Theoretical aspects of contact angle phenomena

Within the core region the profile of a drop is modified by surface forces, such as long-range van der Waals and electrostatic double-layer forces [220], These forces affect the profile in a range of 1-100 nm. They can cause a difference between the microscopic contact angle and the macroscopic one (which enters into Young s equation) [268,269], If the liquid is attracted by the solid surface and this attraction is stronger than the attraction between the 

In many applications it is possible to determine 7l and, with more difficulty, 7s, but not 7sl- Therefore, it would be helpful to express 7sl through 7l and 7s. Since 7sl, 7l, and 7s are independent parameters we can only hope to find an approximate expression and we have to use additional information. Girifalco, Good, and Fowkes considered solids and liquids, in which the molecules are held together by van der Waals forces [270,271], Then, in a thought experiment they separated two materials at the interface (Fig. 7.11). The required work of adhesion per cross-sectional area is w = 71 + 72 — 712. Two new surfaces are formed while the interfacial area disappears. Rearrangement leads to 

Now we recall Section 6.2.3. The work of separating two solids to an infinite distance against the van der Waals attraction, is given by Eq. (6.29) 

Do is a typical interatomic spacing and A12 is the Hamaker constant for the interaction of material 1 with material 2 across a vacuum or gas. According to Eq. (6.28) the mixed Hamaker constant can be expressed by 

The Hamaker constants of the single materials are related to the surface tensions 

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