Polarisation and Cell Losses

In the previous section, we have obtained the open-circuit value (OCV) for a fuel cell as 

This value is considered to be maximum for the ideal case. For example, at 200°C, the AGf = -220 kJ, which yields 

Total voltage y = Open circuit voltage Losses 

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Polarisation is a voltage loss or overpotential, which is a function of current density. It can be broken down into a number of terms, originating in various phenomena that occur when a finite current flows in a cell. The three dominant polarisations are (a) ohmic polarisation or ohmic loss (b) concentration polarisation and (c) activation polarisation. This chapter defines and discusses these polarisations, and describes methods to measure them. 

Electrode polarisations cause large voltage losses in SOFCs and need to be reduced to low levels for increased efficiency. The three polarisations described in this chapter are ohmic polarisation, concentration polarisation, and activation polarisation. The ohmic contribution stems from resistance to electron and ion flows in the materials, and is generally dominated by the electrolyte resistance, with the consequence that SOFCs employing thick (>100 micron) YSZ as electrolj te have high ohmic losses at temperatures below about 900 C. Now that thinner electrolytes are being used in electrode-supported cells, this resistance has dropped and it is possible to use YSZ down to about 700°C. 

As realised from the above issues in the comparison of test results on the electrodes and on the cells, it is a non-trivial task to break down the total loss measured on a single cell into its components using the results from the electrode studies. Impedance spectroscopy on practical cells is, however, a technique by which a partial break down can be made. Though the impedance spectra obtained in general are difficult to interpret due to the many processes involved, the spectra can at least provide a break down of the total loss into an ohmic resistance (Rj = Rgiyt + Rconnect) and a polarisation resistance reflecting losses due to chemical, electrochemical, and transport processes, as described in more detail in Chapter 9. 

At the effective property or continuum level, the simulation of electrode and cell performance basically requires only a parameterised electrochemical model. Such an electrochemical model is usually described as a current-voltage relation, or I-V curve, for a single cell, in terms of parameters that are effective cell properties and operational parameters. The I-V relation describes the voltage (potential) loss at a specified current with respect to the ideal thermodynamic performance, which is called overpotential or polarisation (q). This cell I-V curve is specific for the materials, structural characteristics, and operational parameters (gas compositions, pressure, temperature) of a given PEN element. 

To predict the local polarisation in a full-scale cell or stack at any point, its dependence on composition, pressure, and temperature of the gas flowing in the gas channel contacting the electrode must be known. In a large cell, these bulk gas properties vary from one point to the next. Electrode polarisation or overpotential - the difference between the local potential of the electrode under load and the potential at open circuit (equilibrium potential) - is also a local quantity because it depends not only on the bulk gas composition but also on the current density. In a large cell the current is usually distributed nonuniformly, as discussed in Sections 11.2-11.5. Similar to Eq. 7, one can express the local cell voltage under load, i.e., when current is passed, as the thermodynamic cell potential minus three loss terms the ohmic loss, the cathode polarisation, and the anode polarisation ... 

There is an alternative approach to obtain the effective voltage. The total polarisation can also be summed up for the fuel cell. Usually, the total polarisation is predominantiy due to concentration losses and activation losses i.e.. 

Fig. 1.20 Cell consisting of two reversible Ag /Ag electrodes (Ag in AgN03 solution). The rate and direction of charge transfer is indicated by the length and arrow-head as follows gain of electrons by Ag -he- Ag—> loss of electrons by Ag - Ag + e- —. (o) Both electrodes at equilibrium and (f>) electrodes polarised by an external source of e.m.f. the position of the electrodes in the vertical direction indicates the potential change. (K, high-impedance voltmeter A, ammeter R, variable resistance)...

As a result of the transferred species, loss mechanisms occur. In terms of the first law of thermodynamics these losses are well known as polarisation losses. Polarisation losses are sensitively influenced by numerous mechanisms, which are strongly non-linear with respect to a change of the operational parameters like the current density, electrical potentials, temperature, pressure, gas compositions and material properties. These parameters are assumed to be constant in case of a differential cell area. Thus, the loss mechanisms are summarised in a constant area specific resistance ASR [ 2cm2]. A change of the local overpotential (EN(Uf) — Vceii) at constant ASR complies with a proportional change in the local current density. 

As Manassen et al. (1981) pointed out, the configurations represented in Fig. 10.5 have another disadvantage, namely the disparity between the small surface area desired to minimise the dark current in the storage electrode or half-cell, since this opposes and reduces the photocurrent, and the large surface area necessary to minimise storage polarisation losses and maximise storage capacity. 

The concentrate sample is taken after recirculation of the permeate into the cell, and this way the permeate concentration is accounted for in the concentrate. By recirculating the permeate into the ceil, concentration polarisation effects would be reversed and only irreversible deposition measured. This deposit can also be described as loss of solute Ld (as percent of mass in the feed solution)... 

Three electrodes are necessary to overcome the fact that the potentials of most electrodes change when continuous current is passed (polarisation). In a two-electrode cell the measured voltage is the difference in potential between two changing individual electrode potentials. In these circumstances it is impossible to calculate the potential of any one electrode. Non-aqueous solvents cause problems in terms of solubility of the analyte and supporting electrolyte but principally problems arise because the resistance of the solution rises. This causes loss of potentiostatic control. The reference electrode may also become unstable. 

A schematic representation of this polarisation curve is given in Rg. 15.2. The first part of the curve corresponds to activation loss, mainly the kinetics of oxygen reduction (with jo = 10 -10 A cm ) involved the second part is linear and due to ohmic loss, mainly the electrolyte resistance the third part is due to mass transfer or diffusion loss when the value of becomes close to /umcat or E(j) tends to zero. The optimal operating point is located in the linear part of the curve. These current-density-potential curves are very important for any type of fuel cell, because they summarise the influence of all the important parameters on the performance of a cell. Even though the equation is more complex in the case of high-temperature fuel cells, the general features of the current density vs potential characteristics are similar. 

When the current is decreased, the combined effect of the changes in the partial pressures and the polarisation losses results in the increase of the cell voltage. It is observed that the cell voltage initially overshoots before settling to a steady-state value. The FU and the OU, which are proportional to the current, also decrease. The reverse phenomena are observed with the increase in the external load current. The sudden decrease in the load current results in the decrease in the rate of hydrogen and oxygen consumption and the rate of water vapour formation. In other words, the... 

In addition to these features of a porous electrode, there is another factor that can introduce electrical losses which a-rises from the fact that a porous electrode is not in continuous contact with the electrolyte The result of this discrete contact is that ions and electrons will be restricted in their flow to regions of electrode/electrolyte/gas phase contact, the so-called triple-point contact (T P C ). This introduces a resistive loss which is termed a constriction resistance and is additional to the cell resistance that would be expected on the basis of bulk resistivities and geometry. This type of polarisation will be discussed further in section 3. 

Some general comments were made in section 2(d) relating to polarisation losses at electrodes in prototype multi-cell devices. A more detailed analysis of the kinetics associated with platinum electrodes is now presented, as nearly all the published data on experimental high temperature electrolysers refers to systems incorporating platinum electrodes. This type of electrode is also often employed in commercial high temperature oxygen monitors although of course platinum electrodes would not be used in commercial fuel cells and electrolysers. 

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