The electrolyte in PEM fuel cells is a solid polymer material with covalently bonded sulfonic acid groups. These materials are similar to ion-exchange resins. A cation is associated with each negatively charged sulfonic acid group. For fuel-cell applications, the cations are protons. In other applications, see Chapter 14 and the chlor-alkali process, sodium ions are present rather than protons. PEM is almost synonymous with perfluorinated ionomers known under the trade name Nafion^®. Figure 9.9 shows the structure of the ionomer material. Nafion^® is a copolymer of tetrafluoroethylene (Teflon) and sulfonyl fluoride vinyl ether. The incorporation of ionic groups into the polymer has a dramatic effect on its physicochemical properties. A bicontinuous nanostructure is formed. There are two domains: one that is Teflon like that forms from the backbone of the material, and a second that contains the sulfonic acid groups. These materials segregate into hydrophobic and hydrophilic regions. The sulfonic acid groups arrange themselves to form the hydrophilic regions that are strongly acidic; and the two domains are randomly connected. Equivalent weight, the mass in grams of the polymer per mole of sulfonic acid group, is a key measure of the ion-exchange capacity of the membrane.

The sulfonic acid groups represent fixed anions in the polymer membrane since they are covalently bound to the polymer backbone. When current flows in a PEM fuel cell, protons are transported via two mechanisms as illustrated in Figure 9.10. In the vehicular mechanism, protons are dissociated from the sulfonic groups and hydrated. These move by molecular diffusion. A second mechanism is proton hopping. Here, the proton is closely associated with the sulfonic acid group. During transport, protons hop from acid group to acid group. The only charge carrier is the protons; thus, the transference number of protons is unity.

In addition to the ability of cations to move through these ionomers, a second important aspect of perfluorinated ionomers is their ability to take up large amounts of water and other solvents. It was recognized early on that the water content in ionomer membranes is important for the operation of PEMFCs. The amount of water can be expressed in several ways, but the most common approach is the ratio:

(9.13)

When exposed to water vapor, a relationship exists between the activity of water in the vapor phase and λ. This equilibrium for Nafion is shown in Figure 9.11. When plotted against activity, ∼p_w/p_o, the curve is nearly independent of temperature. The first few molecules of water are associated with high enthalpic changes and are tightly bound to the protons.

An important characteristic of these materials is that the ionomer must be hydrated to allow efficient conduction of protons. The conductivity depends roughly linearly with water content or λ.

(9.15)

Conductivity is the first key transport property of the electrolyte. Compared to other electrolytes used for fuel cells, PEM shows a particularly strong dependence for its conductivity on water content. This behavior has critical implications for PEM cell and system design. For all intents and purposes, the membrane must be close to fully hydrated for good cell performance. Lastly, we note that because the sulfonic acid groups are relatively close to each other in the hydrophilic regions, electrostatic forces repel anions. Effectively, these cation-exchange membranes exclude anions.

Although protons are the only charge carriers in ionomer membranes such as Nafion, the water in the membrane is also mobile. The transport of water influences the design and operation of the PEMFC. A second key transport property is the electroosmotic drag coefficient of water, ξ. This drag may be thought of as the number of water molecules that move with each proton in the absence of concentration gradients. This property is most easily measured with a concentration cell (Chapter 2), which can provide the electroosmotic drag as function of water content, λ. The third transport property is the diffusion coefficient of water in the proton-exchange membrane, D_o.

Accordingly, there are three transport processes that occur in the membrane as highlighted in Figure 9.12. During fuel-cell operation, protons move from the anode to the cathode. Because these protons are hydrated, they “drag” water with them. Finally, concentration gradients can develop, leading to molecular diffusion of water. Thus, we have three species (water, protons, and ionomer) and three transport properties, κ, ξ, and D_o.

Because the ionic current carried by the protons also significantly influences the transport of water (uncharged species), the two processes are coupled. This coupling between ionic current and water transport is not described well with dilute solution theory. The transport described in Chapter 4 focused on the interaction of each species with the solvent. Here, there is no clear choice for the solvent, and further, binary interactions among all three species can be important. Hence, concentrated solution theory is used to derive the equations below. Because of electroneutrality, the concentrations of sulfonic acid groups and protons are equal, and only one composition needs to be specified. Taking the amount of water as the compositional variable, the relevant transport equations are

(9.15)

(9.16)

Equation 9.15 expresses the flux of water as a function of two independent gradients: the chemical potential of water, μ_o, and the electrical potential, ϕ₂. α is a diffusion coefficient of water based on the thermodynamic driving force (i.e., the gradient of the chemical potential of the water rather than its concentration gradient). In addition to molecular diffusion due to a gradient in the chemical potential of water, we see from Equation 9.15 that water movement is also associated with a gradient in potential.

Since protons are the only mobile charged species, the current density is proportional to the molar flux of protons. Therefore, Equation 9.16 is written in terms of current density rather than molar flux. The first term on the right side of Equation 9.16 would be analogous to Ohm’s law. Here we note that there is a second term arising from the gradient in chemical potential of water. ξ is the electro-osmotic coefficient, which represents the number of water molecules that move with each proton in the absence of concentration gradients. Equation 9.16 may be rearranged to

(9.17)

Compare this result with Equation 4.6 for dilute solutions:

(4.6)

In both cases, we see that variations in concentration affect the potential drop across the solution. A key distinction of concentrated solution theory is that coupling goes both ways: namely, variations in potential influence the transport of water. This effect can be seen clearly from the first term in Equation 9.15. There is no analogous phenomenon present with dilute solution theory.

It is also worth noting that, in contrast to the Stefan–Maxwell formulation for concentrated systems to which you may have been previously exposed, nonidealities in the solution are likely to be important, which significantly complicates obtaining the necessary physical parameters. On the positive side, for this three-component system, the three independent binary interaction parameters can be related to three straightforward transport properties: that is, the electrical conductivity (κ), the diffusion coefficient of water (D₀), and the electro osmotic drag coefficient, (ξ).

Equations 9.15 and 9.16 can be simplified to illustrate better the coupling of current flow and water transport in PEM fuel cells.

(9.18)

which is just Ohm’s law, and

(9.19)

Thus, we can see more clearly that water moves due to a concentration gradient, but also from the electroosmotic drag. Let’s examine this behavior in a bit more detail. Imagine that we have a proton-exchange membrane in contact with water vapor on both sides at the same activity. Initially, there is no current flowing and the water content, λ, is determined with the data from Figure 9.11 and is constant across the membrane. Next, we apply a fixed current density of i. What happens to water? Assuming that a positive current is in the direction of left to right, electroosmotic drag will carry water to the right. Unless water can be supplied at the left side and removed at the right side instantaneously, a concentration gradient will develop. Of course, the rate of water supply and removal would be limited by mass transfer of water between the membrane and the vapor. Once a concentration gradient is established, water diffuses down the gradient. Molecular diffusion occurs to counteract the effect of water drag. Depending on the current density, physical properties, and mass transfer on each side, it is possible to have a steady net water movement across the membrane. These phenomena are depicted in Figure 9.13.

What are the implications for the PEMFC? Keep in mind that there is also production of water at the cathode of a PEMFC. This production is an additional source of water that would need to be considered to arrive at a detailed picture of the water content in the membrane. For our purposes, we can refer back to Figure 9.11 to illustrate two possible issues for the operation of PEMFCs. First, note that as the current density increases, the water content on the left side (anode) of the membrane decreases. As we have seen before, the conductivity of the membrane depends on water content. Thus, with increasing current density the anode can “dry out,” resulting in poor performance. At the same time, the water content at the right side grows with increasing current density. What’s more, water is being produced here at the cathode. What if the combined rate transport of water and the rate of production are greater than the rate at which water is removed? In this instance, conductivity is not an issue, but the cathode can “flood”, resulting in severe mass-transfer limitations and poor performance. The excess water can form drops that cover the catalyst sites and prevent access by oxygen.

The PEM material is formed into a thin film, which in addition to serving as the electrolyte, also forms a barrier between the fuel and oxidant. Water balance at the cell sandwich level becomes a key challenge for PEM fuel cells. Too little water, and the membrane conductivity drops; too much water, and the electrode floods. The ideal situation is for the gas in contact with the membrane to be saturated with water vapor. It is impractical to completely avoid liquid water and simultaneously keep the membrane hydrated; therefore, some means of dealing with liquid water is needed for PEMFCs. Further, because of the unique importance of water content in PEMFCs, λ has taken on a special significance to the design of cells and complete systems. The system level analysis is discussed in Chapter 10.

ILLUSTRATION 9.4

Estimate the limiting current in a PEM fuel cell assuming that the conductivity goes to zero as the concentration of water approaches zero. Referring to Figure 9.13, this implies that the minimum concentration of water on the left-hand side of the diagram is zero, since any further increase in the current is not possible because the membrane conductivity without water goes to zero. The maximum current is the current that corresponds to a net water flux of zero. Under limiting current conditions at steady state, Equation 9.19 becomes

The concentration of water can be estimated from the density, equivalent weight, and λ, the ratio of water to sulfonic acid. Taking this concentration to be 15 kmol m⁻³ and using a value for ξ of 1.0 with a membrane thickness of 100 μm, we arrive at

It is clear from the above equation that the limiting current can be increased by reducing the thickness of the separator, which also reduces ohmic losses in the cell.

Whereas Nafion has an electroosmotic drag coefficient of near unity over a wide range of levels of hydration, other membranes show about half the value. If the electroosmotic drag were reduced to 0.4 for an alternative membrane, the limiting current would increase to 36,200 A m⁻².

As noted earlier, a three-dimensional electrode structure is needed in PEMFCs. The flooded-agglomerate model is a reasonable description of electrodes found in PEMFCs. The electrodes for PEMFCs require electrocatalysts to carry out the reactions. At these low temperatures and in acid conditions, platinum and alloys of platinum are the only presently acceptable materials. Given that platinum is a precious metal and therefore expensive, the amount of platinum used in the fuel cell is of critical importance. First, the platinum must be part of the triple phase boundary, and therefore in contact with the gas and the electrolyte, as well as connected electronically with the current collector. Platinum that fails to achieve this is not active toward the desired reactions in the cell. The degree to which the electrode achieves the desired connections defines the gross utilization of platinum. In a well-designed electrode this value is near one. Second, consider a particle of platinum. Only the atoms at the surface participate in the electrochemical reactions. Therefore, it is desirable to have a high surface area to volume ratio; this is achieved by creating small particles of platinum and is characterized by the dispersion of the catalyst, which is defined as the fraction of catalyst atoms that reside at the surface (as opposed to inside the particle). The small catalyst particles are placed on a support material with a high surface area. The most common choice of support material in a fuel-cell electrode is carbon. There are a large variety of carbon materials with high surface area; what’s more, the carbon is conductive and reasonably stable at the conditions found in PEMFCs.

A detailed accounting of the effects of water transport in the membrane, the mechanisms for electrocatalytic reactions, and multicomponent gas diffusion on the polarization curve for PEM fuel cells is beyond the scope of this text. For our purposes we will assume that the polarization curve for a PEM fuel cell can be represented by

(9.20)

As noted earlier, the kinetic polarization of the cathode is much larger than that of the anode for PEMFCs; thus, the kinetic polarization for the hydrogen electrode is neglected. Equation 9.20 includes a term associated with the Tafel slope for the oxygen reduction reaction (ORR) and a second term for the effect of oxygen partial pressure on the kinetics of ORR. All mass-transfer limitations (anode, cathode, membrane) are lumped together with a single term. Again, most often mass-transfer limitations are associated with the cathode. The reasons are as follows. First, the diffusivity of oxygen is much smaller than that of hydrogen. Second, operation is generally on hydrogen/air and therefore the partial pressure of oxygen is lower than that of hydrogen. Lastly, as we saw earlier, high current densities result in high electroosmotic drag that tends to “flood” the cathode. The last term on the right side of Equation 9.20 is the cell resistance, which can be measured from current interruption or by electrochemical impedance spectroscopy. The reference current density and reference pressure are arbitrary. As is done in Illustration 9.5, use i_ref = 1 A m⁻², and p_ref  = 100 kPa.

As a reminder, there is another physical process that can be important in establishing the cell potential at open circuit; hydrogen gas from the anode may diffuse to the cathode where it reacts with oxygen. We will consider this, in addition to the other factors mentioned, in Illustration 9.5, which shows how the polarization curve expressed in Equation 9.20 can be reasonably approximated with just three pieces of information: the mass activity of the catalyst (see definition in box), the membrane resistance, and the permeation of hydrogen across the membrane separator.

MASS ACTIVITY OF PT CATALYSTS

The most common way to describe the effectiveness of the oxygen reduction catalysts for PEM fuel cell is with the mass activity. The current per unit mass of platinum in the cathode is reported. This current is recorded at a cell potential of 0.9 V (iR free) at 80 °C on humidified hydrogen and oxygen at 150 kPa.

ILLUSTRATION 9.5

The mass activity of the catalyst for a PEM fuel cell is 60 A·g⁻¹ (O₂ at 0.9 V). The platinum loading is 5 g·m⁻². The rate of hydrogen crossover is equivalent to 10 A·m⁻², and the membrane separator is 50 μm with a conductivity of 5 S·m⁻¹. The fuel cell will operate at 100 kPa using air at the cathode. Calculate the current–voltage curve, the open-circuit potential, and the maximum power assuming no mass-transfer limitations.

SOLUTION:

We first use the mass activity, measured at 150 kPa, to determine the needed constant in Equation 9.20. The vapor pressure of water at 80 °C is 47 kPa; therefore, the partial pressure of oxygen is 103 kPa and the ratio in Equation 9.20 is close to one. Using the conditions and definition for mass activity, we can determine the constant in Equation 9.20. The potential of 0.9 V (iR free) assumes that the iR contribution has already been accounted for as described on the previous page. Thus,

The resistance is simply

The current density that is used to determine the polarization of the cathode is the sum of the load current density and the crossover of hydrogen.

Equation 9.20 can now be used to yield a reasonable approximation to the polarization curve. In doing so, we include the effect of polarization, the influence of the operating pressure (21 kPa O₂), and the ohmic resistance. We neglect the mass-transfer limitations as specified in the problem statement. The iR resistance is included as shown in Equation 9.20. For each value of the load current we can now calculate the cell potential, V_cell. The results are shown in the plot. The corresponding power curve is also shown. The current–voltage curve is linear at the higher current densities considered, consistent with ohmically limited operation.

The open-circuit potential for this cell corresponds to a load current of zero and is determined by the reaction of oxygen at the cathode with hydrogen that crosses over from the anode; it is not equal to the equilibrium potential. Assuming that the Tafel approximation holds due to sluggish oxygen kinetics, and that the hydrogen crossover rate remains constant, the open-circuit potential is