The Effect of Liquid Saturation Transients on PEM Fuel Cell Impedance: Inductive Loop and Instability of Catalyst Layer Operation

We report a physics--based model for the electrochemical impedance of a PEM fuel cell cathode. The model takes into account the transient behavior of oxygen and proton transport in the cathode catalyst layer caused by variation of the liquid saturation with cell current. Transients of the catalyst layer oxygen diffusivity result in a second capacitive arc in the Nyquist spectrum, while proton conductivity transients lead to formation of an inductive loop. In the range of capillary pressures $p_c$ in which the liquid saturation in the catalyst layer is independent of $p_c$, the loop does not form. Stability analysis of a reduced system of equations reveals that the static solution with inductive loop is unstable with respect to spatial perturbations, implying that the post--oscillatory steady state is impossible to reach. Possible scenarios of instability development are discussed.