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\journal{Journal of Power Technologies}
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\begin{frontmatter}{}

\title{Design of open-porous materials for high-temperature fuel cells}

\author[label1]{T. Wejrzanowski\corref{cor1}}
\ead{twejrzanowski@inmat.pw.edu.pl}
\author[label1]{S. Haj Ibrahim}
\author[label1]{K. Cwieka}
\author[label2]{J. Milewski}
\author[label1]{K. J. Kurzydlowski}
\address[label1]{Warsaw University of Technology, Faculty of Materials Science and Engineering, Woloska 141, 02-507 Warsaw, Poland}
\address[label2]{Institute of Heat Engineering, Warsaw University of Technology, Nowowiejska 21/25, 00-665 Warsaw}
\cortext[cor1]{Corresponding author}

\begin{abstract}
Microstructure, apart from the chemical composition, is one of the major factors influencing material properties. It is especially important for open-porous materials dedicated to catalytic applications, where fraction of pores, their size distribution and specific surface influence diffusion of reactants and kinetics of catalytic reactions.
In these studies the numerical models of the microstructure of open-porous electrodes for molten carbonate fuel cell (MCFC) are presented. The models presented here simulate fabrication routes for real materials including mixing of powders, tape casting and sintering processes. The substrate powders are represented by spheres with defined size distribution. Mixing and compaction of powders with polymeric binder is simulated by granular model implemented in LAMMPS code. In the next step the polymeric phase represented by fine particles and larger porogen addition are removed to form pores. The sintering process is simulated by geometry smoothing what results in spheres aggregation. 
The models presented here were compared with micro computed tomography ($\mu$CT) 3D images of real MCFC materials. Quantitative analysis of $\mu$CT images was performed and it was demonstrated that algorithms used in these studies enable to design materials with desired porous microstructure.
\end{abstract}
\begin{keyword}
Open-porous materials \sep MCFC \sep microstructure\sep  modelling
\end{keyword}
\end{frontmatter}{}




\section{Introduction}
Molten carbonate fuel cells (MCFCs) may be effectively carbon neutral and emit zero net greenhouse gases when it is fed with renewable fuels, such as biogas \cite{modeling_performance}. The carbon dioxide produced on the anode side which is not recirculated to the cathode is simply the result of the carbon-based species that are fed at the inlet. Even if fossil natural gas is used as a fuel, because of the higher efficiency of the MCFC, less CO\textsubscript{2} is emitted as less primary fuel is required to produce a given amount of electricity \cite{milewski2016solid}. In addition, with a radically innovative approach, MCFCs could be used to separate the CO\textsubscript{2} from the flue gas instead, generating power in the process \cite{roshandel2015multi}. The MCFC can be used to separate CO\textsubscript{2} thanks to the functional reactions that occur inside the cell: carbonate ions transport CO\textsubscript{2} directly from the cathode to the anode side (see Figure 1a). Hence, MCFCs offer rich potential to reduce reliance on the already strained power grid, alleviate carbon footprint and provide a source of renewable energy. Most of the key technological and operational issues related with future development of MCFCs is concentrated on materials \cite{selman2006molten,antolini2011stability}. The performance, durability and cost (both manufacturing technology and operational costs) can be improved by application of new materials \cite{Kulkarni2012}. Typically, design of new materials is focused on single cell elements (anode, cathode, electrolyte matrix), which can be stacked into larger device (see Figure 1b).
\begin{figure*}
	\centering
	\includegraphics[width=15cm]{figure1}
	\caption{(a): Schematic illustration of the MCFC operation. (b): The area of the main interest from materials science point of view.}
\end{figure*}
\par The concept of materials design involves mainly the analysis of chemical composition and microstructure effect on the performance and durability of single cell. However, commercial application requires also incorporation of economics. Since MCFCs operate at elevated temperature (typically $\sim$ 650\textsuperscript{o}C) expensive materials (such as platinum) can be replaced by much cheaper ones (i.e. nickel). Moreover, this temperature is high enough to supply MCFC with natural gas or another fuel thus, the use of pure hydrogen is not necessary \cite{Heidebrecht20031029}. This makes MCFCs very promising from the application point of view.
\begin{figure}[t]
	\centering
	\includegraphics[width=7cm]{figure2}
	\caption{Schematic illustration of the numerical methods in design concept. }
\end{figure}
\begin{figure*}[h]
\centering
\includegraphics[width=15cm]{figure3}
\caption{Schematic illustration of the {MCFC} manufacturing process. }
\end{figure*}
\begin{figure*}[t]
	\centering
	\includegraphics[width=15cm]{figure4}
	\caption{(a): SEM image of the anode. (b): SEM image of the cathode. (c): 3D micro-CT image of the cathode.
	(d): 3D vector-like model of the cathode microstructure based on micro-CT image. }
\end{figure*}

All the materials for MCFCs are highly porous (open porosity higher than 50\%). The pore size distribution must be strictly controlled due to gas flow and electrolyte infiltration phenomena. Optimization of these two effects require significantly different microstructures, which results in laminate-like concept of electrodes. There must be also a compromise between relatively high gas flow through electrodes and high efficiency of catalytic ractions \cite{decomposition_CO2}. Variety of possible modifications, both at the chemical composition and microstructure side, open up this field for more extensive studies on the application of novel methods of materials characterization and modeling \cite{Structure_foams,CV_poresize}.
In these studies the numerical models of the microstructure of open-porous electrodes for molten carbonate fuel cells (MCFC) are presented. The models presented here simulate real materials fabrication routes including mixing of powders, tape casting and sintering processes. The results of modelling were compared with computed micro-tomography 3D images of real MCFC materials, and further used as a feedback to the fabrication process optimization. Thus, our studies of the materials design combines three fundamental areas of materials science: characterization, modeling and manufacturing. Advances in compuational science over the past few decades have opened the vista of applying numerical methods in each of the areas (see Figure 2), very often creating a logical sequence in the design of specific materials structure and properties \cite{catlow1990computer,catlow2004computer}.

\section{Experimental}
\subsection{Manufacturing}
Fabrication process applied in these studies typically consist of 3 stages. Initially, the mixture of powders (metallic or ceramic) with polymeric binder and other additives (i.e. porogens) is prepared. Then the green tape is produced by tape casting method. In the last stage of the electrodes fabrication green tapes are fired in the reducing atmosphere. Schematic illustration of the manufacturing process is presented in Figure 3.
The initial composition of the slurry, fraction of polymeric phase, size of powders are of key importance for the final structure of the materials for MCFCs. They also decide on rheology of the slurry, which is important from the technological point of view. Sintering process also needs to be optimized since it is found to have significant influence on materials porosity and specific surface.

\subsection{Characterization}
\begin{figure*}[t]
	\centering
	\includegraphics[width=15cm]{figure5}
	\caption{(a): Device for MCFC performance testing. (b): Example of structure-property relationship for MCFC cathodes with different porosity.}
\end{figure*}

Both, structure and properties of materials are characterized to obtain quantitative structure-property relationships \cite{wejrzanowski2008image, wejrzanowski2010stereology}. Scanning electron microscopy (SEM) and X-ray microtomography ($\mu$-CT) are used to analyze the microstructure of MCFC materials (see Figure 4). These methods (direct) are supported by indirect techniques (i.e. Archimedes density measurements, mercury porosimetry, X-ray diffraction) to study the microstructural parameters such as: porosity (volume fraction of pores), pore size distribution, specific surface, connectivity, etc.
Based on micro-CT images the numerical models (both raster-like and vector-like) can be created. Such data is further used for verification of the models, which incorporates simulation of the processes taking place during fabrication of the materials. 
The properties of materials fabricated within these studies are examined in performance test (see Figure 5). For optimization of the single element (i.e. anode) only this material is replaced (i.e. anode) and other kept unchanged. Such procedure enables to eliminate uncertainty caused by the coincidence of various factors and facilitate the design process.

\section{Modelling}

\begin{figure}[t]
\includegraphics[width=7cm]{figure6}
\caption{(a): Generation of spheres with given distribution. (b): Packing. (c): Deleting unwanted spheres. (d): Geometry smoothing.}
\end{figure}
Numerical models of open-porous materials were generated using multi-step algorithm (see Figure 6). In these algorithms the quantitative results of characterization of the substrates used for materials fabrication and final porous structures are used. The data consisting of particle size distribution of substrate powders is utilized to create initial system with polydisperse spheres for MCFC electrodes. Due to the various manufacturing recipes for MCFC anodes and cathodes, different modeling approaches were necessary. For anode, the slurry was based on the mixture of organic solvent with binder, which were the main factors affecting the porosity. In this case, sphere packing implemented as ANSYS APDL script for simulation of the firing process was applied. Generation of spheres and their packing were performed with algorithm proposed in \cite{Modelling_cellular}. After that, data containing coordinates and radii were exported to ANSYS input file. On the basis of this data, the set of spheres was drawn. The porosity was created by iterative removal of randomly selected spheres and their nearest neighbours, until the desired porosity level is reached. Dilatation of remained spheres was applied to create single volume with connections between spheres.
Structural parameters calculated for the models obtained by means of this algorithm and 3D images obtained for real materials (see Figure 4) were compared, which is common method of validation for porous structures \cite{MorenoAtanasio201081}. It was also needed to fit the parameters controlling the generation of structures. The results for anode validation are presented in Table 1. Comparison of simulated models with the real structures has shown that they are sufficiently accurate for predicting structural properties of anodes with different porosities.

\begin{table}
\caption{Fitting of the anode model.}
\label{fit_anoda} \centering

\begin{tabular}{p{2cm}ccc}
\toprule
	& Mean pore & \multirow{2}*{$S_V$} &
	\multirow{2}*{Porosity} \\
	& size & & \\
	& $\mu$m & 1/$\mu$m &  \% \\
	\midrule
	$\mu$CT model & 10.49 & 0.199 & 46.93 \\
	Representative model & 10.67 & 0.212 & 48.05 \\
	\midrule
	Difference & 1.7\% & 6.5\% & 2.4\%
\end{tabular}
\end{table}

For the cathode based on inorganic solvent, porogen particles were used to obtain desired porosity. Thus, another modelling approach was adopted (see Figure 6), in which porogens and binder were considered as an additional small spheres. System of spheres was based on fraction of each component added to the slurry, their density and size distribution. To reflect the thermal decomposition of hydrocarbons, porogen particles and polymeric phase in cathode model were removed during the stage of sphere packing. User defined potentials between spheres with large energy and very small cutoff were simulating sintering of the particles. Geometry smoothing was performed to obtain narrow connections between spheres, namely necks in real materials. 
Models of real MCFC cathode materials were created, basing on slurry recipes containing respectively 2, 4, 6 and 8g of porogen addition. Similarly to anode, the structures were validated in comparison with $\mu$CT images. Results of porosity and mean pore size validation after fitting of structure generation parameters are presented in Figures 7 and 8. Discrepancy associated with the model did not exceeded 10$\%$ for all specimens. In the light of this fact we can conclude that our methodology enables to model structures based on real slurry mixtures and manufacturing process, which can be invaluable to further optimization of the MCFC cathode material. 

\begin{figure}[h]
	\centering
	\includegraphics[width=7cm]{figure7}
	\caption{Validation of porosity for cathode model.}
	\includegraphics[width=7cm]{figure8}
	\caption{Validation of mean pore size for cathode model.}
\end{figure}

\section{Summary}
In these studies the concept has been applied, where three fundamental areas of materials science: characterization, modeling and manufacturing are used to design materials for MCFC. It had been proved that this methodology can be applied to create representative models of porous materials fabricated by tape casting method, where slurry composed of particles suspended in polymer-based mixtures is first casted and then annealed. Tailoring of wide spectrum of the structure parameters of porous materials enables to design materials for application in catalysis and in particular as the electrode materials in Molten Carbonate Fuel Cells.

\section*{Acknowledgements}
This work was supported by the National Centre for Research and Development in the frames of Applied Research Programme (Grant No. PBS3/B2/24/2015)

\section*{References}
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