Potential differences, Gibbs, Helmholtz

Schofield Phil. Mag. March, 1926) has recently verified this relation by direct experiment. In order to appreciate the significance of this result, it is necessary to consider in more detail the electrical potential difference V and the manner in which it arises. Instead of regarding the phenomenon from the point of view of the Gibbs equation, it has been, until recently, more usual to discuss the subject of electro-capillarity from the conceptions developed by Helmholtz and Lippmann. These views, together with the theory of electrolytic solution pressure advanced by Nemst, are not in reality incompatible with the principles of adsorption at interfaces as laid down by Gibbs. 

Helmholtz and Gibbs energies are almost indistinguishable). Upon charging, or rather charge-separation, a potential difference is created. The electrical work of withdrawing protons against this potential is... 

The potential difference across the electrode/solution interface is dropped by the accumulation of ions of opposite charge in the solution immediately adjacent to the electrode surface in the electrochemical double layer. The spatial distribution of ions gives a potential profile across the double layer into the solution over a distance that is dependent upon the electrolyte concentration. Given this position-dependent potential profile, it is possible that species undergoing electrochemical reaction, which are assumed to reside in the outer Helmholtz plane of the electrical double layer adjacent to the substrate electrode (otherwise known as the plane of closest approach of nonspecifically adsorbed ions), may not actually be at ([is and hence would not experience the full electrical field corresponding to the electrode/solution potential difference. The result of this is that only a part of the measurable applied r] affects the Gibbs energy of activation of the process. The potential at the OHP with respect to solution, (t)s, is denoted t /i and is known as the potential of the (inner limit... 

Equations (4.39), (4.40), (4.41), (4.42), (4.43), (4.44), (4.45), (4.46), and (4.47) allow to calculate all material coefficients related to the Helmholtz free energy from coefficients derived from the Gibbs function and vice versa. In the example worked out above the two thermodynamic potentials differ in two of the independent variables. The same procedure may, in principle, be followed if in the transition from one potential to the other only one variable is exchanged. 

Often, the exponential dependence of the dark current at semiconductor-electrolyte contacts is interpreted as Tafel behavior [49], since the Tafel approximation of the Butler-Volmer equation [50] also shows an exponential increase of the current with applied potential. One should, however, be aware of the fundamental differences of the situation at the metal-electrolyte versus the semiconductor-electrolyte contact. In the former, applied potentials result in an energetic change of the activated complex [51] that resides between the metal surface and the outer Helmholtz plane. The supply of electrons from the Fermi level of the metal is not the limiting factor rather, the exponential behavior results from the Arrhenius-type voltage dependence of the reaction rate that contains the Gibbs free energy in the expraient It is therefore somewhat misleading to refer to Tafel behavior at semiconductor-electrolyte contacts. 

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