Contact Angles and Calculation of Solid Surface Energies

CONTACT ANGLES AND CALCULATION OF SOLID SURFACE ENERGIES 

Using a statistical treatment of the variation of local intermolecular forces as the interface is traversed from the Uquid to the vapor phase, it is possible to calculate the surface tension of a simple Uquid (e.g., argon) that agrees well with experiment. However, such exact methods become quite complex or (currently) impossible for calculating surface tensions in most practical systems. 

As is usually the case when theoretical and experimental science meet, it is necessary to make some simplifying assumptions in order to apply theories to practical systems. Good and Girifalco proposed an empirical approach to the problem based on the Berthelot principle that the interaction constant between two different surfaces or particles will be the geometric mean of the interaction constant for the individual surface units, an approach already introduced in Chapter 4. Good and Girifalco suggested that the work of adhesion between two different liquids could be expressed as a similar function 

For nonpolar liquids with 1 1, results agree reasonably well with experiment. For dissimilar substances, such as water and alkanes or water and mercury, values of 1 between 0.32 and 1.15 must be used to obtain agreement. 

The Good-Girifalco approach has been extended to the use of contact angles in the computation of surface tension values for solid-liquid interfaces. Considering a system where the fluid 2 is either vapor or air (in which case it can be ignored), and combining with Young s equation, one obtains the expression 

---