Helmholtz, layer

Fig. V-14. Energy level diagram and energy scales for an n-type semiconductor pho-toelectrochemical cell Eg, band gap E, electron affinity work function Vb, band bending Vh, Helmholtz layer potential drop 0ei. electrolyte work function U/b, flat-band potential. (See Section V-9 for discussion of some of these quantities. (From Ref. 181.)...

Helmholtz layer Helmholtz layers Helmholtz planes... 

To a first approximation, the ions in both Helmholtz layers can be considered point charges. They induce an equal and opposite image charge inside the conductive electrode. When the electrode is negative to the point of zero charge, cations populate the inner Helmholtz layer. 

The region of the gradual potential drop from the Helmholtz layer into the bulk of the solution is called the Gouy or diffuse layer (29,30). The Gouy layer has similar characteristics to the ion atmosphere from electrolyte theory. This layer has an almost exponential decay of potential with increasing distance. The thickness of the diffuse layer may be approximated by the Debye length of the electrolyte. 

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 inner layer (closest to the electrode), known as the inner Helmholtz plane (IHP), contains solvent molecules and specifically adsorbed ions (which are not hilly solvated). It is defined by the locus of points for the specifically adsorbed ions. The next layer, the outer Helmholtz plane (OHP), reflects the imaginary plane passing through the center of solvated ions at then closest approach to the surface. The solvated ions are nonspecifically adsorbed and are attracted to the surface by long-range coulombic forces. Both Helmholtz layers represent the compact layer. Such a compact layer of charges is strongly held by the electrode and can survive even when the electrode is pulled out of the solution. The Helmholtz model does not take into account the thermal motion of ions, which loosens them from the compact layer. 

The most important quantity that determines the instability in pitting dissolution is the fluctuation of the electrochemical potential of dissolved metal ions in the electric double layer. In the presence of a large amount of supporting electrolyte, the fluctuation can be formulated with the fluctuations of the potential x, y, ff of the Helmholtz layer and the concentration cm (, y, Cfl.0a as follows,... 

The effect of surface deformation in the Helmholtz layer should also be involved in Eq. (35). In consideration of specific adsorption of anions, such effects can be expressed by the potential gradient Lj y, z, as follows,... 

Hence, in Eq. (36), which sign, positive or negative, should be chosen depends on the adsorption state of ionic species in the Helmholtz layer if any kind of specific adsorption is neglected or such adsorption is not so intense, the positive sign can be adopted because there is no inversion of the signs of the electric potentials, as depicted in Fig. 23. This means that the sign of the potential difference in the Helmholtz layer is the same as that of the potential difference in the diffuse layer, i.e.,... 

Figure 23. Electric potential distribution in electric double layer. HL, Helmholtz layer DL, diffuse layer.

In the potential region where nonequilibrium fluctuations are kept stable, subsequent pitting dissolution of the metal is kept to a minimum. In this case, the passive metal apparently can be treated as an ideally polarized electrode. Then, the passive film is thought to repeat more or less stochastically, rupturing and repairing all over the surface. So it can be assumed that the passive film itself (at least at the initial stage of dissolution) behaves just like an adsorption film dynamically formed by adsorbants. This assumption allows us to employ the usual double-layer theory including a diffuse layer and a Helmholtz layer. 

In studying an electrode process there are many things we would like to know. These can be classified according to the locus of the processes that can occur in going from the electrode bulk to the electrode surface, across the Helmholtz layer, and into the bulk of the electrolyte. 

It follows from the definition cited that the size of the zeta potential depends on the structure of the diffuse part of the ionic EDL. At the outer limit of the Helmholtz layer (at X = X2) the potential is j/2, in the notation adopted in Chapter 10. Beyond this point the potential asymptotically approaches zero with increasing distance from the surface. The slip plane in all likelihood is somewhat farther away from the electrode than the outer Helmholtz layer. Hence, the valne of agrees in sign with the value of /2 but is somewhat lower in absolute value. 

According to the literature [21], all reported electrochemical oscillations can be classified into four classes depending on the roles of the true electrode potential (or Helmholtz-layer potential, E). Electrochemical oscillations in which E plays no essential role and remains essentially constant are known as strictly potentiostatic (Class I) oscillations, which can be regarded as chemical oscillations containing electrochemical reactions. Electrochemical oscillations in which E is involved as an essential variable but not as the autocatalytic variable are known as S-NDR (Class II) oscillations, which arise from an S-shaped negative differential resistance (S-NDR) in the current density (/) versus E curve. Oscillations in which E is the autocatalytic variable are knovm as N-NDR (Class III) oscillations, which have an N-shaped NDR. Oscillations in which the N-NDR is obscured by a current increase from another process are knovm as hidden N-NDR (HN-NDR Class IV) oscillations. It is known that N-NDR oscillations are purely current oscillations, whereas HN-NDR oscillations occur in both current and potential. The HN-NDR oscillations can be further divided into three or four subcategories, depending on how the NDR is hidden. 

Figure 3.15 The change in ftee adsorption energy as a function of the electric field. At the top of the figure, we estimate the corresponding potential change by assuming that the potential drops over a Helmholtz layer of thickness 3 A.

The traditional treatment of a double layer at electrode-electrolyte interfaces is based on its separation into two series contributions the compact ( Helmholtz ) layer and the diffusive ( dif ) layer, so that the inverse capacitance is... 

The Gouy-Chapman theory for metal-solution interfaces predicts interfacial capacities which are too high for more concentrated electrolyte solutions. It has therefore been amended by introducing an ion-free layer, the so-called Helmholtz layer, in contract with the metal surface. Although the resulting model has been somewhat discredited [30], it has been transferred to liquid-liquid interfaces [31] by postulating a double layer of solvent molecules into which the ions cannot penetrate (see Fig. 17) this is known as the modified Verwey-Niessen model. Since the interfacial capacity of liquid-liquid interfaces is... 

If the charge osc is fully accommodated by electronic states near the Fermi energy, no space charge is formed in the electrode phase, and any voltage applied to the electrode appears exclusively across the Helmholtz layer, i.e. the system behaves like a metal. 

Equation (2.33) now defines the double layer in the final model of the structure of the electrolyte near the electrode specifically adsorbed ions and solvent in the IHP, solvated ions forming a plane parallel to the electrode in the OHP and a dilfuse layer of ions having an excess of ions charged opposite to that on the electrode. The excess charge density in the latter region decays exponentially with distance away from the OHP. In addition, the Stern model allows some prediction of the relative importance of the diffuse vs. Helmholtz layers as a function of concentration. Table 2.1 shows... 

It can be seen from the table that, in dilute solutions, the diffuse layer may extend some hundreds of angstroms out from the electrode. In contrast, in more concentrated solutions, i.e. 0.1 M, the diffuse layer thickness decreases to < 10 A not much more than the thickness of the Helmholtz layer. As CH has no concentration dependence it remains constant on changing the concentration however, from equations (2.22) and (2,23), CGC decreases as the concentration of the electrolyte increases. Thus, at low concentration ... 

We can progress from here provided that we can find expressions for the partial derivatives of equation (2.99). Provided that the concentration of supporting electrolyte is sufficiently high that all the potential difference across the interface is accommodated within the Helmholtz layer, then transport of O and R near the electrode will only take place via diffusion (i.e. we can neglect migration). The equation of motion for either O or R is given by the differential form of Fick s equation, as discussed in chapter I ... 

Emersion has been shown to result in the retention of the double layer structure i.e, the structure including the outer Helmholtz layer. Thus, the electric double layer is characterised by the electrode potential, the surface charge on the metal and the chemical composition of the double layer itself. Surface resistivity measurements have shown that the surface charge is retained on emersion. In addition, the potential of the emersed electrode, , can be determined in the form of its work function, , since and represent the same quantity the electrochemical potential of the electrons in the metal. Figure 2.116 is from the work of Kotz et al. (1986) and shows the work function of a gold electrode emersed at various potentials from a perchloric acid solution the work function was determined from UVPES measurements. The linear plot, and the unit slope, are clear evidence that the potential drop across the double layer is retained before and after emersion. The chemical composition of the double layer can also be determined, using AES, and is consistent with the expected solvent and electrolyte. In practice, the double layer collapses unless (i) potentiostatic control is maintained up to the instant of emersion and (ii) no faradaic processes, such as 02 reduction, are allowed to occur after emersion. 

The model is most vulnerable in the way it accounts for the number of particles that collide with the electrode [50, 115], In the model, the mass transfer of particles to the cathode is considered to be proportional to the mass transfer of ions. This greatly oversimplifies the behavior of particles in the vicinity of an interface. Another difficulty with the model stems from the reduction of the surface-bound ions. Since charge transfer cannot take place across the non-conducting particle-electrolyte interface, reduction is only possible if the ion resides in the inner Helmholtz layer [116]. Therefore, the assumption that a certain fraction of the adsorbed ions has to be reduced, implies that metal has grown around the particle to cover an identical fraction of the surface. Especially for large particles, it is difficult to see how such a particle, embedded over a substantial fraction of its diameter, could return to the plating bath. Moreover, the parameter itr, that determines the position of the codeposition maximum, is an artificial concept. This does not imply that the bend in the polarisation curve that marks the position of itr is illusionary. As will be seen later on, in the case of copper, the bend coincides with the point of zero-charge of the electrode. 

Depletion and Helmholtz layers, field and potential across a semiconductor-electrolyte interface. 

There are five possible physical phases in the current path in which the current conduction mechanisms are different as illustrated in Figure 19. They are substrate, space charge layer, Helmholtz layer, surface oxide film, and electrolyte. The overall change in the applied potential due to a change of current density in the current path is the sum of the potential drops in these phases ... 

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