Gouy-Chapman layer capacitance

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

An important quantity with respect to experimental verification is the differential capacitance of the total electric double layer. In the Stern picture it is composed of two capacitors in series the capacity of the Stem layer, Cgt, and the capacitance of the diffuse Gouy-Chapman layer. The total capacitance per unit area is given by... 

The ensemble Helmholtz layer/Gouy-Chapman layer constitutes the electrochemical double layer. Its thickness is in the order of a few tens of Angstroms. This layer is generally represented by the series combination of two capacitances relative to the diffuse and compact layers, Cdia and Qomp- The capacity of the double layer, Cd, is thus equal to ... 

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... 

Instead of an exact calculation, Gouy and Chapman have assumed that (4) can be approximated by combining the Poisson equation with a Boltzmann factor which contains the mean electrical potential existing in the interface. (This approximation will be rederived below). From this approach the distribution of the potential across the interface can be calculated as the function of a and from (2) we get a differential capacitance Cqc- It has been shown by Grahame that Cqc fits very well the measurements in the case of low ionic concentrations [11]. For higher concentrations another capacitance in series, Q, had to be introduced. It is called the inner layer capacitance and it was first considered by Stern [1,2]. Then the experimental capacitance Cexp is analyzed according to ... 

Measurements based on the Gouy-Chapman-Stem theory to determine the diffuse double-layer capacitance 10, 24,72, 74... 

It can be shown that the differential capacitance of the diffuse layer, according to Gouy-Chapman theory, CGC, is given by ... 

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 interfacial capacitance increases with the DDTC concentration added. The relationship among potential difference t/ of diffusion layer, the electric charge density q on the surface of an electrode and the concentration c of a solution according to Gouy, Chapman and Stem model theory is as follows. 

However, even taking all these facts into account, this theory is not able to reproduce the capacitance-potential curves in the regions beyond the pzc proximity. The model seems, in fact, to be in sharp disagreement with the experimental behavior. The Gouy-Chapman theory might best be described as a brilliant failure. However, as will be seen, it represents an important contribution to a truer description of the double layer it also finds use in the understanding of the stability of colloids and, hence, of the stability of living systems (see Section 6.10.2.2). 

The Gouy-Chapman theory was tested experimentally on the basis of the double-layer capacity measurements. This theory predicts parabolic capacitance-potential relationship and a square-root dependence on concentration, at constant e and T... 

Compared to the experimental results this clearly shows, that Gouy-Chapman theory fails to describe the capacitance of the double-layer, especially at high salt concentration. 

For the evaluation of the non-faradaic component of the response in a more realistic way, different proposals have been made. A useful idea is that corresponding to the interfacial potential distribution proposed in [59] which assumes that the redox center of the molecules can be considered as being distributed homogeneously in a plane, referred to as the plane of electron transfer (PET), located at a finite distance d from the electrode surface. The diffuse capacitance of the solution is modeled by the Gouy-Chapman theory and the dielectric permittivity of the adsorbed layer is considered as constant. Under these conditions, the CV current corresponding to reversible electron transfer reactions can be written as... 

Although each SCM shares certain common features the formulation of the adsorption planes is different for each SCM. In the DDLM the relationship between surface charge, diffuse-layer potential, d, is calculated via the Gouy-Chapman equation (Table 5.1), while in the CCM a linear relationship between surface potential, s, is assumed by assigning a constant value for the inner-layer capacitance, kBoth models assume that the adsorbed species form inner-sphere complexes with surface hydroxyls. The TLM in its original... 

This model is based on the Gouy-Chapman theory (diffuse double-layer theory). The theory states that in the area of the boundary layer between solid and aqueous phase, independently of the surface charge, increased concentrations of cations and anions within a diffuse layer exists because of electrostatic forces. In contrast to the constant-capacitance model, the electrical potential does not change up to a certain distance from the phase boundaries and is not immediately declining in a linear manner (Fig. 14 a). Diffusion counteracts these forces, leading to dilution with increasing distance from the boundary. This relation can be described physically by the Poisson-Boltzmann equation. 

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