Empirical relationships between effective conductivities in porous and composite materials and their geometric characteristics such as volume fraction e, tortuosity s and constrictivity b are established. (simplified formula) with intrinsic conductivity r 0 , geodesic tortuosity s geod and relative prediction errors of 19% and 18%, respectively. We critically analyze the methodologies used to determine tortuosity and constrictivity. Comparing geometric tortuosity and geodesic tortuosity, our results indicate that geometric tortuosity has a tendency to overestimate the windedness of transport paths. Analyzing various definitions of constrictivity, we find that the established definition describes the effect of bottlenecks well. In summary, the established relationships are important for a purposeful optimization of materials with specific transport properties, such as porous electrodes in fuel cells and batteries.

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.

We develop a stochastic network model for charge transport simulations in amorphous organic semiconductors, which generalizes the correlated Gaussian disorder model to realistic morphologies, charge transfer rates, and site energies. The network model includes an iterative dominancecompetition model for positioning vertices (hopping sites) in space, distance-dependent distributions for the vertex connectivity and electronic coupling elements, and a moving-average procedure for assigning spatially correlated site energies. The field dependence of the hole mobility of the amorphous organic semiconductor, tris-(8-hydroxyquinoline)aluminum, which was calculated using the stochastic network model, showed good quantitative agreement with the prediction based on a microscopic approach.

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Simulations of organic semiconducting devices using drift-diffusion equations are vital for the understanding of their functionality as well as for the optimization of their performance. Input parameters for these equations are usually determined from experiments and do not provide a direct link to the chemical structures and material morphology. Here we demonstrate how such a parametrization can be performed by using atomic-scale (microscopic) simulations. To do this, a stochastic network model, parametrized on atomistic simulations, is used to tabulate charge mobility in a wide density range. After accounting for finite-size effects at small charge densities, the data is fitted to the uncorrelated and correlated extended Gaussian disorder models. Surprisingly, the uncorrelated model reproduces the results of microscopic simulations better than the correlated one, compensating for spatial correlations present in a microscopic system by a large lattice constant. The proposed method retains the link to the material morphology and the underlying chemistry and can be used to formulate structure-property relationships or optimize devices prior to compound synthesis.

The analysis of big data is changing industries, businesses and research as large amounts of data are available nowadays. In the area of microstructures, acquisition of (3-D tomographic image) data is difficult and time-consuming. It is shown that large amounts of data representing the geometry of virtual, but realistic 3-D microstructures can be generated using stochastic microstructure modeling. Combining the model output with physical simulations and data mining techniques, microstructure-property relationships can be quantitatively characterized. Exemplarily, we aim to predict effective conductivities given the microstructure characteristics volume fraction, mean geodesic tortuosity, and constrictivity. Therefore, we analyze 8119 microstructures generated by two different stochastic 3-D microstructure models. This is-to the best of our knowledge-by far the largest set of microstructures that has ever been analyzed. Fitting artificial neural networks, random forests and classical equations, the prediction of effective conductivities based on geometric microstructure characteristics is possible.

Battery technology plays an important role in energy storage. In particular, lithiumion (Li-ion) batteries are of great interest, because of their high capacity, long cycle life, and high energy and power density. However, for further improvements of Li-ion batteries, a deeper understanding of physical processes occurring within this type of battery, including transport, is needed. To provide a detailed description of these phenomena, a 3D representation is required for the morphology of composite materials used in Li-ion batteries. In this paper, we develop a stochastic simulation model in 3D, which is based on random marked point processes, to reconstruct real and generate virtual morphologies. For this purpose, a statistical technique to fit the model to 3D image data gained by X-ray tomography is developed. Finally, we validate the model by comparing real and simulated data using image characteristics which are especially relevant with respect to transport properties.

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