Double layer, electric origin

The name, DLYO, originates from the first letter in the surname of the four authors (Derjaguin, Landau, Verwey and Overbeek) from two different groups, which originally published these ideas. The theory is based on the competition between two contributions, a repulsive electric double layer and an attractive van der Waals force [4,5]. The interaction in the electric double layer was originally obtained from mean field calculations via the Poisson-Boltzmann equation [Eq. (4)]. However, the interaction can also be determined by MC simulations (Sec. II. B) and by approximate integral equations like HNC (Sec. II. C). This chapter will focus on the first two possibilities. 

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. 

Figure 6.13. The electron distribution in the model metal jellium gives rise to an electric double layer at the surface, which forms the origin of the surface contribution to the work function. The electron wave function reaches...

The Nernst equation is of limited use at low absolute concentrations of the ions. At concentrations of 10 to 10 mol/L and the customary ratios between electrode surface area and electrolyte volume (SIV 10 cm ), the number of ions present in the electric double layer is comparable with that in the bulk electrolyte. Hence, EDL formation is associated with a change in bulk concentration, and the potential will no longer be the equilibrium potential with respect to the original concentration. Moreover, at these concentrations the exchange current densities are greatly reduced, and the potential is readily altered under the influence of extraneous effects. An absolute concentration of the potential-determining substances of 10 to 10 mol/L can be regarded as the limit of application of the Nernst equation. Such a limitation does not exist for low-equilibrium concentrations. 

This chapter is devoted to the behavior of double layers and inclusion-free membranes. Section II treats two simple models, the elastic dimer and the elastic capacitor. They help to demonstrate the origin of electroelastic instabilities. Section III considers electrochemical interfaces. We discuss theoretical predictions of negative capacitance and how they may be related to reality. For this purpose we introduce three sorts of electrical control and show that this anomaly is most likely to arise in models which assume that the charge density on the electrode is uniform and can be controlled. This real applications only the total charge or the applied voltage can be fixed. We then show that predictions of C < 0 under a-control may indicate that in reality the symmetry breaks. Such interfaces undergo a transition to a nonuniform state the initial uniformity assumption is erroneous. Most... 

In the closely related coulostatic method based on injection of a charge from a small condenser into an electrode in equilibrium with a redox system. The resulting time dependence of the electrode potential originates from the discharging of the electrical double layer by electrode reactions... 

As regards the origin of the double layer the Helmholtz theory gives no information, but several other theories have been formulated. Modem electrical theories suppose every conducting substance to contain large numbers of negatively charged ions, called electrons, which are exactly alike no matter in what substance they are found. When two s.T. 5... 

The electrified interface is generally referred to as the electric double layer (EDL). This name originates from the simple parallel plate capacitor model of the interface attributed to Helmholtz.1,9 In this model, the charge on the surface of the electrode is balanced by a plane of charge (in the form of nonspecifically adsorbed ions) equal in magnitude, but opposite in sign, in the solution. These ions have only a coulombic interaction with the electrode surface, and the plane they form is called the outer Helmholtz plane (OHP). Helmholtz s model assumes a linear variation of potential from the electrode to the OHP. The bulk solution begins immediately beyond the OHP and is constant in potential (see Fig. 1). 

In solution, all electrodes are surrounded by a layer of water molecules, ions, and other atomic or molecular species. We will not look in depth at this topic, except to refer to the two principle layers, which are named after one of the original pioneers of electrochemistry, namely the nineteen-century great, Hermann Helmholtz. The two Helmholtz layers are often said to comprise the electrode double-layer (or electric double-layer ). 

Equation (1.35) is known as the Debye-Hiickel or Gui-Chapman equation for the equilibrium double layer potential. In terms of the original variable x (1.34), (1.35) suggest e1/2(r(j) is the correct scale of ip variation, that is, the correct scale for the thickness of the electric double layer. At the same time, it is observed from (1.32) that for N 1 the appropriate scale depends on N, shrinking to zero when N — oo (ipm — — oo). This illustrates the previously made statement concerning the meaningfulness of the presented interpretation of relectric potential

(—oo) — 0, < (oo) — —oo). 

In Sect. 2 we reviewed the original Tanaka s treatment of ions in gels. More precise theory should properly account for the chemical dissociation equilibrium in the interior of gels and the Donnan equilibrium at the gel-solvent boundary where an electric double layer is formed [31,97,98]. 

Figure 2.12 Simple capacitor model of electrode-solution interface as a charged double layer (original Helmholtz model). Negatively charged surface. Positively charged ions are attracted to the surface, forming an electrically neutral interphase.

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