Surface excess Helmholtz free energy

CALCULATION OF THE SURFACE TENSION OF LIQUIDS FROM THE EXCESS HELMHOLTZ FREE ENERGY FUNCTION. 

CALCULATION OF THE SURFACE TENSION OF LIQUIDS FROM THE EXCESS HELMHOLTZ FREE ENERGY FUNCTION. //ENGLISH TRANSLATION OF ZH. FIZ. KHIM. 37,622-7,1963.//... 

As indicated in the discussion following Equation 1.29, the interfacial tension Y is equal to the smface excess Helmholtz free energy per unit area (F IA) when the reference surface is chosen to make the surface excess mass T vanish. But... 

With this dividing surface, the surface or excess Helmholtz free energy is the surface tension, as in (2.23). Thus, from the definition of (z) in (3.1)... 

Figure 5.4 To minimize the interfacial Helmholtz free energy a liquid drop shrinks its surface area to the least possible value. As a result, the pressure p" inside the drop is larger than the external pressure p. The excess pressure (p" -p )=27/r.

By analogy with a D-face, new excess quantities have to be introduced for all extensive thermodynamic quantities with respect to the TL. Details are not given here. For brevity, only a result of consideration of the Helmholtz free energy for a three-phase system in thermodynamic equilibrium under the influence of gravity is mentioned. It leads to a condition for the mechanical equilibrium at the TL on a solid with an arbitrary surface profile (roughness) ... 

The excess energy associated with an interface is formally defined in terms of a surface energy. This may be expressed in terms either of Gibbs, G, or Helmholtz, A, free energies. In order to circumvent difficulties associated with the unavoidably arbitrary position of the surface plane, the surface energy is defined as the surface excess [7,8], i.e the excess (per unit area) of the property concerned consequent upon the presence of the surface. Thus Gibbs surface free energy is defined by... 

The surface tension in units of (e(/Vo) is equal to the surface excess free energy (2.23), defined with respect to the dividing surface of (5.97). From the Gibbs-Helmholtz equation... 

At this point is must be emphasized again that a surface or interfacial tension is a tensor by its physical origin (cf O Chap. 4) and hence it may not be split into additive scalar components in general. Such additivity holds for the energy, and referring again to OEq. 6.11 for the specific excess free Helmholtz energy for a surface of phase A in equilibrium with its vapor phase... 

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