Layers electrical double

The inner layer (closest to the electrode), known as the inner Helmholz plane (IHP), contains solvent molecules and specifically adsorbed ions (such as Br or T that are not hydrated in aqueous solutions). It is defined by the locus of points for the specifically adsorbed ions. The next layer, the outer Helmholz plane (OHP), reflects the imaginary plane passing through the 

The outer layer (beyond the compact layer), referred to as the diffuse layer (or Gouy layer), is a three-dimensional region of scattered ions, which extends from the OHP into the bulk solution. Such ionic distribution reflects the counterbalance between ordering forces of the electrical field and the disorder caused by a random thermal motion. The equilibrium between these two opposing effects, indicates that the concentration of ionic species at a given distance from the surface, C(x), decays exponentially with the ratio between the electrostatic energy (zEO) and the thermal energy (RT), in accordance with the Boltzmann equation)  

The electrical double layer resembles an ordinary (parallel-plate) capacitor. For an ideal capacitor, the charge (q) is directly proportional to the potential difference  

The capacitance of the double layer consists of a combination of the capacitance of the compact layer in series with that of the diffuse layer. As is common for two capacitors in series, the total capacitance is given by 

When we have a charged surface in the absence of thermal motion, the charge would be neutralized by adsorption of an equal and opposite number of charged ions (counter ions or gegen ions). In fact, thermal motion prevents formation of such a compact double layer and in practice there is a distribution of counter ions (a screening effect) and a distribution of counter ions in the vicinity of the surface, such that the electrical potential gradually falls to zero at 

Schematic of the ion distribution close to an interface. It is assumed that the particle dispersed in the aqueous phase carries a positive charge and there will be a distribution of negative counter ions in solution. In addition, cations may be present and aid the charge balance. 

The Gouy-Chapman theory leads to an effective electrical double layer whieh is represented by the decay of the potential i//q as a function of distance from the interface. The potential is assumed to decay approximately exponentially. The thickness of this layer is eharacterized by the point at which the potential has dropped to 1/e of its initial value and is defined by the double layer thickness 1/k. The value of k is defined by /c = jrkT, where e is 

Original calculations based on point eharges gave too high an ionic concentration near the surfaee. The refined ealeulations introduce a finite ion size into the calculation that allows for the faet that the ions may have a hydration sheath and allows for specifie interaetions with eounter ions. The theory simply splits the potential funetion into two parts the eompact contaet layer where the potential falls quickly from xj/o to xj/i and a diffuse layer where the potential drops more slowly to zero. 

When an electrode is immersed in an electrolyte, a potential is set up at the electrode-electrolyte interface, where the electronic charge on the electrode attracts ions with opposite charge and orients the solvent dipoles. There exist two layers of charge, one in the electrode and another in the electrolyte. This separation of charge set up is commonly known as the electrical double layer. 

There are several reasons for the electrical double layer at the electrode. One reason is occurrence charge separation during the electron transfer 

Many models have been put forward to explain the electrical, compositional, and structural aspects relevant to the electrochemical reactions that occur in fuel cells. Here, we introduce the evolution of the theoretical aspects that have been used to explain the effects occurring in this region. 

Helmholtz model of double layer and potential distribution. 

While it is easy to say that we can measure the potential difference in an electrochemical cell, the reality of what we are measuring is not obvious. The potential difference between a single 

Subsequently, a vertical line 4 is drawn at this pH value. 

This model indicates that some negatively charge ions are adsorbed on the metal electrode surface and polar water covers the rest of this surface, forming a protective layer. The positively charged hydrogen is in contact with the negatively charge metal surface. Thus, one can conclude that 

2) The Outer Helmholtz Plane (OHP) consists of a plane of adsorbed ions due to electrostatic forces in contact with a diffuse ionic layer at a inner potential 2- 

3) The Diffuse Layer (DL) is a thick layer located in a region of diffusely ions in contact with the OHP and the bulk of solution at a potential range of 4 pDiffuae Thus, the diffuse layer/bulk boundary is at 3 = 4 b.  

In fact, this mathematical model represents an electric potential decay since 

---

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]. 

A number of refinements and applications are in the literature. Corrections may be made for discreteness of charge [36] or the excluded volume of the hydrated ions [19, 37]. The effects of surface roughness on the electrical double layer have been treated by several groups [38-41] by means of perturbative expansions and numerical analysis. Several geometries have been treated, including two eccentric spheres such as found in encapsulated proteins or drugs [42], and biconcave disks with elastic membranes to model red blood cells [43]. The double-layer repulsion between two spheres has been a topic of much attention due to its importance in colloidal stability. A new numeri-... 

Properties of the Electrical Double Layer at the Electrocapillary Maximum... 

The treatment may be made more detailed by supposing that the rate-determining step is actually from species O in the OHP (at potential relative to the solution) to species R similarly located. The effect is to make fi dependent on the value of 2 and hence on any changes in the electrical double layer. This type of analysis has permitted some detailed interpretations to be made of kinetic schemes for electrode reactions and also connects that subject to the general one of this chapter. 

M. J. Spamaay, The Electrical Double Layer, Pergamon, New York, 1972. 

A. L. Loeb, J. Th. G. Overbeek, and P. H. Wiersema, The Electrical Double Layer Around a Spherical Particle, MIT Press, Cambridge, MA, 1961. 

Often the van der Waals attraction is balanced by electric double-layer repulsion. An important example occurs in the flocculation of aqueous colloids. A suspension of charged particles experiences both the double-layer repulsion and dispersion attraction, and the balance between these determines the ease and hence the rate with which particles aggregate. Verwey and Overbeek [44, 45] considered the case of two colloidal spheres and calculated the net potential energy versus distance curves of the type illustrated in Fig. VI-5 for the case of 0 = 25.6 mV (i.e., 0 = k.T/e at 25°C). At low ionic strength, as measured by K (see Section V-2), the double-layer repulsion is overwhelming except at very small separations, but as k is increased, a net attraction at all distances... 

Most studies of the Kelvin effect have been made with salts—see Refs. 2-4. A complicating factor is that of the electrical double layer presumably present Knapp [3] (see also Ref. 6) gives the equation... 

A logical division is made for the adsorption of nonelectrolytes according to whether they are in dilute or concentrated solution. In dilute solutions, the treatment is very similar to that for gas adsorption, whereas in concentrated binary mixtures the role of the solvent becomes more explicit. An important class of adsorbed materials, self-assembling monolayers, are briefly reviewed along with an overview of the essential features of polymer adsorption. The adsorption of electrolytes is treated briefly, mainly in terms of the exchange of components in an electrical double layer. 

Stahlberg has presented models for ion-exchange chromatography combining the Gouy-Chapman theory for the electrical double layer (see Section V-2) with the Langmuir isotherm (. XI-4) [193] and with a specific adsorption model [194]. 

The adhesion between two solid particles has been treated. In addition to van der Waals forces, there can be an important electrostatic contribution due to charging of the particles on separation [76]. The adhesion of hematite particles to stainless steel in aqueous media increased with increasing ionic strength, contrary to intuition for like-charged surfaces, but explainable in terms of electrical double-layer theory [77,78]. Hematite particles appear to form physical bonds with glass surfaces and chemical bonds when adhering to gelatin [79]. 

Much use has been made of micellar systems in the study of photophysical processes, such as in excited-state quenching by energy transfer or electron transfer (see Refs. 214-218 for examples). In the latter case, ions are involved, and their selective exclusion from the Stem and electrical double layer of charged micelles (see Ref. 219) can have dramatic effects, and ones of potential imfKntance in solar energy conversion systems. 

This interface is critically important in many applications, as well as in biological systems. For example, the movement of pollutants tln-ough the enviromnent involves a series of chemical reactions of aqueous groundwater solutions with mineral surfaces. Although the liquid-solid interface has been studied for many years, it is only recently that the tools have been developed for interrogating this interface at the atomic level. This interface is particularly complex, as the interactions of ions dissolved in solution with a surface are affected not only by the surface structure, but also by the solution chemistry and by the effects of the electrical double layer [31]. It has been found, for example, that some surface reconstructions present in UHV persist under solution, while others do not. 

Martynov G A and Salem R R 1983 Electrical Double Layer at a Metal-Dilute Electrolyte Solution Inteiface (Berlin Springer)... 

Miyatani T, Florii M, Rosa A, Fu]ihira M and Marti O 1997 Mapping of electric double-layer force between tip and sample surfaces in water with pulsed-force-mode atomic force microscopy Appl. Phys. Lett. 71 2632... 

Manne S, Cleveland J P, Gaub FI E, Stucky G D and Flansma P K 1994 Direct visualization of surfactant hemimicelles by force microscopy of the electrical double layer Langmuir 10 4409-13... 

Here a few core equations are presented from tire simplest tlieory for tire electric double layer tire Gouy-Chapman tlieory [41]. We consider a solution of ions of valency and z in a medium witli dielectric constant t. The ions... 

Here we consider the total interaction between two charged particles in suspension, surrounded by tlieir counterions and added electrolyte. This is tire celebrated DLVO tlieory, derived independently by Derjaguin and Landau and by Verwey and Overbeek [44]. By combining tlie van der Waals interaction (equation (02.6.4)) witli tlie repulsion due to the electric double layers (equation (C2.6.lOI), we obtain... 

Attard P 1996 Electrolytes and the electric double layer Adv. Chem. Phys. 92 1-159... 

Splelman L A and Friedlander S K 1974 Role of the electrical double layer In particle deposition by convective diffusion J. Colloid. Interfaoe. Sol. 46 22-31... 

A current in an electrochemical cell due to the electrical double layer s formation. 

---