Gibbs energy surface tension relationship

As in so many other fundamental aspects of the thermodynamics of surfaces, we are indebted to Gibbs 6) for pointing out that for solids the surface tension (7) and surface free energy (F ) are not equivalent quantities. Nevertheless, as Shuttleworth (7) mentions in an excellent review, the two terms have been (8) and still are (9) confused. The relationship between the quantities is... 

One important relationship can be derived directly from Eq. (3.29). For pure liquids we choose the Gibbs dividing plane such that T = 0. Then the surface tension is equal to the free surface energy per unit area ... 

The relationship between the surface tension, the chemical potential and the Gibbs surface energy is given by the general relation... 

In Chapter 9 we have shown the thermodynamic relationships among the surface tension, y, (which is the same as the excess surface Gibbs energy), the excess charge density on the metal, qM, the double layer capacitance, Cai, and the surface excess of a particular species, F,- (cf. Eqs. (9.8) to (9.14)). 

An important principle from thermodynamics is the well-known Gibbs adsorption isotherm, which provides a relationship among the bulk-phase concentration c, the interfacial concentration T, and the interfacial tension (essentially the surface free energy per unit area) ... 

In 1805 Young established a relationship between the contact angle of a drop of liquid and the interfacial tensions at the three-phase contact line between a solid, a liquid, and its vapor at equilibrium (Eq. 10.1). J. Willard Gibbs in 1928 then derived the contact angle 9, from thermodynamic quantities, the surface free energies for the three interfaces. Substantial refinements in terms of the nature of the forces involved in the wetting process have been made since then, and interested readers can consult fundamental texts on surface forces. ... 

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