Electric double layer diffuse part

The model more generally accepted for metal/electrolyte interfaces envisages the electrical double layer as split into two parts the inner layer and the diffuse layer, which can be represented by two capacitances in series.1,3-7,10,15,32 Thus, the total differential capacitance C is equal to... 

At present it is impossible to formulate an exact theory of the structure of the electrical double layer, even in the simple case where no specific adsorption occurs. This is partly because of the lack of experimental data (e.g. on the permittivity in electric fields of up to 109 V m"1) and partly because even the largest computers are incapable of carrying out such a task. The analysis of a system where an electrically charged metal in which the positions of the ions in the lattice are known (the situation is more complicated with liquid metals) is in contact with an electrolyte solution should include the effect of the electrical field on the permittivity of the solvent, its structure and electrolyte ion concentrations in the vicinity of the interface, and, at the same time, the effect of varying ion concentrations on the structure and the permittivity of the solvent. Because of the unsolved difficulties in the solution of this problem, simplifying models must be employed the electrical double layer is divided into three regions that interact only electrostatically, i.e. the electrode itself, the compact layer and the diffuse layer. 

The basic difference between metal-electrolyte and semiconductor-electrolyte interfaces lies primarily in the fact that the concentration of charge carriers is very low in semiconductors (see Section 2.4.1). For this reason and also because the permittivity of a semiconductor is limited, the semiconductor part of the electrical double layer at the semiconductor-electrolyte interface has a marked diffuse character with Debye lengths of the order of 10 4-10 6cm. This layer is termed the space charge region in solid-state physics. 

While the lipid bilayer has a very low water content, and therefore behaves quite hydrophobically, especially in its core (see Chapter 2 of this volume), the cell wall is rather hydrophilic, with some 90% of water. Physicochemically, the cell wall is particularly relevant because of its high ion binding capacity and the ensuing impact on the biointerphasial electric double layer. Due to the presence of such an electric double layer, the cell wall possesses Donnan-like features, leaving only a limited part of the interphasial potential decay in the diffuse double layer in the adjacent medium. For a detailed outline, the reader is referred to recent overviews of the subject matter [1,2]. 

Simple electrolyte ions like Cl, Na+, SO , Mg2+ and Ca2+ destabilize the iron(Hl) oxide colloids by compressing the electric double layer, i.e., by balancing the surface charge of the hematite with "counter ions" in the diffuse part of the double... 

For present purposes, the electrical double-layer is represented in terms of Stem s model (Figure 5.8) wherein the double-layer is divided into two parts separated by a plane (Stem plane) located at a distance of about one hydrated-ion radius from the surface. The potential changes from xj/o (surface) to x/s8 (Stem potential) in the Stem layer and decays to zero in the diffuse double-layer quantitative treatment of the diffuse double-layer follows the Gouy-Chapman theory(16,17 ... 

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 ... 

When particles or large molecules make contact with water or an aqueous solution, the polarity of the solvent promotes the formation of an electrically charged interface. The accumulation of charge can result from at least three mechanisms (a) ionization of acid and/or base groups on the particle s surface (b) the adsorption of anions, cations, ampholytes, and/or protons and (c) dissolution of ion-pairs that are discrete subunits of the crystalline particle, such as calcium-oxalate and calcium-phosphate complexes that are building blocks of kidney stone and bone crystal, respectively. The electric charging of the surface also influences how other solutes, ions, and water molecules are attracted to that surface. These interactions and the random thermal motion of ionic and polar solvent molecules establishes a diffuse part of what is termed the electric double layer, with the surface being the other part of this double layer. 

The variation of the electric potential in the electric double layer with the distance from the charged surface is depicted in Figure 6.2. The potential at the surface ( /o) linearly decreases in the Stem layer to the value of the zeta potential (0- This is the electric potential at the plane of shear between the Stern layer (and that part of the double layer occupied by the molecules of solvent associated with the adsorbed ions) and the diffuse part of the double layer. The zeta potential decays exponentially from to zero with the distance from the plane of shear between the Stern layer and the diffuse part of the double layer. The location of the plane of shear a small distance further out from the surface than the Stem plane renders the zeta potential marginally smaller in magnitude than the potential at the Stem plane ( /5). However, in order to simplify the mathematical models describing the electric double layer, it is customary to assume the identity of (ti/j) and The bulk experimental evidence indicates that errors introduced through this approximation are usually small. 

In Eq. 30, Uioo and Fi are the activity in solution and the surface excess of the zth component, respectively. The activity is related to the concentration in solution Cioo and the activity coefficient / by Uioo =fCioo. The activity coefficient is a function of the solution ionic strength I [39]. The surface excess Fi includes the adsorption Fi in the Stern layer and the contribution, f lCiix) - Cioo] dx, from the diffuse part of the electrical double layer. The Boltzmann distribution gives Ci(x) = Cioo exp - Zj0(x), where z, is the ion valence and 0(x) is the dimensionless potential (measured from the Stern layer) obtained by dividing the actual potential, fix), by the thermal potential, k Tje = 25.7 mV at 25 °C). Similarly, the ionic activity in solution and at the Stern layer is inter-related as Uioo = af exp(z0s)> where tps is the scaled surface potential. Given that the sum of /jz, is equal to zero due to the electrical... 

Figure 26-20 (a) Electric double layer created by negatively charged silica surface and nearby cations. (fc>) Predominance of cations in diffuse part of the double layer produces net electroosmotic flow toward the cathode when an external field is applied. 

The electric double layer can be regarded as consisting of two regions an inner region which may include adsorbed ions, and a diffuse region in which ions are distributed according to the influence of electrical forces and random thermal motion. The diffuse part of the double layer will be considered first. 

The calculation of the interaction energy, VR, which results from the overlapping of the diffuse parts of the electric double layers around two spherical particles (as described by Gouy-Chapman theory) is complex. No exact analytical expression can be given and recourse must be had to numerical solutions or to various approximations. 

So far, only non-specific ion adsorption in the diffuse part of the electric double layer has been considered. The broad prediction is that VR should decrease in an approximately exponential fashion with increasing H and that the range of VR should be decreased by... 

The chloride and sodium ions form the diffuse part of the electrical double layer. 

Diffuse layer capacitance — The diffuse layer is the outermost part of the electrical double layer [i]. The electrical double layer is the generic name for the spatial distribution of charge (electronic or ionic) in the neighborhood of a phase boundary. Typically, the phase boundary of most interest is an electrode/solution interface, but may also be the surface of a colloid or the interior of a membrane. For simplicity, we here focus on the metal/solution interface. The charge carriers inside the metal are electrons, which are confined to... 

The presence of salt promotes aggregation due to reduction of the diffuse part of the electric double layer. According to a review by Franks and Eagland, 1975 (6) salt effects on the electric double layer are to be found at I 0.1 for univalent ions. 

Adsorbed ions attract oppositely charged ions from the solution and so form an electrical double-layer. The outer part of the double layer is diffuse as the counterions are held by a dynamical balance between diffusion and the electrical force. The thickness of the double layer is of the order of nanometres, but it gets thirmer when the concentration of ions in the bulk solution is increased. 

At the interface between O and W, the presence of the electrical double layers on both sides of the interface also causes the variation of y with Aq<. In the absence of the specific adsorption of ions at the interface, the Gouy-Chapman theory satisfactorily describes the double-layer structure at the interface between two immiscible electrolyte soultions [20,21]. For the diffuse part of the double layer for a z z electrolyte of concentration c in the phase W whose permittivity is e, the Gouy-Chapman theory [22,23] gives an expression... 

Cantwell and co-workers submitted the second genuine electrostatic model the theory is reviewed in Reference 29 and described as a surface adsorption, diffuse layer ion exchange double layer model. The description of the electrical double layer adopted the Stem-Gouy-Chapman (SGC) version of the theory [30]. The role of the diffuse part of the double layer in enhancing retention was emphasized by assigning a stoichiometric constant for the exchange of the solute ion between the bulk of the mobile phase and the diffuse layer. However, the impact of the diffuse layer on organic ion retention was danonstrated to be residual [19],... 

The stability of inverse micelles has been treated by Eicke (8,9) and by Muller (10) for nonaqueous systems, while Adamson (1) and later Levine (11) calculated the electric field gradient in an inverse micelle for a solution in equilibrium with an aqueous solution. Ruckenstein (5) later gave a more complete treatment of the stability of such systems taking both enthalpic (Van der Waals (VdW) interparticle potential, the first component of the interfacial free energy and the interparticle contribution of the repulsion energy from the compression of the diffuse part of the electric double layer) and entropic contributions into consideration. His calculations also were performed for the equilibrium between two liquid solutions—one aqueous, the other hydrocarbon. 

The model introduced by Stern (2), which is in best agreement with all experimental facts, combines a distribution of charges in a space charge layer (diffuse part of the double layer) and the Helmholtz layer (rigid part of the double layer). Ions are assumed to be adsorbed on the electrode and thus bound to the surface by chemical forces. If strongly adsorbed ions are present at the interface, the rigid double layer predominates in determining the electrical properties of the interface. 

The earlier concepts of microemulsion stability stressed a negative interfacial tension and the ratio of interfacial tensions towards the water and oil part of the system, but these are insuflBcient to explain stability (13). The interfacial free energy, the repulsive energy from the compression of the diffuse electric double layer, and the rise of entropy in the dispersion process give contributions comparable with the free energy, and hence, a positive interfacial free energy is permitted. 

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