Mechanical Basis of Nafion’s High-Frequency Inductive Impedance

Abstract

Recent literature has highlighted how the coupling of electrochemical and mechanical phenomena can affect the way batteries and fuel cells perform [1, 2]. Local volume changes and stresses due to water transport play critical roles in the operation of polymer exchange membranes. A non-isobaric version of Newman’s concentrated-solution theory [3] was applied to study hydrated ionomers, in which mechanical effects intricately entangle the transport of material, momentum, and energy. Electrochemical impedance spectroscopy (EIS) provides a useful tool to study the most pronounced effects arising from this electrochemical/mechanical coupling in Nafion. Nafion is relatively compressible, so changes in pressure affect the concentration of sulfonic acid; thus pressure gradients affect the voltage drop. Also, pressure diffusion can drive proton flux, directly coupling current with mechanical state. When AC signals are driven at low frequencies, these piezoelectric effects are minimal and the Warburg signature of water diffusion dominates the impedance. At higher frequencies, however, current oscillates too fast for the water concentration to respond. Pressure effects dominate the impedance. Strikingly, in this high-frequency regime the membrane can resonate, leading to divergent pressure impedances at a fundamental frequency and its harmonics. This resonance can be related to the speed of sound in the membrane. Above this speed, which is much higher than the characteristic diffusion speed, the signal is carried across the ionomer by elastic (mechanical) waves. Inductive loops on the Nyquist plot, and corresponding peaks in the Bode plots, occur as a consequence of this electrochemical-mechanical coupling above the critical resonant frequency. Various mechanical characteristics can be associated with resistance (viscosity), capacitance (elastic modulus), and inductance (mass). A parametric study reveals how transport and mechanical properties affect the magnitudes and shapes of these impedance signatures. The model rationalizes the inductive responses seen experimentally in several recent high-quality Nyquist plots [4]. [1] A. Kusoglu and A.Z. Weber, Electrochemical/Mechanical Coupling in Ion-Conducting Soft Matter, J. Phys. Chem. Lett., 2015, 6(22), pp 4547-4552 [2] G. Bucci, Formulation of the Coupled Electrochemical-Mechanical Boundary-Value Problem, with Applications to Transport of Multiple Charged Species, Acta Mater., 2016, 104, pp 33-51 [3] P. Goyal and C.W. Monroe, New Foundations of Newman’s Theory for Solid Electrolytes: Thermodynamics and Transient Balances, J. Electrochem. Soc., 2017, 164(11), pp E3647-E3660 [4] B.P. Setzler and T.F. Fuller, A Physics-Based Impedance Model of Proton Exchange Membrane Fuel Cells Exhibiting Low-Frequency Inductive Loops, J. Electrochem. Soc., 2015, 162(6), pp F519-F530