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Random geometric graphs for modelling the pore space of fibre-based materials

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Abstract

A stochastic network model is developed which describes the 3D morphology of the pore space in fibre-based materials. It has the form of a random geometric graph, where the vertex set is modelled by random point processes and the edges are put using tools from graph theory and Markov chain Monte Carlo simulation. The model parameters are fitted to real image data gained by X-ray synchrotron tomography. In particular, they are specified in such a way that the distributions of vertex degrees and edge lengths, respectively, coincide to a large extent for real and simulated data. Furthermore, the network model is used to introduce a morphology-based notion of pores and their sizes. The model is validated by considering physical characteristics which are relevant for transport processes in the pore space, like geometric tortuosity, i.e., the distribution of shortest path lengths through the material relative to its thickness.

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Acknowledgements

This research has been supported by the German Federal Ministry for Education and Science (BMBF) under Grant No. 03SF0324C/E/F.

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Authors and Affiliations

  1. Ulm University, 89069, Ulm, Germany

    Ralf Thiedmann & Volker Schmidt

  2. Helmholtz-Zentrum Berlin für Energie und Materialien, 14109, Berlin, Germany

    Ingo Manke

  3. Forschungszentrum Jülich GmbH, 52425, Jülich, Germany

    Werner Lehnert

Authors
  1. Ralf Thiedmann
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  2. Ingo Manke
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  3. Werner Lehnert
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  4. Volker Schmidt
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Correspondence to Ralf Thiedmann.

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Thiedmann, R., Manke, I., Lehnert, W. et al. Random geometric graphs for modelling the pore space of fibre-based materials. J Mater Sci 46, 7745–7759 (2011). https://doi.org/10.1007/s10853-011-5754-7

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  • DOI: https://doi.org/10.1007/s10853-011-5754-7

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