Surface complexation models capacitance values

The surface charge vs. pH curves of other well studied metal hydroxides can all be described fairly well with the gibbsite one-pKn model [31, 34, 52-54]. The more complex reality that these surfaces are multifunctional does not affect the surface charge of rutile and hematite. Results for rutile are plotted in Fig. 9 for a good fit s.a. of the K+ and NOj ions had to be incorporated. Besides the <7s(pH) curves also, C, the capacitance (dus/dpH) is shown. Around the pzc the capacitance provides a good test for the model description [54]. Experimental capacitance values above pH=10 are unreliable. 

Model h is the so-called four layer model, which, compared to the triple-layer model, introduces one supplementary layer. The major reason for this is that the electrolyte ions typically differ in size. It may be argued that the usually larger anion has to be placed further away from the surface than the more compact cation. The consequence of the additional layer is an additional capacitance value. Furthermore, constraints on electrolyte binding from experimental data, which indicate symmetrical electrolyte binding, become more complicated. This is because in addition to the stability constant for the formation of the outer-sphere complexes, the location of charge also affects the interaction of the ion with the surface. 

Although each SCM shares certain common features the formulation of the adsorption planes is different for each SCM. In the DDLM the relationship between surface charge, diffuse-layer potential, d, is calculated via the Gouy-Chapman equation (Table 5.1), while in the CCM a linear relationship between surface potential, s, is assumed by assigning a constant value for the inner-layer capacitance, kBoth models assume that the adsorbed species form inner-sphere complexes with surface hydroxyls. The TLM in its original... 

Some adsorption models attempt to adjust for the nonconstant nature of the equilibrium constants. The constant-capacitance model uses K values for dissociation and metal complexation that are adjusted for the efiect of the electrical potential at the surface, employing the empirical reaction... 

Constant capacitance model (CCM) was proposed in 1972 by Schindler and Stumm (Schindler, R. W. et at, 1976 Stumm, W. et at, 1980) mostly for the surface of oxides. It is based on the very first model of the dual electric layer developed by Helmholtz. Its core concept is an assumption that only inner-sphere ion complexes form, which are positioned as an individual layer at some distance from the surface, and the diffusion layer is absent. It is believed that Na+, K+, Cb and NO ", as well as inert, do not form bond with the surface and affect only the ion force of the solution. For this reason the model is viewed as two parallel capacitor plates surface of the mineral with charge a, on the one hand, and adsorbed H+, OH and other ions (Figure 2.18, A) with charge + a. on the other. At that, the electric potential value on the surface of the mineral is equal to... 

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