PEM Fuel Cell

## Introduction

Applications for fuel cells range from space applications to micro-fuel cells for cell phones. Fuel cells will become even more important in the future low-carbon economy. Here, we seek to learn the fundamentals of polymer electrolyte membrane (or proton exchange membranes) fuel cells (PEMFCs) and evaluate their performance using characteristic curve and efficiency measurements. We can also compare hydrogen fuel cells to their direct methanol counterparts.

### Pre-Lab Questions

You can download the Pre-Lab questions for this experiment here.

## Background

The literature on fuel cell technology is enormous but only a few key references are needed to complete this lab, at least from a theoretical aspect. More recent journal articles will be helpful to describe the state-of-the-art but the books noted below, particularly the first one, are sufficient to gain an understanding of the fundamentals.

* Fuel Cell Systems Explained. This is an excellent overview of fuel cells and is the basis for the theoretical expressions below. It includes the equations and a MATLAB script for producing a theoretical characteristic curve, and it's recommended that you read and understand Chapters 2-4.
* Fuel Cell Technology Handbook. Less comprehensive and more qualitative. Available in electronic version through our library.
* Key challenges and recent progress in batteries, fuel cells, and hydrogen storage for clean energy systems.
* FuelCells.org. A Washington, D.C.-based non-profit trade group. It's inappropriate to cite them or use their web-based explanations but it's acceptable to use their reports or reports from other agencies. There's a wealth of additional information on this site--newspaper-like tutorials, industrial news, career opportunities, and more.

## Theory

The theory developed here assumes a hydrogen PEMFC and can be reviewed in more detail in Ch. 2-3 of Fuel Cell Systems Explained; Ch. 4 is an excellent introduction to PEMFC assembly and operating considerations. This section does not discuss the operating principles--fuel composition, catalyst selection, water management, and similar topics--but rather a few important concepts to help you get started with the characteristic curve and calculating Faraday efficiency.

Note that we do not consider the initial electrolysis of H2O in the analysis. If we did so in a sloppy manner, we might derive an overall reaction of H2O → H2O + energy, which is clearly impossible (try to identify the mistake).

### Open Cell Voltage

Electrons are liberated in a fuel cell at the anode according to the reaction H2 → 2H+ + 2e- and consumed at the cathode according to the reaction 0.5O2 + 2H+ + 2e- → H2O for an overall reaction of H2 + 0.5O2 → H2O(l). The maximum theoretical potential \(E\_{0,H}\) is

\[E\_{0,H} = \frac{\Delta H\_f}{zF}\]

where \(\Delta H\_f\) is the heat of reaction using enthalpies of formation, \(z\) is the number of electrons liberated in the anode half-reaction, and \(F\) is Faraday's constant. Entropy losses result in the more commonly cited open cell potential \(E\_0\) such that

\[E\_0=-\frac{\Delta G\_f}{zF},\]

where \(\Delta G\_f\) is the Gibbs free energy of formation. Assuming a higher heating value (liquid water product), \(E\_0\approx1.23\textrm{ V}\) at 25 °C for a hydrogen fuel cell. Additional losses at equilibrium due to non-standard operating conditions can be estimated by the Nernst equation such that

\[E\_{0,N} = E\_0 - \frac{RT}{zF} \ln K\]

where \(E\_{0,N}\) is the Nernst potential and \(K\) is the equilibrium constant. Recall that for a general reaction mM + nN → qQ the equilibrium constant is

\[K = \sum a\_i^{\nu\_i} = \frac{a\_Q^q}{a\_M^m a\_N^n},\]

where \(a\_i\) is the activity of species \(i\) and \(\nu\_i\) is the stoichiometric coefficient for species \(i\) (positive for products, negative for reactants). Should you choose to operate a cell (*e.g.*) with air instead of pure oxygen, Eq. (3) provides a means of evaluating changes in \(E\_0\). At typical operating conditions, hydrogen and oxygen can be approximated as ideal gases such that

\[a\_i \approx \frac{P\_i}{P},\]

where \(P\_i\) is the partial pressure of species \(i\) and \(P\) is atmospheric pressure. See Section 2.5.2 in Larmine for an example.

### Characteristic Curve

A plot of cell potential \(E\) as a function of current density \(j\) is called a characteristic curve and is a common tool for analyzing fuel cell performance (**Figure 1**). There are three regions of interest which are described by their reduction of \(E\_0\):

* **Activation losses.** Rapid fall in low-current cell potential due to kinetic limitations at catalyst sites
* **Ohmic losses.** Approximately linear loss region due to resistance to flow of electrons through circuit and ions through membrane.
* **Mass transport losses.** Rapid fall in high-current cell potential due to mass transfer limitations.

Extensive discussions of these regimes are available in the noted references and you should be able to observe each depending on the operating conditions you choose. Note that methanol fuel cells can also suffer from fuel crossover--fuel that diffuses through the membrane without reacting--at high methanol concentrations, but this effect is usually minimal for hydrogen cells.

   A simple empirical equation was proposed by Kim *et al*. as

\[E = E\_{0,R} - b \log j - Rj - me^{nj},\]

where \(E\_{0,R}, b, R,\) and \(m\) are fitted parameters related to the reversible cell potential, oxygen reduction, linear resistance, and mass transfer limitations. Parameters are determined *via* non-linear regression (*e.g.,* MATLAB's `fit()` function or Curve Fitting App, Mathematica's `NonlinearRegress[]` function, or Excel's Solver package). This work provides an extensive comparison of fitted parameters for various cells and operating conditions; if you choose to use Eq. (6) you should also compare your fitted parameters to those of Kim *et al.* or those reported in other works.

### Current Interrupt Test

**Update 7 Feb 2018:** We don't have the sensor set up that's needed for the Current Interrupt Test, so you can ignore this section.

The relative contribution of ohmic and activation losses can be estimated directly from a *current interrupt test* and compared to the predictions of the empirical equation given above for the characteristic curve. To perform a current interrupt test a switch is added to the circuit as shown in **Figure 2(a)**. A fixed load is applied, the system reaches steady state, and the switch is opened. The current immediately goes to zero and hence ohmic losses are immediately recovered, but the recovery to \(E\_0\) is slower because the activation loss is proportional to the concentration of ions and electrons at the electrode surface which accumulate and dissipate relatively slowly (see S. 3.9, The Charge Double Layer in Larminie for more information). Consequently, we can use a plot of voltage as a function of time as in **Figure 2(b)** to determine to determine the relative contributions of ohmic and activation loss.

### Fuel Cell Efficiency

There are many measures of efficiency for fuel cells including the so-called thermodynamic efficiency,

\[\eta\_{\textrm{thermo}} = \frac{\Delta G\_f}{\Delta H\_f} \times 100\%,\]

where these terms have been defined previously; the "fuel cell" efficiency,

\[\eta\_{\textrm{fc}} = \mu\_f \frac{E}{E\_{0,H}} \times 100\%,\]

where \(\mu\_f\) is the fuel utilization coefficient (approximately 0.95); the energy efficiency,

\[\eta\_{\textrm{energy}} = \frac{V\_{\textrm{H}\_2} H\_0}{W},\]

where \(V\_{\textrm{H}\_2}\) is the volume of hydrogen consumed, \(H\_0\) is the energy density of hydrogen, and \(W\) is the energy output of the cell; and finally, the Faraday efficiency,

\[\eta\_{\textrm{Faraday}} = \frac{V\_{\textrm{H}\_2}^{th}}{V\_{\textrm{H}\_2}^c},\]

where \(V\_{\textrm{H}\_2}^{c}\) is the volume of hydrogen consumed in a given time \(t\) and \(V\_{\textrm{H}\_2}^{th}\) is the theoretical volume of hydrogen needed to provide the measured current (the Faraday efficiency is also called the Coulombic efficiency in some sources). To calculate the latter, we assume ideal gas behavior such that

\[V\_{\textrm{H}\_2}^{th} = \frac{nRT}{P},\]

where \(n\) is the moles of H2 consumed, \(T\) and \(P\) are the operating temperature and pressure, and \(R\) is the universal gas constant. The total amount of charge \(Q\) transferred through the system is simply \(nzF\), which is related to the measured current \(I\) through

\[Q = n z F = t I,\]

where \(I\) is assumed to be constant over the time \(t\) of the measurement.

## Standard Operating Procedure

### Safety

* Although most current produced in or by this experiment is quite low, it is nonetheless critical to pay attention to your hands when connecting and disconnecting components. Always connect the voltage sources *last* to avoid accidental shocks.
* Methanol is toxic; wear gloves when working with the methanol fuel cell.
* Relevant chemical information has been listed in **Table 1**.

**Table 1.** Chemicals and their formulas, hazards, and suppliers for fuel cell analysis.

### Tutorial Video

Check out the video below for a brief overview of this experiment, then carefully read the instructions below. Keep in mind that **there may be variations** in the equipment or protocol when you're in the lab compared to when this video was created. Ask a TA or instructor if you're not clear on something.

### Preparation

For most electrical measurements, the circuit shown in **Figure 3** should be used. For the (optional) current interrupt test, the circuit shown in **Figure 2(a)** should be used instead.

If you'd like to attempt the current interrupt test then you'll also need to use the nearby laptop and program a custom LabVIEW program to measure the voltage drop across the fuel cell with a MyDAQ at a rate of at least 20 Hz, corresponding to a loop delay of 50 ms or less, as well as to record your data.

#### Hydrogen Fuel Cell

1. Measure the area of the desired fuel cell (recall that you need current *density*, not current).
2. Connect the tubing between electrolyzer and fuel cell, add tubing to the gas outlets on the fuel cell, and clamp all tubes.
3. Use the electrolyzer to produce to maximum amount of H2 and O2  in their respective reservoirs, then allow this gas to flow through the tubing, cell, and out to atmosphere. Repeat this purge process three times to remove all ambient air from the system.
4. Use the wiring diagram above (**Figure 2(a)** or **Figure 3**) to make electrical connections between the fuel cell, ammeter, voltmeter, and decade box.

#### Methanol Fuel Cell

1. Rinse the fuel cell with the squeeze bottle of deionized (DI) water. Do not dump methanol or rinse down the drain! Collect waste in the appropriate bottle.

### Basic Operation

#### Hydrogen Fuel Cell

1. To produce a characteristic curve, change resistance settings on the resistor box and record the resulting voltage and current (density). Be sure to include the open-cell voltage, and keep the gas volume approximately constant.
2. To collect data for estimation of the Faraday efficiency, produce about 20 mL H2, select a resistance which maximizes power output, then measure voltage, current, and time for every 2 mL H2 consumed.

#### Methanol Fuel Cell

1. Fill the cell with 1, 2, or 3% methanol as desired.
2. Disconnect the fan (we don't use this for any analyses but you're welcome to play with it if you want).
3. To produce a characteristic curve, repeat Step 1 of Basic Operation - Hydrogen Fuel Cell.

### Shutdown

1. Empty all gas from reservoirs.
2. Disconnect all wires and turn off electrometers and electrolyzer.
3. The methanol fuel cell can be left to run unattended until all methanol is consumed.

## Common Report Mistakes and Suggestions

The evaluator(s) for this experiment was asked to list three or more common mistakes often made on the reports for this experiment, or to provide three or more suggestions that could improve the quality of reports for this experiment. The responses were as follows:

1. The most common mistake I observed was that the group members tend to mention fuel cells to be a completely green/ecofriendly option without taking into consideration hydrogen production or byproducts in certain cases.
2. Many groups have not explained the characteristic curve well in the theory section.
3. A schematic diagram of fuel cell was missing in many reports.
4. No/little comparison of experimental results to results found in literature.
5. Too much irrelevant information in describing experimental methods.
6. Poor grammar!!
7. Insufficient explanations of how Faraday efficiency was calculated
8. Making inferences about fuel cell behavior based on naked observation of the characteristic curve. The parameters that affect the curve are what should be compared.
9. Some students claim that the hydrogen PEM fuel cells are inherently "green" or not contributing to greenhouse gases. Many students do not realize that a lot of hydrogen comes from reformation of fossil fuels, not from a convenient electrolysis of water.
10. Most reports include the full reaction of the DMFC, but may be missing the half reactions of the DMFC. This is interesting, because the half reactions show how water must be present at the anode (one reason for methanol in solution and not pure methanol, I believe).

## References

1. ↑ Larmine, J.; Dicks, A. *Fuel Cell Systems Explained,* 2nd Ed., John Wiley & Sons: West Sussex, 2003; Ch. 2-4.
2. ↑ Hoogers, G. *Fuel Cell Technology Handbook.* CRC Press: Boca Raton, 2003.
3. ↑ Chalk, S.G.; Miller, J.F. *J. Power Sources,* **2006,** *159,* 73-80
4. ↑ Fuel Cells 2000. http://fuelcells.org/ (accessed April 14, 2015)
5. ↑ Larmine, J.; Dicks, A. *Fuel Cell Systems Explained,* 2nd Ed., John Wiley & Sons: West Sussex, 2003; pp 38-39.
6. ↑ Kim, J.; Lee, S.; Srinivasan, S. *J. Electrochem. Soc.*, **1995,** *142,* 2670-2674.
7. ↑ Larmine, J.; Dicks, A. *Fuel Cell Systems Explained,* 2nd Ed., John Wiley & Sons: West Sussex, 2003; p 60.
8. ↑ Larminie, J.; Dicks, A. *Fuel Cell Systems Explained*, 2nd ed., Wiley: West Sussex, 2003; pp. 61-66.
9. ↑ Logan *et. al.*, Microbial Fuel Cells: Methodology and Technology, *Environ. Sci. Technol.*, **2006**, *40*, 5181-5192 [web link]
10. ↑ Rabaey, K.; Clauwert, P.; Aelterman, P.; Verstraete, W. Tubular microbial fuel cells for efficient electricity generation. *Environ. Sci. Technol.* **2005**, *39*, 8077-8082.