Colloids and Surfaces A: Physicochemical and Engineering Aspects
Slow kinetics of capillary condensation in confined geometry: experiment and theory
Introduction
Molecules confined in narrow pores, with pore widths of a few molecular diameters, can exhibit a wide range of physical behavior. The introduction of wall forces, and the competition between fluid–wall and fluid–fluid forces, can lead to interesting surface driven phase changes, since for a small confinement the surface effects can be more important than the bulk effects [1]. Such effects can be observed in porous materials which have a large specific area. Porous materials are involved in many physical, chemical or biological processes. Their adsorption properties are known to present a variety of behavior related to the texture of the porous matrix, which provides an experimental way to analyze the pore size distribution. Interpretation of adsorption isotherms in these materials commonly involves a well known phenomenon, capillary condensation [1], [2], [3], which corresponds to the condensation of liquid bridges in the pores. More fundamentally, capillary condensation is a gas–liquid phase transition shifted by confinement. A basic model of confinement is provided by the slab geometry, for which the fluid is confined between two parallel planar solid walls. The classical theory of capillarity [3] predicts that in this geometry the liquid phase condenses when the substrate–liquid surface tension γSL is smaller than the substrate–vapor surface tension γSV, and when the distance between the surfaces is lower than Hc satisfying the Kelvin equation:
Here, Δρ=ρL−ρV is the difference between the bulk densities of the liquid and the gas phase, Δμ=μsat−μ is the (positive) undersaturation and μsat is the chemical potential at bulk coexistence. If the vapor can be considered as an ideal gas, we have: Δμ=kBT ln(psat/pvap), where kB is the Boltzmann's constant, T is the absolute temperature and psat/pvap the saturated vapor pressure divided by the partial pressure of the vapor. Although the equilibrium properties of this transition have motivated many experimental [4], [5], [6], [7] and theoretical studies [8], [3], [9], capillary condensation presents remarkable dynamical features which are still to be explained. The most striking feature is the huge metastability of the coexisting phases, which contrasts with the bulk liquid–vapor transition.
Since capillary condensation is a first order phase transition, one should be able to identify a critical nucleus and a corresponding free energy barrier away from the spinodal. For sufficiently small H, it can be shown that the liquid films coating the solid surfaces become unstable due to fluid–fluid interactions and grow to fill the slab. This has been carefully studied by several authors [7], [11], [12]. In this article we show that, as in the homogeneous nucleation case, the shape of the critical nucleus results from the balance between surface and volume contributions. The height of the activation barrier is so large that it can induce a large metastability of the vapor phase. This first theoretical result is compared to experiments on capillary condensation in a surface forces apparatus (SFA). In the second part of this article, we will discuss the influence of these slow kinetics of capillary condensation on the mechanical properties of a granular material in a humid atmosphere.
Section snippets
Method
Since capillary condensation occurs only in a confined geometry, the problem which arises in computing an energy barrier for the vapor/liquid transition is the validity of the macroscopic concepts of the classical theory of capillarity.
To address this problem we use the following approach:
(i) We use a density functional theory (DFT) model for the fluid phase, taking into account the long range interactions with the solid surfaces, and study the time evolution of a metastable confined vapor with
Humidity induced aging of the avalanche angle of a granular medium
Since the condensation of liquid in a confined geometry can be hindered by high activation energy, one expects that capillary condensation processes may display slow kinetics. We discuss here in more detail the influence of humidity on the slow evolution in time of a macroscopic property: the avalanche angle of granular media.
Solid friction properties of a large number of solid materials are well described by Coulomb's law, which states that the minimum tangential force T that must be applied
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