Double layer, diffuse Helmholtz

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

Figure E.l Electrical double layer (a) Helmholtz double layer (b) diffuse double layer...

Figure 6-1). Inside the double layer (the Helmholtz layer and to a lesser extent the diffuse layer) the charging of the interfaces occurs, resulting in the appearance of large double-layer capacitance... 

By analogy with the Helmholtz condenser formula, for small potentials the diffuse double layer can be likened to an electrical condenser of plate distance /k. For larger yo values, however, a increases more than linearly with o, and the capacity of the double layer also begins to increase. 

IHP) (the Helmholtz condenser formula is used in connection with it), located at the surface of the layer of Stem adsorbed ions, and an outer Helmholtz plane (OHP), located on the plane of centers of the next layer of ions marking the beginning of the diffuse layer. These planes, marked IHP and OHP in Fig. V-3 are merely planes of average electrical property the actual local potentials, if they could be measured, must vary wildly between locations where there is an adsorbed ion and places where only water resides on the surface. For liquid surfaces, discussed in Section V-7C, the interface will not be smooth due to thermal waves (Section IV-3). Sweeney and co-workers applied gradient theory (see Chapter III) to model the electric double layer and interfacial tension of a hydrocarbon-aqueous electrolyte interface [27]. 

Derive the general equation for the differential capacity of the diffuse double layer from the Gouy-Chapman equations. Make a plot of surface charge density tr versus this capacity. Show under what conditions your expressions reduce to the simple Helmholtz formula of Eq. V-17. 

Fig. 1. Schematic representation of the electrochemical or diffuse double layer showing the inner (IHP) and outer (OHP) Helmholtz planes and the...

F r d ic Current. The double layer is a leaky capacitor because Faradaic current flows around it. This leaky nature can be represented by a voltage-dependent resistance placed in parallel and called the charge-transfer resistance. Basically, the electrochemical reaction at the electrode surface consists of four thermodynamically defined states, two each on either side of a transition state. These are (11) (/) oxidized species beyond the diffuse double layer and n electrons in the electrode and (2) oxidized species within the outer Helmholtz plane and n electrons in the electrode, on one side of the transition state and (J) reduced species within the outer Helmholtz plane and (4) reduced species beyond the diffuse double layer, on the other. 

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. 

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... 

By means of the thermodynamic theory of the double layer and the theory of the diffuse layer it is possible to determine the charge density ox corresponding to the adsorbed ions, i.e. ions in the inner Helmholtz plane, and the potential of the outer Helmholtz plane 2 in the presence of specific adsorption. 

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... 

Figure 16.6 The Stern model of the double layer. The outer Helmholtz plane (OHP) and the width of the diffusion layer (8) are indicated. The shaded circles represent solvent molecules. The drawing is not to scale The width of the diffusion layer is several orders of magnitude larger than molecular sizes.

B , while for an n-type semiconductor the reverse is true. An analog to the SCR in the semiconductor is an extended layer of ions in the bulk of the electrolyte, which is present especially in the case of electrolytes of low concentration (typically below 0.1 rnolh1). This diffuse double layer is described by the Gouy-Chap-man model. The Stern model, a combination of the Helmholtz and the Gouy-Chapman models, was developed in order to find a realistic description of the electrolytic interface layer. 

For a long time, the electric double layer was compared to a capacitor with two plates, one of which was the charged metal and the other, the ions in the solution. In the absence of specific adsorption, the two plates were viewed as separated only by a layer of solvent. This model was later modified by Stem, who took into account the existence of the diffuse layer. He combined both concepts, postulating that the double layer consists of a rigid part called the inner—or Helmholtz—layer, and a diffuse layer of ions extending from the outer Helmholtz plane into the bulk of the solution. Accordingly, the potential drop between the metal and the bulk consists of two parts ... 

The Helmholtz model was found not to be able to give a satisfactory analysis of measured data. Later, another theory of the diffuse double layer was proposed by Gouy and Chapman. The interfacial region for a system with charged lipid, R-Na+, with NaCl, is shown in Figure 4.10. 

Figure 7.4. Schematic model of the Electrical Double Layer (EDL) at the metal oxide-aqueous solution interface showing elements of the Gouy-Chapman-Stern-Grahame model, including specifically adsorbed cations and non-specifically adsorbed solvated anions. The zero-plane is defined by the location of surface sites, which may be protonated or deprotonated. The inner Helmholtz plane, or [i-planc, is defined by the centers of specifically adsorbed anions and cations. The outer Helmholtz plane, d-plane, or Stern plane corresponds to the beginning of the diffuse layer of counter-ions and co-ions. Cation size has been exaggerated. Estimates of the dielectric constant of water, e, are indicated for the first and second water layers nearest the interface and for bulk water (modified after [6]).

Consider a simple interfacial region at a mercury/solution interface. The electrolyte is 0.01 M NaF and the charge on the electrode is 10 iC negative to the pzc. The zeta potential is -10 mV on the same scale. What is the capacitance of the Helmholtz layer and that of the diffuse layer Galculate the capacitance of the interfaces. Take the thickness of the double layer as the distance between the center of the mercury atoms and that of hydrated K+in contact with the electrode through its water layer. (Bockris)... 

In considering the effect of the double-layer structure on electrode kinetics (Section 7.3.1), it was pointed out that the existence of a diffuse chaige region causes the concentration at the outer Helmholtz plane to differ from the bulk concentration (Fig. 7.19). The consumption of electron acceptors by the electronation reaction and... 

The Stern surface is drawn through the ions that are assumed to be adsorbed on the charged wall. (This surface is also known as the inner Helmholtz plane [IHP], and the surface running parallel to the IHP, through the surface of shear (see Chapter 12) shown in Figure 11.9, is called the outer Helmholtz plane [OHP]. Notice that the diffuse part of the ionic cloud beyond the OHP is the diffuse double layer, which is also known as the Gouy-Chapman... 

FIG. 12.8 Plot of rju/e versus f/0, that is, the zeta potential according to the Helmholtz-Smoluchowski equation, Equation (39), versus the potential at the inner limit of the diffuse part of the double layer. Curves are drawn for various concentrations of 1 1 electrolyte with / = 10 15 V-2 m2. (Redrawn with permission from J. Lyklema and J. Th. G. Overbeek, J. Colloid Sci., 16, 501 (1961).)... 

Electrode-solution interface. The tightly adsorbed inner layer (also called the compact, Helmholtz, or Stem layer) may include solvent and any solute molecules. Cations in the inner layer do not completely balance the charge of the electrode. Therefore, excess cations are required in the diffuse part of the double layer for charge balance. 

Fig. 2.2 Structure of the electric double layer under different conditions of electrode polarization (a) metal positively charged, anions present at the inner Helmholtz plane (chemically interacting with metal) and in the diffuse double layer beyond the outer Helmholtz plane (b) metal negatively charged, inner Helmholtz plane empty, cations in diffuse layer (c) metal positively charged, strong adsorption of anions in inner Helmholtz plane, balancing cations in the diffuse layer...

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