## Kinetic Performance

When operating on pure hydrogen, the anode stays at a potential close to the theoretical reversible potential of a hydrogen electrode, i.e., Er = 0 V — compare Eq. (4.1). In electrochemical terminology, this corresponds to a low overpotential indicative of a kinetically facile reaction. For the moment, we will therefore neglect the anode contribution towards the cell voltage, assuming an anode potential of 0 V. Since the cell voltage is the difference between anode and cathode potential, the cell voltage will be — to good approximation — identical to the cathode potential, Ec.

In contrast with the anode reaction, the oxygen reduction reaction (ORR) at the cathode is an activated process and therefore exhibits a much higher overpotential. The Butler-Volmer equation, the key equation in electrochemical kinetics, gives a mathematical description of such activated processes. It is presented in Chapter 3, Eq. (3.84).

More useful for practical work on MEAs is the Tafel equation. First formulated from empirical results, it can easily be rationalized by inverting one branch of the Butler-Volmer equation, solving the first term of Eq. (3.84) for the overpotential n = Ec - Er. This leads to the expression for the cell voltage, Ec:

where Er = reversible potential for the cell, i0 = exchange current density for oxygen reduction, b = Tafel slope for oxygen reduction, r = (area specific) ohmic resistance, and i = current density; ohmic losses have been included by adding the term (-ir) = -AE.

The so-called Tafel slope b is determined by the nature of the electrochemical process. Comparison of Eq. (4.3) with Eq. (3.84) reveals that b can be expressed as:

n P Flog10e where R = 8.314 Jmol-1K-1 denotes the universal gas constant, F = 96485 Cmol-1 is the Faraday constant, T is the temperature (in K), and Pis the transfer coefficient, a parameter related to the symmetry of the transition state, usually taken to be 0.5, when no first principle information is available (compare Section 3.5.3). For the oxygen reduction reaction [n = 2, see Eq. (4.2)] in practical fuel cells, b is usually between 40 and 80 mV.

The main factor controlling the activation overpotential and hence the cell potential, Ecell = Ec, is the (apparent) exchange current density i0. Eq. (4.3) demonstrates that, due to the logarithm, a tenfold increase in i0 leads to an increase in cell potential at the given current by one unit of b, or typically 60 mV. It is important to emphasize this point. While the Tafel slope b is dictated by the chemical reaction (and the temperature), the value for i0 depends on reaction kinetics. Ultimately, it depends on the skill of the MEA and electrocatalyst producer to increase this value (compare Chapter 6).

In principle, the following approaches are possible:

• The magnitude of i0 can be increased (within limits) by adding more electrocatalyst to the cathode. However, today's electrocatalysts contain platinum, and economic considerations limit the amount of platinum that MEA makers can put inside their products2.

• Many attempts have been made to do away with platinum as the leading cathode catalyst. Some attempts are discussed in Chapter 6. Unfortunately, to date, no convincing alternative to platinum or related noble metals has been demonstrated. This is not merely due to the lack of catalytic activity of other catalyst systems but is often a result of insufficient chemical stability of the materials considered. For a full discussion of fuel cell catalysis, see Chapter 6.

• A logical and very successful approach is the more effective use of platinum in fuel cell electrodes. A technique borrowed from gas phase catalysis is the use of supported catalysts with small, highly dispersed platinum particles. Of course, electrocatalysts have to use electrically conducting substrate materials, usually specialized carbons, as is discussed in Chapter 6. An extremely fruitful alliance between Ballard and Johnson Matthey has pioneered this approach to PEMFC technology, reducing the electrode platinum loadings in comparison with earlier Ballard work tenfold (Ralph et al., 1997) or, in comparison with pioneering work in the 1950s, one 100-fold (compare Chapters 2 and 6). A transmission electron (TEM) micrograph of a modern carbon-supported electrocatalyst is shown in Fig. 6.12.

• Of course, it is not sufficient to merely improve the surface area of the catalyst employed; good electrochemical contact between the membrane and the catalyst layer is also necessary. In situ measurement of the effective platinum surface area (EPSA) is a critical test for the quality of an electrode structure. The EPSA may be measured by electronic methods or, more commonly, by carbon monoxide adsorption and subsequent electro-oxidation to carbon dioxide with charge measurement (Chapter 6).

2 PEMFCs started in the 1960s with space travel. Platinum loadings of 50 mgcm-2 based on electrode area were then common — compare Chapter 2.

Only after the fuel cell performance has been corrected for ohmic resistance, and the effects of mass transport have been identified or eliminated (by using pure oxygen — see below), can the true kinetic performance of the cathode be studied. For this purpose, resistance corrected data recorded on oxygen are subjected to so-called Tafel analysis (see Fig. 4.9). As Eq. (4.4) suggests, the data fall on a straight line in a semi-logarithmic plot up to a current density, where mass transport effects (compare Fig. 4.3) lead to a sharp drop of the performance curve. The goal of the MEA developer is therefore to lift the overall performance curve in the Tafel plot.

Impedance measurements under practical loads can give valuable information on the catalyst utilization under operating conditions.

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