Youngs Equation for Contact Angle

The change of the interface areas is proportional to +51, 81 cos 9, and -51 for the solid-liquid, liquid-gas, and solid-gas interface, respectively 

It may be noted that the Gibbs free energy contribution from all interfaces is considered in the calculation of total Gibbs energy in equation (5.8). After simplification, one gets Young s equation for the contact angle 6 as 

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Both Equations 1 and 2 can be applied to the Young equation for contact angle. 

All interfacial theories can be used to estimate the theoretical work of adhesion and, in combination with the Young equation for contact angle, also the solid components and solid surface tensions, which cannot be directly measured. Thus, the theories can be used to understand wetting and adhesion phenomena and for characterizing solid surfaces. 

It may be noted that equation (5.19) is same as Young s equation for contact angle equation (5.8). Substituting equation (5.19) in equation (5.18), we have... 

Figure 5.10. Derivation of the Young equation for the equilibrium contact angle.

The Young and Dupre equation for the angle of contact of a liquid resting on a solid surface may be derived as a thermodynamic relationship, but the testing of its validity for the real situation of a nonequilibrium and usually heterogeneous surface presents difficulties. These are discussed first in terms of two simple molecular models and secondly in terms of thermodynamic relationships that should permit an independent verification of the contact angle relationship. 

The Young equation for the contact angle 0 of a liquid on a smooth, rigid solid is... 

Using the above relationships and Young s equation (2.4) for contact angles, one can predict the value Ysl from ... 

Surface and colloid chemistry have only a few fundamental equations that are (almost) always true and they control many practical phenomena. All these general equations were developed more than a century ago. One of these fundamental equations is the Young equation for the contact angle, which is presented next. The other equations are the Young-Laplace, Kelvin and the famous Gibbs adsorption equation. They are also discussed in this chapter. 

There are two important approaches for studying wetting phenomena the Zisman s plot and the associated concept of the critical surface tension and the use of interfacial theories. These two approaches are presented in this section. The approach based on interfacial theories is somewhat more complex but provides more information. When combined with the Young equation for the contact angle (Chapter 4), interfacial theories can be used... 

The key property we can measure of relevance to solid interfaces is the contact angle which, for smooth surfaces, can be related to the surface tensions of the liquid and solid and the solid-liquid interfacial tension via the Young equation. For rough surfaces we need to account for the roughness factor which can be obtained, for example, by atomic force microscopy experiments. For high energy surfaces, the solid-vapour surface tension should be corrected for adsorption phenomena (spreading pressure). 

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. 

The Owens-Wendt method for the interfacial tension combined with the Young equation for the contact angle is given by (assuming zero spreading pressure) ... 

The Neumann equation is rarely used for liquid-liquid interfaces. It is most often used in combination with the Young equation for the contact angle and thus its application is to estimate the surface tension of solids. The p parameter in Equation 15.12 can be solid-specific but average values have been estimated based on three solids (FC-721-coated mica, heat pressed Teflon and PET). Thus, this parameter can be considered to be almost universal. The basic argument of Neumann and co-workers is that for a large number of solids which they have tested they find that... 

Young s equation is not only valid for contact angle measurements of drops of a liquid, L, on a solid, S, in air, but also for the measurement of contact angles of drops of a liquid, L, on a solid, S, immersed in a different liquid which is immiscible in liquid, L, e.g., an oil, O, using ... 

Examination of the Young-Dupre equation (Eq. 6.7) shows that, for the normal application of drop of known liquids on a solid surface of unknown properties, there Me three unknowns, 7 , and 7 . Determination of the values of these unknowns minimally requires three equations, hence contact angles are measined with three different liquids, but two of these liquids must be polar. The contact angles for an apolar liquid yields directly the value of... 

The preceding definitions have been directed toward the treatment of the solid-liquid-gas contact angle. It is also quite possible to have a solid-liquid-liquid contact angle where two mutually immiscible liquids are involved. The same relationships apply, only now more care must be taken to specify the extent of mutual saturations. Thus for a solid and liquids A and B, Young s equation becomes... 

The effect of surface roughness on contact angle was modeled by several authors about 50 years ago (42, 45, 63, 64]. The basic idea was to account for roughness through r, the ratio of the actual to projected area. Thus = rA. lj apparent and similarly for such that the Young equation (Eq.-X-18) becomes... 

Ruch and Bartell [84], studying the aqueous decylamine-platinum system, combined direct estimates of the adsorption at the platinum-solution interface with contact angle data and the Young equation to determine a solid-vapor interfacial energy change of up to 40 ergs/cm due to decylamine adsorption. Healy (85) discusses an adsorption model for the contact angle in surfactant solutions and these aspects are discussed further in Ref. 86. 

Since both sides of Eq. X-39 can be determined experimentally, from heat of immersion measurements on the one hand and contact angle data, on the other hand, a test of the thermodynamic status of Young s equation is possible. A comparison of calorimetric data for n-alkanes [18] with contact angle data [95] is shown in Fig. X-11. The agreement is certainly encouraging. 

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]. 

Methods of Measurement Methods of characterizing the rate process of wetting include four approaches as illustrated in Table 20-37. The first considers the ability of a drop to spread across the powder. This approach involves the measurement of a contact angle of a drop on a powder compact. The contact angle is a measure of the affinity of the fluid for the solid as given by the Young-Dupre equation, or... 

Combination of Eq. 7 or Eq. 8 with the Young-Dupre equation, Eq. 3, suggests that the mechanical work of separation (and perhaps also the mechanical adhesive interface strength) should be proportional to (I -fcos6l) in any series of tests where other factors are kept constant, and in which the contact angle is finite. This has indeed often been found to be the case, as documented in an extensive review by Mittal [31], from which a few results are shown in Fig. 5. Other important studies have also shown a direct relationship between practical and thermodynamic adhesion, but a discussion of these will be deferred until later. It would appear that a useful criterion for maximizing practical adhesion would be the maximization of the thermodynamic work of adhesion, but this turns out to be a serious over-simplification. There are numerous instances in which practical adhesion is found not to correlate with the work of adhesion at ail, and sometimes to correlate inversely with it. There are various explanations for such discrepancies, as discussed below. 

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