Double Helmholtz layer

FIGURE 1.21 Model of the Helmholtz electric double layer. 

When the charge on the solid surface is determined by the specific adsorption of and OH , which is the case for many semiconductors, Vh is determined by the reaction 

Equations (1.31) and (1.32) indicate that [H, which changes linearly with Vh, will vary slowly compared with [HsO, which changes exponentially with Vh. As an approximation we have 

The Helmholtz capacity of a metal electrode is typically on the order of 10 laF/cm, which is much greater than the value for a silicon electrode. It has been reported that the Hehnholtz layer capacitance of silicon in 0.1 M JMFe(CN)6 + 0.5 M KCl aqueous solution is about 3pF/cm. ln 0.1 M tetrabutylammonium perchlorate (TBAP) in acetonitrile it is found to be about 1.5 aF/cm. A larger Ch value, 22 p,F/cm, has been found for deep accumulation of a silicon in acetonitrile and the value varies with the accumulated charge.  

In addition to the intrinsic states, tha-e are also Lewis sites and adsorbed electroactive species. Lewis sites arise from the acid/base properties of the surface. A Lewis acid site is a site attractive to electron pairs from an adsorbing molecule and a Lewis basic site is able to donate electron pairs to an adsorbing molecule. For example, a Lewis acid site M or a basic site N may adsorb a OH ion or a from water, respectively  

Adsorption at acidic sites M causes the solution to become acidic and adsorption of H on Lewis basic sites causes the solution to become basic. Lewis sites are important in two ways they contribute to the Helmholtz double layer, and they result in chemical adsorption and passivation of the intrinsic active surface sites. The surface of sihcon is dominated by basic Lewis sites as manifested by the strong hydrogen adsorption. But the associated surface states are not active because they are located energetically in the valence band.  

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For many practically relevant material/environment combinations, thennodynamic stability is not provided, since E > E. Hence, a key consideration is how fast the corrosion reaction proceeds. As for other electrochemical reactions, a variety of factors can influence the rate detennining step. In the most straightforward case the reaction is activation energy controlled i.e. the ion transfer tlrrough the surface Helmholtz double layer involving migration and the adjustment of the hydration sphere to electron uptake or donation is rate detennining. The transition state is... 

In 1979, a viable theory to explain the mechanism of chromium electroplating from chromic acid baths was developed (176). An initial layer of polychromates, mainly HCr3 0 Q, is formed contiguous to the outer boundary of the cathode s Helmholtz double layer. Electrons move across the Helmholtz layer by quantum mechanical tunneling to the end groups of the polychromate oriented in the direction of the double layer. Cr(VI) is reduced to Cr(III) in one-electron steps and a colloidal film of chromic dichromate is produced. Chromous dichromate is formed in the film by the same tunneling mechanism, and the Cr(II) forms a complex with sulfate. Bright chromium deposits are obtained from this complex. 

The potential for electrochemical corrosion in a boiler results from an inherent thermodynamic instability, with the most common corrosion processes occurring at the boiler metal surface and the metal-BW interface (Helmholtz double layer). These processes may be controlled relatively easily in smaller and simpler design boilers (such as dual-temperature, LPHW heating, and LP steam boiler systems) by the use of various anodic inhibitors. 

The potential between the Helmholtz double layer of a charged particle. Important for assessing the suitability of polyelectrolyte chemicals because it can be easily measured, unlike some other electrokinetic forces. 

On the basis of this argument, the mechanism for the current oscillation and the multilayer formation can be explained as follows. First note that U is kept constant externally with a potentiostat in the present case. In the high-current stage of the current oscillation, the tme electrode potential (or Helmholtz double layer potential), E, is much more positive than U because E is given hy E=U —JAR, where A is the electrode area, R is the resistance of the solution between the electrode surface and the reference electrode, andj is taken as negative for the reduction current. This implies that, even if U is kept constant in the region of the NDR, is much more... 

For moderately doped substrates, when the surface is free of oxide the change of potential is mostly dropped in the space charge layer and in the Helmholtz double layer. The reactions are very sensitive to geometric factors. The reaction that is kinetically limited by the processes in the space charge layer is sensitive to radius of curvature, while that limited by the processes in the Helmholtz layer is sensitive to the orientation of the surface. Depending on the relative effect of each layer the curvature effect versus anisotropic effect can vary. 

An electrode bears a layer of indium-tin oxide (ITO) having an impedance of 25 Q, on which is a layer of adsorbed chromophore having an impedance of 1.0 (all values of Z being cited at fixed frequency). In addition, between the chromophore layer and the bulk electrolyte is the Helmholtz double-layer (see Section 5.1.2), which has an impedance of 120 By assuming that these three layers act as impedances in parallel, calculate the total impedance, Ziotai-... 

Figure 4.5. Electrical equivalent of the Helmholtz double layer a parallel-plate capacitor.

In Section 4.3 it was shown that the electrical equivalent of the Helmholtz double layer is a parallel-plate capacitor (Fig. 4.5). In Section 4.5 (Fig. 4.9) it was shown that... 

Meinert and others [85] have stated that their concept for the electrochemical fluorination of organic compounds is based on the assumption that the first step is the anodic oxidation of the organic molecule. The electrochemical process is promoted by weakening of the C-H bonds due to hydrogen-fluorine bridges. After anodic withdrawal, the C-F bond is formed by insertion of a fluoride ion, present in the Helmholtz-double-layer at the electrode surface. 

Fig.. 1 The electroactive complex diffuses from ihc bulk electrolyte solution tA) through the diffusion layer (B) to the Helmholtz double layer (C) to be discharged as metallic chromium D on Hie cathode surface (Fj. After General Motors color sketch I...

It is to be noted that the Helmholtz double layer plays a significant role in concentration polarization since the concentration of the ions on the electrode surface, and the diffusion of ions from the bulk of the solution into the Helmholtz plane are contributing factors to the limiting current density. This situation may be visualized as shown below ... 

Calculations for two water molecules with their dipole axes and one lone pair each parallel (i.e., in parallel Verwey positions for positive ions, as would be possible in a Helmholtz double layer) in which an accurate DP point charge model was compared with a simple dipole model showed die latter to be 11.6% high at 2.0 A separation, and 4.6%, 1.5%, 0% high at 2.25, 2.5, and 2.75 A, and 1.4%, 2.6%, and 3.3% low at 3.0. 3.5. and 4.0 A. 

Conway, B. E., J. O M. Bockris, and I. A. Ammar. 1951. The dielectric constant of the solution in the diffuse and Helmholtz double layers at a charged interface in aqueous solution. Trans. Farad. Soc. 47 756-766. 

In the non-steady state, changes of stoichiometry in the bulk or at the oxide surface can be detected by comparison of transient total and partial ionic currents [32], Because of the stability of the surface charge at oxide electrodes at a given pH, oxidation of oxide surface cations under applied potential would produce simultaneous injection of protons into the solution or uptake of hydroxide ions by the surface, resulting in ionic transient currents [10]. It has also been observed that, after the applied potential is removed from the oxide electrode, the surface composition equilibrates slowly with the electrolyte, and proton (or hydroxide ion) fluxes across the Helmholtz layer can be detected with the rotating ring disk electrode in the potentiometric-pH mode [47]. This pseudo-capacitive process would also result in a drift of the electrode potential, but its interpretation may be difficult if the relative relaxation of the potential distribution in the oxide space charge and across the Helmholtz double layer is not known [48]. 

When the Fermi level is shifted in the semiconductor under very high anodic polarization, degeneracy of surface states sets in. The surface then behaves like that of a metal and an effective Helmholtz double layer forms at the surface. 

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