Overvoltage, redox

The accumulation is a dynamic process that may turn into a steady state in stirred solutions. Besides, the activity of accumulated substance is not in a time-independent equilibrium with the activity of analyte in the bulk of the solution. All accumulation methods employ fast reactions, either reversible or irreversible. The fast and reversible processes include adsorption and surface complexation, the majority of ion transfers across liquid/liquid interfaces and some electrode reactions of metal ions on mercury. In the case of a reversible reaction, equilibrium between the activity of accumulated substance and the concentration of analyte at the electrode surface is established. It causes the development of a concentration profile near the electrode and the diffusion of analyte towards its surface. As the activity of the accumulated substance increases, the concentration of the analyte at the electrode surface is augmented and the diffusion flux is diminished. Hence, the equilibrium between the accumulated substance and the bulk concentration of the analyte can be established only after an infinitely long accumulation time (see Eqs. II.7.12-II.7.14 and II.7.30). The reduction of metal ions on mercury electrodes in stirred solutions is in the steady state at high overvoltages. Redox reactions of many metal ions, especially at solid... 

According to these results it is favorable to apply semiconductor electrodes which exhibit a large overvoltage concerning the anodic decomposition but not for the oxidation of a redox couple. Unfortunately, there are only few examples which fulfil this condition. Another example was found with n-GaAs in the presence of Eu ... 

The reorganization free energy /.R represents the electronic-vibrational coupling, ( and y are fractions of the overpotential r] and of the bias voltage bias at the site of the redox center, e is the elementary charge, kB the Boltzmann constant, and coeff a characteristic nuclear vibration frequency, k and p represent, respectively, the microscopic transmission coefficient and the density of electronic levels in the metal leads, which are assumed to be identical for both the reduction and the oxidation of the intermediate redox group. Tmax and r max are the current and the overvoltage at the maximum. 

As the electrode potential is polarized fh>m the equilibritun potential of the redox reaction, the Fermi level efcid of electrons in the metal electrode is shifted from the Fermi level erredox) of redox electrons in the redox reaction by an energy equivalent to the overvoltage t) as expressed in Eqn. 8-24 ... 

Fig. 8-5. Electron state density in a metal electrode and in hydrated redox particles, and anodic and cathodic currents of redox electron transfer under cathodic polarization n s cathodic overvoltage (negative) i = anodic current i = cathodic current. [From (lerischer, I960.]...

Then, a concentration gradient of hj lrated redox particles arises in the interfacial diffusion layer and the Fermi level EnitEix ). of redox particles at the interface becomes different from the Fermi level ensEDox) of redox particles outside the diffusion layer as shown in Fig. 8-9(c). The partial overvoltages t]h and iidiff are then given by Eqn. 8-32 ... 

We consider a transfer of redox electrons at semiconductor electrodes polarized at an overvoltage t relative to the equilibrium redox potential (the Fermi level cfcredox)). The transfer current of redox electrons is given in Eqn. 8-54 by the arithmetic sum of the electron current via the conduction band, in(ti) - (0(11) > and the hole current via the valence band, ij(ii) - i (Ti) ... 

Polarization shifts the Fermi level of the electrode epoo from the Fermi level of the redox electron ekredox) by an energy equivalent to an overvoltage tj as described in Eqn. 8-55 ... 

Under the condition of band edge level pinning, where the interfacial electron level of electrode relative to the redox electron level of redox particles is imchanged, the level differences of ej - ered and ej. - eqx remain constant irrespective of any change of the electrode potential. Consequently, the anodic transfer current of redox electrons, in(T ), in Eqn. 8—60 is independent of the overvoltage and remains equal to the exchange current ia.o as expressed in Eqn. 8-62 ... 

Consequently, for the transfer reaction of redox electrons via the conduction band mechanism, the anodic current is constant and independent of the electrode potential whereas, the cathodic current increases with increasing cathodic overvoltage (decreasing electrode potential). 

As the polarization (the overvoltage t) ) increases of a redox reaction that requires the transport of minority charge carriers towards the electrode interface (anodic hole transfer at n-type and cathodic electron transfer at p-type electrodes), the transport overvoltage, t)t, increases from zero at low reaction currents to infinity at high reaction current at this condition the reaction current is controlled by the limiting diffusion current (iu.)tm or ip.um) of minority charge carriers as shown in Fig. 8-25. 

The transfer of anodic holes is associated with the following three processes the generation and transport of holes in the electrode the hole transfer across the compact layer and the diffusion of redox particles in aqueous solution. The total overvoltage, T], is the sum of the three overvoltages np sc for the generation and transport of holes in the electrode, ria for the transfer of holes across the electrode interface, and ii4ur for the diffusion of redox particles in the solution as defined in Eqn. 10-27 ... 

Further, the total overvoltage, ii, is the difference between the polarization potential E(=- aod the equilibrium redox potential (= - BvmvTm /e)... 

The interfadal overvoltage referred to the standard redox potential is defined, generally, by Eqn. 10-41 ... 

Figure 10-23 shows the electron levels and the polarization curves for the transfer of anodic redox holes both at a photoexcited n-fype electrode and at a dark p-type electrode of the same semiconductor. The range of potential where the anodic hole current occurs at the photoexcited n-type electrode is more cathodic (more negative) than the range of potential for the anodic hole current at the dark p-type electrode. The difference between the polarizatitm potential aE(i) (point N in the figure) of the photoexcited n-type electrode and the polarization potential pE(i) (point P in the figme) of the dark p-type electrode at a constant anodic current i is equivalent to the difference between the quasi-Fermi level pej of interfacial holes and the Fermi level bEf of interior holes (electrons) in the photoexcited n-type electrode this difference of polarization potential, in turn, equals the inverse overvoltage rip.sc(i) defined in Eqn. 10-46 ... 

Fig. 10-26. Energy diagram for a cell of photoelectrolytic decomposition of water consisting of a platinum cathode and an n-type semiconductor anode of strontium titanate of which the Fermi level at the flat band potential is higher than the Fermi level of hydrogen redox reaction (snao > epM+zHj) ) he = electron energy level referred to the normal hydrogen electrode ri = anodic overvoltage (positive) of hole transfer across an n-type anode interface t = cathodic overvoltage (negative) of electron transfer across a metallic cathode interface.

In MET, a low-molecular-weight, redox-active species, referred to as a mediator, is introduced to shuttle electrons between the enzyme active site and the electrode.In this case, the enzyme catalyzes the oxidation or reduction of the redox mediator. The reverse transformation (regeneration) of the mediator occurs on the electrode surface. The major characteristics of mediator-assisted electron transfer are that (i) the mediator acts as a cosubstrate for the enzymatic reaction and (ii) the electrochemical transformation of the mediator on the electrode has to be reversible. In these systems, the catalytic process involves enzymatic transformations of both the first substrate (fuel or oxidant) and the second substrate (mediator). The mediator is regenerated at the electrode surface, preferably at low overvoltage. The enzymatic reaction and the electrode reaction can be considered as separate yet coupled. 

The overvoltage may thus be diminished by using as mediator a redox couple that has a high heterogeneous rate constant. 

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