Helmholtz region

What happens when the concentration c0 of ions in solution is very large Equations (6.124) and (6.130) indicate that while CG increases with increasing c0, CH remains constant. Thus, as c0 increases, (1/CG) (1/CH), and for all practical purposes, C CH. That is, in sufficiently concentrated solutions, the capacity of the interface is effectively equal to the capacity of the Helmholtz region, Le., of the parallel-plate model. What this means is that most of the solution charge is squeezed onto the Helmholtz plane, or confined in a region vety near this plane. In other words, little charge is scattered diffusely into the solution in the Gouy-Chapman disarray. 

The relative changes in VH and Vsc as a function of surface state density are shown in Fig. 10.20. At low surface state density (<1012), the potential drop across the Helmholtz layer is small and remains almost constant with a change in electrode potential. However, at high surface state densities (>1013), the potential drop in the Helmholtz region increases and exceeds the potential drop in the space charge region for surface state densities greater than 5 x 1013 cm 2. 

Fig. 10.20. Relative potential drop in the space charge region and in the Helmholtz region as a function of surface state density. (Reprinted from K. Chandresakaran, R. C. Kainthla, and J. O M. Bockris, Elec-trochim. Acta 33 334, Fig. 12, copyright 1988, with permission from Elsevier Science.)...

In the Helmholtz region, the Poisson equation takes the simple form... 

The causes of this anomalous behavior are still not fully understood. It appears likely that many factors are involved surface film formation, varying potential drop across the Helmholtz region caused, for example, by surface state charging, etc. Even crystallographic orientations appear to be important [163]. These aspects have been discussed by other authors [14, 159, 164]. 

The consequences of potential drop variations across the Helmholtz layer in the hole injection process have been examined by a variety of techniques [191, 192]. For example, chemical reaction of the GaAs surface with iodine results in a downward shift of the semiconductor band-edge positions such that the reduction of iodine is mediated by conduction band electrons [192]. When sufficient negative charge accumulates at the surface, the potential is redistributed between the semiconductor space-charge layer and the Helmholtz region. Now iodine is reduced by hole injection as gauged by EL and AC impedance measurements [192]. 

Under conditions of fast surface melting of the 2D condensed layer and negligible desorption of monomers into the outer Helmholtz region, Lorenz [87] and Ran-garajan [165] suggested an ansatz based on the Langmuir isotherm... 

Historically, Frumldn-type models, which represent the Helmholtz region by a network of two or three condensers [449, 520-523] and classical thermodynamics based on a mean-field treatment [524-526], were apphed first to describe 2D phase transitions in organic adlayers at metal-electrolyte interfaces as a function of concentration, potential, and temperature (Sect. 33.2.2). In the simplest... 

Single and multiple potential step experiments demonstrated that the macrokinetics of the formation of the phy-sisorbed uracil film represents a first-order phase transition and follows the exponential law of nucleation (cf. Eq. (34)) in combination with surface diffusion-controlled growth [183]. In situ STM [20, 478, 479] and time-resolved SEIRAS studies [475] suggest that these processes are strongly related to the formation/breaking of uracil-water and water-water hydrogen bonds within the Helmholtz region. 

Hence, the difference between a semiconductor-solution interface and a metal-solution interface is that in the latter the Helmholtz region is the main part of the double layer and in the former there are two, i.e., the... 

Figure 9.16 Potential distribution across the SEI. and 4>yi are potential drops across space charge and Helmholtz regions, respectively. Adapted from reference (14).

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