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Journal of Materials Science

, Volume 46, Issue 24, pp 7745–7759 | Cite as

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

  • Ralf Thiedmann
  • Ingo Manke
  • Werner Lehnert
  • Volker Schmidt
Article

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.

Keywords

Markov Chain Monte Carlo Minimum Span Tree Vertex Degree Markov Chain Monte Carlo Simulation Marked Point Process 

Notes

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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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Ralf Thiedmann
    • 1
  • Ingo Manke
    • 2
  • Werner Lehnert
    • 3
  • Volker Schmidt
    • 1
  1. 1.Ulm UniversityUlmGermany
  2. 2.Helmholtz-Zentrum Berlin für Energie und MaterialienBerlinGermany
  3. 3.Forschungszentrum Jülich GmbHJülichGermany

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