Good-Girifalco approach

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... 

Table 3. Surface tension of RSi03/2 treatments (derived by Good-Girifalco-Fowkes approach except where noted)... 

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. 

There has been considerable elaboration of the simple Girifalco and Good relationship, Eq. XII-22. As noted in Sections IV-2A and X-6B, the surface ftee energies that appear under the square root sign may be supposed to be expressible as a sum of dispersion, polar, and so on, components. This type of approach has been developed by Dann [70] and Kaelble [71] as well as by Schonhom and co-workers (see Ref. 72). Good (see Ref. 73) has preferred to introduce polar interactions into a detailed analysis of the meaning of in Eq. IV-7. While there is no doubt that polar interactions are important, these are orientation dependent and hence structure sensitive. 

A final quasi-thermodynamic approach to molecular structure effects has been proposed by Good et al. (17-18) which relates molar volumes and the Girifalco-Good interaction parameter, as... 

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. 

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... 

Another approach is that of Girifalco and Good (1957-1960) who derived the following important relationship between ysv, yLV and sl ... 

A more theoretical approach to determining whether an adhesive can be expected to wet the surface of a solid has been developed and promoted Girifalco and Good (I9S7) and Fowkes (1964). Utilizing the geometric mean... 

Relevant to the arguments put forward is the relationship introduced by Girifalco and Good [36,39]. Their expression relates the interfacial tension for two immiscible liquid phases to the surface tensions of the individual liquids. The application of this approach to the interpretation of contact angle data was suggested in a later paper by these authors [38]. Our approach, however, is developed under somewhat different basic assumptions and with rather different results. 

Interaction Parameters. A valuable approach to the problem of interpreting contact angle data has been initiated by Good and Girifalco [38]. As noted above, this approach is based on an expression relating the interfacial tension for two immiscible phases to the surface tensions of the individual phases [36,37]. If one of the phases is a solid, this expression is... 

Considerations arising from statistical mechanics and the theory of intermolecular forces can be used to estimate values of the interaction parameter. The pertinent theory has been discussed by Girifalco and Good [36] and independently by Moelwyn-Hughes [54]. However, this approach can be justified only for phases composed of spherical molecules which do not differ greatly in size. The actual importance and usefulness of the interaction parameter are consequently for purposes of correlating existing experimental data. 

As is usually the case when theoretical and experimental science meet, it is necessary to make some simplifying assumptions in order to apply theories to practical systems. Good and Girifalco proposed an empirical approach to the problem based on the Berthelot principle that the interaction constant between two different surfaces or particles will be the geometric mean of the interaction constant for the individual surface units, an approach already introduced in Chapter 4. Good and Girifalco suggested that the work of adhesion between two different liquids could be expressed as a similar function... 

Good and Girifalco [10, 11] proposed a more empirical approach to the problem of calculating the surface and interfacial tension. The interaction constant for two different particles was assumed to be equal to the geometric mean of the interaction constants for the individual particles. This is referred to as the Berthelot principle. 

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. 

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