Double layer theories Gouy-Chapman

FIGURE 5.15 Dimensionless surface potential (y-axis, F< >S/RT) vs. pH U-axis) for three types of carbon electrode materials Cl, acidic carbon (pHIEP = pHPZC = 3.0) C2, typical as-received ( amphoteric ) carbon (pHIEP = pHPZC = 6.5) C3, basic carbon (pi In,. = pHPZC = 10.0). Based on Gouy-Chapman double-layer theory, for a maximum surface charge of 0.03 C/m2 and ionic strength of 10 3 M. 

Stahlberg [134, 135] introduced the application of the Gouy-Chapman double layer theory for the retention of small ionic analytes in ion-exchange and ion-pair chromatography (Figure 4-41). The resulting equation for the retention factor is... 

Tn recent years, the influence of counterions on the properties of A ionized monolayers has received much attention. Even though Davies (I) application of the Gouy-Chapman double layer theory to ionized monolayers represented a major advance in the understanding of the properties of these systems, it has been increasingly recognized that we must account for the different effects (i.e., specific counterion effects) that counterions of the same net charge may have on the charged mono-layer. Because of counterion sequence inversions which have been ob-... 

The Gouy-Chapman double-layer theory neglects the interfacial phase structure of BLMs and hydration effects. As a result, deviations from the expected values of ion conductivity can be observed. This has resulted in the development of refined electrostatic theories which take these factors into consideration [15,44]. 

In most ionic surfactant studies concerning the formation of microemulsions, it is assumed that the brine is a pseudocomponent, one used solely to maintain the mass balance in the system. Recent evidence indicates that this may not be the case with some W/O microemulsions, in which the aqueous core of the W/O structure exhibits a lower salinity and may sometimes even be salt-free. Such segregation has been explained by negative adsorption of the coions according to the Gouy-Chapman double layer theory [136]. 

Dec. 6,1869, Wells, Norfolk, England - Jan. 17,1958, Oxford, England) Chapman studied in Oxford, and then he was a lecturer at Owens College (which later became part of the University of Manchester). In 1907 he returned to Oxford, and led the chemistry laboratories of the Jesus College until his retirement in 1944 [i]. Chapmans research has mostly been focused on photochemistry and chemical kinetics however, he also contributed to the theory of electrical -> double layer [ii]. His treatment of the double layer was very similar to that elaborated by -> Gouy earlier, and what has come to be called the Gouy-Chapman double-layer model [i.iii]. 

Some emphasis is given in the first two chapters to show that complex formation equilibria permit to predict quantitatively the extent of adsorption of H+, OH , of metal ions and ligands as a function of pH, solution variables and of surface characteristics. Although the surface chemistry of hydrous oxides is somewhat similar to that of reversible electrodes the charge development and sorption mechanism for oxides and other mineral surfaces are different. Charge development on hydrous oxides often results from coordinative interactions at the oxide surface. The surface coordinative model describes quantitatively how surface charge develops, and permits to incorporate the central features of the Electric Double Layer theory, above all the Gouy-Chapman diffuse double layer model. 

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. 

The Diffuse-Double-Layer Theory of Gouy and Chapman... 

It is evident now why the Helmholtz and Gouy-Chapman models were retained. While each alone fails completely when compared with experiment, a simple combination of the two yields good agreement. There is room for improvement and refinement of the theory, but we shall not deal with that here. The model of Stem brings theory and experiment close enough for us to believe that it does describe the real situation at the interface. Moreover, the work of Grahame shows that the diffuse-double-layer theory, used in the proper context (i.e., assuming that the two capacitors are effectively connected in series), yields consistent results and can be considered to be correct, within the limits of the approximations used to derive it. 

We use the Gouy-Chapman theory for the diffuse layer which is based on the Poisson-Boltzmann (P.B.) equation for the potential distribution. Although the different corrections to the P.B. equation in double-layer theory have been investigated (20, 21, 22, 23), it is difficult to state precisely the range of validity of this equation. In the present problem the P.B. equation seems a reasonable approximation at 0.1M of a 1-1 electrolyte to 50mV for the mean electrostatic potential pd at the ohp (24) this upper limit for pd increases with a decrease in electrolyte concentration. All the values for pd calculated in Tables I-IV are less than 50 mV— most of them are well below. If n is the volume density of each ion type of the 1-1 electrolyte in the substrate, c the dielectric constant of the electrolyte medium, and... 

The simple condenser model or constant capacitance model has been mentioned above. It is essentially a simplified double layer theory, in which the distance between the plates can be calculated by using part of the Gouy-Chapman theory. See Stumm (1992) for details. 

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... 

R. O. James and G. A. Parks, Characterization of aqueous colloids by their electrical double-layer and intrinsic surface chemical properties. Surface and Colloid Science 12 119 (1982). Perhaps the most complete review of the triple layer model from the perspective of Gouy-Chapman-Stem-Graham e double layer theory. 

Statistical double-layer theory started at the beginning of the last century with the works by Gouy [1] and Chapman [2], two of the most influential papers ever written in electrochemistry. Their theory, which we will briefly review below, explains the double-layer capacity for metal-solution interfaces at low electrolyte concentrations quite well. Unfortunately, further progress has been slow, and during the last decade, there has been more work in simulations of the double layer than in proper theory. 

Considering all the assumptions and approximations involved in the derivation of the Gouy-Chapman model of the double layer, it should be obvious that a real situation is likely to be much more complex. Nevertheless, results obtained based on that model have served (and continue to serve) well in furthering our understanding of electrical phenomena in colloidal systems. Further refinements of double layer theory have succeeded in explaining a number of bothersome observations in specific situations, especially very high surface potentials. However, the complications involved in their application, and the benefits derived, do not generally warrant such effort in most practical situations. 

The early concept of an electrochemical supercapacitor (ES) was based on the electric double-layer existing at the interface between a conductor and its contacting electrolyte solution. The electric double-layer theory was first proposed by Hermann von Helmholtz and further developed by Gouy, Chapman, Grahame, and Stem. The electric double-layer theory is the foundation of electrochemistry from which fhe electrochemical processes occurring at an electrostatic interface... 

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