Young equation, Fowkes

B. Semiempirical Models The Girifalco-Good-Fowkes-Young Equation... 

When the surface density of the solid is essentially that of the amorphous solid or supercooled liquid, Equation 1 becomes the familiar Fowkes-Young expression (18). Based on the generally accepted value of psa for polyethylene, psac values are computed. From these values, the specific volumes are obtained. The percent crystallinity in the surface region is computed from the specific volume. Table II lists the values of psac and the percent crystallinity of these films. 

For the same conditions, a similar result emerges from the Fowkes-Young equation... 

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

Equation (7.29) is known as the Girifalco-Good-Fowkes-Young equation. By using this relationship, the dispersion components of the solid or liquid surface tension could be evaluated. 

According to the Fowkes-Young theory for the interfacial tension and under the assumptions where = y, the Zisman plot is given by the 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]. 

Good-GLrifalco-Fowkes (GGF) equation Using ysi = ysv + yiv - 20(ysvyiv) in Young s equation leads to 1+COS0 2 Uvj Yggf obtained from a plot COS0 versus 4> is solid-liquid interaction parameter 0 = 1 if the interactions are purely dispersive. Based on Berthelot relation for attractive constants valid only when the solid-liquid interactions are dominantly dispersive. [77-82]... 

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 ... 

By combining his equation with the Young equation (Equation (648)), Fowkes obtained the Young-Fowkes equation... 

The empirical nature of is obvious, and it would be helpful to replace y by parameters having a sound basis in thermodynamic or statistical mechanical considerations. Recent efforts by Fowkes [40] to relate y to the dispersion forces between molecules at the interface have been especially promising in leading to tractable equations. An interesting direct correlation has been recently pointed out to us by Gar don [49] between the value of y of a solid polymer and the Hildebrand solubility parameter, 6, which is defined as the square root of the molar energy density—i.e., 6 = n/1E/p A simple consideration of the Young equation and the definition of y indicates that when cos 0=1,... 

Equation 24 is derived from the Young (Eq.21), the Dupre (Eq. 8) and the Fowkes (Eq. 10) equations by assuming complete wetting (cos 0 =0). Measurements with polar solvents give the polar component of the surface tension, but acid/base constants and the corresponding work of adhesion can also be calculated from them ... 

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]. 

Figure 6.2 Combination of Fowkes with the Young equation applied on several low energy surfaces (see Equation 6.2). Reprinted from Zisman (1964), with permission from American Chemical Society...

When the Fowkes equation of the interfacial tension is used together with the Young equation, show that ... 

Despite its simplicity, many success stories have been presented. For example, as already mentioned, using hquid—hquid interfacial tension data for several different mercury—hydrocarbons and water-alkanes, we can estimate ahnosf unique contributions for the dispersion surface tension of mercury (201 mN m ) and water (21.9 mN m ) (Hiemenz and Rajagopalan, 1997 Fowkes, 1964, 1980). These values appear to be reasonable and moreover when used to predict the interfacial tension of water-mercury, quite good agreement is obtained (see Example 3.3 and Problem 3.5). In addition to the success for hquid-hquid interfaces, the Fowkes equation has been used for solid interfaces with good results. As shown in Chapter 6, when combined with the Young equation, we obtain ... 

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. 

Using the Young and Gibbs equation [Eq. (1)] and Fowkes and Harkins (35] assumption that... 

By combining Eq. (13) with the Young equation (7), Fowkes derived the relationship... 

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