Stochastic 3D Models for the Micro-structure of Advanced Functional Materials

Abstract

Optimization of functional materials is a challenging task. Thereby, stochastic morphology models can provide helpful methods. Three classes of stochastic models are presented describing different micro-structures of functional materials by means of methods from stochastic geometry, graph theory and time series analysis. The structures of these materials strongly differ from each other, where we consider organic solar cells being an anisotropic composite of two materials, nonwoven gas-diffusion layers in proton exchange membrane fuel cells consisting of a system of curved carbon fibers, and graphite electrodes in Li-ion batteries which are built up by an isotropic two-phase system (i.e., consisting of a pore and a solid phase). The goal is to give an overview how the stochastic modeling of functional materials can be organized and to provide an outlook how these models can be used for material optimization with respect to functionality.