Helmholtz double layer, transfer across

Fig. 4E Charge transfer across the Helmholtz double layer. The reactant is at the potential ( ), the product is at a potential (j) and the activated complex is at an intermediate position where the...

Metal deposition involves the transfer of mass across the interface, while for outer-sphere charge transfer to occur only electrons have to cross the interface, while both the reactant and the product stay on the solution side of the compact Helmholtz double layer. 

Having shown that charge is transferred across the interface by the metal cations, not by the electrons, one has to propose a mechanism that would explain the observed behavior, particularly the unexpectedly high reaction rate discussed in Section 19.7.1. In the model presented below it is assumed that the ions cross the interface by migration, under the influence of the high electric field in the Helmholtz double layer, caused by application of an overpotential. This field is given by... 

The electric field which actually affects the charge transfer kinetics is that between the electrode and the plane of closest approach of the solvated electroactive species ( outer Helmholtz plane ), as shown in Fig. 2.2. While the potential drop across this region generally corresponds to the major component of the polarization voltage, a further potential fall occurs in the diffuse double layer which extends from the outer Hemlholtz plane into the bulk of the solution. In addition, when ions are specifically absorbed at the electrode surface (Fig. 2.2c), the potential distribution in the inner part of the double layer is no longer a simple function of the polarization voltage. Under these circumstances, serious deviations from Tafel-like behaviour are common. 

The static - double-layer effect has been accounted for by assuming an equilibrium ionic distribution up to the positions located close to the interface in phases w and o, respectively, presumably at the corresponding outer Helmholtz plane (-> Frumkin correction) [iii], see also -> Verwey-Niessen model. Significance of the Frumkin correction was discussed critically to show that it applies only at equilibrium, that is, in the absence of faradaic current [vi]. Instead, the dynamic Levich correction should be used if the system is not at equilibrium [vi, vii]. Theoretical description of the ion transfer has remained a matter of continuing discussion. It has not been clear whether ion transfer across ITIES is better described as an activated (Butler-Volmer) process [viii], as a mass transport (Nernst-Planck) phenomenon [ix, x], or as a combination of both [xi]. Evidence has been also provided that the Frumkin correction overestimates the effect of electric double layer [xii]. Molecular dynamics (MD) computer simulations highlighted the dynamic role of the water protrusions (fingers) and friction effects [xiii, xiv], which has been further studied theoretically [xv,xvi]. 

For one-electron transfer reactions occurring via outer-sphere mechanisms, wp and ws can be estimated on the basis of electrostatic double-layer models. Thus, if the reaction site lies at the outer Helmholtz plane (o.H.p.), wp = ZFd and ws = (Z - 1 )Fcharge number of the oxidized species and (j>d is the potential across the diffuse layer. Rewriting eqn. (7) in terms of rate constants rather than free energies yields the familiar Frumkin equation [8]... 

The double-layer capacitance is taken into account by assuming a simplified Helmholtz parallel plate model (1). On opening the circuit, the potential difference, V, across the double layer must be reduced by diminution of the charge on each plate. For a cathodic reaction, each electron being transferred from the metal to the solution side of the interface effects an elementary act of reaction and reduces the charge, q, on each plate. Consequently the rate of reduction of this charge is equal to the faradaic current, and Eq. (55) follows, y is assumed to differ from rj simply by the value of the reversible potential ... 

Let us consider as an example a metallic iron electrode in an aqueous solution. The anodic metal dissolution is a process in which iron ions in the metallic bonding state in the metal phase transfer across the interfacial compact double layer (Helmholtz layer) into the hydrated state of the ions in the solution ... 

In the case of charge transfer, which occurs in the double layer, the driving force is related to the internal potential difference across the double layer. More precisely, it is linked to the difference between the potentials of the metal and the electrolyte at the Helmholtz plane l... 

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