Gouy-Chapmen space charge layer

The simplest model for the ionic distribution at liquid-liquid interfaces is the Verwey-Niessen model [10], which consists of two Gouy-Chapman space-charge layers back to... 

Elegant studies of electrocapillarity of a nonpolarized ITIES by Gavach et al. [48] showed that the tetraethyl-, tetrapropyl- and tetrabutylammonium ions are not adsorbed within the compact layer and suggested that the interface is made of two space charge layers, described by the Gouy-Chapman theory, on either side of a central compact layer [49-51]. In a nonpolarized ITIES, the potential drop across the interface cannot be altered independently of the chemical potential of a salt of ionic constituents in either of the phases. The degree of specific adsorption cannot therefore be quantitatively estimated at a nonpolarized interface [28]. 

Figure 4.2 Potential changes in the different parts of the double layer. A(p potential drop in the space-charge layer, A

Usually the capacitance of the Helmholtz layer and at higher electrolyte concentrations the capacitance of the Gouy-Chapman layer are much larger than the capacitance of the space-charge layer. Therefore, the reciprocal term can be neglected. The space-charge layer is the dominant element and represents the properties of the double layer for semiconductor electrodes... 

Double-layer capacitance Space-charge layer capacitance Capacitance of the Gouy-Chapman layer Capacitance of the Helmholtz layer Madelung constant Sauerbrey constant Distance... 

By analogy with the charge of the Gouy-Chapman layer, we can calculate for the space-charge layer. For intrinsic semiconductors this yields ... 

The potential difference at the semiconductor-electrolyte interface is the sum of three terms Adi rising from the space-charge layer in the semiconductor A( h from the Helmholtz layer and A0qc from the Gouy-Chapman layer (Figure 3.55). 

Thermal motion of the ions in the EDL was included in the theories developed independently by Georges Gouy in Erance (1910) and David L. Chapman in England (1913). The combined elfects of the electrostatic forces and of the thermal motion in the solution near the electrode surface give rise to a diffuse distribution of the excess ions, and a diffuse EDL part or diffuse ionic layer with a space charge Qy x) (depending on the distance x from the electrode s surface) is formed. The total excess charge in the solution per unit surface area is determined by the expression... 

To evaluate the contribution of the SHG active oriented cation complexes to the ISE potential, the SHG responses were analyzed on the basis of a space-charge model [30,31]. This model, which was proposed to explain the permselectivity behavior of electrically neutral ionophore-based liquid membranes, assumes that a space charge region exists at the membrane boundary the primary function of lipophilic ionophores is to solubilize cations in the boundary region of the membrane, whereas hydrophilic counteranions are excluded from the membrane phase. Theoretical treatments of this model reported so far were essentially based on the assumption of a double-diffuse layer at the organic-aqueous solution interface and used a description of the diffuse double layer based on the classical Gouy-Chapman theory [31,34]. 

A rigorous solution of this problem was attempted, for example, in the hard sphere approximation by D. Henderson, L. Blum, and others. Here the discussion will be limited to the classical Gouy-Chapman theory, describing conditions between the bulk of the solution and the outer Helmholtz plane and considering the ions as point charges and the solvent as a structureless dielectric of permittivity e. The inner electrical potential 0(1) of the bulk of the solution will be taken as zero and the potential in the outer Helmholtz plane will be denoted as 02. The space charge in the diffuse layer is given by the Poisson equation... 

The semiconductor occupies the region to the right of the vertical solid line representing the interface (jc = 0). To the left of it, there is the Helmholtz layer formed by ions attracted to the electrode surface, and also by solvent molecules its thickness, L, is the order of the size of an ion. The space-charge region in the solution (the Gouy-Chapman layer) is adjacent to the Helmholtz layer from the electrolyte side. 

The simplest model of the electrical double layer between a metal and an electrolyte is the simple capacitor visualized by Helmholtz as shown in Figure 14. The diffuse ion distribution in the liquid phase was recognized by Gouy and Chapman- to form a space charge region adjacent to the electrode surface. 

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