The efficiency of polymer solar cells critically depends on the intimacy of mixing of the donor and acceptor semiconductors used in these devices to create charges and on the presence of unhindered percolation pathways in the individual components to transport holes and electrons. The visualization of these bulk heterojunction morphologies in three dimensions has been challenging and has hampered progress in this area. Here, we spatially resolve the morphology of 2%-efficient hybrid solar cells consisting of poly(3-hexylthiophene) as the donor and ZnO as the acceptor in the nanometre range by electron tomography. The morphology is statistically analysed for spherical contact distance and percolation pathways. Together with solving the three-dimensional exciton-diffusion equation, a consistent and quantitative correlation between solar-cell performance, photophysical data and the three-dimensional morphology has been obtained for devices with different layer thicknesses that enables differentiating between generation and transport as limiting factors to performance.

We propose a mathematical model to describe the microstructure of the gas diffusion layer ͑GDL͒ in proton exchange membrane fuel cells ͑PEMFCs͒ based on tools from stochastic geometry. The GDL is considered as a stack of thin sections. This assumption is motivated by the production process and the visual appearance of relevant microscopic images. The thin sections are modeled as planar ͓two-dimensional ͑2D͔͒ random line tessellations which are dilated with respect to three dimensions. Our 3D model for the GDL consists of several layers of these dilated line tessellations. We also describe a method to fit the proposed model to given GDL data provided by scanning electron microscopy images which can be seen as 2D projections of the 3D morphology. In connection with this, we develop an algorithm for the segmentation of such images which is necessary to obtain the required structural information from the given grayscale images.

The efficiency of polymer – metal oxide hybrid solar cells depends critically on the intimacy of mixing of the two semiconductors. The effect of side chain functionalization on the morphology and performance of conjugated polymer:ZnO solar cells is investigated. Using an ester‐functionalized side chain poly(3‐hexylthiophene‐2,5‐diyl) derivative (P3HT‐E), the nanoscale morphology of ZnO:polymer solar cells is significantly more intimately mixed compared to ZnO:poly(3‐hexylthiophene‐2,5‐diyl) (ZnO:P3HT), as evidenced experimentally from a 3D reconstruction of the phase separation using electron tomography. Photoinduced absorption reveals nearly quantitative charge generation for the ZnO:P3HT‐E blend but not for ZnO:P3HT, consistent with the results obtained from solving the 3D diffusion equation for excitons formed in the polymer within the two experimental ZnO morphologies. For thin ZnO:P3HT‐E active layers (∼50 nm) this yields a significant improvement of the solar cell performance. For thicker cells, however, the reduced hole mobility and a reduced percolation of ZnO pathways hinders charge carrier collection, limiting the power conversion efficiency.

Physical properties affecting transport processes inside the gas diffusion layer (GDL) in fuel cells mainly depend on the microscopic structure of its pore space. The presented characterization of the pore space is based on geometric 3D graphs, representing the complex microscopic structure. This description of the open volume contains the essential information on the geometrical structure of the pore space such as its connectivity. Additionally, the geometric structure of the graph, i.e., its vertices and edges, can be marked to display transport related properties such as pore diameters and pore necks. This 3D graph representation allows for an investigation of the local structural characteristics of the GDL by considering local tortuosity characteristics, pore sizes, and connectivity characteristics, respectively. The notion of a local shortest path length through the pore space of the GDL is introduced and the probability distribution of this random variable is computed. Its mean value is related to the (physical) tortuosity which is given by the * Corresponding author: w.lehnert@fz-juelich.de; Electrochemical society active member

A stochastic multi-layer model is developed describing the microstructure of materials which are built up of strongly curved, but almost horizontally oriented fibers. This fully parametrized model is based on ideas from stochastic geometry and multivariate time series analysis. It consists of independent layers which are stacked together, where each single layer is described by a 2D germ-grain model dilated in 3D. The germs form a Poisson point process and the grains are given by random polygonal tracks describing single fibers in terms of multivariate time series. Exemplarily, on the basis of 2D data from SEM images, the parameters of the multi-layer model are fitted to the microstructure of a non-woven material which is used for gas-diffusion layers in PEM fuel cells. Therefore, an algorithm is presented which automatically extracts typical fiber courses from SEM images. Finally, the multi-layer model is validated by comparing structural characteristics computed for 3D data gained by synchrotron tomography from the same material, and for realizations drawn from the multi-layer model.