Polarization Curves

If you work with fuel cells, then you are definitely working with polarization curves. The polarization curve does not have a lot of specificity; however, it is one of the most common methods of testing a fuel cell. It also allows an easy comparison to other published polarization curves. The polarization curve displays the voltage output of the fuel cell for a given current density loading. Polarization curves are usually obtained with a potentiostat/galvanostat, which draws a fixed current from the fuel cell and measures the fuel cell output voltage. By slowly “stepping up” the load on the potentiostat, the voltage response of the fuel cell can be determined. If a potentiostat is unavailable, a more primitive method of determining the current/voltage relationship from the fuel cell is to take several different types of small resistors (to act as a load) and measure the voltage output on a multimeter.

There are three distinct regions of a fuel cell polarization curve:

• At low power densities, the cell potential drops as a result of the activation polarization.
• At moderate current densities, the cell potential decreases linearly with current due to ohmic losses.
• At high current densities, the cell potential drop departs from the linear relationship with current density as a result of a more pronounced concentration polarization.

When the current (load) on a fuel cell is changed, the fuel cell heat and water balance change, and it may take time to reach a new equilibrium point. During testing, a designated time period should be used to allow the fuel cell to reach the new equilibrium. The establishment of an equilibrium period varies depending upon whether the fuel cell load has been increased or decreased.  Relevant test data can be obtained from the fuel cell by adjusting the load in various ways: the load can be programmed to increase or decrease by a certain step-size, or the load can be randomly selected. The most typical method is to have the load increased step-wise. The data can be taken at multiple current or voltage points. A typical method for obtaining measurements is beginning at open-circuit voltage and then collecting five to six points between 600 mV/cell and 850 mV/cell and waiting 15 minutes between each point. The data from the last five minutes should be averaged and then plotted as average current versus average voltage.

Reliable voltage/current curves require a stable environment, where the temperature, pressure, humidity and flow rates maintain the desired level while the test(s) are being conducted. If the conditions are fluctuating, the voltage/current characteristics may change. In addition to keeping the testing environment stable, the fuel cell itself may take a while to stabilize. Depending upon the fuel cell design and size, the fuel cell may take from several to 30 minutes to stabilize after a current or voltage change. For large fuel cell systems, obtaining polarization curves can be tedious and impractical, and only a limited number of points can be taken. An example of a polarization curve is shown in Figure 1.

Figure 1: Example of a PEMFC polarization curve

The polarization curve is useful for troubleshooting issues in the fuel cell stack. If the polarization curve is recorded while increasing and decreasing the current, it may show hysteresis. This typically indicates a change in fuel cell conditions, such as drying or flooding of the membrane. Flooding issues can be characterized by substituting air with pure oxygen. The difference in cell voltage between pure oxygen and air results from the difference in the concentration of oxygen at the catalyst surface—this difference should be nearly constant at any current density. An increase in cell potential difference between oxygen and air at higher current densities indicates mass transport problems.

Voltage Losses

Typical voltage losses seen in a fuel cell are illustrated in Figure 1. The single fuel cell provides a voltage dependent on operating conditions such as temperature, applied load, and fuel/oxidant flow rates. The standard measure of performance for fuel cell systems is the polarization curve, which represents the cell voltage behavior against operating current density.

Electrical energy is obtained from a fuel cell only when current is drawn, and the cell voltage drops due to several irreversible loss mechanisms. The loss is defined as the change in the cell potential (Virrev ) from the theoretical potential (Vrev):

The actual open circuit voltage of a fuel cell is lower than the theoretical model due to species crossover from one electrode through the electrolyte and internal currents. The three major classifications of losses that result in the drop from open circuit voltage are:

(1) activation polarization
(2) ohmic polarization
(3) concentration polarization

Therefore, the operating voltage of the cell can be represented as the departure from ideal voltage caused by these polarizations:

where  represent activation, ohmic (resistive), and mass concentration polarization. As seen in equation 2, activation and concentration polarization occurs at both the anode and cathode, while the resistive polarization represents ohmic losses throughout the fuel cell.

A relationship between the fuel cell potential and current density (fuel cell polarization curve) is:

The shorter version of the equation is:

Activation Polarization: Voltage Loss Due to Voltage Overpotential

Activation polarization is the voltage overpotential required to overcome the activation energy of the electrochemical reaction on the catalytic surface. This type of polarization dominates losses at low current density and measures the catalyst effectiveness at a given temperature. This is a complex three-phase interface problem, since gaseous fuel, the solid metal catalyst, and electrolyte must all make contact. The catalyst reduces the height of the activation barrier, but a loss in voltage remains due to the slow oxygen reaction. The total activation polarization overpotential is 0.1 to 0.2 V, which reduces the maximum potential to less than 1.0 V even under open-circuit conditions. Activation overpotential expressions can be derived from the Butler-Volmer equation. The activation overpotential increases with current density and can be expressed as:

where i is the current density, and i0, is the reaction exchange current density. Exchange current density represents the reaction rate.

The activation losses can also be expressed simply as the Tafel equation:

 

The equation for the anode plus cathode activation overpotential can be represented by:

where n is the number of exchange protons per mole of reactant, F is Faraday’s constant and a is the charge transfer coefficient used to describe the amount of electrical energy applied to change the rate of the electrochemical reaction. The exchange current density, io is the electrode activity for a particular reaction at equilibrium.

• In PEMFC, the anode io for hydrogen oxidation is very high compared to the cathode io for oxygen reduction, therefore, the cathode contribution to this polarization is often neglected.
• DMFCs have approximately equal io for the anode and cathode.
• In high-temperature fuel cells, the operating temperatures are so high that the activation losses are very low.

Based upon equation 7, seems that the activation polarization should increase linearly with temperature. The purpose of increasing temperature is to decrease activation polarization.

Ohmic Polarization: Voltage Loss Due to Charge Transport

Conductors have an intrinsic resistance to charge flow, which results in a loss in cell voltage. This phenomenon is called “ohmic polarization,” and it occurs because of the electrical resistance in the cell components. The cell components that contribute to the electrical resistance are the electrolyte, the catalyst layer, the gas diffusion layer, bipolar plates, interface contacts and terminal connections.  The reduction in voltage is dominated by internal ohmic losses through the fuel cell. This voltage loss is called “ohmic loss,” and includes the electronic (Relec) and ionic (Rionic) contributions to fuel cell resistance. This can be written as:

Rionic dominates the reaction in equation 8 since ionic transport is more difficult than electronic charge transport. Rionic is the ionic resistance of the electrolyte, and Relec includes the electrical resistance of bipolar plates, cell interconnects, contacts, and other cell components through which electrons flow.

Concentration Polarization: Voltage Loss Due to Mass Transport

A fuel cell must continuously be supplied with fuel and oxidant to produce electricity. Products must also be continuously removed to have maximum fuel cell efficiency. The study of mass transfer of uncharged species is important because it can lead to significant fuel cell performance losses if not understood properly. The reactant and product concentrations within the catalyst layer determine the fuel cell performance. Concentration loss can be minimized by optimizing the mass transport in the fuel cell electrodes and flow structures.

The mass transport in the fuel cell electrodes/fuel structures is dominated by convection and the laws of fluid dynamics since the flow channels are macroscale (usually in millimeters or centimeters). The mass transport of the fuel cell electrodes occur on a microscale and are dominated by diffusion. A standard way of calculating fuel cell concentration loss (or mass transport loss), may be expressed by the equation:

where c is a constant and can have the approximate form:

Actual fuel cell behavior frequently has a larger value than what the equation predicts. Due to this, c is often obtained empirically. The concentration loss appears at high current density and is severe. Significant concentration loss limits fuel cell performance.

Conclusion

This post covered the basic electrochemistry concepts to better understand the polarization curve. The catalyst activation barrier must be overcome to convert products into reactants. To lower this activation barrier, a portion of the voltage is lost, and this is called activation overvoltage. The Butler-Volmer equation describes the relationship between the current density and activation overvoltage. The actual fuel cell voltage is also affected by the fuel cell charge and mass transport limitations. Changes in mass and charge transport can be noted by observing changes in the polarization curve.

Dr. Colleen Spiegel Posted by Dr. Colleen Spiegel

Dr. Colleen Spiegel is a mathematical modeling and technical writing consultant (President of SEMSCIO) and Professor holding a Ph.D. and an MSc degree in Engineering. She has seventeen years of experience in engineering, statistics, data science, research & technical writing work for many companies as a consultant, employee, and independent business owner. She is the author of ‘Designing and Building Fuel Cells’ (McGraw-Hill, 2007) and ‘PEM Fuel Cell Modeling and Simulation Using MATLAB’ (Elsevier Science, 2008). She previously owned Clean Fuel Cell Energy, LLC, which was a fuel cell organization that served scientists, engineers, and professors world-wide.

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