Electrochemical mechanisms of the impedance spectrum in polymer electrolyte fuel cells

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

Frequency Transition from Diffusion to Capacitive Response in the Blocked-Diffusion Warburg Impedance for EIS Analysis in Modern Batteries

The use of the Blocked-diffusion Warburg (BDW) impedance within electrochemical impedance spectroscopy (EIS) measurements can unveil diffusion properties of the electroactive material of modern batteries at different states-of-charge. The impedance response of the BDW comprises a diffusion response of charge carriers through a short-diffusion distance (e.g. the solid-phase in electroactive material of battery electrodes) and a capacitive response due to accumulation of charge carriers in a blocked-interface (e.g. impermeable current collector of a thin film electrode). This study has developed a mathematical expression based on the Newton-Raphson iteration method to calculate the frequency and time constant during the transition from diffusion to capacitive response in the BDW impedance. The mathematical procedure to calculate the frequency during the diffusion-capacitive transition response in the BDW has been written in a script in Matlab® software and is applied to BDW impedance responses reported in previous studies and extracted from EIS measurements in Li-ion and NiMH batteries. This study demonstrates that the time constant during the transition from diffusion to capacitive response in the BDW differs from the characteristic time constant commonly represented in the BDW mathematical expression. The characteristic time constant represented in the BDW mathematical expression is related to the rate of accumulation of charge carriers in the blocked-interface of the electrode. On the other hand, the time constant during the transition from diffusion to capacitance responses in the BDW impedance can be related to diffusion properties in solid-phase particles with heterogeneous size distribution in the electroactive material of modern battery electrodes

Further Understanding of Uncertainties in the Impedance Spectrum of the Polymer Electrolyte Fuel Cell due to Inductive Effects and Oxygen Diffusion Time Constant

In this study, uncertainties during the assessment of the electrochemical impedance spectrum of the polymer electrolyte fuel cell (PEFC) attributed to inductive artefacts at high frequencies and inductive loops at low frequencies as well as oxygen diffusion time constant are discussed. A validated impedance model represented as an equivalent electrical circuit of a PEFC allowed the simulation of the effect of inductive artefacts, inductive loops and oxygen diffusion time constant on electrochemical impedance spectroscopy (EIS) measurements represented in the Nyquist plot. This study considers EIS measurements reported in previous studies and provides an insight into the EIS measurements with positive imaginary components at high frequencies attributed to the intrinsic inductance of the measurement cables during EIS tests and at low frequencies attributed to electrochemical mechanisms (e.g. side reactions with intermediate species) during PEFC operation. In addition, an overview of overlapping mechanisms (charge transfer and oxygen transport resistances during the oxygen reduction reaction) on the PEFC impedance spectrum attributed to oxygen diffusion across the cathode catalyst layer is presented. EIS measurements with positive imaginary components and with overlapping effects could yield to ambiguities when studying or relating electrochemical mechanisms (ion conduction, capacitance, charge transfer and mass transport resistances) of the PEFC through a defined single frequency or a single measured value represented in the Nyquist complex-impedance plot

An impedance model for EIS analysis of nickel metal hydride batteries

Based on fundamental electrochemical theory, an impedance model for analysis of electrochemical impedance spectroscopy (EIS) of Nickel-Metal Hydride (NiMH) batteries is presented in this study. The resulting analytical expression is analogous to the impedance response of the Randles electrical circuit used for EIS analysis on NiMH batteries. The impedance model is validated against EIS measurements carried out whilst decreasing the state of charge (SOC) of a NiMH battery pack. The diffusion mechanisms during the discharge of the NiMH battery is modelled through a Warburg element derived from diffusion theory considering reflective boundary conditions. ZView® Scribner Associates Inc. software allowed the estimation of electrochemical and diffusion parameters from EIS measurements of the NiMH battery. The effect of diffusion mechanisms on EIS measurements is discussed. The results demonstrate that ion transport is the rate-limiting process during the discharge of the NiMH battery. This EIS-modelling study has provided an insight into the interpretation of battery electrochemical mechanisms represented in the Nyquist plot from EIS. It can assist to further EIS-modelling to study and correlate State of Health (SOH) in NiMH batteries for different applications

Electrochemical impedance study on estimating the mass transport resistance in the polymer electrolyte fuel cell cathode catalyst layer

In this study the mass transport resistance in the cathode catalyst layer (CCL) of a polymer electrolyte fuel cell (PEFC) is estimated using electrochemical impedance spectroscopy (EIS) measurements. Experimental impedance measurements were carried out in a 6 cm2 PEFC operated with two different relative humidity (RH) values in the cathode and different partial pressures of oxygen in He/O2 and N2/O2 gas mixtures. A mathematical model predicting the CCL impedance response, derived in the authors’ previous study, is applied to EIS measurements to calculate the CCL mass transport resistance. The experimental results show the presence of an overlapped second semicircle at low frequencies which is attributed to an increase in the time constant to diffuse oxygen through the CCL when the PEFC is operated at low oxygen partial pressures, p(O2) 6 20%, in He/O2 or N2/O2 gas mixtures. The results also show that oxygen diluted with nitrogen can reduce the steady state oxygen concentration in the CCL-gas diffusion layer (GDL) interface and can increase CCL mass transport resistance. It is possible, as such, to harness capabilities from both modelling and real-world EIS data in a complementary manner

Start-up vibration analysis for novelty detection on industrial gas turbines

This paper focuses on industrial application of start-up vibration signature analysis for novelty detection with experimental trials on industrial gas turbines (IGTs). Firstly, a representative vibration signature is extracted from healthy start-up vibration measurements through the use of an adaptive neuro-fuzzy inference system (ANFIS). Then, the first critical speed and the vibration level at the critical speed are located from the signature. Finally, two (s- and v-) health indices are introduced to detect and identify different novel/fault conditions from the IGT start-ups, in addition to traditional similarity measures, such as Euclidean distance and cross-correlation measures. Through a case study on IGTs, it is shown that the presented approach provides a convenient and efficient tool for IGT condition monitoring using start-up field data

An electrical circuit for performance analysis of polymer electrolyte fuel cell stacks using electrochemical impedance spectroscopy

In this study, a new electrical equivalent circuit is developed to evaluate the performance of polymer electrolyte fuel cell (PEFC) stacks using electrochemical impedance spectroscopy (EIS). Experimental EIS measurements were carried out in an open-cathode PEFC stack to validate the new electrical equivalent circuit. The electrical equivalent circuit developed in the authors’ previous study, which simulates the impedance response of a single PEFC, is applied to EIS measurements carried out in the open-cathode PEFC stack. However, it cannot reproduce EIS measurements with positive imaginary components at low frequencies. Thus, in this study, the electrical equivalent circuit is modified by adding electrical components which represent intermediate adsorbed species in a two-step electrochemical reaction as reported in the literature. The results show that the new electrical equivalent circuit can accurately reproduce the experimental EIS measurements and can give an insight into the factors that limit the performance of the PEFC stack. This new electrical equivalent circuit can enable an assessment of the state of health and performance of the fuel cell stacks

A generic electrical circuit for performance analysis of the fuel cell cathode catalyst layer through electrochemical impedance spectroscopy

In this study, a generic electrical circuit is presented to characterise the frequency response of the Polymer Electrolyte Fuel Cell (PEFC), Cathode Catalyst Layer (CCL) at different current densities. The new electrical circuit is derived from fundamental electrochemical and diffusion theory. It consists of a transmission line in combination with distributed Warburg elements. The validation of this study is divided into a theoretical validation and an experimental validation. In the theoretical validation the impedance response of the CCL generated from three different circuits reported in the literature was compared with the simulated data from the generic electrical circuit. In the experimental validation, Electrochemical Impedance Spectroscopy (EIS) measurements were carried out in an H2/air PEFC through a three-electrode configuration in the measurement system and were compared with the simulated data from the generic circuit. The results show that the generic circuit is able to accurately reproduce the measured data of the CCL at different current densities and is able to represent the electrochemical and diffusion mechanisms of the CCL in the frequency domain. It is possible to generate a deeper understanding of how and where the chemical energy that is released from the redox reaction is being dissipated and retained within the real physical system

Performance analysis and prediction of compressor fouling condition for a twin-shaft engine

Performance of a twin-shaft Industrial Gas Turbine (IGT) at fouling condition is simulated via a gas turbine model based on fundamental thermodynamics. Measurements across the engine during compressor fouling conditions were considered to validate the outcomes. By implementing correlation coefficients in the compressor model, the performance of the IGT during compressor fouling conditions is predicted. The change in the compressor air flow and the compressor efficiency during fouling conditions is estimated. The results show that the reduction of air flow rate is the dominating parameter in loss of generated power under fouled conditions. The model can provide an insight into the effect of compressor fouling conditions on IGT performance

Analytical Transfer Function to Simulate the Dynamic Response of the Finite-Length Warburg Impedance in the Time-Domain

Based on fundamental electrode theory, an analytical transfer function to simulate the frequency impedance spectrum of the finite-length Warburg (FLW) impedance and the dynamic potential response of the FLW impedance in the time-domain has been developed in this study. Parameters reported in the literature estimated from experimental measurements carried out in polymer electrolyte fuel cells (PEFCs) have been considered to validate the new analytical transfer function. The analytical transfer function representing the FLW impedance can be considered in different equivalent electrical circuit configurations to simulate a more accurate dynamic output voltage of an electrochemical power system under the effect of diffusion phenomena. A Simulink model based on the Randles circuit and the new transfer function representing the FLW impedance is constructed to simulate the dynamic output voltage of a PEFC during a current-interrupt incident. In addition, a Simulink model based on an electrical circuit configuration and the new transfer function representing the FLW impedance is constructed to simulate the dynamic output voltage of a Li-ion battery. This study establishes a wider scope to relate the electrochemical impedance spectroscopy to the dynamic output voltage response of electrochemical power systems