Ralf Thiedmann

The effect of three-dimensional morphology on the efficiency of hybrid polymer solar cells

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.

Local Structural Characteristics of Pore Space in GDLs of PEM Fuel Cells Based on Geometric 3D Graphs

Physical properties affecting transport processes inside the gas diffusion layer (GDL) in polymer electrolyte membrane (PEM) fu cells mainly depend on the microstructure of its pore space. The presented characterization of the complex structure of the po space is based on geometric three-dimensional (3D) graphs, which are marked to display transport-related properties such as po diameters. This representation of the open volume allows for an investigation of local structural characteristics by considering local tortuosity characteristics, pore sizes, and connectivity characteristics, respectively. The notion of local shortest path leng 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 ratio of the mean effective path length through the GDL and i thickness. The developed methods are applied to simulated and to real (experimentally measured) 3D data. The used stochastic 3 model for the GDL is an extended version of the multilayer model proposed by Thiedmann et al. [J. Electrochem. Soc., 155, B39 (2008)], including a more flexible modeling of binder. The numerical results show the sensitivity of the proposed local chara teristics to varying binder modeling.

Stochastic 3D Modeling of the GDL Structure in PEMFCs Based on Thin Section Detection

We propose a mathematical model to describe the microstructure of the gas diffusion layer (GDL) in proton exchange membrane fuel cells (PEMFCs) 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 (2D)] 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.

Spatial modeling of the 3D morphology of hybrid polymer-ZnO solar cells, based on electron tomography data

A spatial stochastic model is developed which describes the 3D nanomorphology of composite materials, being blends of two different (organic and inorganic) solid phases. Such materials are used, for example, in photoactive layers of hybrid polymer zinc oxide solar cells. The model is based on ideas from stochastic geometry and spatial statistics. Its parameters are fitted to image data gained by electron tomography (ET), where adaptive thresholding and stochastic segmentation have been used to represent morphological features of the considered ET data by unions of overlapping spheres. Their midpoints are modeled by a stack of 2D point processes with a suitably chosen correlation structure, whereas a moving-average procedure is used to add the radii of spheres. The model is validated by comparing physically relevant characteristics of real and simulated data, like the efficiency of exciton quenching, which is important for the generation of charges and their transport toward the electrodes.

Comparison of Network Trees in Deterministic and Random Settings using Different Connection Rules

We examine the spatial distribution of network trees, i.e., shortest paths between network devices of different hierarchical levels placed randomly along an underlying infrastructure system. In particular, based on a simulation approach, we analyze the distributional behavior of the network trees obtained through two alternative connection rules. Moreover, we validate by visual comparison that the distributions of these network trees can be regarded as rather similar both in the case where the underlying infrastructure system is based on real road data and in the case where this system is based on a random tessellation model fitted to the real road data. Our study demonstrates that modeling telecommunication networks and the associated mobility along the infrastructure by usage of methods and models from stochastic geometry is feasible from the engineering point of view.

Strukturelle Analyse des Porenraumes von Gasdiffusionslagen in Brennstoffzellen mittels geometrischer 3-D-Graphen

Kurzfassung Eine wichtige Komponente von Polymer-Elektrolyt-Membran-Brennstoffzellen (PEMFC) ist die Gasdiffusionslage (GDL). Sie ist, unter anderem, für die Versorgung der Elektrode mit Reaktionsgasen sowie den Abtransport des entstehenden Wassers verantwortlich. Um einen optimalen Wirkungsgrad der Brennstoffzelle erzielen zu können und eine vorzeitige Alterung zu verhindern, ist eine konstante und gleichmäßige Versorgung der Elektrode mit Reaktionsgasen erforderlich. Dazu muss vor allem sichergestellt werden, dass das bei der Reaktion entstehende Wasser abtransportiert wird, um den Gastransport nicht zu behindern. Um diese Stofftransportprozesse, die im Porenraum der GDL stattfinden, besser verstehen zu können, untersuchen wir in der vorliegenden Arbeit die Struktur des Porenraumes basierend auf einer Graphen-Darstellung. Diese Darstellung des Porenraumes gewinnen wir aus 3-D Synchrotron-Daten mit Hilfe einer Skelettierung. In der vorliegenden Arbeit werden wir damit die Porenräume von zwei verschiedenen Typen von GDL (Papier-Typ und Vlies-Typ) strukturell untersuchen und deren Unterschiede quantitativ beschreiben.

Micro-Scale Transport in the Diffusion Media of Polymer Electrolyte Fuel Cells

This paper reports our recent work on the stochastic-model-based reconstruction of the gas diffusion layer (GDL) of PEFCs and direct numerical simulation and presented the pore-level transport within GDLs of polymer electrolyte fuel cell (PEFC). The carbon-paper-based GDL is modeled as a stack of thin sections with each section described by planar 2D random line tessellations which are further dilated to three dimensions. The reconstruction of the GDL structure is based on given GDL data provided by scanning electron microscopy (SEM) images. Based on the stochastically constructed digital GDL, we further conduct the DNS of the coupled transport processes, including gas flow and species transport, electronic current conduction, and heat transfer. Results indicate remarkable distinction in tortuosities of gas diffusion passage and solid matrix. The numerical tool can be applied to investigate the GDL microstructure and internal pore-level transport in PEFCs.Copyright