Electrochemical exchange potential-energy surfaces

Figure 2. Comparison between component potential-energy surfaces for elementary electrochemical exchange reaction for which the reaction entropy AS is positive (A) and resultant free-energy profile (B), plotted against the nuclear-reaction coordinate.

Figure 27. Representation of the competition between direct electron exchange (at around the conduction band edge at the surface) and exchange mediated by surface electron levels. Surface states may exchange electrons with the redox system in the energy interval at around the electrochemical potential. Surface states exchange electrons with the conduction band by electron capture and thermal electron excitation (vertical arrows).

As = surface area of a semiconductor contact [A ] = concentration of the reduced form of a redox couple in solution [A] = concentration of the oxidized form of a redox couple in solution A" = effective Richardson constant (A/A ) = electrochemical potential of a solution cb = energy of the conduction band edge Ep = Fermi level EF,m = Fermi level of a metal f,sc = Fermi level of a semiconductor SjA/A") = redox potential of a solution ° (A/A ) = formal redox potential of a solution = electric field max = maximum electric field at a semiconductor interface e = number of electrons transferred per molecule oxidized or reduced F = Faraday constant / = current /o = exchange current k = Boltzmann constant = intrinsic rate constant for electron transfer at a semiconductor/liquid interface k = forward electron transfer rate constant = reverse electron transfer rate constant = concentration of donor atoms in an n-type semiconductor NHE = normal hydrogen electrode n = electron concentration b = electron concentration in the bulk of a semiconductor ... 

When a metal, M, is immersed in a solution containing its ions, M, several reactions may occur. The metal atoms may lose electrons (oxidation reaction) to become metaUic ions, or the metal ions in solution may gain electrons (reduction reaction) to become soHd metal atoms. The equihbrium conditions across the metal-solution interface controls which reaction, if any, will take place. When the metal is immersed in the electrolyte, electrons wiU be transferred across the interface until the electrochemical potentials or chemical potentials (Gibbs ffee-energies) on both sides of the interface are balanced, that is, Absolution electrode Until thermodynamic equihbrium is reached. The charge transfer rate at the electrode-electrolyte interface depends on the electric field across the interface and on the chemical potential gradient. At equihbrium, the net current is zero and the rates of the oxidation and reduction reactions become equal. The potential when the electrode is at equilibrium is known as the reversible half-ceU potential or equihbrium potential, Ceq. The net equivalent current that flows across the interface per unit surface area when there is no external current source is known as the exchange current density, f. 

In general, two modes of energy storage are combined in electrochemical capacitors (1) the electrostatic attraction between the surface charges and the ions of opposite charge (electrical double layer) (2) a pseudo-capacitive contribution which is related with quick redox reactions between the electrolyte and the electrode [14,15]. Whereas the redox process occurs at almost constant potential in an accumulator, the electrode potential varies proportionally to the charge-exchanged dq m 2L pseudo-capacitor, what can be summarized by formula (Eq. 12.6) ... 

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