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Advances in Materials Science and Engineering
Volume 2014 (2014), Article ID 562874, 16 pages
Review Article

Geometric Models for Isotropic Random Porous Media: A Review

1Institute for Solid State and Materials Research, IFW Dresden, P.O. Box 270116, 01171 Dresden, Germany
2Institute for Informatics, TU Dresden, 01062 Dresden, Germany

Received 9 October 2013; Accepted 26 February 2014; Published 30 April 2014

Academic Editor: Thomas Hipke

Copyright © 2014 Helmut Hermann and Antje Elsner. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Models for random porous media are considered. The models are isotropic both from the local and the macroscopic point of view; that is, the pores have spherical shape or their surface shows piecewise spherical curvature, and there is no macroscopic gradient of any geometrical feature. Both closed-pore and open-pore systems are discussed. The Poisson grain model, the model of hard spheres packing, and the penetrable sphere model are used; variable size distribution of the pores is included. A parameter is introduced which controls the degree of open-porosity. Besides systems built up by a single solid phase, models for porous media with the internal surface coated by a second phase are treated. Volume fraction, surface area, and correlation functions are given explicitly where applicable; otherwise numerical methods for determination are described. Effective medium theory is applied to calculate physical properties for the models such as isotropic elastic moduli, thermal and electrical conductivity, and static dielectric constant. The methods presented are exemplified by applications: small-angle scattering of systems showing fractal-like behavior in limited ranges of linear dimension, optimization of nanoporous insulating materials, and improvement of properties of open-pore systems by atomic layer deposition of a second phase on the internal surface.