Solid surface tension, contact angle component methods

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... 

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. 

There are three unknowns in the solid surface tension, y v, and Tsv in Eq. (7.15). To calculate/sv. one can use three test liquids with known Tlv> y[y> and values. The component solid surface tensions can be determined from the three contact angles, and /sv is simply the sum of the three components. This method is also known as the three-liquid method. 

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. 

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... 

Two methods can be used for the assessment of y and its components contact angle measurements and inverse gas chromatography (IGC) [31]. Chibowski and Perea-Carpio [32] reviewed the problems encountered when attempting to determine the surface free energy of powered solids, like silica particles, using the contact angle technique. Wu reviewed the different techniques that can be employed to measure the surface tension of polymer melts [30]. These techniques are based on the pendant and sessile drop techniques that require density data or contact angle measurements. 

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. 

Eq. 12 is developed for liquid adsorption on solid, although the molecules adsorbed at infinite dilution do not form an adsorbed liquid film. Schultz et al. demonstrated the validity of this equation, and of the assumptions made, under certain conditions, by comparing the surface energy measured by contact angle method with that determined by gas-solid adsorption on solid surfaces the dispersive component of the surface energy of the liquid equals the surface tension of the alkane probe at the same temperature, i.e., Tl = 7h represents the surface... 

Several authors have tried to determine critical surface tensions for solid surfaces by determining the contact angles for a set of solutions of different concentrations. Zisman s method is, however, not applicable to solutions due to the large probability for specific and selective adsorption of the components constituting the solution. 

The harmonic mean equation is generally considered to be applicable to low surface tension materials such as organic polymers and liquids. If y and y are known for two liquids, and the contact angles of those liquids on the solid of interest are measured, equation 36 produces two simultaneous equations that can be solved to find the surface tension and polarity of a solid polymer surface. Numerous assumptions have been made in developing the theory of fi actional polarity. For example, it ignores the possibility of induced polarity at the interface between polar and nonpolar materials (82). These assumptions limit the application of equation 36 to systems where at least one and preferably both of the components are relatively nonpolar. The theory breaks down when interfacial interactions lead to molecular rearrangements at the interface between solid and liquid. In addition, it was foimd that pairs of liquids with similar dispersive and polar components of surface tension gave umeasonable results for the substrate surface tension calculated by the harmonic mean method (83). 

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