Electrical double layer, Helmholtz

Surface complexation models for the oxide-electrolyte interface are reviewed two models for surface hydrolysis reactions are considered (diprotic surface groups and monoprotic surface groups) and four models for the electric double layer (Helmholtz,... 

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]. 

Pig. 3. Representation of the electrical double layer at a metal electrode—solution interface for the case where anions occupy the inner Helmholtz plane... 

Fig. 1. The structure of the electrical double layer where Q represents the solvent CD, specifically adsorbed anions 0, anions and (D, cations. The inner Helmholtz plane (IHP) is the center of specifically adsorbed ions. The outer Helmholtz plane (OHP) is the closest point of approach for solvated cations or molecules. O, the corresponding electric potential across the double layer, is also shown.

FIGURE 1-11 Schematic representation of the electrical double layer. IHP = inner Helmholtz plane OHP = outer Helmoltz plane. 

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,... 

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

In 1873, Gabriel Lippmann (1845-1921 Nobel prize, 1908) performed extensive experiments of the electrocapiUary behavior of mercury and established his equation describing the potential dependence of the surface tension of mercury in solutions. In 1853, H. Helmholtz, analyzing electrokinetic phenomena, introduced the notion of a capacitor-like electric double layer on the surface of electrodes. These publications... 

Fig. 4.1 Structure of the electric double layer and electric potential distribution at (A) a metal-electrolyte solution interface, (B) a semiconductor-electrolyte solution interface and (C) an interface of two immiscible electrolyte solutions (ITIES) in the absence of specific adsorption. The region between the electrode and the outer Helmholtz plane (OHP, at the distance jc2 from the electrode) contains a layer of oriented solvent molecules while in the Verwey and Niessen model of ITIES (C) this layer is absent...

If the electrolyte components can react chemically, it often occurs that, in the absence of current flow, they are in chemical equilibrium, while their formation or consumption during the electrode process results in a chemical reaction leading to renewal of equilibrium. Electroactive substances mostly enter the charge transfer reaction when they approach the electrode to a distance roughly equal to that of the outer Helmholtz plane (Section 5.3.1). It is, however, sometimes necessary that they first be adsorbed. Similarly, adsorption of the products of the electrode reaction affects the electrode reaction and often retards it. Sometimes, the electroinactive components of the solution are also adsorbed, leading to a change in the structure of the electrical double layer which makes the approach of the electroactive substances to the electrode easier or more difficult. Electroactive substances can also be formed through surface reactions of the adsorbed substances. Crystallization processes can also play a role in processes connected with the formation of the solid phase, e.g. in the cathodic deposition of metals. 

The Frumkin theory of the effect of the electrical double layer on the rate of the electrode reaction is a gross simplification. For example, the electrode reaction does not occur only at the outer Helmholtz plane but also at a somewhat greater distance from the electrode surface. More detailed considerations indicate, however, that Eq. (5.3.20) can still be used to describe the effect of the electrical double layer as a good approximation. 

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. 

Fig. 2. Schematic diagram of the tunnel gap between sample and tip, with the extension of the electric double layers indicated by the outer Helmholtz plane(OHP). (a) No tip interaction at large tip-sample separation, (b) Overlap of the electric double layers at a distance s = 0.6 nm, which can be achieved by conventional imaging conditions (e.g., Uj = 50 mV It = 2 nA Rt = 2.5 x 107 Q). Inset Dependence of the tunnel gap s on the tunnel resistance Rt for a tunnel barrier of 1.5 eV.

The electrified interface is generally referred to as the electric double layer (EDL). This name originates from the simple parallel plate capacitor model of the interface attributed to Helmholtz.1,9 In this model, the charge on the surface of the electrode is balanced by a plane of charge (in the form of nonspecifically adsorbed ions) equal in magnitude, but opposite in sign, in the solution. These ions have only a coulombic interaction with the electrode surface, and the plane they form is called the outer Helmholtz plane (OHP). Helmholtz s model assumes a linear variation of potential from the electrode to the OHP. The bulk solution begins immediately beyond the OHP and is constant in potential (see Fig. 1). 

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 ... 

Fig. 6-99. An interfacial electric double layer on semiconductor electrodes a = charge of surface states 0.1 = interfadal charge of adsorbed ions IHP = inner Helmholtz plane.

In solution, all electrodes are surrounded by a layer of water molecules, ions, and other atomic or molecular species. We will not look in depth at this topic, except to refer to the two principle layers, which are named after one of the original pioneers of electrochemistry, namely the nineteen-century great, Hermann Helmholtz. The two Helmholtz layers are often said to comprise the electrode double-layer (or electric double-layer ). 

Helmholtz [71] first described the interfacial behavior of a metal and electrolyte as a capacitor, or so-called electrical double layer, with the excess surface charge on the metallic electrode remaining separated from the ionic counter charge in the electrolyte by the thickness of the solvation shell. Gouy and Chapmen subsequently... 

The Helmholtz-von Smoluchowski equation indicates that under constant composition of the electrolyte solution, the EOF depends on the magnitude of the zeta potential, which is determined by various factors inhuencing the formation of the electric double layer, discussed above. Each of these factors depends on several variables, such as pH, specihc adsorption of ionic species in the compact region of the double layer, ionic strength, and temperature. 

Not all ceramic materials behave the same at a given pH, however. As the material begins to dissolve, ions form at the snrface, water molecnles orient themselves accordingly, and an electrical double layer is established, as shown in Eigure 3.18. The first layer of charged ions and oriented water molecules is called the inner Helmholtz plane (IHP), and the second layer of oppositely charged particles is called the outer Helmholtz... 

Figure 3.18 Formation of the electrical double layer of a surface in solution, showing the inner Helmholtz plane (IHP) and outer Helmholtz plane (OHP). Reprinted, by permission, from B. D. Craig, Fundamental Aspects of Corrosion Films in Corrosion Science, p. 4. Copyright 1991 by Plenum Press.

To a first approximation, the BLM can be considered to behave like a parallel plate capacitor immersed in a conducting electrolyte solution. In reality, even such a thin insulator as the modified BLM (designated by and R, in Fig. 108) could block the specific adsorption of some species from solution and/or modify the electrochemical behavior of the system. Similarly, System C may turn out to be a semiconductor(l)-insulator-semiconductor(2) (SIS ) rather than a semiconductor(l)-semiconductor(2) (SS ) junction. The obtained data, however, did not allow for an unambiguous distinction between these two alternative junctions we have chosen the simpler of the two [652], The equivalent circuit describing the working (Ew), the reference (Eg), and the counter (Ec) electrodes the resistance (Rm) and the capacitance (C of the BLM the resistance (R ) and capacitance (Ch) of the Helmholtz electrical double layer surrounding the BLM as well as the resistance of the electrolyte solution (RSO ) is shown in Fig. 108a [652],... 

Fig. 108a-c. Proposed equivalent circuits for. a an empty and b a semiconductor-particle-coated BLM. Porous structure of the semiconductor particles allowed c the simplification of the equivalent circuit. Rm, RH, and Rsol are resistances due to the membrane, to the Helmholtz electrical double layer, and to the electrolyte solutions, while C and CH are the corresponding capacitances Rf and Cf are the resistance and capacitance due to the particulate semiconductor film R m and Cm are the resistance and capacitance of the parts of the BLM which remained unaltered by the incorporation of the semiconductor particles R and Csc are the space charge resistance and capacitance at the semiconductor particle-BLM interface and Rss and C are the resistance and capacitance due to surface-state on the semiconductor particles in the BLM [652]... 

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]).

Fig. 3. The structure of electrical double layer at a semiconductor-electrolyte interface (a) and the distribution of the potential (b) and charge (c) at the interface. The electrode is charged negatively. is the space-charge region thickness, La is the Helmholtz layer thickness, Qlc and Qtl are the charge of the semiconductor and ionic plates of the double layer, respectively (for further notations see the text).

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