Adsorption of a fluid in an aerogel: Integral equation approach

Connect the Thermodynamics of Bulk and Confined Fluids: Confinement-Adsorption Scaling

A fluid (a gas or a liquid) adsorbed in a porous material can behave very differently from its bulk counterpart. The advent of various synthesized materials with nanopores and their wide applications have provided strong impetus for studying fluids in confinement because our current understanding is still incomplete. From a large number of Monte Carlo simulations, we found a scaling relation that allows for connecting some thermodynamic properties (chemical potential, free energy per particle, and grand potential per particle) of a confined fluid to the bulk ones. Upon rescaling the adsorbed fluid density, the adsorption isotherms for many different confining environments collapse to the corresponding bulk curve. We also reveal the intimate connection of the reported scaling relation to Gibbs theory of inhomogeneous fluids and morphological thermodynamics. The advance in our understanding of confined fluids, gained from this study, also opens attractive perspectives for circumventing experimental difficulty for directly measuring some fluid thermodynamic properties in nanoporous materials.

Fluids in porous media. IV. Quench effect on chemical potential

It appears to be a common sense to measure the crowdedness of a fluid system by the densities of the species constituting it. In the present work, we show that this ceases to be valid for confined fluids under some conditions. A quite thorough investigation is made for a hard sphere (HS) fluid adsorbed in a hard sphere matrix (a quench-annealed system) and its corresponding equilibrium binary mixture. When fluid particles are larger than matrix particles, the quench-annealed system can appear much more crowded than its corresponding equilibrium binary mixture, i.e., having a much higher fluid chemical potential, even when the density of each species is strictly the same in both systems, respectively. We believe that the insight gained from this study should be useful for the design of functionalized porous materials.

Statistical mechanics of homogeneous partly pinned fluid systems

The homogeneous partly pinned fluid systems are simple models of a fluid confined in a disordered porous matrix obtained by arresting randomly chosen particles in a one-component bulk fluid or one of the two components of a binary mixture. In this paper, their configurational properties are investigated. It is shown that a peculiar complementarity exists between the mobile and immobile phases, which originates from the fact that the solid is prepared in presence of and in equilibrium with the adsorbed fluid. Simple identities follow, which connect different types of configurational averages, either relative to the fluid-matrix system or to the bulk fluid from which it is prepared. Crucial simplifications result for the computation of important structural quantities, both in computer simulations and in theoretical approaches. Finally, possible applications of the model in the field of dynamics in confinement or in strongly asymmetric mixtures are suggested.

Random sequential adsorption of objects of decreasing size

We consider the model of random sequential adsorption, with the depositing objects, as well as those already at the surface, decreasing in size according to a specified time dependence, from a larger initial value to a finite value in the large-time limit. Numerical Monte Carlo simulations of two-dimensional deposition of disks and one-dimensional deposition of segments are reported for the density-density correlation function and gap-size distribution function, respectively. Analytical considerations supplement numerical results in the one-dimensional case. We investigate the correlation hole-the depletion of correlation functions near contact and, for the present model, their vanishing at contact-that opens up at finite times, as well as its closing and reemergence of the logarithmic divergence of correlation properties at contact in the large-time limit.

Mode-coupling theory for the slow collective dynamics of fluids adsorbed in disordered porous media

We derive a mode-coupling theory for the slow dynamics of fluids confined in disordered porous media represented by spherical particles randomly placed in space. Its equations display the usual nonlinear structure met in this theoretical framework, except for a linear contribution to the memory kernel which adds to the usual quadratic term. The coupling coefficients involve structural quantities which are specific of fluids evolving in random environments and have expressions which are consistent with those found in related problems. Numerical solutions for two simple models with pure hard core interactions lead to the prediction of a variety of glass transition scenarios, which are either continuous or discontinuous and include the possibility of higher-order singularities and glass-glass transitions. The main features of the dynamics in the two most generic cases are reviewed and illustrated with detailed computations. Moreover, a reentry phenomenon is predicted in the low fluid-high matrix density regime and is interpreted as the signature of a de-correlation mechanism by fluid-fluid collisions competing with the localization effect of the solid matrix.

Fluids in porous media. I. A hard sponge model

The morphology of many porous materials is spongelike. Despite the abundance of such materials, simple models which allow for a theoretical description of these materials are still lacking. Here, we propose a hard sponge model which is made by digging spherical cavities in a solid continuum. We found an analytical expression for describing the interaction potential between fluid particles and the spongelike porous matrix. The diagrammatic expansions of different correlation functions are derived as well as that of grand potential. We derived also the Ornstein-Zernike (OZ) equations for this model. In contrast to Madden-Glandt model of random porous media [W. G. Madden and E. D. Glandt, J. Stat. Phys. 51, 537 (1988)], the OZ equations for a fluid confined in our hard sponge model have some similarity to the OZ equations of a three-component fluid mixture. We show also how the replica method can be extended to study our sponge model and that the same OZ equations can be derived also from the extended replica method.

Gas adsorption and desorption in silica aerogels: a theoretical study of scattering properties

We present a numerical study of the structural correlations associated with gas adsorption and desorption in silica aerogels in order to provide a theoretical interpretation of scattering experiments. Following our earlier work, we use a coarse-grained lattice-gas description and determine the nonequilibrium behavior of the adsorbed gas within a local mean-field analysis. We focus on the differences between the adsorption and desorption mechanisms and their signature in the fluid-fluid and gel-fluid structure factors as a function of temperature. At low temperature, but still in the regime where the isotherms are continuous, we find that the adsorbed fluid density, during both filling and draining, is correlated over distances that may be much larger than the gel correlation length. In particular, extended fractal correlations may occur during desorption, indicating the existence of a ramified cluster of vapor filled cavities. This also induces an important increase of the scattering intensity at small wave vectors. The similarity and differences with the scattering of fluids in other porous solids such as Vycor are discussed.

Computer simulation of the phase diagram for a fluid confined in a fractal and disordered porous material

We present a grand canonical Monte Carlo simulation study of the phase diagram of a Lennard-Jones fluid adsorbed in a fractal and highly porous aerogel. The gel environment is generated from an off-lattice diffusion limited cluster-cluster aggregation process. Simulations have been performed with the multicanonical ensemble sampling technique. The biased sampling function has been obtained by histogram reweighting calculations. Comparing the confined and the bulk system liquid-vapor coexistence curves we observe a decrease of both the critical temperature and density in qualitative agreement with experiments and other Monte Carlo studies on Lennard-Jones fluids confined in random matrices of spheres. At variance with these numerical studies we do not observe upon confinement a peak on the liquid side of the coexistence curve associated with a liquid-liquid phase coexistence. In our case only a shouldering of the coexistence curve appears upon confinement. This shoulder can be associated with high density fluctuations in the liquid phase. The coexisting vapor and liquid phases in our system show a high degree of spatial disorder and inhomogeneity.

Vapor-liquid transitions of dipolar fluids in disordered porous media: Performance of angle-averaged potentials

Using replica integral equations in the reference hypernetted-chain (RHNC) approximation we calculate vapor-liquid spinodals, chemical potentials, and compressibilities of fluids with angle-averaged dipolar interactions adsorbed to various disordered porous media. Comparison with previous RHNC results for systems with true angle-dependent Stockmayer (dipolar plus Lennard-Jones) interactions indicate that, for a dilute hard sphere matrix, the angle-averaged fluid-fluid (ff) potential is a reasonable alternative for reduced fluid dipole moments m( *2)=mu(2)/(epsilon(0)sigma(3))< or =2.0. This range is comparable to that estimated in bulk fluids, for which RHNC results are presented as well. Finally, results for weakly polar matrices suggest that angle-averaged fluid-matrix (fm) interactions can reproduce main features observed for true dipolar (fm) interactions such as the shift of the vapor-liquid spinodals towards lower temperatures and higher densities. However, the effective attraction induced by dipolar (fm) interaction is underestimated rather than overestimated as in the case of angle-averaged ff interactions.

Water in nanopores. I. Coexistence curves from Gibbs ensemble Monte Carlo simulations

Coexistence curves of water in cylindrical and slitlike nanopores of different size and water-substrate interaction strength were simulated in the Gibbs ensemble. The two-phase coexistence regions cover a wide range of pore filling level and temperature, including ambient temperature. Five different kinds of two-phase coexistence are observed. A single liquid-vapor coexistence is observed in hydrophobic and moderately hydrophilic pores. Surface transitions split from the main liquid-vapor coexistence region, when the water-substrate interaction becomes comparable or stronger than the water-water pair interaction. In this case prewetting, one and two layering transitions were observed. The critical temperature of the first layering transition decreases with strengthening water-substrate interaction towards the critical temperature expected for two-dimensional systems and is not sensitive to the variation of pore size and shape. Liquid-vapor phase transition in a pore with a wall which is already covered with two water layers is most typical for hydrophilic pores. The critical temperature of this transition is very sensitive to the pore size, in contrast to the liquid-vapor critical temperature in hydrophobic pores. The observed rich phase behavior of water in pores evidences that the knowledge of coexistence curves is of crucial importance for the analysis of experimental results and a prerequiste of meaningful simulations.

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.