Gouy-Chapman theory, electrode-electrolyte

Figure 2.11 According to the Gouy-Chapman theory, the capacity of the electrode/electrolyte interface should be a cosh function of the potential difference across it (see text). Concentration of electrolyte in (b) > than that in (a).

The electrode roughness factor can be determined by using the capacitance measurements and one of the models of the double layer. In the absence of specific adsorption of ions, the inner layer capacitance is independent of the electrolyte concentration, in contrast to the capacitance of the diffuse layer Q, which is concentration dependent. The real surface area can be obtained by measuring the total capacitance C and plotting C against Cj, calculated at pzc from the Gouy-Chapman theory for different electrolyte concentrations. Such plots, called Parsons-Zobel plots, were found to be linear at several charges of the mercury electrode. ... 

The concentration of ions near the electrode surface depends on charge density and hence on potential. For example, in 0.1 M solution of a 1 -1 electrolyte at a rational potential of + 0.5 V, the concentration of anions at the outer Helmholtz plane, calculated from the Gouy-Chapman theory, is 4.7 M. At this concentration. 

Reference electrodes of mercury have been used by several investigators in an attempt to measure single electrode potentials. Stastny and Strafelda (5 ) concluded that the zero charge potential of such an electrode in contact with an infinitely dilute aqueous solution is -0.1901V referred to the standard hydrogen electrode. Hall ( ) states that the potential drop across the double layer under these conditions is independent of solution composition when specific adsorption is absent. Daghetti and Trasatti (7, ) have used mercury reference electrodes to study the absolute potential of the fluoride ion-selective electrode and have compared their estimates of ion activities in NaF solutions with those provided by other methods. Their method is based on the assumption that the potential drop across the mercury I solution interface is independent of the electrolyte concentration once the diffuse layer effects are accounted for by the Gouy-Chapman theory. 

As the electrode surface will, in general, be electrically charged, there will be a surplus of ionic charge with opposite sign in the electrolyte phase in a layer of a certain thickness. The distribution of jons in the electrical double layer so formed is usually described by the Gouy— Chapman—Stern theory [20], which essentially considers the electrostatic interaction between the smeared-out charge on the surface and the positive and negative ions (non-specific adsorption). An extension to this theory is necessary when ions have a more specific interaction with the electrode, i.e. when there is specific adsorption of ions. 

Parsons and Zobel plot — In several theories for the electric - double layer in the absence of specific adsorption, the interfacial -> capacity C per unit area can formally be decomposed into two capacities in series, one of which is the Gouy-Chapman (- Gouy, - Chapman) capacity CGC 1/C = 1 /CH + 1 /CGC. The capacity Ch is assumed to be independent of the electrolyte concentrations, and has been called the inner-layer, the - Helmholtz, or Stern layer capacity by various authors. In the early work by Stern, Ch was attributed to an inner solvent layer on the electrode surface, into which the ions cannot penetrate more recent theories account for an extended boundary region. In a Parsons and Zobel plot, Ch is determined by plotting experimental values for 1/C vs. 1/Cgc- Specific adsorption results in significant deviations from a straight line, which invalidates this procedure. 

There have been considerable efforts to move beyond the simplified Gouy-Chapman description of double layers at the electrode-electrolyte interface, which are based on the solution of the Poisson-Boltzmann equation for point charges. So-called modified Poisson-Boltzmann (MPB) models have been developed to incorporate finite ion size effects into double layer theory [61]. An early attempt to apply such restricted primitive models of the double layer to the ITIES was made by Cui et al. [62], who treated the problem via the MPB4 approach and compared their results with experimental data for the more problematic water-DCE interface. This work allowed for the presence of the compact layer, although the potential drop across this layer was imposed, rather than emerging as a self-consistent result of the theory. The expression used to describe the potential distribution across this layer was... 

Measurements of the surface tension and surface stress of solids are not easy. Some attempts have been made to measure the surface energy, or at least to determine the PZC, of solid electrodes attached to piezoelectric materials (36, 37). More often there is a reliance on studies of differential capacitance (Section 13.4.3) (35, 38). In principle, these measurements could provide all of the information needed to describe the surface charges and relative excesses however, one must first know the PZC. Evaluating it for a solid electrode/electrolyte system is not straightforward, and indeed, as discussed below, the PZC is not uniquely defined for a polycrystalline electrode. The most widely used approach is to evaluate the potential of minimum differential capacitance in a system involving dilute electrolyte. The identification of this potential as the PZC rests on the Gouy-Chapman-Stem theory discussed in Section 13.3,... 

To date, it has been documented that ILs can be adsorbed onto various electrode surfaces. For example, Nanjundiah et al. found that several ILs used as electrolytes can induce double-layer capacitance phenomena on the surface of an Hg electrode and obtained the respective capacitance values for various ILs. Hyk and Stojek have also studied the IL thin layer on electrode surfaces and suggested that counterions substantially influence the distribution of IL. Kornyshev further discussed IL formations on electrode surfaces, suggesting that IL studies should be based on modern statistical mechanics of dense Coulomb systems or density-functional theory rather than classical electrochemical theories that hinge on a dilute-solution approximation. There are three conventional models that describe the charge distribution of an ion near a charged surface the Helmholtz model, the Gouy-Chapman model, and the Stern model. In the case of ILs, it remains controversial which model can best explain and lit the experimental data. 

Gouy and Chapman developed the theory for the diffuse part of the double layer in front of the electrode. In a first approximation and for a z/z valent electrolyte, an exponential... 

Gouy and Chapman realised that in an electrolyte solution, the charges are free to move and are subject to thermal motion. They retained the concepts of the electrostatic theory to describe the coulombic metal-counter ion interaction but, in addition, they allowed for the random motion of the ions. The result is a diffuse layer of charge in which the concentration of counter ions is greatest next to the electrode surface and decreases progressively towards a homogeneous distribution of ions within the bulk electrolyte (Fig. 5.1b). 

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