## Ohmic Resistances

Electronic resistances are located in a number of fuel cell stack components and, inside the MEA, in the electrode substrates and the two catalyst layers. Ionic resistances occur where proton transport takes place, i.e., inside the membrane electrolyte and inside the catalyst layers.

The total resistance controls the slope of the pseudo-linear middle portion of the current/voltage curve shown in Fig. 4.3. The larger the resistance, the faster the drop of the current/voltage curve with increasing current density.

Electronically, a fuel cell can be regarded as a serial circuit of an ideal voltage source, Eo, and a total internal resistance, R (see Fig. 4.4). The higher the current flow, the larger the ohmic voltage drop across the sum of all internal resistances inside the fuel cell. The total ohmic resistance, R, is therefore the

1.4 __________________________________________________________________________^

♦ Fuel Cell - Equivalent Circuit

ae = e2 - ej = i * R L----------------------------------i

FIGURE 4.4 A potential transient recorded in a current interrupt measurement (for example, using an oscilloscope). The cell current is interrupted at t = 50 |ls, and the ohmic (ionic) resistance is obtained from the fast potential jump AE divided by the cell current before breaking the circuit. Eventually, the cell potential will relax toward the open circuit potential on a much larger time scale.

Eoi R

Fuel Cell - Equivalent Circuit

h combination of the electronic and ionic resistances of various fuel cell components; i.e., ohmic losses occur during transport of electrons and ions (protons).

In order to separate the different influences on performance, ohmic correction of the data is the first step in analyzing fuel cell current/voltage curves. This can be done by numerical fitting (see below) to data recorded on pure oxygen, by impedance spectroscopy, or, more commonly, by the current interrupt technique.

This technique relies on the fact that the potential drop across the internal resistance (AE = IR) vanishes when the steady-state current I is momentarily interrupted, as is illustrated in Fig. 4.4 by the open switch. The value of R is then calculated from the ratio of AE and I.

Clearly, the resulting potential step is not infinitely fast due to the capacitances (and possibly inductances) present in the electrodes. But these changes occur on a much faster time scale than the electrochemical processes that subsequently cause the cell potential to relax slowly towards the open circuit value (compare Fig. 4.4). Therefore, there is a need not only for instantaneous switching but also for fast sampling of the potential response in order to provide a clean separation of these two processes (Buchi et al., 1995a). Sampling is usually performed by a storage oscilloscope.

Current interrupt is probably the most important technique in the routine performance analysis of MEAs. The technique can be employed such that the switch is closed sufficiently fast for the fuel cell performance not to be affected by the measurement, for example by recording a response such as the one shown in Fig. 4.4 for a few tens of microseconds before turning the current back on. In other words, the fuel cell "does not notice" the short interruption of the current. The need for interrupting currents of several hundred amperes on a timescale of microseconds clearly requires careful choice of the electronic circuitry (Buchi et al., 1995).

Because fuel cell electrodes and MEAs are essentially "flat" items of varying areas, A, depending on fuel cell design, for easy performance comparison one usually works with current densities, i, rather than with currents, I, and accordingly with area specific resistances, r = RA, rather than with resistances, R.

For example, the MEA in a cell of Aj = 200 cm2 active area delivering a current of 200 A (not an unusual figure) runs at a current density of 1.0 Acm-2. If 100 mV of cell voltage are lost due to ohmic effects (for example, measured by current interrupt), the whole MEA has a resistance of R1 = AER/I = 0.5 mQ. The lab may have a second cell of only A2 = 10 cm2 active area. In order to be able to predict the likely ohmic loss of a similar (but smaller) MEA in the small cell, one better works with the area specific resistance r = R1A1. Here, r = 0.5 mQ • 200 cm2 = 100 mflcm2 = 0.1 Qcm2. In the small cell running at 1.0 Acm-2, presuming identical operation, this of course also leads to an ohmic loss of AER = 0.1 Qcm2 ■ 1.0 Acm-2 = 100 mV. But here the total cell resistance is much larger, R2 = r/A2 = 0.1 Qcm2/ 10cm2 = 10 mQ, rather than 0.5 mQ for the large cell.

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