Surface Tension Component Methods

The method of equation of state is totally different from aU the surface tension component methods described in Sect. 7.2.2. The equation of state method assumes that the interfacial surface tension ysL depends on the surface tension of the liquid ytv and solid ysv only, i.e., ygL = /(/sv /lv)- Tho method was mainly developed in Neumann s laboratory [33-37]. Neumann et al. formulated three versions of the equation of state. The first version was based on Zisman s data comprising eight solid surfaces with low surface tensions [33,34]. According to Girifalco and Good [38], the liquid-solid interfacial surface tension between dissimilar molecules can be formulated as... 

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-... 

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. 

Two-liquid geometric and two-liquid harmonic methods are applied to calculate surface tension components of the TLCP films, as tabulated in Tables 6.3 and 6.4. For both tables, calculated values from various pairs of liquids are shown in the third, fourth, and fifth columns, respectively. Columns 6, 7, and 8 give their corresponding average values. In Table 6.3, it is found that three liquid pairs (water-diiodomethane, glycerol-diiodomethane, and formamide-diiodomethane) give comparable ys for each of the TLCPs by using the... 

TABLE 6.9. Surface Tension Components of 73/23 ABA/ANA Copolymers (Calculated with 3-Liquid LWAB method). 

In Table 11.3 are reported the COSMO volumes and areas and the surface tension components for a number of common solvents as calculated by the preceding method. In the last column are reported the total surface tensions as obtained from DIPPR [27]. It should be stressed that the values of the surface tension components in Table 11.3 are predicted ones and not fitted to experimental data other than the overall surface tension of the compound. 

The calculations with Equation 11.23 and Table 11.3 are in reasonably good agreement with the reported values for the Lifshitz-van der Waals surface tension component in the literature [4-6,28]. As an example, the y calculated from Equation 11.23 for methanol, ethanol, glycerol, and water are 17.23, 18.03, 31.97, and 21.13 mN/m, respectively, while the corresponding reported values [28] are 18.5, 20.1, 34.0, and 21.8 mN/m, respectively. Having the partial surface tensions of pure solvents, we may now proceed to the next step and propose a method for the surface-tension characterization of polymers and solid surfaces. 

Estimate using the Hansen-Beerbower method the surface tension components of ethyl acetate (surface tension equal to 23.9 mN m ). Then, using plausible assumptions estimate the surface tension of n-butyl acetate. 

Estimate the LW, acid/base and the total surface tension of all three epoxies. Surface tension components for the van Oss-Good method for water and MEG are given in Table 3.4, while for benzaldehyde it can be assumed that only LW contribution exists and the surface tension is 38.5 mN m. Comment on the values obtained for the individual components of the surface tensions for the three epoxies. 

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... 

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). 

Apply both methods (after having estimated suitable values for the surface tension components) to the interface between mercury and ethanol (22.27 mN m ) and mercury and methylene iodide (30.1 mN m ). Compare the results to the experimental values which are equal to 389 and 304 mN m respectively. 

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. 

It was made clear in Chapter II that the surface tension is a definite and accurately measurable property of the interface between two liquid phases. Moreover, its value is very rapidly established in pure substances of ordinary viscosity dynamic methods indicate that a normal surface tension is established within a millisecond and probably sooner [1], In this chapter it is thus appropriate to discuss the thermodynamic basis for surface tension and to develop equations for the surface tension of single- and multiple-component systems. We begin with thermodynamics and structure of single-component interfaces and expand our discussion to solutions in Sections III-4 and III-5. 

In general, the surface tension of a Hquid mixture is not a simple function of the pure component surface tensions because the composition of the mixture surface is not the same as the bulk. For nonaqueous solutions of n components, the method of Winterfeld, Scriven, and Davi is apphcable ... 

Defoamers, 3 236-254 9 23 applications, 3 245-249 commercial sources, 3 240, 241t components, 3 237-240 defoaming theory, 3 241-245 economic aspects, 3 249-250 health and safety factors, 3 251-252 in paper manufacture, 13 118 in polymer colloids, 20 386 silica in, 22 376 surface tension, 8 244t test methods, 3 250-251 Defoaming, 3 240-242 Defoaming (antifoaming) agents, 25 in diesel fuel, 12 428 in food, 12 63-64... 

Strictly speaking, Equation (2) allows the vertical component of surface tension to be measured. Since this equals 7 cos 0, we are actually making a single measurement that involves two parameters. If 7 were independently known, the Wilhelmy plate method could also be used to determine 0. Whether we seek to evaluate 7, 0, or both, two experiments are needed, and these may not both involve the factor cos 0. In Section 6.8a we discuss a second type of measurement that can be made with the Wilhelmy apparatus that supplies a complementary observation so both 7 and 0 can be determined on a single instrument. 

---