Application of finite Gaussian process distribution of relaxation times on SOFC electrodes

Electrochemical impedance spectroscopy (EIS) is a powerful tool in characterisation of processes in electrochemical systems, allowing us to elucidate the resistance and characteristic frequency of physical properties such as reaction and transport rates. The essence of EIS is the relationship between current and potential at a given frequency. However, it is often the case that we do not understand the electrochemical system well enough to fit a meaningful physical model to EIS data. The distribution of relaxation times (DRT) calculation assumes an infinite series of relaxation processes distributed over a characteristic timescale. The DRT calculation may identify the number of processes occurring, as well as their respective resistivity and characteristic timescale, and may resolve processes which have relatively similar timescales. Using a nonparametric tool known as Gaussian process (GP) regression, we showcase a method of finding a unique solution to the ill-posed DRT problem by optimising kernel hyperparameters as opposed to ad-hoc regularisation. In this work, we use finite GP regression under inequality constraints (fGP) to analysed EIS data generated by a (Ni/CGO|CGO|YSZ|Reference Cathode) solid-oxide fuel cell in a gas mixture of 0.5 bar H₂/0.5 bar H₂O and at a temperature of 600 °C. By varying the current density, we can characterise the current-voltage relationship of the electrode and shed light on the reaction mechanism governing charge transfer at the solid-gas interface. Our findings also show that even at relatively high current densities (±600mAcm^-2) the electrode process is limited by charge transfer.