Double layer structure Compact

Double-layer structure. It is generally assumed that the ions can approach the electrode only at a distance of a few angstroms. Their centers are located in a plane (called Helmholte plane). The Helmholtz layer (or compact layer) would contain only solvent molecules oriented by the electric field. 

ME, but of less mathematical rigour, is the singularity method (SM), which reconstructs the potential field by a superposition of singularity fields from point charges (Phillips 1995). Additionally, it is possible to approximate compact, isometric aggregates as porous spheres (PS), for which analytical expressions of the double layer structure are available (Ohshima 2008). Some of the mentioned methods assume a certain shape of the aggregates or primary particles, some of them are based on the Unearised PBE (BEM, ME, PS). Only a few have already been employed for particle clusters (CoeUio et al. 1996 Kwon et al. 1998 Schiefil et al. 2012). 

The subsequent three chapters are devoted to the electric double-layer structure at the interface between immiscible electrolytes examined by the electrocapillary curves method (Prof. Senda and coauthors) and by measurement of the electric double-layer capacity (Dr. Samec and Dr. Mare ek) as well as to the investigation of the Galvani and Volta potentials in the above-mentioned systems (Prof. Koczorowski). These chapters will be of interest to many electrochemists since the results obtained here are comparable with the thoroughly studied metal/electrolyte solution interface. An insignificant potential shift in the compact layer at the interface between immiscible electrolytes in the absence of specific ion adsorption - this is the main conclusion arrived at by the authors of Chaps. 4 and 5. Chapter 6 deals with the scale of potentials in a system of immiscible electrolytes and the thermodynamic relation between the distribution coefficients and the Volta potentials. 

The double-layer structure at ITIES shows different features than that formed at the metal/electrolyte interface. The charge distribution in the both phases preserves its diffuse property even in rather concentrated solutions [7]. The potential difference in the compact double-layer is much smaller than the potential differences in the adjacent diffuse layers. Thus, practically, the overall potential difference only consists of the potential difference in the diffuse layers 02(w) and (f) o)... 

The double-layer capacitance is composed of several contributions. In a geometrical sense the double layer in "supported" systems is represented by the compact "Helmholtz" or "Stem" layer. The electrostatically attracted solvated species reside in the "outer Helmholtz plane" (OHP), and specifically adsorbed species reside closer to the electrode in the "inner Helmholtz plane" (IHP). The double-layer structure is completed by a "diffuse" layer, composed of electrostatically attracted species at some distance from the electrode surface. The fuU thickness of the double layer can be defined as the external boundary of the diffuse layer separating it from the bulk solution, where the measured potential becomes equal to that of the bulk solution and no local potential gradient driven by the difference between the electrode potential ( )j and the solution potential can be determined (Figure 5-4). 

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 central issue which has to be addressed in any comprehensive study of electrode-surface phenomena is the determination of an unambiguous correlation between interfacial composition, interfacial structure, and interfacial reactivity. This principal concern is of course identical to the goal of fundamental studies in heterogeneous catalysis at gas-solid interfaces. However, electrochemical systems are far more complicated since a full treatment of the electrode-solution interface must incorporate not only the compact (inner) layer but also the boundary (outer) layer of the electrical double-layer. The effect of the outer layer on electrode reactions has been neglected in most surface electrochemical studies but in certain situations, such as in conducting polymers and... 

In the active state, the dissolution of metals proceeds through the anodic transfer of metal ions across the compact electric double layer at the interface between the bare metal and the aqueous solution. In the passive state, the formation of a thin passive oxide film causes the interfadal structure to change from a simple metal/solution interface to a three-phase structure composed of the metal/fUm interface, a thin film layer, and the film/solution interface [Sato, 1976, 1990]. The rate of metal dissolution in the passive state, then, is controlled by the transfer rate of metal ions across the film/solution interface (the dissolution rate of a passive semiconductor oxide film) this rate is a function of the potential across the film/solution interface. Since the potential across the film/solution interface is constant in the stationary state of the passive oxide film (in the state of band edge level pinning), the rate of the film dissolution is independent of the electrode potential in the range of potential of the passive state. In the transpassive state, however, the potential across the film/solution interface becomes dependent on the electrode potential (in the state of Fermi level pinning), and the dissolution of the thin transpassive film depends on the electrode potential as described in Sec. 11.4.2. 

The fundamental electrochemical event, that is, electron transfer, occurs at the electrode surface. Peculiarities of electrochemical reactions include an electrical field, which in a special way complicates the phenomena of adsorption and desorption at the surface. The first layer of the solution, which is in contact with the electrode, possesses a specific structure. It is important for charged particles that the orientation of medium molecules in the vicinity of the electrode produces a decrease in dielectric permeability in the compact part of the double layer (Damaskin and Kryshtalik 1984). 

The simplest model of the structure of the metal-solution interphase is the Helmholtz compact double-layer model (1879). According to this model, all the excess charge... 

The simplest model of the structure of the metal-solution interphase is the Helmholtz compact double-layer model (1879). According to this model, all the excess charge on the solution side of the interphase, qs. is lined up in the same plane at a fixed distance away from the electrode, the Helmholtz plane (Fig. 4.4). This fixed distance xH is determined by the hydration sphere of the ions. It is defined as the plane of the centers of the hydrated ions. All excess charge on the metal, qM, is located at the metal surface. 

In the discussion of the different models for the structure of double layer developed up to this point, no specific interactions have been considered. However, specific adsorption is a common phenomena in electrochemistry. Since the interactions implied have to be very short range in nature, the chemisorbed species are strongly bound to the electrode surface with the locus of their centers being the inner Helmholtz plane (IHP, see Fig. 1.10), or compact part of the double layer. 

The structure of the electric double layers has been described by different models. All models consider the charges on solid phase to be compact, forming... 

The solvent also acts as a dielectric medium, which determines the field diji/dx and the energy of Interaction between charges. Now, the dielectric constant e depends on the inherent properties of the molecules (mainly their permanent dipole moment and polarizability) and on the structure of the solvent as a whole. Water is unique in this sense. It is highly associated in the liquid phase and so has a dielectric constant of 78 (at 25 C), which is much higher than that expected from the properties of the individual molecules. When it is adsorbed on the surface of an electrode, inside the compact double layer, the structure of bulk water is destroyed and the molecules are essentially immobilized... 

Activation-limited growth tends to favor compact columnar or equiaxed deposits, while mass transport-limited growth favors formation of loose dendritic deposits. The deposit morphology is modified by using additives. Additives act as grain refiners and levelers because of their effects on electrode kinetics and the structure of the electrical double layer at the cathode surface. Additives that reduce primarily the nucleation overpotential can be considered to be grain-refining additives because of increased secondary nucleation events. 

The electric field across electrochemical interfaces is of key importance to understanding electrochemical processes. The barrier heights for the charge transfer processes at such interfaces depend on the field, which in turn depends on the overall electronic properties of the interface. To understand the effect of the field on these barriers requires quantitative insight into the electronic structure of the interface. Theoretical treatments of the physics of electrochemical interfaces are needed. These must handle more effectively such questions as the role of electronic surface states and the interactions of the solvent and ions of the compact double layer with the metal orbitals, as well as the spillover of the conduction band electrons into the interface. The experimental techniques described in the previous section of this chapter will exert a significant influence on the development of such understanding, but this will require the combined efforts of theorists and experimentalists. 

Many properties of disperse systems are related to the distribution of charges in the vicinity of the interface due to the adsorption of electrolytes. The adsorption of molecules is driven by the van der Waals attraction, while the driving force for the adsorption of electrolytes is the longer-range electrostatic (Coulomb) interaction. Because of this, the adsorption layers in the latter case are less compact than in the case of molecular adsorption (i.e., they are somewhat extended into the bulk of the solution), and the discontinuity surface acquires noticeable, and sometimes even macroscopic thickness. This diffuse nature of the ionized adsorption layer is responsible for such important features of disperse systems as the appearance of electrokinetic phenomena (see Chapter V) and colloid stability (Chapters VII, VIII). Another peculiar feature of the adsorption phenomena in electrolyte solutions is the competitive nature of the adsorption in addition to the solvent there are at least two types of ions (even three or four, if one considers the dissociation of the solvent) present in the system. Competition between these ions predetermines the structure of the discontinuity surface in such systems -i.e. the formation of spatial charge distribution, which is referred to as the electrical double layer (EDL). The structure and theory of the electrical double layer is described in detail in textbooks on electrochemistry. Below we will primarily focus on those features of the EDL, which are important in colloid... 

Stern in 1924 combined the structures to form a compact double layer at the electrode surface with a... 

Not only do surfactants and cosurfactants lower the interfacial tension, but also their molecular structures affect the curvature of the interface as shown schematically in Fig. 3. The hydrocarbon chains are rather closely packed (about 0.25 nm per chain) they repel one another sideways and as a result have a tendency to bend the interface around the water side. The counterions of the ionic headgroups also repel one another sideways and thus tend to curve the interface around the oil side. The bullQ polar groups of nonionic surfactants have a similar effect. So we understand qualitatively that more cosurfactant promotes W/O rather than O/W microemulsions. More electrolyte compresses the double layer, diminishes the sideways pressure of the double layer, and also promotes W/O microemulsions. The polar groups of PEO nonionics become more compact (less soluble) at higher temperatures, and so with this type of surfactants high temperature leads to W/O microemulsions. 

When a metal electrode is placed in an electrolyte solution, an equilibrium difference usually becomes established between the metal and solution. Equilibrium is reached when the electrons left in the metal contribute to the formation of a layer of ions whose charge is equal and opposite to that of the cations in solution at the interface. The positive charges of cations in the solution and the negative charges of electrons in the metal electrode form the electrical double layer [4]. The solution side of the double layer is made up of several layers as shown in Fig. 2.7. The inner layer, which is closest to the electrode, consists of solvent and other ions, which are called specifically adsorbed ions. This inner layer is called the compact Helmholtz layer, and the locus of the electrical centers of this inner layer is called the inner Helmholtz plane, which is at a distance of di from the metal electrode surface. The solvated ion can approach the electrode only to a distance d2. The locus of the centers of the nearest solvated ion is called the outer Helmholtz plane. The interaction of the solvated ion with metal electrode only involves electrostatic force and is independent of the chemical properties of the ions. These ions are called non-specifically adsorbed ions. These ions are distributed in the 3D region called diffusion layer whose thickness depends on the ionic concentration in the electrolyte. The structure of the double layer affects the rate of electrode reactions. 

In experiments covering a larger potential region, from the oxidized state until the complete neutral state, a new resonance circuit was found not described by the transmission line model. A new model was suggested by Pickup et al., which was used and modified later by Rammelt and Plieth et This model is corroborated by the duplex film structure (Figure 11.9). A compact layer on the metal/polymer interface with neutral state properties in the neutral state and double-layer properties in the oxidized state describes the compact polymer film the transmission fine model represents the porous part (Figure 11.17). 

Two planes are usually associated with the double layer. The first one, the inner Helmholtz plane (IHP), passes through the centers of specifically adsorbed ions (compact layer in the Helmholtz model), or is simply located just behind the layer of adsorbed water. The second plane is called the outer Helmholtz plane (OHP) and passes through the centers of the hydrated ions that are in contact with the metal surface. The electric potentials linked to the IHP and OHP are usually written as 4 2 and 4f, respectively The diffuse layer develops outside the OHP. The concentration of cations in the diffuse layer decreases exponentially vs. the distance from the electrode surface. The hydrated ions in the solution are most often octahedral complexes however, in Fig. 1.1.2. they are shown as tetrahedral structures for simplification. 

Figure 1.6 (a) Structure of the double layer at the electrode/solution interface. Note the highly ordered structure of the compact layer the diffuse layer is less ordered but is not the random arrangement of the solution away from the interface, (b) Potential field resulting from this model. 

Orientation and interactions of adsorbed molecules From measurements of the differential capacitance of the electrode double layer or from electrocapillary measurements the surface concentration of the adsorbed molecules and the area A required for an adsorbed molecule in the electrode surface can be determined [18, 27, 28, 30, 69, 70]. Using data obtained for the crystal structure of bases the area which would be occupied by one adsorbed molecule in different surface orientations can be evaluated and compared with the experimentally-determined area A. From these calculations it has been concluded that at low surface concentrations (the so-called dilute adsorption region) the adsorbed bases lie flat at the electrode surface. In compact layer the adsorbed bases seem to adopt a perpendicular surface orientation [18, 45]. Similar reorientation from flat to perpendicular stance has been observed with... 

Figure 10 (a) Tlic double-iayer structure at the solid—solution interface according to the Gony-Chapman-Steni-Grahame model, (b) Tlie electrostatic potential in the compact and diffuse parts of the double layer, (Taken from Ref. 6, with permission.)... 

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