Girifalco-Good theory

The Good-Girifalco theory [77-82] was originally formulated to make an attempt to correlate the solid-liquid interfacial tension to the solid surface energy and the liquid surface tension through an interaction parameter, basic formulation of the theory is ... 

He wrote about 160 research papers, including those about the well-known theories for interfa-cial tensions discussed in this book, such as the earlier Good-Girifalco theory and the more modern acid-base theory of Card van Oss and M. K. Chaudhury. The first papers from these two theories have so far (2014) received about 1800 citations. 

Many different measures may be used to specify this fundamental adhesion. It may be expressed in terms of forces or in terms of energies. Again, depending on the context, these may be forces or energies of attachment or else of detachment. Sometimes values of fundamental adhesion can be calculated from a theoretical model (see Electrostatic theory of adhesion, Good-Girifalco interaction parameter) occasionally, they may be deduced from experimental measurement (see Adhesion-fundamental and practical) for many practical adhesive bonds, they are not available by either route. 

Further insight comes from consideration of the Good-Girifalco interaction parameter theory, which gives the following equation. 

The theory of the Good-Girifalco interaction parameter can be developed to give some support for this relationship. This was not accepted by Fowkes, who argued that the principal non-dispersion interactions are Acid-base interactions, for which a geometric mean relationship does not apply. 

The authors postulate that a solid and a liquid of similar polarity will give a minimum value of y%. Kitazaki and Hata also discuss the ramifications of their postulates and experimeiital results on adhesion measurements. Overall their conclusion is that a maximum is achieved when the polarities of the solid surface and the adhesive are as similar as possible. From the Good and Girifalco theory, a maximum in would also be expected when the interparticle forces across the interface are at a maximum. Wu has also analyzed the separation of the force components of the interfacial and surface tensions. Wu, however, chooses to make an arithmetic mean approximation rather than the geometric mean approximation used by Good and by Fowkes. He bases this choice on an analogy with the form of the expressions for the interparticle forces, which are more closely mimicked by an arithmetic mean. Wu contends that his use of the arithmetic mean yields results closer to measured values. 

L. A. Girifalco, R.J. Good, A theory for the estimation of surface and interfacial energies. 

Girifalco, L.A. and Good. R.J. A theory for the estimation of surface and interfacial energies I. Derivation and application to interfacial tension, J. Phys. Chem., 61(7) 904-909,1957. 

One of the major problems of the application of the theory to sohds is the determination of the interfacial tension. For such systems it cannot be determined by direct measurements, it is usually derived from thermodynamic calculations. Good and Girifalco [31] developed the first theory for the calculation of Yab> because it contained an adjustable parameter it did not gain practical use. The most widely accepted solution was suggested by Fowkes [32,33]. He assumed that surface tension can be divided as shown in Eq. 9 ... 

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. 

Good and Girifalco defined an interaction parameter (cp) from molecular interaction theory, which is given in terms of and Wc by... 

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... 

The Owens-Wendt theory (Good and Girifalco, 1960 Owens and Wendt, 1969) accounts for local interactions and separates the surface tension into dispersive and polar components (o and O ) for the solid-vapor, and liquid-vapor interfaces (Osv and Olv) (Parry et al, 2010 Wood et al., 2010b) ... 

Good, R. J. and Girifalco, L. A. 1960. A theory for estimation of surface and interfacial energies. III. Estimation of surface energies of solids from contact angle data. The Journal of Physical Chemistry 64 561-565. 

The theory of Good and Girifalco is easily derived We will review the theoretical basis here, in order to introduce a contribution to the theory of contact angles which has not been published heretofore. 

Similarly good agreement between experiment and theory in this case, an analytically derived, rather than DFT, prediction - is observed for the Ceo-Ceo potential shown in Fig. 15(b). The Girifalco potential accurately models our experimental data both in terms of the depth and the width of the intermolecular interaction curve. Deviations at intermolecular... 

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). 

All theories have strengths and weaknesses and it may be difficult to decide a priori which theory is the best. Perhaps for this reason, several textbooks (Shaw, 1992 Hamley, 2000 Goodwin, 2004 Israelachvilli, 1985) present only the very simple theories of Fowkes and Girifalco-Good, possibly for illustration purposes, while others (Pashley and Karaman, 2004) do not present any theories at all for estimating the interfacial tension( ). 

Many theories have been proposed for the estimation of interfacial tensions, many more than just the Fowkes, Girifalco-Good and Hansen-Beerbower. These theories can be tested against experimental data for liquid—liquid interfaces but testing is more difficult for solid-liquid interfaces (where the interfacial tension cannot be measured directly). 

The Fowkes, Girifalco-Good and Hansen are all theories for estimating the interfacial tension of solid-liquid (and other) interfaces. Which statement is always correct ... 

A very simple theory for the interfacial tension that performs satisfactorily in some simple cases is given by a modified form of the Girifalco-Good equation (using a correction parameter equal to one) ... 

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