CREDs

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Assuming that the target interface can be modeled as a quiescent, sharp boundary, with Eq. (30) initially at equilibrium there is zero net flux of species Red across the interface and each phase has a uniform composition of Red, CRed, (where the integer i = 1 or 2). The initial condition is identical to Eqs. (11) and (12). 

However, at a less negative potential the limiting current is not attained, so that there is a dynamic equilibrium between cox and cred at the electrode therefore, according to eqn. 3.3 we obtain for ox... 

As [Ox] = cRed for quinhydrone, the second term on the right-hand side of this equation equals zero and the first and third are combined in the constant Eqh. The fourth term is simplified in different pH ranges as follows ... 

The charge transfer coefficient oc can be found from the dependence of j0 on C0x Or cRed-... 

When A—or A—>0, then cRed- 0 or cOx- 0. A limiting current is then formed on the polarization curve that is independent of the electrode potential (see page 286). If the initial concentration, e.g. of the oxidized... 

In the general case, the initial concentration of the oxidized component equals Cqx and that of the reduced component cRed. If the appropriate differential equations are used for transport of the two electroactive forms (see Eqs 2.5.3 and 2.7.16) with the corresponding diffusion coefficients, then the relationship between the concentrations of the oxidized and reduced forms at the surface of the electrode (for linear diffusion and simplified convective diffusion to a growing sphere) is given in the form... 

For the sake of simplicity, it will further be assumed that cRed = 0. 

The effect of transport phenomena on the overall electrode process can also be expressed in terms of the concentration or transport overpotential. The original concentration of the oxidized form cQx decreases during the cathodic process through depletion in the vicinity of the electrode to the value (c0x)x=o and, similarly, the concentration of the reduced form cRed increases to the value (cRed)A.=0. It follows from Eqs (5.4.18), (5.4.19) and (5.4.20) that... 

The first two terms on the right-hand side of this equation express the proper overpotential of the electrode reaction rjr (also called the activation overpotential) while the last term, r)c, is the EMF of the concentration cell without transport, if the components of the redox system in one cell compartment have concentrations (cOx)x=0 and (cRed)x=0 and, in the other compartment, Cqx and cRcd. The overpotential given by this expression includes the excess work carried out as a result of concentration changes at the electrode. This type of overpotential was called the concentration overpotential by Nernst. The expression for a concentration cell without transport can be used here under the assumption that a sufficiently high concentration of the indifferent electrolyte suppresses migration. 

The equilibration proceeds by electron transfer between the semiconductor and the electrolyte. The solution levels are almost intact ( REdox — redox)> since the number of transferred electrons is negligible relative to the number of the redox system molecules (cox and cred). On the other hand, the energy levels of the semiconductor phase may shift considerably. The region close to the interface is depleted of majority charge carriers and the energy bands are bent upwards or downwards as depicted in Fig. 5.60b. 

For simplicity we assume that the intermediate stays at the electrode surface, and does not diffuse to the bulk of the solution. Let (j>l0 and 0oo denote the standard equilibrium potentials of the two individual steps, and cred, Cint, cox the surface concentrations of the three species involved. If the two steps obey the Butler-Volmer equation the current densities j and j2 associated with the two steps are ... 

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