Extended Fowkes equation

They extended Fowkes equation [liquation (7)] to a more general form as follows ... 

This represents the dispersion component of surface free energy, taken from reference 66 Calculated using extended Fowkes equation to two components, taken from reference 68 from reference 64... 

Calculated using extended Fowkes equation to three components, taken from reference 19... 

Following Fowkes proposition, various workers postulated, more or less successfully, extensions to Eq. 6.31 in order to include other types of interphase interactions. It must be emphasized that the term extended Fowkes equations is really a misnomer, since Fowkes did not condone their use. However, the two best-known versions are attributable to Owens and Wendt (1969) ... 

Chen et al. (1999) treated polyester films with plasma in six kinds of gases (O, Nj, He, Ar, H, and CH ). Results in terms of surface tension and three components, and and the critical surface tension of the polyester film are summarized in Table 3.9 (Chen et al., 1999). It is evident that the value of the surface tension of polyester film obtained by the extended Fowkes s equation (Fowkes, 1964) corresponds highly to y of Zisman s plots (Zisman, 1964), which coincides with the theory of (Kitazaki and Hata (1972). Surface tensions of polyester films treated with O, ... 

Keywords Solid surface tension Solid surface energy Contact angle Work of adhesion Zisman method Surface tension component mefliod Fowkes method Owais-Wendt-Rabel-Kaelble mefliod Extended Fowkes mefliod Equation of state... 

In addition to the methods discussed above, there are a few other solid surface tension determination methods, such as the Wu method [29, 30] and the Schultz methods [31, 32], which also fall into the category of partitioning surface tensions into independent components. Wu used the harmonic means to describe the interfacial surface tension instead of the geometric mean, based on a few slightly different assumptions to derive the equations for Wu s model. The Schultz methods can be considered as a special case of the extended Fowkes method. The contact angle of a polar liquid (usually water) on the solid is conducted in another nonpolar liquid medium (e.g., pure hydrocarbon compounds), or the contact angle of a nonpolar liquid on the solid is measured in another polar liquid medium. 

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]... 

Fowkes also extended this concept to solid surfaces. Going back to the equation for the work of adhesion (Eq. 36), neglecting the spreading pressure and using Eq. (87) allows the relationship shown in Eq. (88) to be derived. 

Fowkes [59,60] confirmed the validity of these equations by experimental and theoretical approaches, and has extended these concepts to solid/liquid systems by combining Equation 2.3 with Equation 2.15 to give ... 

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