Girifalco-Good parameter

In a similar manner, an expression for the interfacial tension, Yf can be written using the geometric mean definition for work of adhesion, Wa (see Figure 8), and the Girifalco-Good interaction parameter (17-18), as. 

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 many applications it is possible to determine 7l and, with more difficulty, 7s, but not 7sl- Therefore, it would be helpful to express 7sl through 7l and 7s. Since 7sl, 7l, and 7s are independent parameters we can only hope to find an approximate expression and we have to use additional information. Girifalco, Good, and Fowkes considered solids and liquids, in which the molecules are held together by van der Waals forces [270,271], Then, in a thought experiment they separated two materials at the interface (Fig. 7.11). The required work of adhesion per cross-sectional area is w = 71 + 72 — 712. Two new surfaces are formed while the interfacial area disappears. Rearrangement leads to... 

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 second problem involves interpretation of the interfacial tension ysL (there is no difficulty concerning = y since the liquid must coexist with its vapour). The interfacial tension must be lower than the snm of the two individual surface tensions (otherwise the interface would not form) by an amount related to them (it is a consequence of the same forces that give rise to the individual surface tension). Good and Girifalco expressed this (see Good-Girifalco interaction parameter) as... 

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 concept of surface energy components provides one route to interfacial tensions and solid surface energies and others include the Good-Girifalco interaction parameter and Acid-base interactions. 

Good-Girifalco interaction parameter D E PACKHAM Definition of (p evaluation for dispersion force interface interfacial tension solid surface energies... 

Values for the Girifalco and Good Parameter for Water/Liquid Interfaces... 

From Eq. (84), which describes the components of the Good and Girifalco interaction parameter, g, it can be seen that the components of the forces which interact across interfaces are considered to be additive, as shown in Eq. (85),... 

Appendix 3.2 The V parameter of the Girifalco-Good equation (Equation 3,16) for liquid-liquid interfaces. Data from Girifalco and Good (1957,1960)... 

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) ... 

Good-Girifalco interaction parameter mechanical loss function... 

The dimensionless interaction parameter (p expresses implicitly the effect of all interactions in the given interphase on the interfacial tension 7sl- the framework of the Girifalco-Good concept, Eq. 6.20a represents the form proposed for the equation of state 6.13. Hence, Eq. 6.20a has to refer to all phases involved and should be written more precisely as... 

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 ... 

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 ... 

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. 

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... 

The factor denoted in these equations by Z 3 is called here the interaction parameter. (The symbol was employed for this quantity by Good and Girifalco.)... 

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... 

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]... 

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