## HTPEM Fuel Cell Impedance: Mechanistic Modelling and Experimental Characterisation

Research output: Book/Report › Ph.D. thesis › Research

### Abstract

This Ph.D. Thesis investigates this type of fuel cells through experimental studies and mathematical modelling. These studies all revolve around the electrochemical impedance spectroscopy (EIS) characterisation method. EIS is performed by applying a sinusoidal current or voltage signal to the fuel cell and calculating the impedance from the response. This is repeated over the frequency range covering the processes of interest. A representation of the impedance across this frequency range is called an impedance spectrum.

The first experimental investigation treats the effects of adding CO and CO2 to the hydrogen which is fed to the cell. Since the effects on the steady state performance are well documented, the focus is on the effect on the impedance spectrum. It is concluded that the entire impedance spectrum is affected by even small amounts of CO. This questions parts of the way that HTPEM impedance spectra are often interpreted in the literature.

The second experimental investigation applies EIS to the investigation of the break-in process of two sub-types of HTPEM fuel cells. One type is the Celtec®-P from BASF which utilises a membrane based on the sol-gel process. The other type is the Dapozol® 77 from Danish Power Systems® which is based on a membrane that has been doped with phosphoric acid after casting. The two types show different development of voltage and impedance with time. The sol-gel based cells take the longest to reach a stable development rate. For both types, the results indicate that break-in times for HTPEM fuel cells can be significantly shortened with respect to the guide lines from BASF.

The main focus of this project is on mechanistic modelling of the interplay of polarisation curves and impedance spectra for HTPEM fuel cells. The aim is to develop a model that can extract information about critical electrode parameters from these two types of measurements. Such a model can potentially be applied to the analysis of degradation phenomena or the effects of different electrode designs. To this end a 1+1D model, taking into account the dynamics of gas transport and electrode kinetics on the cathode side, has been developed. The model takes into account the interplay between the concentration of phosphoric acid in the catalyst layer and the solubility and diffusivity of oxygen, the exchange current density, and the proton conductivity.

Fitting the model to a dataset consisting of polarisation curves and impedance spectra is attempted under different assumptions. These assumptions affect the resulting fitting parameters and the fit quality to varying degree. It is concluded that the requirement of simultaneous fitting of both polarisation curves and impedance spectra makes it much harder to achieve agreement between the model and the data. This can, however be interpreted as a strength, since it makes identification of erroneously assumption and parameter combinations which can otherwise appear credible if only the polarisation curves are considered.

The ability of the model to reproduce the data outside the fitted area is investigated. Here it is concluded that the effects of the current density is acceptably reproduced but the temperature dependence is problematic. The reason for the unrealistic temperature dependence is assumed to be twofold. In part, the models of the ohmic losses in the fuel cell are too simplistic and, besides, the balance between the diffusion losses in the gas phase and the acid phase is deemed unrealistic. A number of possible improvements to the model to correct these shortcomings are suggested.

In spite of the shortcomings of the model, the results achieved through this project demonstrate the strengths inherent in this modelling philosophy. To the extent it is possible to improve the agreement between the model and the data across operating points, it is deemed feasible for the model to eventually achieve the initial aim.

### Details

This Ph.D. Thesis investigates this type of fuel cells through experimental studies and mathematical modelling. These studies all revolve around the electrochemical impedance spectroscopy (EIS) characterisation method. EIS is performed by applying a sinusoidal current or voltage signal to the fuel cell and calculating the impedance from the response. This is repeated over the frequency range covering the processes of interest. A representation of the impedance across this frequency range is called an impedance spectrum.

The first experimental investigation treats the effects of adding CO and CO2 to the hydrogen which is fed to the cell. Since the effects on the steady state performance are well documented, the focus is on the effect on the impedance spectrum. It is concluded that the entire impedance spectrum is affected by even small amounts of CO. This questions parts of the way that HTPEM impedance spectra are often interpreted in the literature.

The second experimental investigation applies EIS to the investigation of the break-in process of two sub-types of HTPEM fuel cells. One type is the Celtec®-P from BASF which utilises a membrane based on the sol-gel process. The other type is the Dapozol® 77 from Danish Power Systems® which is based on a membrane that has been doped with phosphoric acid after casting. The two types show different development of voltage and impedance with time. The sol-gel based cells take the longest to reach a stable development rate. For both types, the results indicate that break-in times for HTPEM fuel cells can be significantly shortened with respect to the guide lines from BASF.

The main focus of this project is on mechanistic modelling of the interplay of polarisation curves and impedance spectra for HTPEM fuel cells. The aim is to develop a model that can extract information about critical electrode parameters from these two types of measurements. Such a model can potentially be applied to the analysis of degradation phenomena or the effects of different electrode designs. To this end a 1+1D model, taking into account the dynamics of gas transport and electrode kinetics on the cathode side, has been developed. The model takes into account the interplay between the concentration of phosphoric acid in the catalyst layer and the solubility and diffusivity of oxygen, the exchange current density, and the proton conductivity.

Fitting the model to a dataset consisting of polarisation curves and impedance spectra is attempted under different assumptions. These assumptions affect the resulting fitting parameters and the fit quality to varying degree. It is concluded that the requirement of simultaneous fitting of both polarisation curves and impedance spectra makes it much harder to achieve agreement between the model and the data. This can, however be interpreted as a strength, since it makes identification of erroneously assumption and parameter combinations which can otherwise appear credible if only the polarisation curves are considered.

The ability of the model to reproduce the data outside the fitted area is investigated. Here it is concluded that the effects of the current density is acceptably reproduced but the temperature dependence is problematic. The reason for the unrealistic temperature dependence is assumed to be twofold. In part, the models of the ohmic losses in the fuel cell are too simplistic and, besides, the balance between the diffusion losses in the gas phase and the acid phase is deemed unrealistic. A number of possible improvements to the model to correct these shortcomings are suggested.

In spite of the shortcomings of the model, the results achieved through this project demonstrate the strengths inherent in this modelling philosophy. To the extent it is possible to improve the agreement between the model and the data across operating points, it is deemed feasible for the model to eventually achieve the initial aim.

Original language | English |
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Place of Publication | Aalborg |
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Publisher | Department of Energy Technology, Aalborg University |

Number of pages | 186 |

ISBN (Print) | 978-87-92846-47-1 |

State | Published - Dec 2014 |

Publication category | Research |

- HTPEM, HT-PEM, HT-PEMFC, HTPEMFC, EIS, Imdpedance Spectroscopy, Electrochemical Impedance Spectroscopy, Modelling, Matlab

### Research areas

### Projects

- COmmercial BReak-through of Advanced Fuel Cells, COBRA
Project: Research