The Helmholtz Double Layer

As already discussed in Section 3.2, the potential across a single solid-liquid interface cannot be measured. One can only measure the potential of an electrode vs a reference electrode. It has already been shown in Section 3.2 that a certain 

As already mentioned, the charges are concentrated within the iimer and outer Helmholtz layer at high ion concentrations. In this case, the double layer acts as parallel-plate capacitor. The charge density Qj stored in such a capacitor, is related to the voltage drop U by 

Using e = 20 and Xi = 5x 10 cm, one obtains 3X 10 Fcm . This capacity value agrees with the experimental data within an order of magnitude. This Helmholtz capacity is independent of the electrode potential, that is, in the case of a metal electrode any external variation of the electrode potential leads only to a corresponding change of the charges on both sides of the interface. 

Considering at first a metal electrode and assuming that cations are specifically adsorbed at the electrode surface, then the equivalent negative counter charge occurs just below the metal surface, as indicated in Fig. 5.3. This charge separation causes a corresponding potential across the interface as also shown in Fig. 5.3. It is partly determined by the specifically adsorbed ions and in addition by the solvated ions 

As already discussed in Section 3.2 the potential across a single solid-liquid interface cannot be measured. One can only measure the potential of an electrode vs. a reference electrode. It has already been shown in Section 3.2 that a certain potential is produced at a metal or semiconductor electrode upon the addition of a redox system, because the redox system equilibriates with the electrons in the electrode, i.e. the Fermi level on both sides of the interface must be equal under equilibrium. It should be emphasized here that the potential caused upon addition of a redox couple to the solution occurs in addition to that already formed by the specific adsorption of, for instance, hydroxyl ions. A variation in the relative concentrations of the oxidized and reduced species of the redox system leads to a corresponding change of the potential across the outer Helmholtz layer, as required by Nernst s law (see Eq. 3.47), which can be detected by measuring the electrode potential vs, a reference electrode. However, there still exists a potential across the inner Helmholtz layer which remains unknown. 

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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. 

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 ... 

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]. 

Since the space charge capacity is usually much smaller than the capacity Ch of the Helmholtz double layer, it can easily be determined experimentally. 

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...

The numerical value of p = 1.8x10 esu used for the dipole moment of water, taken from gas-phase measurements, may be criticized. Mutual depolarization of the closely packed dipoles on the surface may lead to a smaller effective value of p. Also, taking the diameter of a water molecule to represent 8, the thickness of the Helmholtz double layer, probably constitutes an underestimate. The use of more accurate values for these parameters may decrease the numerical parameter in Eq. 36L from 0.14 to perhaps 0.10. Since n is an adjustable parameter (within certain limits), this does not affect our considerations. 

Tafel slopes for the anodic and the cathodic process double-layer capacitance ( lF/cm ) capacitance of the Helmholtz double layer capacitance of the diffuse double layer double-layer capacitance at 0 = 0 double-layer capacitance at 0 = 1 adsorption pseudocapacitance (llF/cm ) adsorption pseudocapacitance derived from the Langmuir isotherm... 

During anodic dissolution, the applied potential is partitioned between the space charge layer in the semiconductor, C/jc and the Helmholtz double layer, C/h ... 

Buffering in an aprotic medium is sometimes a problem. Proton donors, such as a suitable phenol, malonic ester, or amine salt, together with the corresponding base, may be an acceptable solution. Guanidine perchlorate [472] has been proposed as an efficient proton donor (and supporting electrolyte) in aprotic solvents, as it brings the protons into the Helmholtz double layer. 

Numerous models of the electrode-electrolyte interface have been developed. The simplest of these is the Helmholtz double-layer model, which posits that the charge associated with a discrete layer of ions balances the charge associated with electrons at the metal surface. The Helmholtz double-layer model predicts incorrectly that the interfacial capacitance is independent of potential. Nevertheless, cvurent models of the charge redistribution at electrode-electrolyte interfaces owe their terminology to the original Helmholtz model. 

FIGURE 1.3. Schematic illustration of the double layers in the semiconductor/electrolyte interface at an equilibrium condition. K is the potential drop across the space charge layer and Vh is the potential drop across the Helmholtz double layer. After Morrison. " ... 

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. ... 

FIGURE 1.10. An equivalent circuit for the electrical components at the semiconductor/electrolyte interface in the absence of an oxide. represents the resistance of the electrolyte Ch is the capacity of the Helmholtz double layer and Rf is the charge transfer resistance 0, and Ru are the capacitance and resistance associated with the space charge layer in the semiconductor C, and are the capacitance and resistance of the surface states. 

For heavily doped materials, either notp type, the surface is degenerated and the material behaves like a metal electrode, meaning that the charge transfer reaction in the Helmholtz double layer is the rate-determining step. This is supported by the lack of an impedance loop associated with the space charge for the heavily doped materials. Also, for heavily doped n-Si large current in the dark is due to electron injection, which is not characterized by a slope of 60 mV/decade. For p-Si, electron injection into the conduction band may also occur during the anodic dissolution. 

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