Slow kinetics of capillary condensation in confined geometry: experiment and theory

Abstract

When two solid surfaces are brought in contact, water vapor present in the ambient air may condense in the region of the contact to form a liquid bridge connecting the two surfaces: this is the so-called capillary condensation. This phenomenon has drastic consequences on the contact between solids, modifying the macroscopic adhesion and friction properties. In this paper, we present a survey of the work we have performed both experimentally and theoretically to understand the microscopic foundations of the kinetics of capillary condensation. From the theoretical point of view, we have computed the free energy barrier associated with the condensation of the liquid from the gas in a confined system. These calculations allow understanding of the existence of very large hysteresis, which is often associated with capillary condensation. These results are compatible with experimental results obtained with a surface forces apparatus in a vapor atmosphere, showing a large hysteresis of the surface energy of two parallel planes as a function of their distance. In the second part, we present some experiments on the influence of humidity on the avalanche angle of granular media. We show that the aging in time of this avalanche angle can be explained by the slow kinetics of capillary condensation in a random confined geometry.

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 γ_SL is smaller than the substrate–vapor surface tension γ_SV, and when the distance between the surfaces is lower than H_c satisfying the Kelvin equation:

$$\text{Δ}\text{ρ}\text{Δ}\text{μ≃2(γ}{}_{\mathrm{<mtext>SV</mtext>}}\text{−γ}{}_{\mathrm{<mtext>SL</mtext>}}\text{)/H}{}_{\mathrm{<mtext>c</mtext>}}$$

Here, Δρ=ρ_L−ρ_V is the difference between the bulk densities of the liquid and the gas phase, Δμ=μ_sat−μ is the (positive) undersaturation and μ_sat is the chemical potential at bulk coexistence. If the vapor can be considered as an ideal gas, we have: Δμ=k_BT ln(p_sat/p_vap), where k_B is the Boltzmann's constant, T is the absolute temperature and p_sat/p_vap 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.