Diffuse double layer potential drop across

The same system has been studied previously by Boguslavsky et al. [29], who also used the drop weight method. While qualitatively the same behavior was observed over the broad concentration range up to the solubility limit, the data were fitted to a Frumkin isotherm, i.e., the ions were supposed to be specifically adsorbed as the interfacial ion pair [29]. The equation of the Frumkin-type isotherm was derived by Krylov et al. [31], on assuming that the electrolyte concentration in each phase is high, so that the potential difference across the diffuse double layer can be neglected. 

The description of the ion transfer process is closely related to the structure of the electrical double layer at the ITIES [50]. The most widely used approach is the combination of the BV equation and the modified Verwey-Niessen (MVN) model. In the MVN model, the electrical double layer at the ITIES is composed of two diffuse layers and one ion-free or inner layer (Fig. 8). The positions delimiting the inner layer are denoted by X2 and X2, and represent the positions of closest approach of the transferring ion to the ITIES from the organic and aqueous side, respectively. The total Galvani potential drop across the interfacial region, AgCp = cj) — [Pg.545]

Figure 1.5 shows a schematic representation of the double layer at a planar solid-liquid interface. The potential drop across the Helmholz layer is shown as linear (in the presence of specific adsorption, it will not be completely linear), followed by a tailing-off of the potential into the diffuse layer. For concentrated solutions (>0.1 M) the diffuse layer is typically a nanometer or less, while for dilute solutions it may be tens or even hundreds of nanometers. 

The electric field which actually affects the charge transfer kinetics is that between the electrode and the plane of closest approach of the solvated electroactive species ( outer Helmholtz plane ), as shown in Fig. 2.2. While the potential drop across this region generally corresponds to the major component of the polarization voltage, a further potential fall occurs in the diffuse double layer which extends from the outer Hemlholtz plane into the bulk of the solution. In addition, when ions are specifically absorbed at the electrode surface (Fig. 2.2c), the potential distribution in the inner part of the double layer is no longer a simple function of the polarization voltage. Under these circumstances, serious deviations from Tafel-like behaviour are common. 

At oxide semiconductor electrode-electrolyte interfaces, with no contribution from surface states, the electrical potential drop exhibits three components the potential drop across the space-charge region, sc, across the Helmholtz layer, diffuse double layer, d, the latter becoming negligible in concentrated electrolytes... 

Recent statistical-mechanical theories [62] and Monte Carlo simulations of the diffuse double layer [63, 64] predict that the potential of the outer Helmholtz plane is generally overestimated in the Gouy-Chapman theory. If this is the case, the potential drop across the inner layer can be even greater, e.g., by c. 15% if a hypernetted-chain approximation is applied to the primitive model of the diffuse layer [12]. 

Following Hueing et al., ° a notation is presented in Section 7.5.2 that addresses the concepts of a global impedance, which involved quantities averaged over the electrode surface a local interfacial imgedance, which involved both a local current density and the local potential drop V — Oo(r) across the diffuse double layer a local impedance, which involved a local current density and the potential of the electrode V referenced to a distant electrode and a local Ohmic impedance, which involved a local current density and potential drop Oo(r) from the outer region of the diffuse double layer to the distant electrode. The corresponding list of symbols is provided in Table 7.2. 

The total potential drop Apotential drop at the metal/oxide interface, the potential drop in the oxide, the potential drop in the Helmholtz layer and the potential drop in the electrolyte (diffuse double layer) ... 

Girault (lb) pointed out that the apparent potential dependence of the ET rate may be attributed to the change in concentration of the reactants near the interface rather than to activation control. This model, further developed by Schmickler (9), postulates that the rate constant is essentially potential-independent because the potential drop across the compact part of the double-layer at the ITIES is small. In this model, the ET rate dependence on the interfacial potential drop is only due to the diffuse layer effect similar to Frumkin effect at metal electrodes. 

The structure of the double layer can affect the rates of electrode processes. Consider an electroactive species that is not specifically adsorbed. This species can approach the electrode only to the OHP, and the total potential it experiences is less than the potential between the electrode and the solution by an amount 2 — which is the potential drop across the diffuse layer. For example, in 0.1 M NaF, 2 - (f> is -0.021 V at = -0.55 V vs. SCE, but it has somewhat larger magnitudes at more negative and more positive potentials. Sometimes one can neglect double-layer effects in considering electrode reaction kinetics. At other times they must be taken into account. The importance of adsorption and double-layer structure is considered in greater detail in Chapter 13. 

The electrophoretic mobility permits one to calculate the f potential. Often g, the potential drop across the diffuse part of the double layer, is taken to be identical to f. Hence, the electrokinetic charge may also be set approximately equal to the diffuse charge. 

Three interface layers occur within the electrical or the diffuse double layer (DDL) of a clay particle the inner Helmholtz plane (IHP) the outer Helmholtz plane (OHP) with constant thicknesses of Xi and X2, respectively and third is the plane of shear where the electro kinetic potential is measured (Rg. 2.10). This plane of shear is sometimes assumed to coincide with the OHP plane. The IHP is the outer limit of the specifically adsorbed water, molecules with dipoles, and other species (anions or cations) on the clay solid surface. The OHP is the plane that defines the outer limit of the Stem layer, the layer of positively charged ions that are condensed on the clay particle surface. In this model, known as the Gouy-Chapman-Stera-Grahame (GCSG) model, the diffuse part of the double layer starts at the location of the shear plane or the OHP plane (Hunter, 1981). The electric potential drop is linear across the Stem layer that encompasses the three planes (IHP, OHP, and shear planes) and it is exponential from the shear plane to the bulk solution, designated as the reference zero potential. 

In this model, there exist two charge-free layers and a diffuse double layer. The potential determining ions are located on a surface, designated by subscript 0, and are responsible for developing surface charge (qq). The surface potential at this plane ( /o) drops linearly across the inner Helmholtz layer to v]/p at the inner Helmholtz plane (denoted by (3), where most specifically adsorbing ions along... 

Reference electrodes of mercury have been used by several investigators in an attempt to measure single electrode potentials. Stastny and Strafelda (5 ) concluded that the zero charge potential of such an electrode in contact with an infinitely dilute aqueous solution is -0.1901V referred to the standard hydrogen electrode. Hall ( ) states that the potential drop across the double layer under these conditions is independent of solution composition when specific adsorption is absent. Daghetti and Trasatti (7, ) have used mercury reference electrodes to study the absolute potential of the fluoride ion-selective electrode and have compared their estimates of ion activities in NaF solutions with those provided by other methods. Their method is based on the assumption that the potential drop across the mercury I solution interface is independent of the electrolyte concentration once the diffuse layer effects are accounted for by the Gouy-Chapman theory. 

In electrochemistry, the potential drop across the double-layer is described by the potential difference (A( )J H/s) between the irmer potential at a point in the metal electrode (( )ai) and the irmer potential at the end point of the diffuse layer in electrolyte solution (( ) (A( )jh/ = (< )m) - (< ) - This is called the absolute potential difference. The other expression of the potential drop is... 

The potential drop across the diffuse layer is normally expressed as the outer potential drop rather than the inner potential drop. The outer potential drop (Av /jj/s) is expressed as /i. As shown in Figure 2.3, and >i are the potential drops across the entire double-layer and the potential drop across the diffuse layer, respectively. Therefore the potential drop across the Helmholtz layer should be (A /m/s - Vi)/ and the potential across the entire double-layer can be expressed as ... 

Figure 2.9 indicates that the potential of the Helmholtz layer is smaller than that of the diffuse layer with diluted electrolyte solutions. However, when increasing the electrolyte concentration, the potential of the diffuse layer becomes much smaller than that of the Helmholtz layer. This observation reinforces the notion that at dilute electrolyte concentrations the potential drop of the entire double-layer is dominated by that of the diffuse layer, and at high electrolyte concentrations the dominating potential drop will be that of the Helmholtz layer. Furthermore, Equation (2.20) also indicates that the potential drop across the Helmholtz layer is not only a function of the square root of the electrolyte concentration, but also a function of the square root of the dielectric constant (e,eo)/ suggesting that different electrolyte solutions can cause different potential drops across the diffuse and Helmholtz layers, and the dielectric constant has the same effect on the potential drop distribution. 

Potential determining salts, also referred to as phase transfer agents for a future objective of electrochemistry at the oil-water interface in microemulsions are considered. Reasearchers have studied these salts, composed of a hydrophilic and a hydrophobic ion, in microemulsion stabilized by nonionic surfactants with an oligo ethylene oxide head-group. NMR measurements show that the salts preferentially dissoc. across the surfactant interface between the oil and water domains, and hence create a potential drop across the surfactant film, and back to back diffuse double layers in the oil and water phases. These observations are also supported by Poisson-Boltzmann calcns. ... 

There are effectively two components which make up the total potential drop across the interface viz., j/o across the diffuse part, and (i// — j/o) across the fixed part. The total capacitance of the double layer, C, is made up of that due to the inner (adsorption) layer, which we may designate Ch, and that due to the diffuse layer, Cq. Since these capacitances are connected in series... 

X10 cm sec and the double-layer corrected rate constant is 2X10 cm sec [45]. In this case the double-layer correction decreases the rate because the potential drop across the diffuse layer is negative. In view of aU the approximations and corrections involved, the calculations provide a reasonable estimate of the experimental rate. 

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