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Research Papers

# HeteroFoaMs: Electrode Modeling in Nanostructured Heterogeneous Materials for Energy Systems

[+] Author and Article Information
W. K. S. Chiu1

Department of Mechanical Engineering,  University of Connecticut, Storrs, CT 06269-3139

A. V. Virkar, F. Zhao

Department of Materials Science and Engineering,  University of Utah, Salt Lake City, UT 84112

K. L. Reifsnider

HeteroFoaM Center, Department of Mechanical Engineering,  University of South Carolina, Columbia, SC 29208

G. J. Nelson

Department of Mechanical Engineering,  University of Connecticut, Storrs, CT 06269-3139

F. Rabbi, Q. Liu

HeteroFoaM Center, Department of Mechanical Engineering,  University of South Carolina, Columbia, SC 29208

1

Corresponding author: wchiu@engr.uconn.edu

J. Fuel Cell Sci. Technol 9(1), 011019 (Dec 27, 2011) (6 pages) doi:10.1115/1.4005142 History: Received September 07, 2011; Revised September 18, 2011; Published December 27, 2011; Online December 27, 2011

## Abstract

Heterogeneous functional materials, e.g., “HeteroFoaMs” are at the heart of countless energy systems, including heat storage materials, batteries, solid oxide fuel cells, and polymer electrolyte fuel cells. HeteroFoaMs are generally nanostructured and porous to accommodate transport of gasses or fluids, and must be multifunctional (i.e., active operators on mass, momentum, energy, or charge, in combinations). This paper will discuss several aspects of modeling the relationships between the constituents and microstructure of these material systems and their device functionalities. Technical advances based on these relationships will also be identified and discussed. Three major elements of the general problem of how to model HeteroFoaM electrodes will be addressed. Modeling approaches for ionic charge transfer with electrochemistry in the nanostructured porosity of the electrode will be discussed. Second, the effect of morphology and space charge on conduction through porous doped ceria particle assemblies, and their role in electrode processes will be modeled and described. And third, the effect of local heterogeneity and morphology on charge distributions and polarization in porous dielectric electrode materials will be analyzed using multiphysics field equations set on the details of local morphology. Several new analysis methods and results, as well as experimental data relating to these approaches will be presented. The value, capabilities, and limitations of the approaches will be evaluated.

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## Figures

Figure 1

Charge transfer (1/Rpol ) in variable cross-section pin fin structures with periodic structure geometries, where fins are prescribed a base radius (rbase ), tip radius (rtip ), ionic resistivity (ρ), and charge transfer resistance (Rct ). Electrochemical fin modeling predictions (curves) were validated to experimental results (symbols) from Kenjo [2] for well sintered and poorly sintered electrodes.

Figure 2

Fin efficiency defined in [1] as a function of ionic resistivity ratio for the geometries investigated for various SOFC electrode materials. The well sintered and poorly sintered lines correspond to the geometries shown in Fig. 1 (well sintered: rtip  = 1.85 μm; poorly sintered: rtip  = 0.15 μm). Results indicate that surface area gains may increase charge transfer, but a trade-off exists in balancing ohmic losses incurred by constrictions in the microstructure for specific SOFC electrode materials.

Figure 3

An idealized composite cathode showing the distributed nature of the electrochemical reaction. Ionic conduction through the solid portion of the porous regions has a major effect on the polarization resistance. Space charge effects dominate transport across the boundaries and also influence the polarization resistance.

Figure 4

The effective resistivity is high for small grains and narrow necks, and small for large grains and wide necks

Figure 5

Polarization resistance as a function morphology and space charge. Note that the polarization resistance is high at large grain and small necks; and small at small grains and large necks.

Figure 6

Cage points

Figure 7

Two conductor particles with imposed voltage: (a) exact potential distribution Vexact and (b) numerical error: Vexact – Vcomp

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