Electrochemical impedance spectroscopy (EIS) is a powerful technique that can be applied in-situ to deconvolute the various loss mechanisms in the polymer electrolyte fuel cell (PEFC) that occur at different rates. The frequency response of a PEFC that results from EIS is in essence characterised by energy dissipating and energy storing elements of the cell. It can be represented by an equivalent circuit that is composed of resistors and capacitors respectively. By understanding the arrangement and magnitude of the electrical components in the equivalent electrical circuit, it is possible to generate a deeper understanding of how and where the electrical energy that is generated due to the redox reaction is being dissipated and retained within the real physical system. Although the use of equivalent circuits is often an adequate approach, some electrochemical processes are not adequately described by electrical components. In which case, it is necessary to adopt a more rigorous approach of describing processes through the use of differential equations to describe the physics of the electrochemical system at the frequency domain.
Studies in the literature have attempted to construct mathematical models to describe the impedance response of the cathode catalyst layer (CCL) based on conservation equations describing the electrochemical and diffusion processes. However this has resulted in a complicated mathematical analysis which in turn results in complicated solutions. The resulting equations cannot be easily validated against real-world EIS measurements and only analytical results have been reported. In this thesis a mathematical model to describe the impedance response of the CCL has been developed. This model is derived from fundamental electrochemical theory describing the physics of the CCL. The mathematical treatment is simplified by taking into account some considerations based on the EIS theory. The resulting model can be easily applied to real-world EIS measurements of PEFCs and presents parameters commonly known in the electrochemical area. The scientific contribution of this doctoral thesis is mainly divided in two sections: Modelling and Application.
The first step of the modelling section develops an equation describing charge conservation in the CCL and together with Ohm s Law equation accounting for ionic conduction, predicts the impedance response of the CCL at low currents. The second step includes the change of oxygen concentration during the oxygen reduction reaction (ORR) into the equation accounting for CCL low current operation. The study of mass transport in the CCL is very complex; the literature has treated it with simplifications and approximations. The finite diffusion distance for oxygen to reach the reaction sites in the CCL forms a complicated network of multi-phase parallel and serial paths and can change in dimension at different operating conditions (flooding, drying). In the mathematical treatment of this doctoral thesis the finite diffusion distance and surface concentration of oxygen in the CCL are considered to be independent of the thickness of the CCL. EIS reflects only bulk measurements based on the total CCL thickness. Even though this results in an over-simplification for the oxygen diffusion in the total CCL, this approach simplifies the mathematical treatment to predict the impedance response of the CCL at high current operation, and as result it can be successfully validated against real-world EIS measurements.
In the application section the model is applied with real-world EIS measurements of PEFCs. First the model is applied with EIS measurements presenting inductive effects at high frequencies. The model reveals mechanisms masked at high frequencies of the impedance spectrum by inductance effects. The results demonstrate that the practice of using the real part of the Nyquist plot where the imaginary part is equal to zero to quantify the ohmic resistance in PEFCs can be subject to an erroneous interpretation due to inductive effects at high frequencies. Secondly the model is applied to cathode impedance data obtained through a three-electrode configuration in the measurement system and gives an insight into the mechanisms represented at low frequencies of the impedance complex-plot. The model predicts that the low frequency semicircle in PEFC measurements is attributed to low equilibrium oxygen concentration in the CCL-gas diffusion layer (GDL) interface and low diffusivity of oxygen through the CCL. In addition the model is applied with simultaneous EIS measurements in an Open-Cathode PEFC stack. The factors that limit the performance of the PEFC stack are evaluated with simultaneous EIS measurements and the model. The results show that the change in impedance response of individual cells within the stack is attributed to oxygen limitations, degradation in membrane electrode assemblies (MEAs) and temperature distribution. This EIS knowledge enables an assessment of the state of health in operational fuel cell stacks. In the last section of the application section, the mathematical model translated in the time domain via reverse Laplace Transform predicts the current distribution through the CCL. This provides information to improve the performance of the CCL as well as determine the uptake of product water in the membrane.
Finally the conclusions and future work are presented. This doctoral thesis has established a backbone understanding of how the electrochemical and diffusion mechanisms relate to the electrochemical impedance spectra of PEFCs. The goal of a future work is to develop this EIS knowledge into a real-time EIS system for non-intrusive diagnostics of degradation in operational PEFCs. This implies a modification of the model to consider oxygen transport through the CCL thickness as part of a multi-species mixture using mass transport theory including concentrated solution theory to fuel cell engineering.
A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy of Loughborough University.
Mexican National Council for Science and Technology (CONACYT)