Electrical contribution, free energy interface

The first integral in Equation 17 is identified as the electrical contribution to the change in free energy in forming the charged interface (3) and may be evaluated using Equation 12... 

We recall that the first integral in Equation 23a represents the change in electrical free energy in forming the diffuse double layer. This contribution to f, the free energy of formation of the charged interface, is positive and hence represents an unfavourable component which opposes the formation of the charged interface. 

The free energy barrier for the flow of ionic charge across the oxide electrode-electrolyte interface has an electrical contribution and consequently the reaction rate can be formally described by Butler-Volmer-type equations [38]. The cation current density corresponding to the process... 

The adsorption of either ions or neutral molecules on the electrode surface depends on qn, i.e., on the apphed electric potential. Correspondingly, the electric field at the electrochemical interface is an additional free-energy contribution that either favors or restricts the adsorption of species on the electrode from the ionic conducting phase. A variety of adsorption isotherms has been proposed to account for the behavior of different electrochemical systems. Among them are the Langmuir, Frumkin, and Temkin isotherms [2]. Frumkin and Temkin isotherms, at variance with the Langmuir one, include effects such as adsorbate—adsorbate or adsorbate—surface interactions. 

The reorganization free energy is usually split in two parts. The local mode contribution is obtained in standard routines which require local potentials (say harmonic potentials) and vibrational frequencies in the reactants and products states. The collective modes associated with the proteins and the solvent, however, pose complications. One complication arises because classical electrostatics needs modification when the spatial extension of the electric field and charge distributions are comparable with the local structure extensions of the environment. Other complications are associated with the presence of interfaces such as metal/solution, protein/solution, and metal/film/solution interfaces. These issues are only partly resolved, say by nonlocal dielectric theory and dielectric theory of anisotropic media. 

If, on the other hand, the lamellae are perpendicular to the conductor surfaces, all the interfaces are parallel to the field and so there will be no excess polarization charges. The electric field will be a constant VId throughout the material. The electrostatic contribution to the free energy can be easily calculated to be... 

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