Electric double layer definition

Clavilier eta/.196,794-796have studied CO adsorption on electrochemi-cally faceted Pt(lll) and Pt(110) electrodes and from the charge transients, with the provision that the CO dipole has a negligible contribution to the electrical double-layer potential these authors have provided a definite determination of ( =o- However, electrochemically faceted Pt(lll) electrodes have a polycrystalline surface structure, and thus the value of Eq-q for such electrodes lies between fiULO for terraces and forst s.197 786 787... 

The concept of surface concentration Cg j requires closer definition. At the surface itself the ionic concentrations will change not only as a result of the reaction but also because of the electric double layer present at the surface. Surface concentration is understood to be the concentration at a distance from the surface small compared to diffusion-layer thickness, yet so large that the effects of the EDL are no fonger felt. This condition usually is met at points about 1 nm from the surface. 

Double integration with respect to EA yields the surface excess rB+ however, the calculation requires that the value of this excess be known, along with the value of the first differential 3TB+/3EA for a definite potential. This value can be found, for example, by measuring the interfacial tension, especially at the potential of the electrocapillary maximum. The surface excess is often found for solutions of the alkali metals on the basis of the assumption that, at potentials sufficiently more negative than the zero-charge potential, the electrode double layer has a diffuse character without specific adsorption of any component of the electrolyte. The theory of diffuse electrical double layer is then used to determine TB+ and dTB+/3EA (see Section 4.3.1). 

A classic definition of electrochemical ultracapacitors or supercapacitors summarizes them as devices, which store electrical energy via charge in the electrical double layer, mainly by electrostatic forces, without phase transformation in the electrode materials. Most commercially available capacitors consist of two high surface area carbon electrodes with graphitic or soot-like material as electrical conductivity enhancement additives. Chapter 1 of this volume contains seven papers with overview presentations, and development reports, as related to new carbon materials for this emerging segment of the energy market. 

Since the electro-osinotic flow is induced by the interaction of the externally applied electric field with the space charge of the diffuse electric double layers at the channel walls, we shall concentrate in our further analysis on one of these 0 1 2) thick boundary layers, say, for definiteness, at... 

The definition of Cei given here is somewhat different from that previously stated (see Section 3.4.2). Here Ce/,cr is the electrolyte concentration up to which the foam film thickness decreases. Above it the film thickness is constant, but greatly exceeds the thickness of a bilayer. A rough estimate of the electrical double layer (l/ cr) thickness may be obtained... 

This is a somewhat academic question because the answer depends on the definition of this. Two possibilities for this have been given in fig. 2.6. Nevertheless, for interpretational purposes it is sometimes useful to have some feeling for the thickness t. The issue may be compared with that of defining the thickness of an electric double layer. Strictly speaking such layers are infinitely thick but for many practical purposes, like colloid stability and electrokinetics, it has proved convenient to introduce the Debye length, v" as a representative measure of t. Making this choice for double layers involves three elements ... 

The models describing hydrolysis and adsorption on oxide surfaces are called surface complexation models in literature. They differ in the assumptions concerning the structure of the double electrical layer, i.e. in the definition of planes situation, where adsorbed ions are located and equations asociating the surface potential with surface charge (t/> = f(5)). The most important models are presented in the papers by Westall and Hohl [102]. Tbe most commonly used is the triple layer model proposed by Davis et al. [103-105] from conceptualization of the electrical double layer discussed by Yates et al. [106] and by Chan et al. [107]. Reviews and representative applications of this model have been given by Davis and Leckie [108] and by Morel et al. [109]. We will base our consideration on this model. 

At least two of the recognized mechanisms for the formation of electrical double layers (Hunter, elal. 1981 Russel etal., 1989) are relevant to LB film depositions (1) ionization of carboxylic acid group and amphoteric acid groups on solid surfaces, and (2) differences between the affinities of two phases for ions or ionizable species. The latter mechanism includes the uneven distribution of anions and cations between two immiscible phases, the differential adsorption of ions from an electrolyte solution to a solid surface, and the differential solution of one ion over the other from a crystal lattice. Since the solid-liquid and the film-liquid interfaces are flat, large surfaces and since both have a large, solid-like concentration, the analysis that follows applies to both interfaces. For an interface conformed by a thin film of an amphiphilic compound with the hydrophilic end of the molecule in contact with the water subphase, the equilibrium of charges is based on pH and subphase concentration. The effect of pH is highlighted by the definition of the of the carboxylic acid ... 

In addition, immersion and removal speeds play a definite role in LB depositions because they disturb equilibrium of charges at the electrical double layer. When the solid is immersed, the double layer begins to form and ions must diffuse toward and away from the solid surface before equilibrium is reached. When the solid is removed, the double layer is partially wiped out by the flow but metal cations are retained on the film deposited on the solid substrate. On the other hand, during film deposition, the mechanical barriers designed to keep the surface pressure constant move the film on the air-water interface and disturb the double layers under the film. At this point, we do not have a quantitative way to estimate the disturbance to the double layer caused by the movement of the solid substrate, but we can introduce the following assumptions ... 

The applicability of continuum theories, such as the Poisson-Boltzmann model, in nanoscale is the most concerned issue in this field yet. Numerous conflicting results were reported in literature. We have done careful MD simulations of EOF and compared the ion distributions with the PB predictions rigorously to clarify the applicability of the continuum theory. To compare the descriptions from two different scales, above all, the observers have to be stand on the same base to avoid definition gaps. First, when presenting the MD results, the bin size should not be smaller than the solvent molecular diameter in comparison with the continuum theory otherwise, the MD results are not the macroscopic properties at the same level of the continuum. A second gap which departs the MD results from the PB predictions is the effect of the Stem layer. As well known, the PB equation describes only the ion distribution in diffusion (outer) layer of the electric double layer (EDL) [1]. In the continuum theory, the compact (iimer) layer of EDL is too thin (molecular scale) to be considered, and therefore, the PB equation almost governs the ion distribution in the whole domain. However, in nanofluidics the iimer layer which is also termed as Stem layer is comparable to the channel in size. The PB equation is not able to govern the ion behavior in the Stem layer in theory. Therefore, if one compares the MD... 

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