Characterization and modeling of nanoporous carbon structures

The aim of the work presented here is to optimize nanoporous carbon materials by means of 'virtual material design'. On this length scale (ca. 10nm) Focused Ion Beam - Scanning Electron Microscopy Nanotomography (FIB-SEM) is the only imaging technique providing three-dimensional geometric information. Yet, for the optimization, the pore space of the materials must be reconstructed from the resulting image data, which was a generally unsolved problem so far. To overcome this problem, a simulation method for FIB-SEM images was developed. The resulting synthetic FIB-SEM images could then be used to test and validate segmentation algorithms. Using simulated image data, a new algorithm for the morphological segmentation of the highly porous structures from FIB-SEM data was developed , enabling the reconstruction of the three-dimensional pore space from FIB-SEM images. Two case studies with nanoporous carbons used for energy storage are presented, using the new techniques for the characterization and optimization of electrodes of Li-ion batteries and electric double layer capacitors (EDLC's), respectively. The reconstructed pore space is modeled geometrically by means of stochastic geometry. Finally, the electrical properties of the materials were simulated using both imaged real and modeled structures. In the first part of the thesis, a novel simulation program for FIB-SEM nanotomography is described. The program can, for the first time, generate completely artificial FIB-SEM tomographic images of highly porous materials, described by Boolean models of spheres or cylinders. The computation of which, using standard methods, would have taken weeks, even on high-performance machines. To this end, new acceleration techniques were developed and combined with existing techniques, reducing the simulation time by several orders of magnitude, without loss of physical accuracy. Results of simulated FIB-SEM nanotomograms of highly complex structures are presented, consisting of more than one hundred 2D images. In the second part, a new segmentation algorithm for FIB-SEM data is presented, enabling the reconstruction of the three-dimensional structure of highly porous materials, imaged by FIB-SEM nanotomography. The new method uses mathematical morphology, and is shown to be the best performing documented in literature so far. For the first time, simulated FIB-SEM data has been used to verify the correctness of the new method. In two case studies, the geometric structure of a nanoporous additive for Li-ion battery electrodes and nanoporous carbon electrodes for electric double layer capacitors (EDLC's) are reconstructed. The optimization of porous materials requires virtual representations of their pore space. This is achieved by using models from stochastic geometry, as described in the third part of the thesis. Virtual models are described, representing the nanoporous additive as well as the EDLC electrodes. The additive is modeled by level sets of a Gaussian random field, while for the EDLC electrodes a modified version of the Boolean model of spheres has been used. The modified Boolean model has been fitted to the observed structure by means of simulating realizations of the model and minimizing a similarity measure using stochastic optimization. The models, fitted to the reconstructed pore spaces of both materials, show good agreement. In the final part of the thesis, electrical properties of the electrodes made from the nanoporous carbons are predicted using physical simulations. For Lithium-Ion batteries, the in influence of the nanoporous carbon on the charging behavior is investigated using simulations. A multi-scale model is employed using the segmented FIB-SEM and synchrotron radiation computed tomography data. This establishes for the first time a multi-scale process for simulations, combining both experimental techniques. The additive is homogenized on the nanoscale and inserted as an effective medium into the microscale electrode. It is found, that the additive has a non negligible in influence on the charging behavior. Multi-scale simulations are also used to investigate the electrical behavior of nanoporous carbon electrodes for EDLC's. To this end, the effective resistivities and capacitances of the electrodes are computed using the segmented FIB-SEM data sets. Then, a macro- homogeneous model is fitted to a measured electric impedance spectrum of one of the samples, using the computed effective properties. Finally, the microscale simulations are performed on model realizations with a given parameter range. This enables us to optimize the resistance and the capacitance of the electrode.