G-C theory

FIGURE 15.8 Electrostatic potential as a function of the distance from a surface according to the G-C theory for three different bulk concentrations of a 1 1 electrolyte 1, 50, and 500mM, respectively. The surface charge density is kept constant at -0.1 C/m. ... 

Equations 15.43 through 15.45 in combination with Equation 15.23 constitute the result of the G-C theory. 

In the ideal case 4, =4 o, i.e., the surface potential obtained from the G-C theory. At first sight Equations 15.48 and 15.53 may seem to be contradictory. However, by inserting Equation 15.23 into Equation 15.53 under the condition that... 

There are two versions of the physical description of this system. According to the Gouy-Chapman (G-C) theory, counter ion thermal energy runs counter to the electrostatic attraction and a secondary diffuse layer in which the potential decays almost exponentially because of screening effects is generated. Both layers are under dynamic equilibrium. The electrical potential difference, between the stationary phase and the bulk eluent can be theoretically estimated. Figure 3.2 depicts the G-C model. 

The variations of the capacity of the diffuse part of the dl with the potential at the electrode surface has the shape of a hyperbolic cosine (G-C theory for a symmetrical electrolyte) the minimum of capacity corresponds to zero-charge density on the metal. This density of charge corresponds to a potential imposed on the electrode. This potential of zero charge (pzc) varies with the co (see Section V.l). 

When there is ionic adsorption, there are ions on the metal side of the oHp (substitution for the water molecule). These metalion interactions cannot be described by the G-C theory [see Section... 

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Heibst, E. In Atomic, Molecular, Optical Physics Handbook Drake, G., Ed. AIP Press New Yoik, 1996, p 429 Adams, N. G. In Atomic, Molecular, Optical Physics Handbook Drake, G., Ed. AIP Press New Yoik, 1996, p 441. For three-body systems, a slightly more complex temperature dependence is observed. For saturated systems, more complex treatments are needed —see Gilbert, R. G. Smith, S. C. Theory erf Unimolecular and Recombination Reactions Blackwell Oxford, 1990. 

Golab J.T., Sprague J.R., Carron K.T., Schatz G.C., Vanduyne R.P., A surface enhanced hyper-Raman scattering study of pyridine adsorbed onto silver - experiment and theory, J. Chem. Phys. 1988 88 7942-7951. 

In theory, this model can be used to fix up to three moments of the mixture fraction (e.g., (c), ( 2), and (c3)). In practice, we want to choose the CFD transport equations such that the moments computed from Eqs. (34) and (35) are exactly the same as those found by solving Eqs. (28) and (29). An elegant mathematical procedure for forcing the moments to agree is the direct quadrature method of moments (DQMOM), and is described in detail in Fox (2003). For the two-environment model, the transport equations are... 

A great many of the difficulties (and sometimes the misunderstandings) arise from point (c). It is however important to notice that the APM describes the properties of solutions as finite differences between suitable composition-dependent averages and the properties of the pure components. Series expansions in powers of 6, p, 6, and a were introduced afterwards for the purpose of qualitative discussion and comparison with other treatments, e.g., the theory of conformal solutions.34>85>36 They introduce artificial difficulties due to their slow convergencef which have nothing to do with the physical ideas of the APM. Therefore expansions of this type should be proscribed for all quantitative applications one should instead use the compact expressions of the excess functions. 

Gostoli, C., Pilati, F., Sarti, G. C. and Di Giacomo, B Chemical kinetics and diffusion in poly(butylene terephthalate) solid-state poly condensation experiments and theory, J Appl. Polym. Sci., 29, 2873-2887 (1984). 

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