We study water adsorption-induced deformation of a monolithic, mesoporous silicon membrane traversed by independent channels of ∼8 nm diameter. We focus on the elastic constant associated with the Laplace pressure-induced deformation of the membrane upon capillary condensation, i.e., the pore-load modulus. We perform finite-element method (FEM) simulations of the adsorption-induced deformation of hexagonal and square lattices of cylindrical pores representing the membrane. We find that the pore-load modulus weakly depends on the geometrical arrangement of pores, and can be expressed as a function of porosity. We propose an analytical model which relates the pore-load modulus to the porosity and to the elastic properties of bulk silicon (Young's modulus and Poisson's ratio), and provides an excellent agreement with FEM results. We find good agreement between our experimental data and the predictions of the analytical model, with the Young's modulus of the pore walls slightly lower than the bulk value. This model is applicable to a large class of materials with morphologies similar to mesoporous silicon. Moreover, our findings suggest that liquid condensation experiments allow one to elegantly access the elastic constants of a mesoporous medium.
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29 June 2015
Research Article|
June 29 2015
Elastic response of mesoporous silicon to capillary pressures in the pores
Gennady Y. Gor;
Gennady Y. Gor
a)
1NRC Research Associate, resident at Center for Computational Materials Science,
Naval Research Laboratory
, Washington, DC 20375, USA
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Luca Bertinetti;
Luca Bertinetti
2Department of Biomaterials, Max-Planck Institute of Colloids and Interfaces,
Research Campus Golm
, 14424 Potsdam, Germany
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Noam Bernstein;
Noam Bernstein
3Center for Computational Materials Science,
Naval Research Laboratory
, Washington, DC 20375, USA
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Tommy Hofmann;
Tommy Hofmann
4
Helmholtz-Centre Berlin for Materials and Energy
, D-14109 Berlin, Germany
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Peter Fratzl;
Peter Fratzl
2Department of Biomaterials, Max-Planck Institute of Colloids and Interfaces,
Research Campus Golm
, 14424 Potsdam, Germany
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Patrick Huber
Patrick Huber
2Department of Biomaterials, Max-Planck Institute of Colloids and Interfaces,
Research Campus Golm
, 14424 Potsdam, Germany
5Institute of Materials Physics and Technology,
Hamburg University of Technology (TUHH)
, Eißendorfer Str. 42, D-21073 Hamburg-Harburg, Germany
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Appl. Phys. Lett. 106, 261901 (2015)
Article history
Received:
April 23 2015
Accepted:
June 16 2015
Citation
Gennady Y. Gor, Luca Bertinetti, Noam Bernstein, Tommy Hofmann, Peter Fratzl, Patrick Huber; Elastic response of mesoporous silicon to capillary pressures in the pores. Appl. Phys. Lett. 29 June 2015; 106 (26): 261901. https://doi.org/10.1063/1.4923240
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