Specific surface free energy and the intermolecular potential

6 Specific surface free energy and the intermolecular potential 

While bearing in mind the conclusions that liquid surfaces contain a fraction of vacancies and that solid surfaces are seldom equilibrium structures, an estimate of the specific surface free energy of a condensed phase can be made using the method of separating a column of material into two parts. 

Let the mean equilibrium spacing of the molecules in the condensed phase be ro. Then, in a column of cross-sectional area a, the number of molecules in any layer perpendicular to the axis of the column is a/r . When the column is separated under reversible, isothermal conditions, the area of new surface produced 

For solids and liquids q is approximately 10 and, at sufficiently low temperatures, e is approximately the potential energy of a pair of molecules at the equilibrium separation, Uq. For the Mie potential (see section 1.3)  

Sublimation, for solids, and vaporisation, for liquids, correspond to the breaking of all the bonds between a molecule and its neighbours. Therefore, the molar enthalpy for sublimation or vaporisation (as is appropriate) is equal to qeNp jl where is the Avogadro constant. Hence  

---