Interfacial tension Fowkes theory

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 ... 

If Fowkes semiempirical interfacial tension theory (as described on pages 65-67) is applied to the solid-liquid interface, then... 

The logical next step in the process of extending the utility of theory to practical systems is to include polar molecular interactions. For this step, Fowkes suggested that the intermolecular forces contributing to surface and interfacial tensions, and subsequent phenomena such as wetting, could be broken down into independent and additive terms. For example, a polar molecule such as an ester would have two terms making up its surface tension—dispersion forces (d) and dipolar interactions (p)—so that... 

The success of the Fowkes equation, but also the need for better theories, has been illustrated in Examples 3.3 and 3.4. Extensions of the Fowkes equation have been proposed, which account explicitly for polar and hydrogen bonding effects in the expression for the interfacial tension using geometric-mean rules for all terms. Two such well-known theories are the Owens-Wendt theory, which is often used for polymer surfaces, and the Hansen/Skaarup (van Krevelen and Hoftyzer, 1972 Hansen, 2000) model. Both models are presented below. The Hansen/Skaarup... 

It can be seen that these theories resemble the Fowkes equation but one or two additional cross terms are added to account for the specific interactions (a combined specific terms is used for Owens-Wendt while both polar and hydrogen bonding terms are used in the Hansen equation). The relevant equations for the surface and interfacial tensions for these two theories are given in Equations 3.22-3.24 ... 

A major observation from the van Oss-Good theory is that, unlike other theories, the interfacial tension may be positive or negative. Note that the LW term is given by a geometric-mean Fowkes equation, but this is not the case for the Lewis AB asymmetric term. 

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 ... 

Which of the two classical theories, of Fowkes and Owens-Wendt, will perform best in describing or predicting the interfacial tensions for these three mixtures ... 

Compare the Fowkes, Owens-Wendt and van Oss-Good theories for these non-aqueous liquid-liquid interfacial tensions. Which model performs best ... 

Problem 15.15 Validation of various theories using data for squalane liquid liquid interfacial tensions (data are from Fowkes et al., 1990)... 

According to the Fowkes-Young theory for the interfacial tension and under the assumptions where = y, the Zisman plot is given by the equation ... 

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. 

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