Interfacial region, Helmholtz free

If the monolayer and its associated double layer occupy a separate phase which lies between two homogeneous bulk phases, then for constant temperature, volume, and total number densities of species in this phase, the total differential Helmholtz free energy for a planar interfacial region is given by (20) ... 

The Helmholtz free energy F for the interfacial region is defined in the usual way ... 

Fig. 5.2 - Grahame s model of the interfacial region in the immediate vicinity of the electrode 0 and 0 represent cations and anions respectively, andtl is a water molecule which may be free or involved in primary solvation. IHP is the inner Helmholtz plane, OHP is the outer Helmholtz plane.

Let us consider a multicomponent two-phase system with a plane interface of area A in complete equilibrium, and let us focus on the inhomogeneous interfacial region. Our approach is a point-thermodynamic approach [92-96], and our key assumption is that in an inhomogeneous system, it is possible to define, at least consistently, local values of the thermodynamic fields of pressure P, temperature T, chemical potential p, number density p, and Helmholtz free-energy density xg. At planar fluid-fluid interfaces, which are the interfaces of our interest here, the aforementioned fields and densities are functions only of the height z across the interface. 

Figure 19. The electronic structure of an n-type semiconductor/electrolyte solution interface under conditions of free electron depletion at the surface. Shown are the conduction and valence band edges as a function of the distance from the surface. The interfacial potential drop is distributed over a region in the solid (depletion region, width 4c) and the molecular Helmholtz layer at the liquid side (not shown). The interfacial capacitance is represented by a series connection of the capacitance of the depletion layer (Csc) and the Helmholtz layer (Csoi).

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