Scattering signatures of invasion percolation.

Motivated by recent experiments, we investigate the scattering properties of percolation clusters generated by numerical simulations on a three-dimensional cubic lattice. Individual clusters of given size are shown to present a fractal structure up to a scale of order of their extent, even far away from the percolation threshold p_{c}. The influence of intercluster correlations on the structure factor of assemblies of clusters selected by an invasion phenomenon is studied in detail. For invasion from bulk germs, we show that the scattering properties are determined by three length scales, the correlation length ξ, the average distance between germs d_{g}, and the spatial scale probed by scattering, set by the inverse of the scattering wave vector Q. At small scales, we find that the fractal structure of individual clusters is retained, the structure factor decaying as Q^{-d_{f}}. At large scales, the structure factor tends to a limit, set by the smaller of ξ and d_{g}, both below and above p_{c}. We propose approximate expressions reproducing the simulated structure factor for arbitrary ξ, d_{g}, and Q, and illustrate how they can be used to avoid to resort to costly numerical simulations. For invasion from surfaces, we find that, at p_{c}, the structure factor behaves as Q^{-d_{f}} at all Q, i.e., the fractal structure is retained at arbitrarily large scales. Results away from p_{c} are compared to the case of bulk germs. Our results can be applied to discuss light or neutrons scattering experiments on percolating systems. This is illustrated in the context of evaporation from porous materials.

Evaporation Process in Porous Silicon: Cavitation vs Pore Blocking.

We measured sorption isotherms for helium and nitrogen in wide temperature ranges and for a series of porous silicon samples, both native samples and samples with reduced pore mouth, so that the pores have an ink-bottle shape. Combining volumetric measurements and sensitive optical techniques, we show that, at a high temperature, homogeneous cavitation is the relevant evaporation mechanism for all samples. At a low temperature, the evaporation is controlled by meniscus recession, the detailed mechanism being dependent on the pore length and mouth reduction. Native samples and samples with ink-bottle pores shorter than 1 µm behave as an array of independent pores. In contrast, samples with long ink-bottle pores exhibit long-range correlations between pores. In this latter case, evaporation takes place by a collective percolation process and not by heterogeneous cavitation as previously proposed. The variety of evaporation mechanisms points to porous silicon being an anisotropic three-dimensional pore network rather than an array of straight independent pores.

On Condensation and Evaporation Mechanisms in Disordered Porous Materials.

Sorption isotherm measurement is a standard method for characterizing porous materials. However, such isotherms are generally hysteretic, differing between condensation and evaporation. Quantitative measurement of pore diameter distributions requires proper identification of the mechanisms at play, a topic which has been and remains the subject of intensive studies. In this paper, we compare high-precision measurements of condensation and evaporation of helium in Vycor, a prototypical disordered porous glass, to a model incorporating mechanisms on the single pore level through a semimacroscopic description and collective effects through lattice simulations. Our experiment determines both the average of the fluid density through volumetric measurements and its spatial fluctuations through light scattering. We show that the model consistently accounts for the temperature dependence of the isotherm shape and of the optical signal over a wide temperature range as well as for the existence of thermally activated relaxation effects. This demonstrates that the evaporation mechanism evolves from pure invasion percolation from the sample's surfaces at the lowest temperature to percolation from bulk cavitated sites at larger temperatures. The model also shows that the experimental lack of optical signals during condensation does not imply that condensation is unaffected by network effects. In fact, these effects are strong enough to make most pores to fill at their equilibrium pressure, a situation deeply contrasting the behavior for isolated pores. This implies that, for disordered porous materials, the classical Barrett-Joyner-Halenda approach, when applied to the condensation branch using an extended version of the Kelvin equation, should properly measure the true pore diameter distribution. Our experimental results support this conclusion.

Condensation of helium in aerogel and athermal dynamics of the random-field Ising model.

High resolution measurements reveal that condensation isotherms of (4)He in high porosity silica aerogel become discontinuous below a critical temperature. We show that this behavior does not correspond to an equilibrium phase transition modified by the disorder induced by the aerogel structure, but to the disorder-driven critical point predicted for the athermal out-of-equilibrium dynamics of the random-field Ising model. Our results evidence the key role of nonequilibrium effects in the phase transitions of disordered systems.