Owens-Wendt equation

The poly(MPC) brush gave a quite wettable surface. The contact angle of the water droplet (2.0 pL) on poly(MPC) brush surface was very low (below 5°). The contact angles of methylene iodide and hexadecane were 45° and <5°, respectively. Using the Owens-Wendt equation [49], the surface free energy of the poly(MPC) brush surface was estimated to be 73 mJ/m, which is quite similar to that of water. Therefore, water plays the role of a good solvent, resulting in low friction of the poly(MPC) brush. Ho et al. [50] prepared a low-friction surface on polyurethane... 

To do so, we must perform contact angle measurements for different liquids on the same solid. The minimum number of required data depends on the theory. In the case of Owens-Wendt we need data for two liquids on the same solid, while the most advanced theories (Hansen/Beerbower and van Oss-Good) require data for at least three liquids on the same solid. Graphical methods can also be used, e.g. the Owens-Wendt equation can be written in the form ... 

The Owens-Wendt theory often performs better than Fowkes equation for polar systems, but problems have been often reported, e.g. for systems like ethanol-water and acetone-water, which are erroneously predicted to be as immiscible as benzene-water. Nonetheless, Owens-Wendt is an old theory, well-established in certain fields, with extensive parameter tables and many successful appKcations, particularly for polymers. Table 6.2 shows some parameters of the Owens-Wendt equation for liquids and some polymers. 

In the Fowkes and many subsequent equations, it is assumed that the surface tension can be divided into imaginary contributions from the various intermo-lecular forces, e.g. dispersion and remaining specific forces in the Fowkes and subsequently in the Owens-Wendt equation (OW) (Equations 3.19 and 3.22a). These theories have since been known as surface component or simply component theories . It is a very useful concept in the sense that, if these surface components could be calculated reliably, we could obtain information about the contribution of the various intermolecular forces on the... 

Apply the Fowkes and Owens-Wendt equations to these interfaces. What do you conclude on the apphcabUity of these methods for these interfaces ... 

Evaluate the GG (without the correction parameter ( ) ), the Fowkes and the Owens-Wendt equations for the squalane systems with water, aniline, pyridine, ethanol and acetone as well as for the ethanol-acetone system (whieh is miscible). Provide a discussion. 

The geometric-mean approach has been in constant use for more than three decades, even though many articles have been published proving it to be incorrect. The Owens and Wendt equation falsely predicts ethanol and acetone to be as immiscible in water as benzene The main problem is the incorrect assumption that all polar materials interact with all other polar materials as a function of their internal polar cohesive forces. That is... 

This method utilizes a similar approach to Owens and Wendt s method but uses a harmonic-mean equation to sum the dispersion and polar contributions. Wu reported that the Owens and Wendt equation was giving surface tension values for polymers in error by as much as 50-100% when compared with their melt values, particularly for polar polymers. He suggested that a harmonic (or reciprocal) mean approximation might be better for polar polymers as given ... 

Owens, Wendt, Kaelble and others (see ref. (22)) argued that the polar interaction could be computed by using the same geometric mean mixing rule as for the dispersion force interaction. One then obtains the following equation ... 

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 ... 

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). 

Considering ten different polymeric sohds (PS, PE, PET, PMMA, PVC, etc.) he found that the /-parameter is proportional to a polar surface tension component of the liquid but he states that it is possibly a complex function of the polar contributions to the surface tension from both liquids and sohds. There is also some scatter in these plots and he does not propose the simple square root expression adopted by Owens and Wendt (Equation 3.22b). Similar results were presented with the same method by others as well (Schultz et al, 1977a,b) who used it to determine the surface energy components of high... 

The Owens-Wendt method for the interfacial tension combined with the Young equation for the contact angle is given by (assuming zero spreading pressure) ... 

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. 

The van Oss-Good equation can result in either positive or negative interfacial tensions, the latter simply meaning miscible liquids. Thus, it is possible for the van Oss-Good theory to predict repulsive van der Waals forces which can be present in certain systems (van Oss et al, 1988, 1989). Because van Oss-Good can also predict negative interfacial tensions, it has been shown to predict well the solubility in aqueous polymer solutions (van Oss and Good, 1992) where Owens-Wendt fails. It has also been applied with success to biopolymers (van Oss et al,... 

Compare the Fowkes, Owens-Wendt and Harmonic Wu equations for the four polymer mixtures for which experimental data were provided. Which method performs best Provide a short discussion. 

Water was chosen as a polar, and di-iodomethane as a non-polar liquid to compare the surface properties of the hybrid polymer layers containing different commercially available long chain perfluoroalkyl silanes (1 mol% each) with those of other surfaces. The measured contact angles and the surface energy data of the solids calculated according to the Owens and Wendt equation [24] are given in Table 6.3. The increase in the contact angles as a measure for a clearly reduced wettability can be observed with both test substances. 

Contact angles are measured with two liquids (e.g., water and methylene iodide) and values are substituted into the Owens-Wendt-Kaelble equation (4,5,26,31,32)... 

Owens-Wendt-Rabel-Kaelble (OWRK) method. Owens and Wendt [19] modified the Fowkes model by assuming that solid surface tension and liquid surface tensions are composed of two components, namely, a dispersion component and a hydrogenbonding component. The nondispersive interaction was included into the hydrogenbonding component. Nearly at the same time, Rabel [20] and Kaelble [21] also published a very similar equation by partitioning the solid surface tension into dispersion and polar components. Subsequent researchers called this as the OWRK method, and ysv and jiv can be expressed as... 

Owens and Wendt proposed an even more general equation for the work of adhesion between two arbitrary media [1121. In analogy to dispersion forces they used the geometric mean also for the other force components ... 

In 1969, based on the Fowkes equation, Owens and Wendt proposed a new expression by dividing the surface tension into two components, dispersive, yf, and polar, y , using a geometric mean approach to combine their contributions. They assumed that the free energy of adhesion of a polymer in contact with a liquid can be represented by the equation... 

Owens and Wendt applied only two liquids to form drops in their experimental surface tension determinations. They used fw = 21.8 and y(v =51.0 for water, and y= 49.5 and y[v = 1.3 mj m 2 for methylene iodide, in their calculations. After measuring the contact angles of these liquid drops on polymers, they solved Equation (693) simultaneously for two unknowns of yfv and y( v, so that it would then be easy to calculate the total surface tension of the polymer from the (ysv = yfv + 7sv) equation. Later, Kaelble extended this approach and applied determinant calculations to determine ysv and y(v- When the amount of contact angle data exceeded the number of equations, a non-linear programming method was introduced by Erbil and Meric in 1988. 

It is obvious that the harmonic-mean approach has the same defects as the Owens and Wendt approach, and that internal cohesive polar interaction properties cannot determine the interfacial interaction energy between two dilferent materials. This equation was also abandoned. 

For the values of the surface energies which must be inserted in the Dupre equation, recent surface energy data for the polymers used in this study, which were determined by Erhard (21) could be used. Erhard determined experimentally the surface free energies of the polymers and computed the work of adhesion with the method of Owens and Wendt. Table II shows the data of the work of... 

The surface free energy of a solid/iiquid interface can be described as a function of individual force components of the solid and liquid. For the relationship, the following equation, which was assumed by Owens and Wendt [21], is most reliable for polymeric solids ... 

Equation 2.7 is also referred as the Girifalco-Good equation. Alternative equahons have been proposed by Owens and Wendt [34] ... 

Table 59.3 is based primarily on the Zisman critical surface tension of wetting and Owens and Wendt approaches because most of the polymer data available is in these forms. The inadequacies of equations such as Eq. (59.7) have been known for a decade, and newer, more refined approaches are becoming established, notably these of van Oss and coworkers [24]. A more limited number of polymers have been examined in this way and the data (at 20 °C) are summarized in Table 59.4. is the component of surface free energy due to the Lifshitz-van der Waals (LW) interactions that includes the London (dispersion, y ), Debye (induction), and Keesom (dipolar) forces. These are the forces that can correctly be treated by a simple geometric mean relationship such as Eq. (59.6). y is the component of surface free energy due to Lewis acid-base (AB) polar interactions. As with y and yP the sum of y and y is the total solid surface free energy, y is obtained from... 

The validity of this equation is now well established. By analogy with the work of Fowkes, Owens and Wendt [4] and then Kaelble and Uy [5] have suggested that the non-... 

Here andy are the acid components of the surface free energy for phases 1 and 2, and 7, and 7a are the basic components. This equation is similar to that of Owens and Wendt in that it contains geometric mean terms, but effectively the polar contribution to van der Waals forces have been replaced by two... 

The Ys values are obtained by the Owens and Wendt approach [10] (Equation 9.3) using water and diiodomethane, where y is the sum of the dispersion force component of surface tension, y, and the polar component, and the subscripts LV and SV refer to the liquid/vapor and solid/vapor interfaces, respectively. 

Tamai et al. [61] and Dann [62] introduced an energy term, —lab, into Equation 2.14 to account for the stabilization by non-dispersion forces. However, yf cannot be evaluated merely by the introduction of this term. Consequently, Owens and Wendt [63] and Kaelble and Uy [64], by analogy with the work of Fowkes, have proposed that Ub may be expressed by the relation 2 yly Y. This expression may be introduced into Equation 2.15 to give ... 

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) ... 

Kaelble and Uy together with Owens and Wendt suggested that the effects of all polar interactions, including hydrogen-bonding interactions, could be considered as one term in equations (10) and (11) the work of adhesion then simplifies to two terms, W% and By assuming that polar interactions between two phases could be approximated by a geometric mean expression, they obtained from equation (12)... 

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