Gouy-Chapman-Stem

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

The description of the double layer reported in Figures 3 and 22 is only approximate the composition of the electrode/solution region is somewhat more complex. The double layer has been studied in most detail for a mercury electrode immersed in an aqueous solution. According to Gouy-Chapman-Stem there are several layers of solution in contact with the electrode, see Figure 25. 

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

Later, the Gouy-Chapman-Stem model [2,19, 22-24] describes the interface in the absence of specific adsorption by assuming that the ions can approach the... 

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...

Many more-sophisticated models have been put forth to describe electrokinetic phenomena at surfaces. Considerations have included distance of closest approach of counterions, conduction behind the shear plane, specific adsorption of electrolyte ions, variability of permittivity and viscosity in the electrical double layer, discreteness of charge on the surface, surface roughness, surface porosity, and surface-bound water [7], Perhaps the most commonly used model has been the Gouy-Chapman-Stem-Grahame model 8]. This model separates the counterion region into a compact, surface-bound Stern" layer, wherein potential decays linearly, and a diffuse region that obeys the Poisson-Boltzmann relation. 

Figure 13.3.6 (a) A view of the differential capacitance in the Gouy-Chapman-Stem (GCS) model as a series network of Helmholtz-layer and diffuse-layer capacitances. (b) Potential profile through the solution side of the double layer, according to GCS theory. Calculated from (13.3.23) for 10 M 1 1 electrolyte in water at 25°C. 

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,... 

An important feature of the biogeochemistry of trace elements in the rhizosphere is the interaction between plant root surfaces and the ions in the soil solution. These ions may accumulate in the aqueous phases of cell surfaces external to the plasma membranes (PMs). In addition, ions may bind to cell wall (CW) components or to the PM surface with variable strength. In this chapter, we shall describe the distribution of ions among the extracellular phases using electrostatic models (i.e. Gouy-Chapman-Stem and Donnan-plus-binding models) for which parameters are now available. Many plant responses to ions correlate well with computed PM-surface activities, but only poorly with activities in the soil solution. These responses include ion uptake, ion-induced intoxication, and the alleviation of intoxication by other ions. We illustrate our technique for the quantitative resolution of multiple ion effects by inserting cell-surface activities into nonlinear equations. 

Eq. (11) does not take into account surface-potential effects, but it may be modified to incorporate surface potentials computed by a Gouy-Chapman-Stem model and surface ion activities computed by the Nemst equation. Thus /zjout / become / pM° and the outer and inner surface activities, and t ,... 

Silva, I.R., Smyth, T.J., Israel, D.W., Raper, C.D., Rufty, T.W., 2001. Magnesium is more efficient than calcium in alleviating aluminum rhizotoxicity in soybean and its ameliorative effect is not explained by the Gouy-Chapman-Stem model. Plant Cell Physiol. 42, 538-545. 

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. 

Specific double-layer capacitance Cdi is given by Gouy-Chapman-Stem (GCS) model [13-14] as follows ... 

Summarizing, the main hypotheses and simplifications of the Gouy-Chapman-Stem approach are [5] ... 

Where Ns is the site density, Ka and Kb are equilibrium constants, and Col is a simple capacitance (derived from the Gouy-Chapman-Stem) model. 

In Figure 9.11, the expulsion of co-ions is depicted for a Gouy-Chapman-Stern double layer. Let c+ be the concentration of co-ions at a positively charged surface. In a Gouy-Chapman-Stem double layer, the co-ion expulsion per unit surface area, that is, the negative adsorption of co-ions F+ is given by... 

To solve Equation 9.44, an approximate expression for /(x) must be taken. Here, we elaborate this further assuming a Gouy-Chapman-Stem double layer in which the Stem potential t r does not exceed, say, 50 mV. For most surfaces in media of not too low ionic strength (i.e., > 10" M), this is a reasonable condition. Hence, substituting Equation 9.41 in 9.44 and subsequent integration yield... 

Figure 2.26. Gouy-Chapman-Stem model of the double layer from T. Dong s thesis )...

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