The electric double layer

A net surface charge can be acquired by the unequal adsorption of oppositely charged ions. Ion adsorption may involve positive or negative surface excess concentrations. 

Surfaces in contact with aqueous media are more often negatively charged than positively charged. This is a consequence of the fact that cations are usually more hydrated than anions and so have the greater tendency to reside in the bulk aqueous medium whereas the smaller, less hydrated and more polarising anions have the greater tendency to be specifically adsorbed. 

Surfaces which are already charged (e.g. by ionisation) usually show a preferential tendency to adsorb counter-ions, especially those with a high charge number. It is possible for counter-ion adsorption to cause a reversal of charge. 

If surfactant ions are present, their adsorption will usually determine the surface charge. 

Hydrated (e.g. protein and polysaccharide) surfaces adsorb ions less readily than hydrophobic (e.g. lipid) surfaces. 

This chapter is about charged solid surfaces in liquids. The most important liquid is water. Because of its high dielectric constant, water is a good solvent for ions. For this reason, most surfaces in water are charged. Different processes can lead to charging. Ions adsorb to a surface or dissociate from a surface. A protein might, for instance, expose an amino group on its surface. This can become protonated and 

In the years 1910-1917, Gouy and Chapman went a step further. They took into account a thermal motion of the ions. Thermal fluctuations tend to drive the 

1) Hermann Ludwig Ferdinand Helmholtz, 1821-1894. German physicist and physiologist, professor in Konigsberg, Bonn, Heidelberg, and Berlin. 

2) Louis George Gouy, 1854-1926. French physicist, professor in Lyon. 

3) David Leonard Chapman, 1869-1958. English chemist, professor in Manchester and Oxford. 

In the years 1910-1917 Gouy2 and Chapman3 went a step further. They took into account a thermal motion of the ions. Thermal fluctuations tend to drive the counterions away form the surface. They lead to the formation of a diffuse layer, which is more extended than a molecular layer. For the simple case of a planar, negatively charged plane this is illustrated in Fig. 4.1. Gouy and Chapman applied their theory on the electric double layer to planar surfaces [54-56], Later, Debye and Hiickel calculated the potential and ion distribution around spherical surfaces [57], 

the Gouy-Chapman and Debye-Hiickel are continuum theories. They treat the solvent as a continuous medium with a certain dielectric constant, but they ignore the molecular nature of the liquid. Also the ions are not treated as individual point charges, but as a continuous charge distribution. For many applications this is sufficient and the predictions of continuum theory agree with experimental results. At the end of this chapter we discuss the limitations and problems of the continuum model. 

Among different liquid-solid interfaces, fhe boundary between an electrolyte and a metal electrode is the one which has been most investigated in surface science. This is dictated by its importance for elecfrochemisfry and by a rich variety of interesting phenomena. In some respect the relevant processes are similar to those at the gas-solid interface. On the other hand, the electrified character of the electrolyte-solid interface resulfs in some peculiarities. One can control interface properties through external manipulation of the interfacial potential difference. All reactions that involve charge transfer respond directly to this quantity. In this section we shall consider the structure of the electric double layer which takes place at an electrolyte-solid interface and the basic principles of control for various reactions at this boundary. 

Consider the structure of an interface layer between a metal electrode and an electrolyte solution kept under a potential difference p. Due fo electrostafic forces, the ions from the solution are attracted by the electrode electrostatic adsorption) and the dipolar molecules are oriented along the lines of the electric force. They can also be physically or chemically adsorbed specifically adsorbed) on the electrode. In the case of electrostatic adsorption alone, ions can approach the electrode to a distance given by their primary solvation shells. The plane parallel to the electrode surface through the centers of elecfrostatically adsorbed ions at their maximum approach to the electrode is called the outer Helmholtz plane (OFIP) and the solution region between the OHP and the electrode surface is called the Helmholtz or compact layer. Due to thermal motion the ions are not confined within the compact layer, but are distributed over the so-called diffuse layer. The plane through the centers of specifically adsorbed ions is referred to as the inner Helmholtz plane (IHP) (Fig. 2.21). 

The distance between the plates of the first capacitor is fixed, whereas that of the second one varies as a function of the electrolyte concentration. At low concentrations, the diffuse layer is extended deeply into the solution and the capacitance of the electric double layer is determined mainly by the value of Q. If has a minimum af 2 = 0. Thus the applied potential equals the PZC. This observation can be used for determining the PZC. 

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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. 

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... 

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]. 

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. 

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 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. 

The 2eta potential (Fig. 8) is essentially the potential that can be measured at the surface of shear that forms if the sohd was to be moved relative to the surrounding ionic medium. Techniques for the measurement of the 2eta potentials of particles of various si2es are collectively known as electrokinetic potential measurement methods and include microelectrophoresis, streaming potential, sedimentation potential, and electro osmosis (19). A numerical value for 2eta potential from microelectrophoresis can be obtained to a first approximation from equation 2, where Tf = viscosity of the liquid, e = dielectric constant of the medium within the electrical double layer, = electrophoretic velocity, and E = electric field. 

On the electrode side of the double layer the excess charges are concentrated in the plane of the surface of the electronic conductor. On the electrolyte side of the double layer the charge distribution is quite complex. The potential drop occurs over several atomic dimensions and depends on the specific reactivity and atomic stmcture of the electrode surface and the electrolyte composition. The electrical double layer strongly influences the rate and pathway of electrode reactions. The reader is referred to several excellent discussions of the electrical double layer at the electrode—solution interface (26-28). 

Pig. 3. Representation of the electrical double layer at a metal electrode—solution interface for the case where anions occupy the inner Helmholtz plane... 

Electrically, the electrical double layer may be viewed as a capacitor with the charges separated by a distance of the order of molecular dimensions. The measured capacitance ranges from about two to several hundred microfarads per square centimeter depending on the stmcture of the double layer, the potential, and the composition of the electrode materials. Figure 4 illustrates the behavior of the capacitance and potential for a mercury electrode where the double layer capacitance is about 16 p.F/cm when cations occupy the OHP and about 38 p.F/cm when anions occupy the IHP. The behavior of other electrode materials is judged to be similar. 

Activation Processes. To be useful ia battery appHcations reactions must occur at a reasonable rate. The rate or abiUty of battery electrodes to produce current is determiaed by the kinetic processes of electrode operations, not by thermodynamics, which describes the characteristics of reactions at equihbrium when the forward and reverse reaction rates are equal. Electrochemical reaction kinetics (31—35) foUow the same general considerations as those of bulk chemical reactions. Two differences are a potential drop that exists between the electrode and the solution because of the electrical double layer at the electrode iaterface and the reaction that occurs at iaterfaces that are two-dimensional rather than ia the three-dimensional bulk. 

Fig. 7. (a) Simple battery circuit diagram where represents the capacitance of the electrical double layer at the electrode—solution interface, W depicts the Warburg impedance for diffusion processes, and R is internal resistance and (b) the corresponding Argand diagram of the behavior of impedance with frequency, for an idealized battery system, where the characteristic behavior of A, ohmic B, activation and C, diffusion or concentration (Warburg... 

Fig. 1. The structure of the electrical double layer where Q represents the solvent CD, specifically adsorbed anions 0, anions and (D, cations. The inner Helmholtz plane (IHP) is the center of specifically adsorbed ions. The outer Helmholtz plane (OHP) is the closest point of approach for solvated cations or molecules. O, the corresponding electric potential across the double layer, is also shown.

The physical separation of charge represented allows externally apphed electric field forces to act on the solution in the diffuse layer. There are two phenomena associated with the electric double layer that are relevant electrophoresis when a particle is moved by an electric field relative to the bulk and electroosmosis, sometimes called electroendosmosis, when bulk fluid migrates with respect to an immobilized charged surface. 

Two kinds of barriers are important for two-phase emulsions the electric double layer and steric repulsion from adsorbed polymers. An ionic surfactant adsorbed at the interface of an oil droplet in water orients the polar group toward the water. The counterions of the surfactant form a diffuse cloud reaching out into the continuous phase, the electric double layer. When the counterions start overlapping at the approach of two droplets, a repulsion force is experienced. The repulsion from the electric double layer is famous because it played a decisive role in the theory for colloidal stabiUty that is called DLVO, after its originators Derjaguin, Landau, Vervey, and Overbeek (14,15). The theory provided substantial progress in the understanding of colloidal stabihty, and its treatment dominated the colloid science Hterature for several decades. 

Fig. 7. The van der Waals potential between droplets is increasingly negative with reduced interdroplet distance, whereas the electric double-layer potential...

The relative value of the two potentials reveals the destabdization action of salts added to the emulsion. Addition of an electrolyte to the continuous phase causes a reduction of the electric double-layer repulsion potential, whereas the van der Waals potential remains essentially unchanged. Hence, the reduced electric double-layer potential causes a corresponding reduction of the maximum in the total potential, and at a certain concentration of electrolyte the maximum barrier height is reduced to a level at which the stabdity is lost. 

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