Double layer defined

For the capacitance (per unit interfacial area) of the double layer, defined as Oo/t /o, it follows for low potentials ... 

Recall that 6 = /i Dt is the electric double-layer defined in Chapter 3. Experimentally, 0.3 mm < 6 < 0.5 mm for most practical electrochemicd cells under diffusion and natural convection [2]. The latter topic will be dealt with in a later section. In this section, 6 is due to diffusion and migration and its value is normally 6 < 1 mm. 

The treatment in the case of a plane charged surface and the resulting diffuse double layer is due mainly to Gouy and Qiapman. Here may be replaced by d /dx since is now only a function of distance normal to the surface. It is convenient to define the quantities y and yo as... 

In the preceding derivation, the repulsion between overlapping double layers has been described by an increase in the osmotic pressure between the two planes. A closely related but more general concept of the disjoining pressure was introduced by Deijaguin [30]. This is defined as the difference between the thermodynamic equilibrium state pressure applied to surfaces separated by a film and the pressure in the bulk phase with which the film is equilibrated (see section VI-5). 

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. 

The potential difference across the electric double layer A. This cannot be determined in absolute terms but must be defined with reference to another charged interface, i.e. a reference electrode. In the case of a corroding metal the potential is the corrosion potential which arises from the mutual polarisation of the anodic and cathodic reactions constituting the overall corrosion reaction see Section 1.4). 

The surface potential of a liquid solvent s, %, is defined as the difference in electrical potentials across the interface between this solvent and the gas phase, with the assumption that the outer potential of the solvent is zero. The potential arises from a preferred orientation of the solvent dipoles in the free surface zone. At the surface of the solution, the electric field responsible for the surface potential may arise from a preferred orientation of the solvent and solute dipoles, and from the ionic double layer. The potential as the difference in electrical potential across the interface between the phase and gas, is not measurable. However, the relative changes caused by the change in the solution s composition can be determined using the proper voltaic cells (see Sections XII-XV). 

The main idea of a lattice model is to assume that atomic or molecular entities constituting the system occupy well-defined lattice sites in space. This method is sometimes employed in simulations with the grand canonical ensemble for the simulation of surface electrochemical proceses. The Hamiltonians H of the lattice gas for one and two adsorbed species from which the ttansition probabilities 11 can be calculated have been discussed by Brown et al. (1999). We discuss in some detail MC lattice model simulations applied to the electrochemical double layer and electrochemical formation and growth two-dimensional phases not addressed in the latter review. MC lattice models have also been applied recently to the study the electrox-idation of CO on metals and alloys (Koper et al., 1999), but for reasons of space we do not discuss this topic here. 

Although not the subject of this article, double layer studies are briefly discussed in this paragraph in order to demonstrate that ex situ XPS studies indeed provide information about the state of the electrode exposed to an electrochemical environment at a defined potential. A crucial step in any ex situ experiment is the emersion of the electrode. Here the question arises whether the electrochemical double layer or part of it is preserved at the interface after emersion and transfer. Winograd et al. [10,11] first demonstrated that the electrode under UHV conditions still remembers the electrode potential applied at the time of emersion. These authors investigated oxide formation on Pt and the underpotential deposition of Cu and Ag on Pt by means of XPS and proved that the electrochemically formed oxide layer and... 

The dependence of dx on qM is central in a model, proposed by Price and Halley,93 for the metal surface in the double layer which is related to that discussed above. The positively charged ion background profile p+(z) is assumed uniform, with a value equal to the bulk density pb, from z = -oo to z = 0, with the electronic density profile n(z) more diffuse. In contrast to the previous model30 which emphasizes penetration by the conduction electrons of the region of solvent, this model93 supposes that the density profile n(z) is zero for z > dx, where z > dx defines the region of the electrolyte. Then the potential at dx is given by... 

The pores of the silica template can be filled by carbon from a gas or a liquid phase. One may consider an insertion of pyrolytic carbon from the thermal decomposition of propylene or by an aqueous solution of sucrose, which after elimination of water requires a carbonization step at 900°C. The carbon infiltration is followed by the dissolution of silica by HF. The main attribute of template carbons is their well sized pores defined by the wall thickness of the silica matrix. Application of such highly ordered materials allows an exact screening of pores adapted for efficient charging of the electrical double layer. The electrochemical performance of capacitor electrodes prepared from the various template carbons have been determined and are tentatively correlated with their structural and microtextural characteristics. 

Carbonaceous materials play a key role in achieving the necessary performance parameters of electrochemical capacitors (EC). In fact, various forms of carbon constitute more than 95% of electrode composition [1], Double layer capacity and energy storage capacity of the capacitor is directly proportional to the accessible electrode surface, which is defined as surface that is wetted with electrolyte and participating in the electrochemical process. 

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... 

As was discussed in section 2.1.1, electrocapillarity measurements at mercury electrodes, which have well-defined and measurable areas, allow the double-layer capacitance, CDL, to be obtained as Fm-2. Bowden assumed that the overpotential change at the very beginning of the anodic run in H2-saturated solution was a measure of the double-layer capacity. The slope of the E vs. Q plot in this region was taken as giving 1/CDL, and this gave 2 x 10 5 F. He then assumed that, under these same conditions, the double-layer capacity, in Fm-2, of the mercury electrode is the same. This gave the real surface area of the electrode as 3.3cm 2, as opposed to its geometric area of I cm2. 

The electroosmotic pumping is executed when an electric field is applied across the channel. The moving force comes from the ion moves in the double layer at the wall towards the electrode of opposite polarity, which creates motion of the fluid near the walls and transfer of the bulk fluid in convection motion via viscous forces. The potential at the shear plane between the fixed Stem layer and Gouy-Champmon layer is called zeta potential, which is strongly dependent on the chemistry of the two phase system, i.e. the chemical composition of both solution and wall surface. The electroosmotic mobility, xeo, can be defined as follow,... 

Figure 4. a) Model for the double-layer structure on Pt(lll) as viewed both normal to (111) plane and parallel to the (111) plane at the potential 0TOin. The potential 0ro n is defined in the voltammetry curve in b). 

Mass transfer phenomena usually are very effective on distance scales much larger than the dimensions of the cell wall and the double layer dimensions. Thicknesses of steady-state diffusion layers1 in mildly stirred systems are of the order of 10 5 m. Thus, one may generally adopt a picture where the local interphasial properties define boundary conditions while the actual mass transfer processes take place on a much larger spatial scale. 

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