Stem-Graham model

The earliest models used to describe the distribution of charges in the edl are, besides the Helmholz model, the Gouy-Chapman diffuse layer model and the Stem-Graham model. Details of these models are given in Westall and Hohl (1980), Schindler (1981, 1984) and Schindler and Stumm (1987). 

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. 

The Triple-Layer Model (TLM) This model, first developed by Yates et al. (1974) and Davis (1978), is essentially an expanded Stem-Grahame model the specifically adsorbed ions are placed as partially solvated ions at a plane of closest approach. Additional capacitances are introduced. Subsequently, Hayes (1987) had to modify the earlier TLM by moving specifically adsorbed ions to the mean plane of the surface. 

Figure 10. Electrical double layer models. Top right (a) typical type of potential vs. composition plot for a charged surface compared to (b) constant capacitance model. Top left Two double-layer models, (a) diffuse double layer, (b) part parallel plate capacitor and part diffuse layer.. Bottom left Stem layer model. Incorporation of adsorbed ions to surface. From Hiemenz and Rajagopalan (1997) Bottom right Comparison of Gouy-Chapman and Stem-Grahame models of the electrical double layer. From Davis and Kent (1990).

According to the Stem-Graham model, the dense part of the EDL, adjacent to the solid surface charged with the potential determining ions, may, in turn, consist of inner and outer layers. The inner part, located in the direct vicinity of the charged surface, is formed by the specifically adsorbed ions, which are completely, or partially dehydrated (the so-called inner Helmholtz plane). The outer part, referred to as the outer Helmholtz plane, consists of hydrated ions that do not reveal such strong specific adsorption. The ions, specifically adsorbed within the inner part of Stem- Helmholtz plane, may... 

Figure 10.7. Schematic representation of the Stem-Graham model of the electrical double-layer (a) distribution of counterions in the vicinity of the charged surface (b) variation of electrical potential with distance from the surface...

In this way, the Gouy-Chapman-Stem-Grahame model of the electrical double layer was bom (5). This model is stiU qualitatively accepted, although a number of additional parameters have... 

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. 

Thus, Grahame modified Stem s model by introducing the inner plane of closest approach (IHP inner Helmholtz plane), which is located at the distance jc, from the electrode (Fig. 4.11). The IHP is the plane of centers of partially or fully dehy-... 

Fuerstenau") was the first who used the Stern-Grahame model of EDL to describe the adsorption of long-chain surfactants for the equilibrium in heterogeneous systems. The adsorption density in the Stem plane is given by the equation... 

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. 

FIGURE 1.4 Double-layer models (a) Helmholtz model, (b) Gouy-Chapman model, (c) Stem model, and (d) Grahame model. (With kind permission from Springer Science+Business Media Electrochemical Supercapacitors Scientific Fundamentals and Technological Applications, 1999, Conway, B.E. Originally published by Kluwer Academic/ Plenum Pubhshers, New York in 1999.)... 

FIGURE 12.18 Schematic representation of the model for two parallel plane snrfaces in the charge regulation approach, assumed to he oxide surfaces in equilihrium with the solution. (Adapted from Journal of Colloid and Interface Science, 296, Chan, D. Y. C. et al.. Electrical double layer interactions between dissimilar oxide surfaces with charge regulation and Stem-Grahame layers, no. 1 (April 1), 150-158, Copyright (2006), with permission from Elsevier.)... 

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. 

The simplest model for the electrical double layer is the Helmholtz condenser. A distribution of counterions in the bulk phase described by a Boltzmann distribution agree with the Gouy-Chapman theory. On the basis of a Langmuir isotherm Stem (1924) derived a generalisation of the double layer models given by Helmholtz and Gouy. Grahame (1955) extended this model with the possibility of adsorption of hydrated and dehydrated ions. This leads to a built-up of an inner and an outer Helmholtz double layer. Fig. 2.14. shows schematically the model of specific adsorption of ions and dipoles. 

Figure 3. Highly schematic view of the electrical double layer (EDL) at a metal oxide/aqueous solution interface showing (1) hydrated cations specifically adsorbed as inner-sphere complexes on the negatively charged mineral surface (pH > pHpzc of the metal oxide) (2) hydrated anions specifically and non-specifically adsorbed as outer-sphere complexes (3) the various planes associated with the Gouy-Chapman-Grahame-Stem model of the EDL and (4) the variation in water structure and dielectric constant (s) of water as a function of distance from the interface, (from Brown and Parks 2001, with permission)...

---