Thin inclusion approach for modelling of heterogeneous conducting materials

Experimental data show that heterogeneous nanostructure of solid oxide and polymer electrolyte fuel cells could be approximated as an infinite set of fiber-like or penny-shaped inclusions in a continuous medium. Inclusions can be arranged in a cluster mode and regular or random order. In the newly proposed theoretical model of nanostructured material, the most attention is paid to the small aspect ratio of structural elements as well as to some model problems of electrostatics. The proposed integral equation for electric potential caused by the charge distributed over the single circular or elliptic cylindrical conductor of finite length, as a single unit of a nanostructured material, has been asymptotically simplified for the small aspect ratio and solved numerically. The result demonstrates that surface density changes slightly in the middle part of the thin domain and has boundary layers localized near the edges. It is anticipated, that contribution of boundary layer solution to the surface density is significant and cannot be governed by classic equation for smooth linear charge. The role of the cross-section shape is also investigated. Proposed approach is sufficiently simple, robust and allows extension to either regular or irregular system of various inclusions. This approach can be used for the development of the system of conducting inclusions, which are commonly present in nanostructured materials used for solid oxide and polymer electrolyte fuel cell (PEMFC) materials.