Surface tension component approach

Several other approaches have been developed to calculate the solid-vapour surface tension from contact angle measurements (22). The surface tension component approach was pioneered by Fowkes. He postulated that the total surface tension can be expressed as a sum of different surface tension components, each of which arises due to a specific type of intermolecular forces. Fowkes (e.g. see ref. (22)) argued that in van der Waals systems, only dispersion forces could effectively operate across the interface. Therefore, he obtained the following expression ... 

Surface tension component approaches do not reflect physical reality. Intermolecular forces do not have additional and independent effects on the contact angle. ... 

While intermolecular forces determine the interfacial tensions, they do not have additional effects on the contact angles hence the surface tension component approaches cannot describe physical reality. ... 

Good, van Oss, and Caudhury [208-210] generalized this approach to include three different surface tension components from Lifshitz-van der Waals (dispersion) and electron-donor/electron-acceptor polar interactions. They have tested this model on several materials to find these surface tension components [29, 138, 211, 212]. These approaches have recently been disputed on thermodynamic grounds [213] and based on experimental measurements [214, 215]. 

Some researchers [30-33] have challenged the validity of the equation of state. For example, to verify the equation of state experimentally. Spelt et al. [34] reported that the contact angles of two different testing liquids on a solid surface were identical when the liquid surface tensions were equal. On the contrary, van Oss et al. [31] showed that testing liquids of different surface tension values produced the same contact angle on the same solid, so that the results of Spelt et al. [34] could be completely explained by the theory of surface tension component. Johnson et al. [32] and Morrison [33] also criticized the method using Neumann s equation of state for its thermodynamic basis. However, Neumann et al. [35,36] rejected these criticisms and insisted on the thermodynamic validity of their approach. 

Thus by contact angle measurements using three different liquids (L), of which two must be polar, with known y Y and y values, the ys", Ys and ys of any solid (S) can, in principle, be determined. The value of yl must be known or determined independently [108]. The apolar component of the surface tension of solids (yj" ) can be determined by contact angle measurements using strictly apolar liquids for which yL = y These surface tension components can be related to experimentally determined pull-off forces between chemically modified AFM tips and an oxyfluorinated isotactic polypropylene surface in CFM approaches [110]. It was observed that the pull-off force measured with carboxylic acid tips in ethanol depended hnearly on the basic term of the surface tension (y,") on the modified polymer surface. 

In conclusion, the present approach to surface tension components has some apparent similarities with the vOCG model [4-6,28] but, in essence, it is a drastically different approach. The key feature is that it provides with a sound basis for the interactions dictating interfacial phenomena, which is fully compatible with the picture we have about intermolecular interactions from quantum chemical calculations. The new approach has not been tested extensively yet, but the tests of this woik are indicating a rather satisfactory agreement with experiment. Work is underway in our laboratory toward a more extensive testing of the new approach against experimental data. 

FIGURE 2.1 Left) Various surface tension components y (mJ/m ) for materials discussed in the text ( from 24 mJ/m assuming that y+/y = 1). (Right) Adhesive pressure versus interlayer thickness as predicted by eq. (2.3) for two flat montmorillonite surfaces separated by apolar organic films (e.g., an olefin). For small film thicknesses (<2.5 to 3 nm) this continuum approach is not valid rather, the adhesive pressure has discontinuous stable maxima (much higher than the dashed line) which correspond to integer numbers of monomer layers. 

Wu, W. Giese, R.F. van Oss, C.J. Evaluation of the Lifshitz-van der Waals/acid-base approach to determine surface tension components. Langmuir, 1995, 11, 379-382. 

Kwok D. (1999) The usefulness of the Lifshitz-van der Waals/acid-base approach for surface tension components and interfacial rensions. Colloids Surfa-Physicochem Eng Asp 156 191-200. 

Neumann and co-workers not only have presented a completely different approach but they do not believe in the surface tension component theories at all. They have stated this clearly many times. For example, Kwok and Neumann (2000a, p. 47) ... 

It is worth mentioning that Professor Good has not always been so critical. In his 1977 review (Good, 1977) he sees much promise in the - then - recently appeared Neumann theory, while he mentioned several reasons why the surface tension component theory could break down, among others the importance of entropic effects (incidentally discussed by others later, e.g. Douillard, 1997). Nevertheless, Professor Good and Professor Fowkes clearly converged to the notion that the surface tension component theories constitute the most successful approach, with special emphasis on the explicit treatment of the very important acid-base interactions. 

However, the most important difference between the two approaches lies on the way the surface tension components are estimated. In the van Oss-Good approach, the surface tension components for liquids and for solids are estimated from a wide range of experimental data (liquid-liquid interfacial tensions, contact angles, etc.) often regressed simultaneously for various solids and liquids. As we discussed, there are no predictive or estimation methods proposed by van Oss-Good for calculating these surface tension components. 

On the other hand, Panayiotou has proposed a novel and potential groundbreaking method for estimating the surface tension components. This is a method based on a quantum mechanical approach and, in particular, the COSMO-RS method pioneered by Klamt and co-workers (see Klamt (2005) for a detailed review of the method). 

In summary, there are three basic approaches to use contact angle data to determine the surface tensions of solid surfaces. These approaches are the Zisman method, the surface tension component methods, and the equation of state. Within these three approaches, there are many variants. It is reasonable to wonder the merit, accuracy, and limitation of some of the methods. The Zisman method is an empirical approach based on the correlation between the cosines of the contact angles on a solid surface versus the surface tensions of the test liquids. With alkanes, linear plots are usually obtained, and the critical solid surface tension (yc) is determined by extrapolating... 

The surface tension component method assumes that surface tension can be partitioned into different components, which address different intermolecular interactions individually. The overall surface tension will be the sum of all the components according to the linear free energy relationship. In the original Fowkes method [14], only the dispersion interaction is considered. The component method has been subsequentiy extended to include polar component and later divided the polar component into dipolar interaction and H-bonding interaction. The vOCG model appeared as a refined version of the surface tension component methodology. It assumes the existence of both additive and nonadditive components. The Lifshitz-van der Waals component (/ ) is additive, and the electron donor and acceptor components (7 and 7" ) are nonadditive. The solid surface tension (7sv) can be calculated by using three Uquids with known y, y and y values. Since this is a semiempirical approach, the calcu-... 

Liquid-Phase Components. It is usual to classify organic Hquids by the nature of the polar or hydrophilic functional group, ie, alcohol, acid, ester, phosphate, etc. Because lowering of surface tension is a key defoamer property and since this effect is a function of the nonpolar portion of the Hquid-phase component, it is preferable to classify by the hydrophobic, nonpolar portion. This approach identifies four Hquid phase component classes hydrocarbons, polyethers, siHcones, and duorocarbons. 

In the majority of continuum solvation models incorporating a surface-tension approach to estimating the non-electrostatic solvation components, the index k in Eq. (11.22) runs over a list of atom types, and die user assigns the appropriate type to each atom of the solute. This is particularly straightforward for MM models, like the Generalized Bom/Surface Area (GB/SA) model (Still el al. 1990 see also Best, Merz, and Reynolds 1997), since atom types are already intrinsic to the force field approach. This same formalism has been combined with the CHARMM and Cornell et al. force fields (see Table 2.1) to define GB models for proteins and nucleic acids (Dominy and Brooks 1999 Jayaram, Sprous, and Beveridge 1998). Considering this approach applied within the QM arena, the MST-ST models of Orozco and Luque have been the most extensively developed (see, for instance, Curutchet, Orozco, and Luque 2001). 

The same logic that we used to obtain the Girifalco-Good-Fowkes equation in Section 6.10 suggests that the dispersion component of the surface tension yd may be better to use than 7 itself when additional interactions besides London forces operate between the molecules. Also, it has been suggested that intermolecular spacing should be explicitly considered within the bulk phases, especially when the interaction at d = d0 is evaluated. The Hamaker approach, after all, treats matter as continuous, and at small separations the graininess of matter can make a difference in the attraction. The latter has been incorporated into one model, which results in the expression... 

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