Helmholtz/Gouy-Chapman model

Figure 1. Schematic diagram (top) of electric potential across the double layer based on Gouy-Chapman-Stem model in which the solvent is a continuum dielectric. The cartoon (bottom) depicts a hypothetical arrangement of solvent and ions near a charged surface. Similar pictures are found in electrochemical texts. The labels IHP and OHP mark the inner and outer Helmholtz planes.

Since the interface behaves like a capacitor, Helmholtz described it as two rigid charged planes of opposite sign [2]. For a more quantitative description Gouy and Chapman introduced a model for the electrolyte at a microscopic level [2]. In the Gouy-Chapman approach the interfacial properties are related to ionic distributions at the interface, the solvent is a dielectric medium of dielectric constant e filling the solution half-space up to the perfect charged plane—the wall. The ionic solution is considered as formed... 

The Gouy-Chapman theory for metal-solution interfaces predicts interfacial capacities which are too high for more concentrated electrolyte solutions. It has therefore been amended by introducing an ion-free layer, the so-called Helmholtz layer, in contract with the metal surface. Although the resulting model has been somewhat discredited [30], it has been transferred to liquid-liquid interfaces [31] by postulating a double layer of solvent molecules into which the ions cannot penetrate (see Fig. 17) this is known as the modified Verwey-Niessen model. Since the interfacial capacity of liquid-liquid interfaces is... 

The Gouy-Chapman theory treats the electrolyte as consisting of point ions in a dielectric continuum. This is reasonable when the concentration of the ions is low, and the space charge is so far from the metal surface that the discrete molecular nature of the solution is not important. This is not true at higher electrolyte concentrations, and better models must be used in this case. Improvements on the Gouy-Chapman theory should explain the origin of the Helmholtz capacity. In the last section we have seen that the metal makes a contribution to the Helmholtz capacity other contributions are expected to arise from the molecular structure of the solution. 

Fig. 1 Double layer model for a cathode, (a) Helmholtz model (b) Gouy-Chapman model (c) Stern model. 

B , while for an n-type semiconductor the reverse is true. An analog to the SCR in the semiconductor is an extended layer of ions in the bulk of the electrolyte, which is present especially in the case of electrolytes of low concentration (typically below 0.1 rnolh1). This diffuse double layer is described by the Gouy-Chap-man model. The Stern model, a combination of the Helmholtz and the Gouy-Chapman models, was developed in order to find a realistic description of the electrolytic interface layer. 

Of course, when the volume concentration of mobile charges is sufficiently high that the Debye length is comparable with the ionic radius of the mobile ion(s), a combination of the Helmholtz and Gouy-Chapman models is required. This is achieved by assuming that the measured Cdi value is a series combination of that due to the Gouy-Chapman model (Cgc) and that due to the Helmholtz model (Ch), i.e. 

The next question concerns how these excess charges are distributed on the metal and solution sides of the interphase. We discuss these topics in the next four sections. Four models of charge distribution in the solution side of the interphase are discussed the Helmholtz, Gouy-Chapman, Stern, and Grahame models. 

The Helmholtz model was found not to be able to give a satisfactory analysis of measured data. Later, another theory of the diffuse double layer was proposed by Gouy and Chapman. The interfacial region for a system with charged lipid, R-Na+, with NaCl, is shown in Figure 4.10. 

Figure 7.4. Schematic model of the Electrical Double Layer (EDL) at the metal oxide-aqueous solution interface showing elements of the Gouy-Chapman-Stern-Grahame model, including specifically adsorbed cations and non-specifically adsorbed solvated anions. The zero-plane is defined by the location of surface sites, which may be protonated or deprotonated. The inner Helmholtz plane, or [i-planc, is defined by the centers of specifically adsorbed anions and cations. The outer Helmholtz plane, d-plane, or Stern plane corresponds to the beginning of the diffuse layer of counter-ions and co-ions. Cation size has been exaggerated. Estimates of the dielectric constant of water, e, are indicated for the first and second water layers nearest the interface and for bulk water (modified after [6]).

What are the implications of Eq. (6.132) The Stem synthesis of the two models implies a synthesis of the potential-distance relations characteristic of these two models [Fig. 6.66(b)] a Z/ncar variation in the region from. v = 0 to the position of the OHP according to the Helmholtz-Perrin model (see Section 6.6.2), and an exponential potential drop in the region from OHP to the bulk of solution according to the Gouy-Chapman model (see Section 6.6.4), as shown in Fig. 6.67. 

What happens when the concentration c0 of ions in solution is very large Equations (6.124) and (6.130) indicate that while CG increases with increasing c0, CH remains constant. Thus, as c0 increases, (1/CG) (1/CH), and for all practical purposes, C CH. That is, in sufficiently concentrated solutions, the capacity of the interface is effectively equal to the capacity of the Helmholtz region, Le., of the parallel-plate model. What this means is that most of the solution charge is squeezed onto the Helmholtz plane, or confined in a region vety near this plane. In other words, little charge is scattered diffusely into the solution in the Gouy-Chapman disarray. 

Fig. 6.67. Helmholtz-Perrin, Gouy-Chapman, and Stem models of the double layer.

When we revised the different models of the interface, namely, the Helmholtz-Perrin, Gouy-Chapman, and Stem models, we left the corresponding section (Section 6.6.6) with the idea that these models were not able to reproduce the differential capacity curves [Fig. 6.65(b)]. We said that when ions specifically adsorb on the electrode, the models fail to explain the experimental facts. 

Figure 2.13 illustrates what is currently a widely accepted model of the electrode-solution interphase. This model has evolved from simpler models, which first considered the interphase as a simple capacitor (Helmholtz), then as a Boltzmann distribution of ions (Gouy-Chapman). The electrode is covered by a sheath of oriented solvent molecules (water molecules are illustrated). Adsorbed anions or molecules, A, contact the electrode directly and are not fully solvated. The plane that passes through the center of these molecules is called the inner Helmholtz plane (IHP). Such molecules or ions are said to be specifically adsorbed or contact adsorbed. The molecules in the next layer carry their primary (hydration) shell and are separated from the electrode by the monolayer of oriented solvent (water) molecules adsorbed on the electrode. The plane passing through the center of these solvated molecules or ions is referred to as the outer Helmholtz plane (OHP). Beyond the compact layer defined by the OHP is a Boltzmann distribution of ions determined by electrostatic interaction between the ions and the potential at the OHP and the random jostling of ions and... 

Figure 4.1 Helmholtz and Gouy-Chapman model of the electric double layer.

Fig. 1.10 Schematic view of the electrical double layer in agreement with the Gouy-Chapman-Stem-Grahame models. The metallic electrode has a negative net charge and the solvated cations define the inner limit of the diffuse later at the Helmholtz outer plane (OHP). There are anions adsorbed at the electrode which are located at the inner Helmholtz plane (IHP). The presence of such anions is stabilized by the corresponding images at the electrode in such a way that each adsorbed ion establishes the presence of a surface dipole at the interface...

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