Contact angle Fowkes equation

The extensive use of the Young equation (Eq. X-18) reflects its general acceptance. Curiously, however, the equation has never been verified experimentally since surface tensions of solids are rather difficult to measure. While Fowkes and Sawyer [140] claimed verification for liquids on a fluorocarbon polymer, it is not clear that their assumptions are valid. Nucleation studies indicate that the interfacial tension between a solid and its liquid is appreciable (see Section K-3) and may not be ignored. Indirect experimental tests involve comparing the variation of the contact angle with solute concentration with separate adsorption studies [173]. 

Laplace equation A thermodynamic derivation Determining surface tension from the Kelvin equation Heat of immersion from surface tension and contact angle Surface tension and the height of a meniscus at a wall Interfacial tensions from the Girifalco-Good-Fowkes equation... 

The values obtained for n-hexanol-water were = 24.6 and = 1.9 dynes/cm and for water-hexanol, = 22 and yf = 12.4 dynes/cm. As regards the contact angle results obtained with n-hexanol, values of Oow obtained from Equations 14 and 15 and by experiment show a wide disparity. See Tables IV-VII. For paraffin wax, both equations predict zero contact angle for n-hexanol whereas the experimental values are 45° 6a) and 37°C Or), As discussed earlier, adsorption of alcohols at the solid/liquid interface may affect the wetting behavior of substrates. These effects are not accounted for by the Fowkes or Wu treatment, and hence it is not unexpected that these equations do not correlate with experimental Oow values for hexanol/water. 

Combining the Fowkes (22) equation for the Interfacial tension, Ya between two phases with Young s equation for the contact angTe, 6, of a liquid, l, and a solid, s, when only London forces operate across the Interface, a relationship Is obtained between the equilibrium contact angle, 9, and the various tensions ... 

The dispersive component is associated with polymer-filler interaction and the specific component is associated with filler networking and agglomeration. The dispersive component of different fillers is more conveniently measured by inverse gas chromatography although it can also be measured by contact angle methods. The work of adhesion is given by the following equation, which has been modified to account for Fowkes theoiy. 

Some experiments very similar to these outlined above were carried out by Ruch and Bartell [31]. Metal surfaces were equilibrated with aqueous decylamine, and the air-liquid-solid contact angles were then measured, using small air bubbles. The degree of adsorption of the decylamine was determined by optical measurements of the thickness of the film, but could be only approximately related to actual amounts adsorbed. While the results correlated well with a semi-empirical analysis, they unfortunately do not allow a verification of Equation 25. As shown in Figure 5, a qualitative calculation of > using the solution adsorption data, then allows calculation of TTgyo, assuming Equation 25 to hold. Clearly this last quantity is far from zero, as opposed to the situation assumed by Fowkes and Harkins for their system. Ruch and Bartell in fact took the adsorbed film to be identical in nature at the SL and the SV interfaces, but without any independent verification of the assumption. 

Fluorocarbon and hydrocarbon modified PDMS surfaces are compared in Table 2. The contact angle data are obtained by the Good-Girifalco-Fowkes equation. It is striking that the hydrocarbon contact angle liquid gives better agreement with the JKR result for the hydrocarbon surface whereas the fluorocarbon liquid data better fit the fluorocarbon surface... 

From a practical applications point of view, both the critical surface tension approach and the use of contact angles with the Good-Girifalco-Fowkes equation represent handy tools for the characterization of the wettability, and therefore something of the chemical nature, of solid surfaces. The choice of technique is basically one of preference and convenience. 

In this table, is calculated from the Girifalco-Good-Fowkes-Young equation [20] using -hexadecane as the sole contact angle test liquid ... 

Similar equations can be written for the solid/liquid interface. Fowkes derived an expression for the contact angle [12],... 

Fowkes [12] obtained the following equation for the contact angle of a liquid on a... 

In order to calculate polymer/filler interaction, or more exactly the reversible work of adhesion characterizing it, the surface tension of the polymer must also be known. This quantity is usually determined by contact angle measurements or occasionally the pendant drop method is used. The former method is based on the Young, Dupre and Fowkes equations (Eqs. 21,8, and 10), but the result is influenced by the surface quality of the substrate. Moreover, the surface (structure, orientation, density) of polymers usuaUy differs from the bulk, which might bias the results. Accuracy of the technique maybe increased by using two or more liquids for the measurements. The use of the pendant drop method is limited due to technical problems (long time to reach equilibrium, stability of the polymer, evaluation problems etc.). Occasionally IGC is also used for the characterization of polymers [30]. 

The /-parameter is obtained in the usual way by combining this equation with the Young equation for the contact angle and by subtracting the experimental spreading coefficient from the one estimated fi om the Fowkes equation. 

Compare your results to these diverse values from the literature and provide an explanation for the wide range of contact angle values reported. What type of contact angle is calculated with the Fowkes equation and how can the Fowkes equation be used to analyse the PE surfaces in this case ... 

Fowkes and Maruchi tested Drago s hypothesis applied to the interaction of liquids with a solid surface by measuring the contact angles of various acidic and basic liquids (which had been characterized by Drago in terms of their E and C parameters) on different acidic and basic surfaces. Fowkes calculated and for the liquid and solid and examined the difference between these two quantities, which according to the preceding equations is given by... 

A frequently used method to measure the Hamaker constant of solids is based on the idea that the interaction of a solid surface with nonpolar liquids will mainly occur through the London dispersion interaction. One can therefore define a dispersive surface tension 7° that contains only the dispersive contribution. The value of Ys can be determined from contact angle measurements with nonpolar liquids using the Fowkes equation [83]... 

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. 

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