Materials containing nanoparticles or -tubes, provide many interesting properties for modern applications. For proton exchange membrane fuel cells (PEMFCs), titanoxid-nanotubes (TNT), embedded in a matrix material, are a promising candidate for aging-resistant electrodes. Thus, there is an urgent demand to characterize these novel materials to optimize their performance. However, experimental methods are often not sufficient to investigate the influence of nanotube parameters on the behavior of the overall material. We propose a combination of statistical and numerical simulation to close this gap to achieve a detailed understanding of the material properties, e.g. fill factor or average segment length. Random walk algorithms can generate nanotube networks, that consist of a cluster of bent tubes. These networks are defined by macroscopic properties such as electrical conductivity, which can be investigated in experiments.

The numerical simulation of these networks is a challenging task. On the one hand, the diameter of the tubes is only a few tens of nanometers and on the other hand, the overall simulation domain can extend over a few micrometers. These types of multi-scale FEM simulations are costly in terms of computing time. However, the symmetry of unit cells, which accurately represent larger domains, can be exploited to reduce the simulation time, while achieving reliable results. In this research, we present a random walk algorithm generating bent nanotube networks of a defined size, which can then form unit cells for larger structures. We investigate how the volume of the unit cell and tube parameters influence the usability of the unit cell to represent a larger volume. Eventually, the approach is used to determine the probability of a percolation path for relevant dimensions of PEMFC electrodes.