkes modification of it. 

Fluorocarbon and hydrocarbon modified PDMS surfaces are compared in Table 2. The contact angle data are obtained by the Good-Girifalco-Fowkes equation. It is striking that the hydrocarbon contact angle liquid gives better agreement with the JKR result for the hydrocarbon surface whereas the fluorocarbon liquid data better fit the fluorocarbon surface... 

Good-Girifalco-Fowkes (GGF) equation Using Xsi = Xsv + yiv - 2(ysvyiv) in Young s equation leads to 1+COS0 Xggf obtained from a plot COS0 versus 4> is solid-liquid interaction parameter 0 = 1 if the interactions are purely dispersive. Based on Berthelot relation for atuactive constants valid only when the solid-liquid interactions are dominantly dispersive. [77-82]... 

If one combines the suggestion of Good and Girifalco with the modifications proposed by Fowkes, one may rewrite Equation (17.30) in the form... 

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. 

For a given pair of liquids, the first three terms can be measured experimentally, and if one is nonpolar then Ya = Ya. and hence Ys of a polar liquid can be experimentally determined. This equation is due to Fowkes (1963) and constitutes a special case of the more general equation of Girifalco and Good (1957), in which the last term of Equation 2.14 is mulitplied by a correction factor. It is noteworthy that Equation 2.14 is derived when the interaction between A and B occurs through dispersion only. This is true when at least one of A and B is nonpolar. When both are nonpolar, Y/i = y1 nd Ys = Ys. and Equation 2.14 becomes... 

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. 

When polar contributions are neglected, (27) reduces to the Fowkes equation [196]. In terms of the Good-Girifalco equation (21), the interaction parameter is given by ... 

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