Capillary condensation in disordered porous materials: hysteresis versus equilibrium behavior

Modeling desorption of fluids from disordered mesoporous materials

The desorption mechanism of fluids in disordered mesoporous glasses is studied by Monte Carlo simulations of a coarse-grained lattice model with realistic matrix configurations representative of Vycor. Two methods of simulation are considered: grand canonical ensemble Monte Carlo simulations and dynamic Monte Carlo simulations which mimic the diffusion of the fluid in and out of the material using Kawasaki dynamics. In the grand canonical simulations, cavitation via nucleation of bubbles inside the pores plays the dominant role in determining the fluid configurations along the desorption isotherm. The Kawasaki dynamics simulations indicate that such configurations are achieved dynamically via the gradual advancement of macroscopic front interfaces toward the interior. This is made possible by the bubble nucleation mechanism operating on a length scale that is determined by both the typical pore size and the strength of the solid-fluid interaction.

Capillary condensation in linear mesopores of different shape

The hysteresis and kinetics of capillary condensation of N2 and Ar in linear mesopores, produced by etching of Si wafers, have been studied for different pore shapes, including the ink bottle geometry. Pore blocking has been observed in the solid state of the pore fillings, but not in the liquid state. We conclude that individual local geometries such as the pore mouth, a blind end, or a single constriction have no effect on the shape of sorption isotherms, that the pore space should be regarded as a statistical ensemble of pore segments with a lot of quenched disorder.

Adsorption/desorption hysteresis in inkbottle pores: a density functional theory and Monte Carlo simulation study

The mechanisms of adsorption and desorption in inkbottle-shaped pores are considered for lattice models using grand canonical mean field density functional theory and Monte Carlo simulation. We find that they depend significantly on the particular pore geometry, the nature of the fluid-solid interaction, and the temperature. We find two mechanisms for desorption. One mechanism involves the emptying of the main cavity even as the density of fluid in the necks remains high, a mechanism observed recently in studies of an off-lattice model of an inkbottle. The other is a simultaneous desorption from the entire pore space, behavior that is more closely related to the traditional picture of pore blocking in the inkbottle system.

Intrusion and extrusion of water in hydrophobic mesopores

We present experimental and theoretical results on intrusion-extrusion cycles of water in hydrophobic mesoporous materials, characterized by independent cylindrical pores. The intrusion, which takes place above the bulk saturation pressure, can be well described using a macroscopic capillary model. Once the material is saturated with water, extrusion takes place upon reduction of the externally applied pressure. Our results for the extrusion pressure can only be understood by assuming that the limiting extrusion mechanism is the nucleation of a vapor bubble inside the pores. A comparison of calculated and experimental nucleation pressures shows that a proper inclusion of line tension effects is necessary to account for the observed values of nucleation barriers. Negative line tensions of order 10(-11) J m(-1) are found for our system, in reasonable agreement with other experimental estimates of this quantity.

Density functional theory for nearest-neighbor exclusion lattice gases in two and three dimensions

To speak about fundamental measure theory obliges us to mention dimensional crossover. This feature, inherent to the systems themselves, was incorporated in the theory almost from the beginning. Although at first it was thought to be a consistency check for the theory, it rapidly became its fundamental pillar, thus becoming the only density functional theory which possesses such a property. It is straightforward that dimensional crossover connects, for instance, the parallel hard cube system (three dimensional) with that of squares (two dimensional) and rods (one dimensional). We show here that there are many more connections which can be established in this way. Through them we deduce from the functional for parallel hard (hyper)cubes in the simple (hyper)cubic lattice the corresponding functionals for the nearest-neighbor exclusion lattice gases in the square, triangular, simple cubic, face-centered-cubic, and body-centered-cubic lattices. As an application, the bulk phase diagram for all these systems is obtained.

Local mean-field study of capillary condensation in silica aerogels

We apply local mean-field (i.e., density functional) theory to a lattice model of a fluid in contact with a dilute, disordered gel network. The gel structure is described by a diffusion-limited cluster aggregation model. We focus on the influence of porosity on both the hysteretic and the equilibrium behavior of the fluid as one varies the chemical potential at low temperature. We show that the shape of the hysteresis loop changes from smooth to rectangular as the porosity increases and that this change is associated with disorder-induced out-of-equilibrium phase transitions that differ in adsorption and in desorption. Our results provide insight in the behavior of 4He in silica aerogels.

Capillary condensation and interface structure of a model colloid-polymer mixture in a porous medium

We consider the Asakura-Oosawa model of hard sphere colloids and ideal polymers in contact with a porous matrix modeled by immobilized configurations of hard spheres. For this ternary mixture a fundamental measure density functional theory is employed, where the matrix particles are quenched and the colloids and polymers are annealed, i.e., allowed to equilibrate. We study capillary condensation of the mixture in a small sample of matrix as well as demixing and the fluid-fluid interface inside a bulk matrix. Density profiles normal to the interface and surface tensions are calculated and compared to the case without matrix. Two kinds of matrices are considered: (i) colloid-sized matrix particles at low packing fractions and (ii) large matrix particles at high packing fractions. These two cases show fundamentally different behavior and should both be experimentally realizable. Furthermore, we argue that capillary condensation of a colloidal suspension could be experimentally accessible. We find that in case (ii), even at high packing fractions, the main effect of the matrix is to exclude volume and, to high accuracy, the results can be mapped onto those of the same system without matrix via a simple rescaling.

Hard sphere fluids at surfaces of porous media

An adsorbate fluid of hard spheres is brought into contact with a semi-infinite porous matrix modeled by immobilized configurations of freely overlapping spheres with a sharp kink one-body density distribution. Comparison of results from a recent density-functional approach to those of our computer simulations yields good agreement for the adsorbate density profile across the matrix surface. We show how the matrix can be replaced by a fictitious external potential that only depends on the distance from the interface, and that leads to the same adsorbate density profile. This potential is found to be a smooth function of distance, due to the geometry of the matrix particles. For high matrix densities, the porous medium becomes practically impenetrable, and its surface behaves like a rough hard wall whose roughness decreases with increasing matrix density.

Phase behavior and dynamics of fluids in mesoporous glasses

Equilibrium and dynamical relaxation behavior of fluids confined in disordered mesoporous glasses such as Vycor are studied based on a lattice model using mean field theory and Monte Carlo simulations. Preferential attractive interactions between the solid surfaces and the fluid suppresses macroscopic phase separation, while making the relaxation rate increasingly slow. The free energy landscape characterized by the presence of the many metastable minima separated by finite barriers dominates both the static and dynamic behavior of fluids at low temperature. Our results provide additional insight into the nature of hysteresis in adsorption measurements of gases in porous glasses.

Effects of pore walls and randomness on phase transitions in porous media

We study spin models within the mean field approximation to elucidate the topology of the phase diagrams of systems modeling the liquid-vapor transition and the separation of 3He-4He mixtures in periodic porous media. These topologies are found to be identical to those of the corresponding random field and random anisotropy spin systems with a bimodal distribution of the randomness. Our results suggest that the presence of walls (periodic or otherwise) are a key factor determining the nature of the phase diagram in porous media.

Density-functional theory for fluids in porous media

As models for substances adsorbed within amorphous solid matrices, we consider mixtures of spheres with either hard or ideal interactions where several (matrix) components are quenched and the remaining (adsorbate) components are equilibrated. We propose a density-functional theory, based on the exact zero-dimensional limit, which treats both matrix and adsorbate components on the level of the respective one-body density profiles. As a test, we calculate pair correlation functions for hard spheres adsorbed in either a hard sphere or an ideal sphere matrix, and find good agreement with our computer simulation results.

Inside the hysteresis loop: multiplicity of internal states in confined fluids

We study the equilibrium and stability of metastable states and capillary condensation hysteresis of a Lennard-Jones fluid in cylindrical pores by means of the canonical ensemble density functional theory and gauge cell Monte Carlo simulations. We demonstrate a possibility for the existence of multiple laterally uniform internal states of equal density inside the hysteresis loop. The region of multiple states is bounded by the states of zero compressibility. The internal states can be stabilized in Monte Carlo simulations constraining the density fluctuations.

Lattice model of adsorption in disordered porous materials: mean-field density functional theory and Monte Carlo simulations

We present mean-field density functional theory calculations and Monte Carlo simulations for a lattice model of a fluid confined in a disordered porous material. The model is obtained by a coarse graining of an off-lattice model of adsorption of simple molecules in silica xerogels. In some of our calculations a model of a porous glass is also considered. The lattice models exhibit behavior that is qualitatively similar to that of their off-lattice counterparts but the computations required are much more tractable and this makes it feasible to investigate the effects of porous material microstructure at longer length scales. We focus on exploring in detail the behavior in the adsorption/desorption hysteresis region for these models. In agreement with recent results for a model that uses a random distribution of solid sites on the lattice [Kierlik et al., Phys. Rev. Lett. 87, 055701 (2001)] we show that the disorder of the solid matrix induces multiple metastable states within the hysteresis region, which are evident in both the mean-field theory calculations and the Monte Carlo simulations. These multiple metastable states can be connected by scanning curves that are very similar to those seen in experimental studies of adsorption hysteresis. The results from mean-field theory predict that while there is hysteresis in the adsorption/desorption isotherms it is not possible to locate a condition of phase equilibrium that satisfies thermodynamic consistency. A wider significance of these results is discussed.