Helmholtz double-layer properties

In fig. 3.20b specific adsorption Is also accounted for. The notion of specific adsorption has been defined In sec. 3.3. In disperse systems, its occurrence is de facto Inferred from the dependence of certain double layer properties on the natures of counter- and co-lons Generally, ions interacting specifically (non-electrostatlcally) with the surface approach it to shorter distance p < d). The plane where these specifically adsorbed ions reside is called the inner Helmholtz plane (iHp) In colloid science, the model of fig. 3.20b Is also known as the triple layer model. In this model three charges and three capacitances can be distinguished. For the two inner layer differential capacitances... 

Assuming once more that the Helmholtz double layer has the properties of a condenser for which... 

TTius, it is quite obvious that purity of the used IL is for many studies and in particular for electrochemical investigations of an enormous importance Water but in particular ionic impurities from the reaction process can lead to a completely different behavior at the interface, because a hard inorganic cation such as sodium or lithium disturb the formation of an ideal, homogeneous Helmholtz-double-layer (Figure 22.2) and should have - even in low concentrations - a significant on fundamental properties. 

The description of the double layer properties by the Stem-Gouy model is a very crude one. A veiy weak point is the assumption that the dielectric contact suddenly changes from that of the solution to that of the Helmholtz double layer. The main information comes, therefore, from the minimum which indicates the potential of zero excess charge on the metal. This is, however, only correct in the absence of specific adsorption of ions. If ions are adsorbed, the counter charge for the diffuse double layer is the sum of the surface charge in the metal and of the adsorbed ions. Since the concentration of adsorbed ions also varies with the applied potential, this effect increases the apparent capacity of the Helmholtz double layer. 

Inhibitors can act on the medium by modifying its properties, thus reducing its aggressiveness towards the metal. Them action is probably mainly within the volume of the Helmholtz double layer. 

IHP) (the Helmholtz condenser formula is used in connection with it), located at the surface of the layer of Stem adsorbed ions, and an outer Helmholtz plane (OHP), located on the plane of centers of the next layer of ions marking the beginning of the diffuse layer. These planes, marked IHP and OHP in Fig. V-3 are merely planes of average electrical property the actual local potentials, if they could be measured, must vary wildly between locations where there is an adsorbed ion and places where only water resides on the surface. For liquid surfaces, discussed in Section V-7C, the interface will not be smooth due to thermal waves (Section IV-3). Sweeney and co-workers applied gradient theory (see Chapter III) to model the electric double layer and interfacial tension of a hydrocarbon-aqueous electrolyte interface [27]. 

In this chapter, mathematical procedures for the estimation of the electrical interactions between particles covered by an ion-penetrable membrane immersed in a general electrolyte solution is introduced. The treatment is similar to that for rigid particles, except that fixed charges are distributed over a finite volume in space, rather than over a rigid surface. This introduces some complexities. Several approximate methods for the resolution of the Poisson-Boltzmann equation are discussed. The basic thermodynamic properties of an electrical double layer, including Helmholtz free energy, amount of ion adsorption, and entropy are then estimated on the basis of the results obtained, followed by the evaluation of the critical coagulation concentration of counterions and the stability ratio of the system under consideration. 

In order to determine a system thermodynamically, one has to specify some independent parameters (e.g. N, T, P or V) besides the composition of the system. The most common choice in MC simulation is to specify N, V and T resulting in the canonical ensemble, where the Helmholtz free energy A is the natural thermodynamical potential. However, MC calculations can be performed in any ensemble, where the suitable choice depends on the application. It is straightforward to apply the Metropolis MC algorithm to a simple electric double layer in the iVFT ensemble. It is however, not so efficient for polymers composed of more than a few tens of monomers. For long polymers other algorithms should be considered and the Pivot algorithm [21] offers an efficient alternative. MC simulations provide thermodynamic and structural information, but time-dependent properties are not accessible. If kinetic or time-dependent properties are of interest one has to use molecular dynamic or brownian dynamic simulations. 

Porous and nanocrystalline semiconductor electrodes have unusual properties because the semiconductor/electrolyte interphase is three-dimensional. The Helmholtz electrical double layer can extend throughout the... 

Since charged particles involve all these processes, including the formation of edge charges (Equations 2.3-2.5), first, the electric properties of interfaces have to be determined. A simple way to do so is the application of a support electrolyte in high concentration. The electric double layer, in this case, behaves as a plane and, as a first approach, the Helmholtz model, that is, the constant capacitance model, can be used (Chapter 1, Section 1.3.2.1.1, Table 1.7). It is important to note that the support electrolyte has to be inert. A suitable support electrolyte (such as sodium perchlorate) does not form complexes (e.g., with chloride ions, Section 2.3) and does not cause the degradation of montmorillonite (e.g., potassium fixation in the crystal cavities). In this case, however, cations of the support electrolyte, usually sodium ions, can also neutralize the layer charges ... 

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. 

Figures 3.23a-d illustrate the properties of the double layer for the simple case of adsorption at the outer Helmholtz plane, as in fig. 3.21. A capacitance of 20 pF cm" (figs, a and b) is more representative for hydrophobic surfaces, whereas that of 100 pF cm" (figs, c and d) is more typical for hydrophilic ones.

The properties of the surface layers have a strong effect on the deposition process. The driving force of the electrochemical reaction is the potential difference over the electrochemical double layer. Adsorption of species can change this potential. For example, the additives used in electrodeposition adsorb in the Helmholtz layer. They can change the local potential difference, block active deposition sites, and so on. The thickness of the diffusion layer affects the mass-transfer rate to the electrode. The diffusion layer becomes thinner with increasing flow rate. When the diffusion layer is thicker than the electrode surface profile, local mass-transfer rates are not equal along the electrode surface. This means that under mass-transfer control, metal deposition on electrode surface peaks is faster than in the valleys and a rough deposit will result. 

An important aspect of analyzing the double layer data in the presence of specific adsorption is the determination of the dielectric properties of the irmer layer. In the Grahame model for ionic adsorption [Gl], the adsorbed ions are assumed to have their charge centers located on the inner Helmholtz plane (iHp). Furthermore, the iHp is closer to the electrode surface than the oHp. This is due to the fact that the adsorbed ions replace solvent molecules on the electrode surface, whereas the counter ions on the oHp do not. Another feature of the following treatment is that the charge on the adsorbed ions is assumed to be located on the iHp. Accordingly, the potential drop across the inner layer is given by... 

Let us now discuss in some detail the peculiarities of particle motion during electrophoresis and some other electrical properties of free disperse systems. Electrophoresis usually takes place in a stationary liquid. In a moving fluid the motion of particles occurs only in thin flat gaps and capillaries (microelectrophoresis), where the fluid motion is caused by electroosmosis. If fairly large non-conducting particles are dispersed in a rather dilute electrolyte solution, the ratio of particle radius to the double layer thickness may be substantially greater than 1, i.e., r/8 = kt 1. The streamlines of outer electric field surround the particle and are parallel to most of its surface, as shown in Fig. V-9. In this case the particle velocity, v0, can be with good precision described by Helmholtz-Smoluchowski equation. 

To study the effects of electrochemical properties on passive ion transport processes, we developed a model that focuses on ionic processes at membrane and channel surfaces (14). The surface compartment model (SCM) is based on a Helmholtz electrical double layer, where the enhanced concentration of counterions and the depletion of co-ions at charged surfaces is described by straight line gradients. Treatment of the electrical double layer as a compartment greatly simplifies the calculation of ion transport. 

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. 

Usually the capacitance of the Helmholtz layer and at higher electrolyte concentrations the capacitance of the Gouy-Chapman layer are much larger than the capacitance of the space-charge layer. Therefore, the reciprocal term can be neglected. The space-charge layer is the dominant element and represents the properties of the double layer for semiconductor electrodes... 

Helmholtz-Smoluchowski Equation The most common simplification encountered in electroosmotic flow analysis is the Helmholtz-Smoluchowski approximation. To derive this, we begin by eliminating the nonlinear and transient terms in Eq. 1 as described above and assume that the pressure gradient, Vp, is zero everywhere. The latter of these assumptions is generally valid for pure electroosmotic flow (no applied pressure) with uniform surface ( -potential) and solution (viscosity and conductivity) properties. We also replace — VO with the local applied electric field strength and use Poisson s equation (Eq. 4) to express the net charge density in terms of the double layer potential, v[/. This yields... 

Electrical double layer EDI). Favorable electron-transfer capabilities make ionic hquids good conductive media and vahd substitutes for conventional electrolytes. Electrolytic properties of ionic hquids were studied to determine the capacitance-layer thickness relationship of the EDL by electrochemical impedance spectroscopy (EIS). EIS data combined with supporting SFG analysis indicate that the EDL formed by ionic hquids at the electrode-ioitic liquid interface follows the Helmholtz model and corresjtonds to a Helmholtz layer of one ion thickness [35,36]. 

Different theoretical models have been developed to describe the electrical properties of the double layer. The simplest of these, proposed by Helmholtz (Figure 3.45), assumes that the positive and negative charges are located in two planes separated by a distance Lh of about 0.2 to 0.3 nm, which corresponds to the minimum distance separating hydrated ions from the electrode surface. 

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