Potentiostatic operation

3 Instabilities in High-Temperature Fuel Cells due to Combined Heat and Charge Transport Table 3.1. Parameter values used in the simulations, if not given differently in the text. 

This section treats the steady-state behavior of the cell for the case of fixed cell voltage. In the first part, a cell of infinite length is considered. This reduces the problem to the analysis of two ordinary differential equations in space describing the stationary energy balance. The second part deals with a fuel cell of finite length and includes the boundary conditions of Eq. (11) in the investigation. 

In the steady-state case, the energy balance (11) can be transformed to two first-order differential equations in space  

The newly introduced variable Qp is the spatial temperature gradient. As the cell voltage pm is given, the steady-state system is completed by the three implicit algebraic correlations (12-14) for the unknowns A pA, A pc, and i. The solution of the steady-state system can be visualized in a phase diagram, where 0 is plotted against 0. The result for the parameter values listed in Tab. 3.1 is shown in Fig. 3.2. 

An equilibrium point of (16, 17), where = =o, corresponds to a solution with a 

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Conclusion when using ionic conductors where the conducting, i.e. backspillover ion participates in the catalytic reaction under study (e.g. O2 ions in the case of catalytic oxidations) then both galvanostatic and potentiostatic operation lead to a steady-state and allow one to obtain steady-state r vs Uwr plots. 

FIGURE 11.4 Distributions of reactant concentration near the electrode after different times of potentiostatic operation t, < tj < tum-... 

For batch operation (see Sect. 2.3.4), the limiting current density is going to zero for increasing degree of conversion (see reactant 1 in Fig. 1). Here, the galvanostatic operation may only be acceptable if exclusively unproblematic side reactions occur, such as water electrolysis as solvent decomposition. In all other cases, better results can be expected using the potentiostatic operation (see next section). 

In some problematic cases, there will be no obvious limits available for the choice of the current density in galvanostatic operation. Concurrent reactions take place, resulting in a poor selectivity. But here the potentiostatic operation also cannot demonstrate its advantages, and probably the simpler galvanostatic operation may be applied. To find relatively suitable operation conditions, an experimental optimization of the current density should be carried out, perhaps including parameters... 

Operation with Constant Electrode Potential (Potentiostatic Operation)... 

Fig. 3 Scheme of potentiostatic operation for a preparative eiectroiysis, using in principie a simpiified cyciovoitammetry equipment. The potentiai of the working eiectrode is measured by a Luggin capiiiary, coupied with a reference eiectrode (RE, see Sect. 2.5.1.6). The controi circuit in the potentiostat adjusts the ceii current untii the potentiai of the working eiectrode is equai to the voitage at the controi input. 

The central importance of the electrode potential has been discussed in Sect. 2.3.2. The potentiostatic operation mode evidently requires a reliable potential measurement. Only experiments at constant current can operate without knowledge of the potential. But here too the potential of the working electrode imparts interesting information, for example, a change in this potential - probably not detectable in the... 

Potentiostatic operating mode is applied - that is, the cell voltage is taken as an input parameter. 

It is the objective of this chapter to study this effect by a model-based analysis. The spatially distributed model used here will be derived in the next section. In a first step, the steady-state behavior of the model will be investigated by a phase plane analysis for the case of potentiostatic operation of the cell. In the second step, numerical bifurcation analysis of the model will be used to study the technically more interesting case of galvanostatic operation. 

Fig. 3.2. Steady-state solutions of an infinite length system for potentiostatic operation

One purpose of the investigation of the potentiostatic operation is to motivate the numerical results obtained for the galvanostafic operation mode and presented in the next section. Furthermore, the described phase plane analysis does not provide any information on the stability of the found solutions. The stability analysis will be included in the numerical studies of Section 3.4. 

In contrast to classical chemical reactors, a fuel cell provides the possibility to control the reaction rate directly from outside by setting the cell current, because the local cell current density and the local reaction rate are related by a constant factor. This operation of a fuel cell at constant cell current is more important than the potentiostatic operation from a technical point of view, as fuel cells typically are characterized by current-voltage plots. Because the integral Eq. (15) has to be included in the analysis, the investigation of the galvanostatic operation is more difficult and requires numerical methods. In the following, numerical bifurcation... 

Nonaqueous systems are generally more resistive than aqueous ones, and thus the IR drop in potentiostatic operation may be pronounced. The IR drop should be taken into account especially in fine measurements, such as mechanistic research, and potentiostats with IR drop compensation devices should be used. 

Figure 67. Local current distribution during the transition from an oscillatory state in the transpassive region to a state in the oxygen evolution region measured under potentiostatic operation. (Reprinted from O. Lev, M. Sheintuch, H. Yarnitsky, and L. M. Pismen, Chem. Eng. Sci. 45, 839, 1990. Copyright 1990 with kind permission from Elsevier Science Ltd., Kidlington, U.K.)...

An AMEL 553 galvanostat-potentiostat was used in order to supply constant currents (galvanostatic operation) or potentials (potentiostatic operation) [8] between the working and counter, or the working and reference electrodes, respectively. Most experiments were carried... 

Electrochemical reactors can be operated under conditions of constant electrode potential, constant current, or constant cell voltage. The first two are referred to as potentiostatic and galvanostatic modes of operation, respectively. The potenti-static method is characterized by constant values of the kinetic parameters and hence enables integration of the dififerential equations describing the different reactors. On the other hand, galvanostatic operation is characterized by an inevitable change of electrode potential with time, leading to variations in the kinetic parameters. Hence we restrict our treatment to potentiostatic operation. 

Fig.2. The potentiostat. Operational amplifiers LF 356, Burr-Brown 3554, and Apex PA83.

Complete filling of the template was acheived in a standard manner by monitoring the electrochemical cell current under potentiostatic operation as shown in Figs. 2.22 and 2.23. 

Scan rates typically vary from 10 mV/s to 1 V/s. The lower limit is due to thermal convection, which is always present in an electrolyte. To record faster responses, an oscilloscope or fast transient recorder used to be required all modern potentiostats operate at fast scan voltages. The limit is determined by the sampling rate and the rise time of the op-amps. The currents in successive scans differ from those recorded in the first scan. For quantitation purposes, the first scan should always be used. 

Because the current is not constant during the potentiostatic operation, it has to be integrated during the experiment for calculating the charge transfer and the current efficiency. Coulometers or electronic integrators are commercially available. If a computer data acquisition system is used, the current integration is possible by software. 

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