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A meaningful design and an efficient operation of fuel cells require a comprehensive understanding of the underlying physico-chemical processes. Intensive fuel cell research carried out over the last decades led to the development of fundamental concepts which in the meantime have found entry into text books and standard works. However, special attention needs to be paid, when the system under consideration exhibits nonlinear operating behavior. The fuel cell literature contains various relevant experimental reports and theoretical predictions on nonlinear phenomena in fuel cells. Among them are several instances of bistability, observed e.g. in proton-exchange membrane (PEM) fuel cells or high-temperature fuel cells (e.g. [1-3]). Furthermore, oscillatory conditions and pattern formation have been reported especially in PEM fuel cells (e.g. [4,5]). A careful analysis of these studies reveals that the understanding of nonlinear effects in fuel cells
is not only of academic interest, but is crucial for improved operation and process design.
Within the present contribution a prototype model is suggested [6], which allows for a systematic discussion of the findings on nonlinear operating behavior of fuel cells, mentioned above. The model consists of Kirchhoff’s loop law for the determination of the cell voltage, a generic charge balance and a generic mass and energy balance. The model is used to illustrate that nonlinear operating behavior, such as bistability or oscillations, can be traced back to a branch of the current-voltage-curve exhibiting a negative differential resistance (NDR) [7]. Two different types of such an NDR-branch can be distinguished. An N-type NDR-branch ends in two vertical tangents in the iU-phase-plane. Systems possessing such an NDR-branch can exhibit bistability under galvanostatic control but not under potentiostatic control. A S-type NDR-branch ends in two horizontal tangents in the iU-phase-plane. Such systems can exhibit bistability under potentionstatic control but not under galvanostatic conditions. A careful analysis of the prototype model reveals the existence of three main classes of system properties leading to a NDR-branch. The first class of phenomena originates from the ion transport trough the electrolyte material. In order to create a negative differential resistance, a state-dependent electrolyte resistance is required. Clear examples for such a behavior can be found in PEM fuel cells operated under reduced feed stream humidification at constant flow rate, as well as in high-temperature fuel cells. In both cases, a product of the electrochemical reaction – product water in case of the PEM fuel cell and thermal energy released in the electrochemical reaction in case of the high-temperature fuel cell – leads to a decrease of the electrolyte resistance. Bistable iU-curves of the S-type have been observed or predicted under such conditions.
The second class of phenomena originates from nonlinear electrochemical surface kinetics at one of the electrodes of the fuel cell. In order to create a negative differential resistance, a potential dependent transport step is required. The PEM fuel cell exposed to H2/CO-mixtures gives a clear example for this class. Here, the surface coverage of hydrogen, which is the reactant of the main Faradaic reaction at the anode, is influenced at elevated electrode potentials by the dissociation of water towards the catalyst surface. As a consequence a N-type NDR-branch is formed, which however gets hidden under steady-state conditions by the CO electro-oxidation. Due to an interaction of the fast N-NDR system with the slower dynamics of the CO, oscillations occur under galvanostatic control. The third class of phenomena originates from nonlinearities other than ion transport in the membrane or electrochemical surface kinetics. So far, one example for this last class can be identified in the relevant literature. The self-inhibition of the transport of product water within the porous structures was found to lead to bistability. As the oxygen transport towards the cathode catalyst layer gets affected by the presence of the product water, this non-electrochemical nonlinearity projects a N-type NDR-branch into the iU-curve of the cell.
Furthermore, the present contribution places some remarks on the technical relevance of the reviewed findings. In general, it can be stated that the knowledge and the understanding of nonlinear effects in fuel cells are essential for preventing them, for mastering them or for exploiting them systematically in order to ensure a reasonable and efficient operation of fuel cells.
[1]Moxley et al., Chem. Eng. Sci. 58, 4705 (2003)
[2]Hanke-Rauschenbach et al., J. Electrochem. Soc. 155, B97 (2008)
[3]Katsaounis et al., Solid State Ionics 177, 2397 (2006)
[4]Zhang and Datta, J. Electrochem. Soc. 149, A1423 (2002)
[5]Hanke-Rauschenbach et al., J. Electrochem. Soc. 157, B1521 (2010)
[6]Hanke-Rauschenbach et al., Rev. Chem. Eng. (2011), submitted
[7]K. Krischer , Adv. in Electrochem. Sci. and Eng. 8, p. 89 (2003)
