Gouy-Stem model

Gouy-Chapman and Stem Models of the Double Layer... 

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. 

Fig. 6.66. The Stem model, (a) A layer of ions stuck to the electrode and the remainder scattered in cloud fashion, (b) The potential variation according to this model, (c) The corresponding total differential capacity C is given by the Helmholtz and Gouy capacities in series.

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. 

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. 

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... 

The charge potential relationship is given by the Stem-Gouy-Chapmann model. In this model it is assumed that the Stem layer is a region of constant capacitance, Cj, separating the surface plane from the plane where the diffuse layer starts. The charge-potential relationship in the Stem layer is... 

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 jigsaw puzzle was put together by Stem in 1926. Agreement between theory and experiment can be achieved once it is realized that both the Helmholtz and the Gouy-Chapman models are valid and exist simultaneously. Thus, there is a layer of ions on the surface that... 

The most basic problems to solve are (i) dealing with the potential near or in the surface this Is a non-thermodynamlc parameter. (11) matching the smeared-out Gouy-Stem double layer to the localized site binding model of the first layeifs) and (ill) identify the proper binding sites and their numbers. 

Stem improved the Gouy-Chapman theory of the DDL by assuming that some ions are tightly retained immediately next to colloid surfaces in a layer of specifically adsorbed or Stem- layer cations. The double layer is diffuse beyond this layer. A satisfactory approximation of the Stem model can be made by assuming that the specifically adsorbed ions quantitatively reduce the surface density of the colloid. The diffuse portion of the double layer then is assumed to develop on a colloid surface of correspondingly reduced charge density. Sample Stem-modification calculations for a series of monovalent cations are shown in Fig. 8.10, Relatively few of the... 

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)...

Figure 26. Schematics of the electrical double layer at a solid-liquid interface, (a) the Helmholtz model, (b) the Gouy-Chapman model, and (c) the Stem model.

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