Nemst model

To determine the flux, Nemst model of stationary diffusion with linear distribution of the concentration across the layers of the constant thickness is used, and the concentration of the intermediate is assumed to be zero, i.e. the anode discharge proceeds at limit current condition. Then... 

Figure Bl.28.6. (a) Convection within the electrolyte solution, due to rotation of the electrode (b) Nemst diflfiision model for steady state.

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. 

FIGURE 36.5 Model calculation employed to study the dependence of the cluster diameter on the distance between the STM and the substrate surface for localized electrochemical nucle-ation and growth. The lower part of the figure shows the profile of the Nemst potential for the Co /Co potential as a function of the distance from the tip center. The fines indicate a constant Co concentration. (From Schindler et al., 2000, with permission from the American Institute of Physics.)... 

The question arises of the extent to which the build-up of an electrode potential may significantly alter the original concentration of the solution in which the electrode is placed. Let us take the example of a silver electrode. Once the electrode has been immersed in an Ag+ solution, part of the Ag+ ions will be discharged by precipitation of the corresponding amount of Ag and to an extent such that the Nemst potential has been reached. In fact, a double layer at the electrode/solution interface has been formed whose structure cannot be as precisely described as has appeared from the model proposed by... 

The pH (or pI) term of the Nemst equation contains the electrode slope factor as a linear temperature relationship. This means that a pH determination requires the instantaneous input, either manual or automatic, of the prevailing temperature value into the potentiometer. In the manual procedure the temperature compensation knob is previously set on the actual value. In the automatic procedure the adjustment is permanently achieved in direct connection with a temperature probe immersed in the solution close to the indicator electrode the probe usually consists of a Pt or Ni resistance thermometer or a thermistor normally based on an NTC resistor. An interesting development in 1980 was the Orion Model 611 pH meter, in which the pH electrode itself is used to sense the solution temperature (see below). 

Fig. 15 Two of the simplest theories for the dissolution of solids (A) the interfacial barrier model, and (B) the diffusion layer model, in the simple form of Nemst [105] and Brunner [106] (dashed trace) and in the more exact form of Levich [104] (solid trace). c is the concentration of the dissolving solid, cs is the solubility, cb is the concentration in the bulk solution, and x is the distance from the solid-liquid interface of thickness h or 8, depending on how it is defined. (Reproduced with permission of the copyright owner, John Wiley and Sons, Inc., from Ref. 1, p. 478.)...

Comprehensive discussions of fuel cells and Camot engines Nemst law analytical fuel cell modeling reversible losses and Nemst loss and irreversible losses, multistage oxidation, and equipartition of driving forces. Includes new developments and applications of fuel cells in trigeneration systems coal/biomass fuel cell systems indirect carbon fuel cells and direct carbon fuel cells. 

It was shown by Roux (1974) that the two ideal sites model applies perfectly to partitioning of Rb distribution between nepheline and hydrothermal solutions. Based on the experimental work of Roux (1974), deviation from ideality in the normalized Rb/Na distribution between nepheline (X.) and hydrothermal solution (Xaq) is detectable for X, values higher than 10 (figure 10.3A) Distribution constant Xin the Nemst s law range is Kq = 0.82 (Roux, 1974), and the modification of K with increasing X, is well described by equation 10.20, within experimental approximation (figure 10.3B). 

The same authors (2001) studied the common case of bivalent (liquid phase)-monova-lent (solid phase) exchange. In this study, two isotopic models, i.e. Vermeulen s and Patterson s and the Nemst-Plank model for the exchange of ions of different valence, were compared in terms of applicability (Table 4.16). Specifically, the authors studied the range... 

In a hydrodynamically free system the flow of solution may be induced by the boundary conditions, as for example when a solution is fed forcibly into an electrodialysis (ED) cell. This type of flow is known as forced convection. The flow may also result from the action of the volume force entering the right-hand side of (1.6a). This is the so-called natural convection, either gravitational, if it results from the component defined by (1.6c), or electroconvection, if it results from the action of the electric force defined by (1.6d). In most practical situations the dimensionless Peclet number Pe, defined by (1.11b), is large. Accordingly, we distinguish between the bulk of the fluid where the solute transport is entirely dominated by convection, and the boundary diffusion layer, where the transport is electro-diffusion-dominated. Sometimes, as a crude qualitative model, the diffusion layer is replaced by a motionless unstirred layer (the Nemst film) with electrodiffusion assumed to be the only transport mechanism in it. The thickness of the unstirred layer is evaluated as the Peclet number-dependent thickness of the diffusion boundary layer. 

Based on the previous description of the double layer, it is logical to assume that a direct relationship between the absolute charge at the interface and the concentration of ions in the vicinity of the interface exists. Indeed, several models have been developed in the past that describe the ion concentration as a function of the actual surface charge at a specific distance jc from the interface. Furthermore, the famous Nemst equation, which is the basis for understanding many electrochemical reactions, proves to be helpful as it relates the ion concentration to a quantity called the electrical potential ( j/). The electrical potential is the work (W) required to move a unit charge (q) through the electrical field ... 

The equations (19) may be considered as refined Nemst-Planck equations. These equations combined with the M.S.T. model are treated by F. Helfferich (55) in a very exhaustive manner in the chapter on ion-exchange resin membranes of his book on ion-exchange resins. Extensive literature references are also given here. 

I.2. Interdiffusion. F. Helfferich and H. D. Ocher (54) studied the interdiffusion of counterions through an ion-exchange membrane. Bases for their calculations were the Nemst-Planck flux equations combined with the M.S.T. model. Ion-fluxes and concentration profiles in the membrane were calculated. 

R. ScHLOGL and U. Schodel 146) have supplied another proof for the usability of the Nemst-Planck flux equations combined with the M.S.T. model, also for the case that an electric current flows through an ion-selective membrane. They determined the concentration profiles of the mobile ions for the case of a cation selective membrane on the basis of phenol sulfonic acid and NaCl solutions, under application of an electric current. 

Uf < 1 in the real operation regime of a SOFC. This model based on the thermodynamic equilibrium already shows the principal influences of the system pressure p, SOFC temperature sofc, excess air X and fuel utilisation Uf on the Nemst voltage En. 

The Nemst voltage En is shown as a function of the fuel utilisation Uf in a SOFC in Figure 2.4 with H2 as a fuel and with the system pressure p as a parameter. The excess air and the SOFC temperature are the fixed parameters. The range of practical interest between Uf = 0.1 and Uf = 0.9 can be well approximated with the model of the ideal gas. The dotted lines show the adaptation of the model for a high fuel utilisation. The amount of the water fraction and the decrement in the hydrogen and oxygen fraction within the SOFC reduces En between Uf = 0.1 and Uf = 0.9 by about more than 200 mV An increment of the system pressure from... 

Some models use the average Nemst voltage, according to Equation (2.61), to determine the cell voltage and cell power from a given current density and ASR. The results of this common approach are in deviation to the results of the integral determination according to Equation (2.59). 

The electric potential ip is assumed to be continuous throughout the electrodes and electrolyte except at the electrode/electrolyte interfaces. These discontinuities are usually modeled by Nemst s law. The model to calculate the potential jumps at each electrolyte/electrode interface is described in Celik et al. (2005). The source term in Equation (5.24) is non-zero only near the electrode/electrolyte interfaces to account for the potential jumps. 

We consider here Equations (9.10), (9.11) and (9.12) in the analysis of a coupled lumped SOFC. Because we now resolve the anode and cathode regions in this analysis (thereby temporally resolving the reactant concentrations, pressures and temperatures), the cell voltage versus, time can also be determined (using the Nemst equation). The anode gas phase lumped model is provided by integrating Equations (9.10) and (9.11) in the x-direction ... 

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