Mixed potential model

Otherwise it has been shown that the accumulation of electrolytes by many cells runs at the expense of cellular energy and is in no sense an equilibrium condition 113) and that the use of equilibrium thermodynamic equations (e.g., the Nemst-equation) is not allowed in systems with appreciable leaks which indicate a kinetic steady-state 114). In addition, a superposition of partial current-voltage curves was used to explain the excitability of biological membranes112 . In interdisciplinary research the adaptation of a successful theory developed in a neighboring discipline may be beneficial, thus an attempt will be made here, to use the mixed potential model for ion-selective membranes also in the context of biomembrane surfaces. 

Fig. 5. Tentative mixed potential model for the sodium-potassium pump in biological membranes the vertical lines symbolyze the surface of the ATP-ase and at the same time the ordinate of the virtual current-voltage curves on either side resulting in different Evans-diagrams. The scale of the absolute potential difference between the ATP-ase and the solution phase is indicated in the upper left comer of the figure. On each side of the enzyme a mixed potential (= circle) between Na+, K+ and also other ions (i.e. Ca2+ ) is established, resulting in a transmembrane potential of around — 60 mV. This number is not essential it is also possible that this value is established by a passive diffusion of mainly K+-ions out of the cell at a different location. This would mean that the electric field across the cell-membranes is not uniformly distributed.

Ni(I), of course, is not known as a stable, naturally occurring entity. Epelboin et al. conjectured that it may exist on the surface in a more or less solvated state, and possibly complexed, perhaps as NiOHa(is [72], It is not clear what the concentration of Ni ds is likely to be on the surface, other than that likely to be associated with a propagating kink site. If a Ni.[ds species is involved in the anodic processes in electroless deposition as suggested by Touhami et al. [71], this accounts in substantial part for the interdependence between the anodic and cathodic processes, and lack of adherence to a mixed potential model for electroless deposition in their mildly alkaline solution. 

Interactions between Collector and Sulphide Minerals and Mixed Potential Model... 

The mixed-potential model demonstrated the importance of electrode potential in flotation systems. The mixed potential or rest potential of an electrode provides information to determine the identity of the reactions that take place at the mineral surface and the rates of these processes. One approach is to compare the measured rest potential with equilibrium potential for various processes derived from thermodynamic data. Allison et al. (1971,1972) considered that a necessary condition for the electrochemical formation of dithiolate at the mineral surface is that the measmed mixed potential arising from the reduction of oxygen and the oxidation of this collector at the surface must be anodic to the equilibrium potential for the thio ion/dithiolate couple. They correlated the rest potential of a range of sulphide minerals in different thio-collector solutions with the products extracted from the surface as shown in Table 1.2 and 1.3. It can be seen from these Tables that only those minerals exhibiting rest potential in excess of the thio ion/disulphide couple formed dithiolate as a major reaction product. Those minerals which had a rest potential below this value formed the metal collector compoimds, except covellite on which dixanthogen was formed even though the measured rest potential was below the reversible potential. Allison et al. (1972) attributed the behavior to the decomposition of cupric xanthate. 

Abstract In the beginning, the mixed potential model, which is generally used to explain the adsorption of collectors on the sulphide minerals, is illustrated. And the collector flotation of several kinds of minerals such as copper sulphide minerals, lead sulphide minerals, zinc sulphide minerals and iron sulphide minerals is discussed in the aspect of pulp potential and the nature of hydrophobic entity is concluded from the dependence of flotation on pulp potential. In the following section, the electrochemical phase diagrams for butyl xanthate/water system and chalcocite/oxygen/xanthate system are all demonstrated from which some useful information about the hydrophobic species are obtained. And some instrumental methods including UV analysis, FTIR analysis and XPS analysis can also be used to investigated sulphide mineral-thio-collector sytem. And some examples about that are listed in the last part of this chapter. 

Ever since the mixed potential model has been proposed, the interaction mechanism between thio-collector and sulphide minerals has been usually explained on the basis of this model. The principle of the mixed potential model can be schematically shown in Fig. 4.1. Here, E respectively... 

Table 4.1 shows the measured rest potential of sulphide electrode in thio collector solutions at pH = 6.86 and the equilibrium potential calculated for possible processes. In terms of the mixed potential model, the reaction products should be metal collector salts between four thio collectors and galena and jamesonite and should be disulphide between four thio collectors and pyrite and... 

Figure 4.1 The mixed potential model of redox reaction on sulphide surface...

From the point of view of electrochemistry of flotation, a depressant is, however, defined as a reagent by the addition of which the oxidation of the mineral surface occurs at lower potential than collector oxidation or formation of metal collector salt which may be also decomposed imder the conditions given in the discussions which follow. Under these conditions, the mixed potential model becomes one of mineral oxidation and oxygen reduction, the oxidation of the thio collector or the formation of the metal collector is suppressed, and the mineral will remain... 

The Tafel expressions for both the anodic and the cathodic reaction can be directly incorporated into a mixed potential model. In modeling terms, a Tafel relationship can be defined in terms of the Tafel slope (b), the equilibrium potential for the specific half-reaction ( e), and the exchange current density (70), where the latter can be easily expressed as a rate constant, k. An attempt to illustrate this is shown in Fig. 10 using the corrosion of Cu in neutral aerated chloride solutions as an example. The equilibrium potential is calculated from the Nernst equation e.g., for the 02 reduction reaction,... 

Relationships such as that in Eq. (12) offer convenient means of testing the validity of mixed potential models by comparing electrochemically determined parameters (in this case, a reaction order based on measured Tafel slopes) to values measured by other means. One such example would be the corrosion of U02 (nuclear fuel) in aerated neutral solutions containing added carbonate (6). In the presence of carbonate, corrosion product deposits are avoided, since the U02+ corrosion product is solubilized by complexation with the carbonate. Measured Tafel slopes yield a predicted reaction order of n0l = 0.67 with respect to 02 for the overall corrosion reaction ... 

Many of these approaches have been used in mixed potential models to predict the behavior of copper nuclear waste containers in a compacted clay environment (22), and to predict the corrosion rate of nuclear fuel inside these containers once they have failed and water allowed to contact the nuclear fuel (U02) wasteform (6). The container is lined with a carbon shell liner to give it mechanical integrity. Consequently, when the container floods with water on failure, two corrosion processes are possible, corrosion of the U02 wasteform (conservatively assumed to be unprotected by the Zircalloy cladding within which it is encapsulated) and corrosion of the carbon steel liner. The reaction scheme underlying... 

Figure 21 Schematic illustrating the one-dimensional array of layers considered in the mixed potential model of nuclear fuel corrosion in a failed (flooded) nuclear waste container.

Other examples of such mixed potential models include that developed by Macdonald and Urquidi-Macdonald to predict water radiolysis effects in thin condensed water layers on metal surfaces (24), and the models of Marsh and Taylor (25), and Kolar and King (22) to predict the corrosion of carbon steel and copper waste containers surrounded by a low permeability material such as clay. 

Figure 1.9 is the Pourbaix diagram for iron and some of its compounds in an aqueous system at 25°C. The equilibrium potential of the reaction Fe° = Fe2+ + 2e falls outside the stability region of water represented by dashed lines. Hence, measurement of the equilibrium electrode potential is complicated by the solvent undergoing a reduction reaction, while the iron is undergoing electrochemical oxidation. This is the basis of the mixed potential model of corrosion. 

The two cases described above were chosen to demonstrate that useful predictions can be made of the behavior of the materials on the basis of mixed-potential models. These calculations also highlight the critical role played by the electrochemical potential in determining whether failure will or will not occur, and they demonstrate the promising methods for calculating the ECP in various environments that are practically important. 

Only a few systematic studies have been made of the effect of fluid flow on the ECP of power plant alloys in high-temperature water, even though theory suggests that the effect should be substantial under certain conditions [43]. Because the theoretical predictions, from the mixed-potential model (MPM) [43] and more recently the advanced mixed-potential model (AMPM) [47], preceded systematic experimental studies, it is appropriate to discuss the theoretical predictions first. 

Active mass utilization 326, 371, 373 Active material 369, 376 Advanced Mixed Potential Model (AMPM) 152... 

Mixed Potential Model and the Electrochemical Corrosion Potential. 673... 

After the concentration of each radiolysis species is calculated, the corrosion potential of the component can be estimated using a mixed potential model (MPM) [35], The MPM is based on the physico-electrochemical condition that charge conservation must be fulfilled at the corroding interface. Because electrochemical reactions transfer charge across a metal/solution interface at rates measured by the partial currents, the following... 

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