Electrical double layer charge distribution

A charged surface and the ions, which neutralize the surface, together create an electric double layer. The distribution of the ions can be evaluated from the Poisson-Boltzmann equation where the ions are treated as point particles and the primitive model is used. Further, all correlations between the ions are neglected, which means that the ions are interacting directly only with the colloids and through an external field given by the average distribution of the small ions. The distribution of the particles are assumed to follow Boltzmann s theorem [11]... 

FIGURE 2-1 Helmholtz model of the electrical double layer, (a) Distribution of counterions in the vicinity of the charged surface. (b) Variation of electrical potential with distance from the charged surface. 

Electric double layer The distribution of charges around a colloid suspended in an ionic solution. 

When two conducting phases come into contact with each other, a redistribution of charge occurs as a result of any electron energy level difference between the phases. If the two phases are metals, electrons flow from one metal to the other until the electron levels equiUbrate. When an electrode, ie, electronic conductor, is immersed in an electrolyte, ie, ionic conductor, an electrical double layer forms at the electrode—solution interface resulting from the unequal tendency for distribution of electrical charges in the two phases. Because overall electrical neutrality must be maintained, this separation of charge between the electrode and solution gives rise to a potential difference between the two phases, equal to that needed to ensure equiUbrium. 

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). 

Previous considerations have shown that the interface between two conducting phases is characterised by an unequal distribution of electrical charge which gives rise to an electrical double layer and to an electrical potential diflFerence. This can be illustrated by considering the transport of charge (metal ions or electrons) that occurs immediately an isolated metal is immersed in a solution of its cations ... 

Surface forces measurement is a unique tool for surface characterization. It can directly monitor the distance (D) dependence of surface properties, which is difficult to obtain by other techniques. One of the simplest examples is the case of the electric double-layer force. The repulsion observed between charged surfaces describes the counterion distribution in the vicinity of surfaces and is known as the electric double-layer force (repulsion). In a similar manner, we should be able to study various, more complex surface phenomena and obtain new insight into them. Indeed, based on observation by surface forces measurement and Fourier transform infrared (FTIR) spectroscopy, we have found the formation of a novel molecular architecture, an alcohol macrocluster, at the solid-liquid interface. 

When an electrode is in contact with an electrolyte, the interphase as a whole is electroneutral. However, electric double layers (EDLs) with a characteristic potential distribution are formed in the interphase because of a nonuniform distribution of the charged particles. 

Consider a system of two solvents in contact in which a single electrolyte BA is dissolved, consisting of univalent ions. A distribution equilibrium is established between the two solutions. Because, in general, the solvation energies of the anion and cation in the two phases are different so that the ion with a certain charge has a greater tendency to pass into the second phase than the ion of opposite charge, an electrical double layer appears at... 

As depicted in Fig. 5, both the protein molecule and the sorbent surface are electrically charged. In an aqueous environment, they are surrounded by counterions, which, together with the surface charge, form the so-called electrical double layer. The Gibbs energy of an electrical double layer, may be calculated as the isothermal, isobaric reversible work required to invoke the charge distribution in the double layer... 

The second term in equation (9) is the usual electrostatic term. Here vA is the valency of the unit and e is the elementary charge, and ip(z) is the electrostatic potential. This second term is the well-known contribution accounted for in the classical Poisson-Boltzmann (Gouy -Chapman) equation that describes the electric double layer. The electrostatic potential can be computed from the charge distribution, as explained below. 

As we have seen, the electric state of a surface depends on the spatial distribution of free (electronic or ionic) charges in its neighborhood. The distribution is usually idealized as an electric double layer one layer is envisaged as a fixed charge or surface charge attached to the particle or solid surface while the other is distributed more or less diffusively in the liquid in contact (Gouy-Chapman diffuse model, Fig. 3.2). A balance between electrostatic and thermal forces is attained. 

Most particles acquire a surface electric charge when in contact with a polar medium. Ions of opposite charge (counter-ions) in the medium are attracted towards the surface and ions of like charge (co-ions) are repelled, and this process, together with the mixing tendency due to thermal motion, results in the creation of an electrical double-layer which comprises the charged surface and a neutralising excess of counter-ions over co-ions distributed in... 

In the case of an interface between a metal and an aqueous solution, the space charge layer on the metal side is less than a monatomic layer, hence, the charge in the space charge layer is included in the interfadal charge of the compact layer although, as is discussed in Sec. 5.5, a charge distribution in the atomic dimension exists on the metal side of the electric double layer. 

The presence of a net charge at the particle surface produces an asymmetric distribution of ions in the surrounding region. This means that the concentration of counterions close to the surface are higher than the ions with the same charge as the particle. Thus, an electrical double layer is measured around such a particle placed in water. 

How Is the Charge Distributed inside a Solid Electrode Phenomena that depend on electric double layers comprise a general and very widespread part of the science of surfaces. They occur whoever phases (containing charged... 

Fig. 3. The structure of electrical double layer at a semiconductor-electrolyte interface (a) and the distribution of the potential (b) and charge (c) at the interface. The electrode is charged negatively. is the space-charge region thickness, La is the Helmholtz layer thickness, Qlc and Qtl are the charge of the semiconductor and ionic plates of the double layer, respectively (for further notations see the text).

The purpose of this chapter is to introduce the basic ideas concerning electrical double layers and to develop equations for the distribution of charges and potentials in the double layers. We also develop expressions for the potential energies and forces that result from the overlap of double layers of different surfaces and the implication of these to colloid stability. 

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