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Condensation capillaire et transitions hors d'équilibre dans les milieux poreux désordonnés : l'exemple des aérogels de silice.

Abstract : This work aims at the theoretical understanding of adsorption phenomena in silica aerogels. In spite of their very high porosity, the aerogels dramatically affect the properties of the adsorbed fluid. The out-of-equilibrium character of the system manifests itself in the hysteresis behaviour of the adsorption isotherms. Several experimental groups have shown the remarkable influence of porosity and temperature on the shape of the hysteresis loop. Neither the traditional approach to capillary condensation in disordered mesoporous solids nor the equilibrium properties of the random field Ising model (RFIM) can rationalize these results.

Our modeling fully takes into account the disordered and out-of-equilibrium character of the fluid-aerogel system. The fluid is described by a lattice gas and the aerogel structure is generated by a diffusion-limited cluster-cluster aggregation algorithm (DLCA). The coarse-grained character of our description enables the study of collective phenomena occuring on length scales beyond the cavities of the aerogel. The model is treated within a local mean-field theory, which defines a grand potentiel landscape. As suggested by experiments, activated processes are negligible, and the system evolves in the landscape according to a zero temperature dynamics, changing only when an external parameter (chemical potentiel) is varied.

This modeling gives insight into the nature of adsorption phenomena. At low enough temperature, the disorder due to the aerogel induces a complex grand potentiel landscape, with a large number of metastable states. The system evolves in this landscape by a series of avalanches, which are irreversible, usually microscopic, condensation or evaporation events. This avalanche dynamics in a complex landscape is at the origin of hysteresis. The shape of the hysteresis loop depends on the mechanism at work; these mechanisms are different on adsorption and desorption and change with temperature and porosity. In particular, we find out-of-equilibrium phase transitions similar to those observed in the RFIM at zero temperature. On adsorption, the isotherm is either continuous, if all avalanches are microscopic, or discontinuous, if there is a macroscopic avalanche ; those two regimes are separated by a critical line corresponding to the \og avalanche transition\fg. Desorption can occur through three distinct mechanisms: the first one is cavitation, the other are phase transitions involving the interface between the adsorbed fluid and the gaz reservoir: invasion percolation and depinning transition. We find that it is most often difficult to relate the characteristics of the isotherms to the structure of the aerogel.

In the final part of this work, we study the link between metastability and hysteresis, taking the exemple of the RFIM on a Bethe lattice at zero temperature. Using analytical computation, we show how the hysteresis loop relates to the distribution of metastable states in the magnetization-magnetic field plane.
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Contributor : François Detcheverry <>
Submitted on : Sunday, December 18, 2005 - 1:03:31 AM
Last modification on : Tuesday, December 8, 2020 - 3:44:59 AM
Long-term archiving on: : Friday, September 14, 2012 - 4:35:11 PM



  • HAL Id : tel-00011232, version 1


François Detcheverry. Condensation capillaire et transitions hors d'équilibre dans les milieux poreux désordonnés : l'exemple des aérogels de silice.. Analyse de données, Statistiques et Probabilités []. Université Pierre et Marie Curie - Paris VI, 2005. Français. ⟨tel-00011232⟩



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