Morphological and electrochemical modeling of SOFC composite cathodes with distributed porosity
Highlights
• A model of charge and mass transport in porous composite SOFC cathodes is presented. • Accounting for the distribution of morphological properties along the thickness. • The model reproduces the dependence of polarization resistance on thickness. • The exchange current of oxygen reduction reaction follows an Arrhenius law. • The exchange current depends on the square root of oxygen partial pressure.
Introduction
Fuel cells are energy conversion devices in which the chemical energy of a fuel and a combustive agent (for example, hydrogen and air, respectively) is electrochemically transformed into electric energy. The electrochemical conversion avoids the use of a direct combustion process and of a Carnot thermodynamic cycle, thus reducing pollution levels in exhaust gases while increasing the energetic efficiency [1], [2]. Solid oxide fuel cells (SOFCs), characterized by a solid electrolyte which transports oxygen ions at high temperature (usually higher than 600 °C), have attracted research and technology interest due to the expected advantages if compared with other types of fuel cells, such as the broader fuel flexibility [3], [4], [5] and the high efficiency of energy conversion [6], [7], which can be further increased by the possibility of co-generation with gas turbine power systems [8], [9].
A single SOFC consists of two electrodes, namely the cathode and the anode, where the oxygen reduction and the fuel oxidation respectively occur, separated by a dense anion-conducting electrolyte, which is dedicated to the transport of oxygen ions from the cathode towards the anode. In hydrogen fed SOFCs, the cathode represents the main source of energy loss [10], [11], [12]. Porous composite cathodes, which consist in sintered random structures of electron-conducting (e.g., strontium-doped lanthanum manganite, LSM) and ion-conducting particles (e.g., yttria-stabilized zirconia, YSZ), are often used in order to promote the oxygen reduction [13].
In a composite cathode, the molecular oxygen in gas phase reacts with electrons, transported by the electron-conducting phase, to form oxygen ions, which are transported by the ion-conducting particles towards the electrolyte. Therefore, the reaction occurs in the proximity of the contact perimeter between electron-conducting, ion-conducting and gas phase, where the reaction participants can coexist, which is called three phase boundary (TPB) [10], [14].
The rate at which the current is converted within the cathode, from the electronic form to the ionic form, depends not only on the catalytic activity of the materials and the extension of the reaction zone, but also on the relative facility at which charges and chemical species are transported to and from the reaction sites [15], [16]. The effective transport properties of the composite structure, as well as the density of reacting sites, depend on the microstructural characteristics of the electrode, such as the particle diameter, the porosity and the composition [17]. Thus, the interplay of material, catalytic, geometric and microstructural characteristics determines the cathode efficiency [14], [18], which is inversely proportional to its polarization resistance.
In this study, a mechanistic model, based on steady-state balance equations of the reaction participants, is developed and applied to porous composite LSM/YSZ cathodes. The conservation equations are applied to the domain modeled as a continuum phase (continuum approach) [15], [19], [20], [21], [22], [23], [24], characterized by effective transport and kinetic parameters (e.g., electric and ionic conductivity, gas permeability, TPB length per unit volume). The model accounts for a coherent description of the microstructure through the percolation theory [25], which is used to estimate the effective properties from the morphological cathode characteristics. As a new feature of the model herein presented, the variation of the porosity along the cathode thickness, as experimentally found on the electrodes investigated [26], is considered. The model represents the refinement of a previous work [27], in which the polarization behavior was interpreted without coherently relating the porosity distribution to the variation of morphological effective properties and, consequently, to the electrochemical performance (as, instead, developed here) and without taking into account the effects of the gas phase.
The comparison of simulation results with experimental data allows to obtain information about the macrokinetics of oxygen reduction, in particular regarding its dependence on temperature and oxygen partial pressure.
Section snippets
General aspects and model assumptions
Within the cathode, the molecular oxygen in gas phase is reduced through the electrons, coming from the current collector and transported by the electron-conducting phase, into oxygen ions, transported by the ion-conducting phase, following the stoichiometry:
The reaction, which represents the conversion of the current from the electronic form into the ionic form, may take place at any TPB, provided that the paths transporting the reaction participants are connected to the
Results and discussion
The model of the cathode described in Section 2 is used to interpret the experimental data, provided by Barbucci et al. [26], regarding porous composite cathodes of different thicknesses in different operating conditions. LSM was used as electronic conductor and YSZ as ion-conducting phase. From scanning electron microscope images, all the samples were found to show a porosity linearly distributed along the thickness, increasing up from the current collector to the electrolyte interface as
Conclusions
A mathematical model of porous composite SOFC cathodes, based on the application of local mass and charge balance equations, was developed. The model also comprised, through the extended percolation theory, a coherent morphological description, which allowed to take into account non-uniform effective properties along the cathode thickness. The model was applied to interpret experimental data of polarization resistance as a function of thickness, temperature and oxygen partial pressure of porous
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