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

How 2D Nanoflakes Improve Transport in Mixed Matrix Membranes: Insights from a Simple Lattice Model and Dynamic Mean Field Theory

Mixed matrix membranes (MMMs), incorporating graphene and graphene oxide structural fragments, have emerged as promising materials for challenging gas separation processes. What remains unclear is the actual molecular mechanism responsible for the enhanced permeability and perm-selectivity of these materials. With the fully atomistic models still unable to handle the required time and length scales, here, we employ a simple qualitative model based on the lattice representation of the physical system and dynamic mean field theory. We demonstrate that the performance enhancement results from the flux-regularization impact of the 2D nanoflakes and that this effect sensitively depends on the orientation of the nanoflakes and the properties of the interface between the nanoflakes and the polymer.

A New Statistical Theory for Constructing Sorption Isotherms in Mesoporous Structures Represented by Bethe Lattices

In the present work, a new statistical theory is developed to describe adsorption and desorption in mesoporous materials (pore sizes ranging from 2 to 50 nm) represented by pore networks in the form of Bethe lattices. The new theory is an extension of a previous theory applied for Statistically Disordered Chain Model (SDCM) structures and incorporates the cooperative effects emerging during phase transitions in pore networks. The theory is validated against simulations and algorithmic models that describe sorption of lattice and real fluids in Bethe lattices. It is seen that the pore network coordination number, or pore connectivity, z, has a significant impact on two important processes observed in pore networks: pore assisting condensation during adsorption and evaporation by percolation during desorption. The inclusion of pore connectivity in the earlier developed framework accounting for cooperativity effects is an important step, rendering the existing models to mimic fluid behavior in real materials more accurately. Hence, the new theory inherently contains all essential elements that may offer the extraction of more reliable pore size distributions utilizing both the adsorption and desorption branches of the isotherm.

Artifacts and misinterpretations in gas physisorption measurements and characterization of porous solids

This contribution provides a critical review of gas physisorption in the textural characterization of porous solids, with the focus on the artifacts in experimental data that lead to serious misinterpretation of the results derived from the analysis of adsorption isotherms. Apart from the problems related to the determination and interpretation of the BET area, we paid particular attention to the issues associated with the determination of pore size distribution; for example, the choice of the correct branch of the hysteresis loop and the network effects. Pitfalls in the analyses using either the classical macroscopic or the advanced microscopic (DFT, GCMC) methodology are addressed. The ultimate aim is to provide guidance for proper calculations and correct interpretation of physisorption data.

Application of the dynamic mean field theory to fluid transport in slit pores

We explore the applicability of the lattice model and dynamic mean field theory as a computationally efficient tool to study transport across heterogeneous porous media, such as mixed matrix membranes. As a starting point and to establish some basic definitions of properties analogous to those in the off-lattice systems, we consider transport across simple models of porous materials represented by a slit pore in a chemical potential gradient. Using this simple model, we investigate the distribution of density and flux under steady state conditions, define the permeability across the system, and explore how this property depends on the length of the pore and the solid-fluid interactions. Among other effects, we observe that the flux in the system goes through a maximum as the solid-fluid interaction is varied from weak to strong. This effect is dominated by the behavior of the fluid near the walls and is also confirmed by off-lattice molecular dynamics simulations. We further extend this study to explore transport across heterogeneous slit pore channels composed of two solids with different values of solid-fluid interaction strengths. We demonstrate that the lattice models and dynamic mean field theory provide a useful framework to pose questions on the accuracy and applicability of the classical theories of transport across heterogeneous porous systems.

Reduced Model for Properties of Multiscale Porous Media with Changing Geometry

In this paper, we consider an important problem for modeling complex coupled phenomena in porous media at multiple scales. In particular, we consider flow and transport in the void space between the pores when the pore space is altered by new solid obstructions formed by microbial growth or reactive transport, and we are mostly interested in pore-coating and pore-filling type obstructions, observed in applications to biofilm in porous media and hydrate crystal formation, respectively. We consider the impact of these obstructions on the macroscopic properties of the porous medium, such as porosity, permeability and tortuosity, for which we build an experimental probability distribution with reduced models, which involves three steps: (1) generation of independent realizations of obstructions, followed by, (2) flow and transport simulations at pore-scale, and (3) upscaling. For the first step, we consider three approaches: (1A) direct numerical simulations (DNS) of the PDE model of the actual physical process called BN which forms the obstructions, and two non-DNS methods, which we call (1B) CLPS and (1C) LP. LP is a lattice Ising-type model, and CLPS is a constrained version of an Allen–Cahn model for phase separation with a localization term. Both LP and CLPS are model approximations of BN, and they seek local minima of some nonconvex energy functional, which provide plausible realizations of the obstructed geometry and are tuned heuristically to deliver either pore-coating or pore-filling obstructions. Our methods work with rock-void geometries obtained by imaging, but bypass the need for imaging in real-time, are fairly inexpensive, and can be tailored to other applications. The reduced models LP and CLPS are less computationally expensive than DNS, and can be tuned to the desired fidelity of the probability distributions of upscaled quantities.

Advancing Computational Analysis of Porous Materials-Modeling Three-Dimensional Gas Adsorption in Organic Gels

Assessing the efficacy of specific porous materials for use in various applications has been a central focus for many experimental studies over the years, with a view to altering the material properties according to the desired characteristics. The application potential for one such class of nanoporous materials-organic resorcinol-formaldehyde (RF) gels-is of particular interest, due to their attractive and adjustable properties. In this work, we simulate adsorption analysis using lattice-based mean field theory, both in individual pores and within three-dimensional porous materials generated from a kinetic Monte Carlo cluster aggregation model. We investigate the impacts of varying pore size and geometry on the adsorptive behavior, with results agreeing with those previously postulated in the literature. The adsorption analysis is carried out for porous materials simulated with varying catalyst concentrations and solids contents, allowing their structural properties to be assessed from resulting isotherms and the adsorption and desorption processes visualized using density color maps. Isotherm analysis indicated that both low catalyst concentrations and low solids contents resulted in structures with open transport pores that were larger in width, while high catalyst concentrations and solids contents resulted in structures with bottleneck pores that were narrower. We present results from both the simulated isotherms and pore size analysis distributions, in addition to results from RF gels synthesized in the lab and analyzed experimentally, with significant similarities observed between the two. Not only do the results of this comparison validate the kinetic Monte Carlo model's ability to successfully capture the formation of RF gels under varying synthesis parameters, but they also show significant promise for the tailoring of material properties in an efficient and computationally inexpensive manner-something which would be pivotal in realizing their full application potential, and could be applied to other porous materials whose formation mechanism operates under similar principles.

Molecular simulations of water adsorption and transport in mesopores with varying hydrophilicity arrangements

The adsorption and transport of water in an open cylindrical mesopore with two different inner surface arrangements of hydrophilicities were examined by molecular simulations. The first model has a weak hydrophilic surface at both entrances of the pore and a stronger hydrophilic surface in the mid-section. The second pore has stronger hydrophilic surfaces at the entrances and weaker in the middle region. The simulation results show that the water adsorption isotherms obtained from Grand Canonical Monte Carlo simulations and pore filling curves acquired from Grand Canonical Molecular Dynamics simulations change depending on the arrangement of the strong and weak hydrophilic surfaces. In the first model, water condensation focuses on the mid-section forming a liquid bridge or a film, which creates a concave meniscus accelerating subsequent adsorption within the pore. Two bridges form in the entrance regions, where a cavity naturally occurs in between the films, in the second model. The different filling and emptying mechanisms clearly change the adsorption-desorption characteristics for the two pore types, but the second type generally showed faster transitions overall. Flux and meniscus analysis also reveals a circulating flow at the menisci of the interfaces within the pore. The results are expected to be valuable in understanding the effects of interior surface modification of nanopores in future applications.

Stochastic analysis of capillary condensation in disordered mesopores

Most mesoporous materials of practical interest are inherently disordered, which has a significant impact on the condensation and evaporation of vapours in their pores. Traditionally, the effect of disorder is theoretically analyzed in a perturbative approach whereby slight elements of disorder (constriction, corrugation) are added to geometrically ideal pores. We propose an alternative approach, which consists of using a stochastic geometrical model to describe both the porous material and the condensate within the pores. This is done through a multiphase generalisation of the standard Gaussian random field model of disordered materials. The model parameters characterising the condensate provide a low-dimensional approximation of its configuration space, and we use a Derjaguin-Broekhoff-de Boer approximation to calculate the free-energy landscape. Our analysis notably questions the existence of vapour-like metastable states in realistically disordered mesoporous materials. Beyond capillary condensation, our general methodology is applicable to a broad array of confined phenomena.

A single-walker approach for studying quasi-nonergodic systems

The jump-walking Monte-Carlo algorithm is revisited and updated to study the equilibrium properties of systems exhibiting quasi-nonergodicity. It is designed for a single processing thread as opposed to currently predominant algorithms for large parallel processing systems. The updated algorithm is tested on the Ising model and applied to the lattice-gas model for sorption in aerogel at low temperatures, when dynamics of the system is critically slowed down. It is demonstrated that the updated jump-walking simulations are able to produce equilibrium isotherms which are typically hidden by the hysteresis effect characteristic of the standard single-flip simulations.

Hidden Nanobubbles in Undersaturated Liquids

Here, we propose theoretically the existence of a new type of nanobubble in undersaturated liquids. These nanobubbles have a concave vapor-liquid interface featured with a negative curvature rather than a positive curvature for nanobubbles in supersaturated liquids, so that they often hide inside of the substrate textures and it might not be easy to characterize them through atomic force microscopy (AFM) measurements. However, these hidden nanobubbles are still stabilized by the contact line pinning effect and stay at the thermodynamically metastable state. We further demonstrate that similar to the nanobubbles in supersaturated liquids the contact angle of the hidden nanobubbles is more sensitive to the nanobubble size rather than the substrate chemistry, and their curvature radius is dependent on the chemical potential but independent of the base radius. Finally, we show several potential situations for the appearance of the hidden nanobubbles.

Modeling the Interaction between AFM Tips and Pinned Surface Nanobubbles

Although the morphology of surface nanobubbles has been studied widely with different AFM modes, AFM images may not reflect the real shapes of the nanobubbles due to AFM tip-nanobubble interactions. In addition, the interplay between surface nanobubble deformation and induced capillary force has not been well understood in this context. In our work we used constraint lattice density functional theory to investigate the interaction between AFM tips and pinned surface nanobubbles systematically, especially concentrating on the effects of tip hydrophilicity and shape. For a hydrophilic tip contacting a nanobubble, its hydrophilic nature facilitates its departure from the bubble surface, displaying a weak and intermediate-range attraction. However, when the tip squeezes the nanobubble during the approach process, the nanobubble shows an elastic effect that prevents the tip from penetrating the bubble, leading to a strong nanobubble deformation and repulsive interactions. On the contrary, a hydrophobic tip can easily pierce the vapor-liquid interface of the nanobubble during the approach process, leading to the disappearance of the repulsive force. In the retraction process, however, the adhesion between the tip and the nanobubble leads to a much stronger lengthening effect on nanobubble deformation and a strong long-range attractive force. The trends of force evolution from our simulations agree qualitatively well with recent experimental AFM observations. This favorable agreement demonstrates that our model catches the main intergradient of tip-nanobubble interactions for pinned surface nanobubbles and may therefore provide important insight into how to design minimally invasive AFM experiments.

Capillary condensation in one-dimensional irregular confinement

A lattice-gas model with heterogeneity is developed for the description of fluid condensation in finite sized one-dimensional pores of arbitrary shape. Mapping to the random-field Ising model allows an exact solution of the model to be obtained at zero-temperature, reproducing the experimentally observed dependence of the amount of fluid adsorbed in the pore on external pressure. It is demonstrated that the disorder controls the sorption for long pores and can result in H2-type hysteresis. Finite-temperature Metropolis dynamics simulations support analytical findings in the limit of low temperatures. The proposed framework is viewed as a fundamental building block of the theory of capillary condensation necessary for reliable structural analysis of complex porous media from adsorption-desorption data.

Capillary condensation of adsorbates in porous materials

Hysteresis in capillary condensation is important for the fundamental study and application of porous materials, and yet experiments on porous materials are sometimes difficult to interpret because of the many interactions and complex solid structures involved in the condensation and evaporation processes. Here we make an overview of the significant progress in understanding capillary condensation and hysteresis phenomena in mesopores that have followed from experiment and simulation applied to highly ordered mesoporous materials such as MCM-41 and SBA-15 over the last few decades.

The differences in surfactant adsorption on carbon nanotubes and their bundles

Dissipative particle dynamics simulations of a mesoscale model are performed to investigate the concentration dependence of surfactant adsorption on small-diameter carbon nanotubes and their bundles. Adsorption is found to follow fundamentally different mechanisms in the two cases because of the heterogeneity of the bundle surface and the difference in diameter of bundles compared to that of individual tubes. Whereas aggregation dominates adsorption on individual tubes, on bundles it is largely a Langmuir-type process. High adsorption energy sites on the outer surface of bundles, where surfactant molecules can interact with two tubes simultaneously, dominate at low coverage. They also cause adsorption on bundles to become significant well before adsorption on individual tubes starts. The difference in the adsorption mechanisms leads to a crossover point at higher concentrations, where the adsorbed amount per surface area on individual tubes becomes larger than that for the bundles.

Understanding adsorption and desorption processes in mesoporous materials with independent disordered channels

Using a lattice-gas model in mean-field theory, we discuss the problem of how adsorption and desorption of fluids in independent cylinderlike pores is influenced by variations in the pore diameter along the length of the pore, surface roughness of the pore walls, and chemical heterogeneity. We also consider the impact of contact with the bulk phase via the pore opening and the possibility of interactions between neighboring pores via a liquid film on the external surface of the material. We find that a combination of pore size variation along the length of the pore and surface roughness yields sorption hysteresis similar to that found in systems with three-dimensional disordered pore networks such as porous glasses. Our results are especially relevant to adsorption and desorption in porous silicon materials with independent linear pores and apparently anomalous features of the behavior in these systems can be accounted for within the context of the present model.

Nucleation and hysteresis of vapor-liquid phase transitions in confined spaces: effects of fluid-wall interaction

In this work, we propose a method to stabilize a nucleus in the framework of lattice density-functional theory (LDFT) by imposing a suitable constraint. Using this method, the shape of critical nucleus and height of the nucleation barrier can be determined without using a predefined nucleus as input. As an application of this method, we study the nucleation behavior of vapor-liquid transition in nanosquare pores with infinite length and relate the observed hysteresis loop on an adsorption isotherm to the nucleation mechanism. According to the dependence of hysteresis and the nucleation mechanism on the fluid-wall interaction, w , in this work, we have classified w into three regions ( w>0.9 , 0.1< or =w< or =0.9 , and w<0.1 ), which are denoted as strongly, moderately, and weakly attractive fluid-wall interaction, respectively. The dependence of hysteresis on the fluid-wall interaction is interpreted by the different nucleation mechanisms. Our constrained LDFT calculations also show that the different transition paths may induce different nucleation behaviors. The transition path dependence should be considered if morphological transition of nuclei exists during a nucleation process.

Effect of the reservoir size on gas adsorption in inhomogeneous porous media

We study the influence of the relative size of the reservoir on the adsorption isotherms of a fluid in disordered or inhomogeneous mesoporous solids. We consider both an atomistic model of a fluid in a simple, yet structured pore, whose adsorption isotherms are computed by molecular simulation, and a coarse-grained model for adsorption in a disordered mesoporous material, studied by a density functional approach in a local mean-field approximation. In both cases, the fluid inside the porous solid exchanges matter with a reservoir of gas that is at the same temperature and chemical potential and whose relative size can be varied, and the control parameter is the total number of molecules present in the porous sample and in the reservoir. Varying the relative sizes of the reservoir and the sample within experimental range may change the shape of the hysteretic isotherms, leading to a 're-entrant' behavior compared to the grand-canonical isotherm when the latter displays a jump in density. We relate these phenomena to the organization of the metastable states that are accessible for the adsorbed fluid at a given chemical potential or density.

Test particle limit for the pair structure of quenched-annealed fluid mixtures

A density functional route to the pair structure of quenched-annealed fluid mixtures is presented. The bulk two-body partial pair correlation functions of the mixture are identified with the one-body density distributions in an external potential that models a fixed test particle. Quenched-annealed (replica) density functional theory is used to calculate the inhomogeneous one-body density distributions. A closed theory is obtained by using an exact sum rule that equates two different expressions for the cross pair correlation function between unlike species. Results for binary quenched-annealed hard sphere mixtures are found to agree well with computer simulation data, improving over results from the replica Ornstein-Zernike equations using the direct correlation functions, obtained as second functional derivatives of the quenched-annealed excess free energy functional, as input. The proposed framework allows for the independent determination of the blocked part of the fluid-fluid partial pair correlation function.

Probing helium interfaces with light scattering: from fluid mechanics to statistical physics

We have investigated the formation of helium droplets in two physical situations. In the first one, droplets are atomised from superfluid or normal liquid by a fast helium vapour flow. In the second, droplets of normal liquid are formed inside porous glasses during the process of helium condensation. The context, aims, and results of these experiments are reviewed, with focus on the specificity of light scattering by helium. In particular, we discuss how, for different reasons, the closeness to unity of the index of refraction of helium allows in both cases to minimise the problem of multiple scattering and obtain results which it would not be possible to get using other fluids.

Tortuosity of unsaturated porous fractal materials

The tortuosity of a capillary-condensed film of inviscid fluid adsorbed onto fractal substrates as a function of the filling fraction of the fluid has been calculated numerically. This acts as a way of probing the multiscale structure of the objects. It is found that the variation of tortuosity alpha with filling fraction varphi is found to follow a power law of the form alpha approximately varphi- for both deterministic and stochastic fractals. These numerically calculated exponents are compared to exponents obtained from a phenomenological scaling and good agreement is found, particularly for the stochastic fractals.

Adsorption of fluids in a pore with chemical heterogeneities: the cooperative effect

In this work, we study the cooperative adsorption of fluids in a heterogeneous pore, in which the pore walls are composed of homogeneous substrates with chemical groups (CGs) decorating them. The adsorption caused by the homogeneous substrates alone and that by CGs do not add up to the overall adsorption, indicating the existence of a cooperative effect. The cooperative effect is the source of cooperative adsorption, and is characterized in this work by the ratio of the overall adsorption to the sum of adsorption by the substrate only and that by CGs. It is found that the cooperative adsorption does not depend monotonically on the substrate or the CGs. Two different origins of the cooperative adsorption play different roles depending on which one dominates the overall adsorption. Our simulations reveal that, when the homogeneous substrate dominates the overall adsorption, weakening of the attractive fluid-substrate interaction or alternatively strengthening of the fluid-CGs interaction leads to a stronger cooperative effect and enhances the cooperative adsorption. However, when CGs dominate the overall adsorption, weakening of the attractive fluid-CG interaction or strengthening the fluid-substrate interaction results in strong cooperative adsorption. In order to investigate the effects of the distribution of CGs on cooperative adsorption, a design-test method is generalized and used in this work. Simulation results show that the overall adsorption can be significantly affected by the CG distribution.

Capillary condensation in porous materials. Hysteresis and interaction mechanism without pore blocking/percolation process

We have performed measurements of boundary hysteresis loops, reversal curves, and subloops in p+-type porous silicon, a porous material composed of straight non-interconnected pores. These data show that a strong interaction mechanism exists between the pores. The pores of porous silicon are non-independent, whereas they are not interconnected. This hysteretic behavior is very similar to that observed in porous glass, which consists of cavities connected to each other by constrictions. This questions the so-called pore blocking/percolation model developed to explain the behavior of fluid in porous glass. More generally, if we disregard the shape of the boundary hysteresis loops which depends on the porous material (H1 for MCM-41 and SBA-15, H2 for porous glass and p+-type porous silicon), the hysteretic features inside the main loop are qualitatively the same for all these porous systems. This shows that none of these systems are composed of independent pores. A coupling between the pores is always present whether they are interconnected or not and whatever the shape of the main loop is.

Fluid bridges confined between chemically nanopatterned solid substrates

We discuss equilibrium properties of classical fluids confined to nanoscopic volumes by solid substrates. The substrates themselves are endowed with wettable chemical patterns of variable symmetry. We develop a thermodynamic description suitable for these highly anisotropic systems. Based upon a combination of Monte Carlo simulations in the grand canonical ensemble and lattice density functional theory at mean-field level we analyze the structure and phase behaviour of the confined fluid. Under suitable thermodynamic conditions the fluid may condense partially in regions controlled by the wettable nanopatterns. The resulting fluid bridges are established as thermodynamic phases and exhibit unique rheological features.

Mercury porosimetry in mesoporous glasses: a comparison of experiments with results from a molecular model

We present results from experiments and molecular modeling of mercury porosimetry into mesoporous Vycor and controlled pore glass (CPG) solid materials. The experimental intrusion/extrusion curves show a transition from a type H2 hysteresis for the Vycor glass to a type H1 hysteresis for the CPG. Mercury entrapment is observed in both materials, but we find that the amount of entrapped mercury depends on the chosen experimental relaxation time. No additional entrapment is found in a second intrusion/extrusion cycle, but hysteresis is still observed. This indicates that hysteresis and entrapment are of different origin. The experimental observations are qualitatively reproduced in theoretical calculations based on lattice models, which provide significant insights of the molecular mechanisms occurring during mercury porosimetry experiments in these porous glasses.

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.

Wetting of rings on a nanopatterned surface: a lattice model study

We perform mean-field density functional theory calculations on a lattice model to study the wetting of a solid substrate decorated with a ring pattern of nanoscale dimensions. We have found three different liquid morphologies on the substrate: a ring morphology where the liquid covers the pattern, a bulge morphology where a droplet is forming on one side of the ring, and a morphology where the liquid forms a cap spanning the nonwetting disk inside the pattern. We investigate the relative stability of these morphologies as a function of the ring size, wall-fluid interaction, and temperature. The results found are in very good agreement with experiments and calculations performed on similar systems at a micrometer length scale. The bulge morphology has also been observed in Monte Carlo simulations of the lattice model. Our results show that (i) morphologies of wetting patterns previously observed on a much larger (microm) scale can also form on a nm length scale, (ii) whether or not this happens depends crucially on the size of the wettable pattern, and (iii) the wettable ring may only be partially wet by the bulge morphology of the fluid. This morphology is a result of a spontaneously broken symmetry in the system.

Mean-field theory of liquid droplets on roughened solid surfaces: application to superhydrophobicity

We present calculations of the density distributions and contact angles of liquid droplets on roughened solid surfaces for a lattice gas model solved in a mean-field approximation. For the case of a smooth surface, this approach yields contact angles that are well described by Young's equation. We consider rough surfaces created by placing an ordered array of pillars on a surface, modeling so-called superhydrophobic surfaces, and we have made calculations for a range of pillar heights. The apparent contact angle follows two regimes as the pillar height increases. In the first regime, the liquid penetrates the interpillar volume, and the contact angle increases with pillar height before reaching a constant value. This behavior is similar to that described by the Wenzel equation for contact angles on rough surfaces, although the contact angles are underestimated. In the second regime, the liquid does not penetrate the interpillar volume substantially, and the contact angle is independent of the pillar height. This situation is similar to that envisaged in the Cassie-Baxter equation for contact angles on heterogeneous surfaces, but the contact angles are overestimated by this equation. For larger pillar heights, two states of the droplet can be observed, one Wenzel-like and the other Cassie-like.

Soft core fluid in a quenched matrix of soft core particles: a mobile mixture in a model gel

We present a density-functional study of a binary phase-separating mixture of soft core particles immersed in a random matrix of quenched soft core particles of larger size. This is a model for a binary polymer mixture immersed in a cross-linked rigid polymer network. Using the replica "trick" for quenched-annealed mixtures we derive an explicit density functional theory that treats the quenched species on the level of its one-body density distribution. The relation to a set of effective external potentials acting on the annealed components is discussed. We relate matrix-induced condensation in bulk to the behavior of the mixture around a single large particle. The interfacial properties of the binary mixture at a surface of the quenched matrix display a rich interplay between capillary condensation inside the bulk matrix and wetting phenomena at the matrix surface.

Knowledge-based reconstruction of random porous media

An evolutionary optimization technique is used to reconstruct digitized material models of 300(3) nm3 size for mesoporous two-phase systems. The models are adapted to the two-point probability (TPP) and to a volume-based pore-size distribution (PSD) which were derived from SANS and adsorption experiments and which carry statistical information about morphology and topology of the pore system. To avoid extreme update-costs, the bulk of mutations are assessed by means of a suitable approximation of the PSD; it is demonstrated that a sporadic insertion of the PSD suffices to drive the algorithm towards satisfactory models in acceptable time. Our approach is knowledge-based in the sense that (i) the mutations are restricted to expedient exchanges of phase-voxels by a heuristic rule, and (ii) the sporadic calculation of the PSD from the current state of the model, in essence, provides an efficient self-control for the evolutionary process. We applied the method to reconstruct periodic models of the xerogel Gelsil 200. Such reconstructs of real mesoporous solids could be utilized, for instance, to verify theories of adsorption and capillary condensation.

Lattice density functional for colloid-polymer mixtures: comparison of two fundamental measure theories

We consider a binary mixture of colloid and polymer particles with positions on a simple cubic lattice. Colloids exclude both colloids and polymers from nearest neighbor sites. Polymers are treated as effective particles that are mutually noninteracting, but exclude colloids from neighboring sites; this is a discrete version of the (continuum) Asakura-Oosawa-Vrij model. Two alternative density functionals are proposed and compared in detail. The first is based on multioccupancy in the zero-dimensional limit of the bare model, analogous to the corresponding continuum theory that reproduces the bulk fluid free energy of free volume theory. The second is based on mapping the polymers onto a multicomponent mixture of polymer clusters that are shown to behave as hard cores; the corresponding property of the extended model in strong confinement permits direct treatment with lattice fundamental measure theory. Both theories predict the same topology for the phase diagram with a continuous fluid-fcc freezing transition at low polymer fugacity and, upon crossing a tricritical point, a first-order freezing transition for high polymer fugacities with rapidly broadening density jump.

Application of percolation theory to the drainage of liquid nitrogen from mesoporous silica xerogel Gelsil 50

Previous in situ small-angle neutron scattering studies of nitrogen adsorption and desorption at 78 K on the mesoporous silica xerogels Gelsil 50 and Gelsil 75 revealed the formation of ramified clusters of vapor-filled pores on desorption, which is characteristic for a percolation process. In the present work, we check whether the adsorption/desorption isotherm data for a monolithic sample of Gelsil 50 can be analyzed in terms of a bond-percolation model. Three powder samples were studied too. Percolation probability data are presented and the effects of heterogeneous nucleation, finite size, and surface clusters on drainage from Gelsil 50 are addressed. The mean coordination number was derived. The results of the analysis are discussed with respect to recent theoretical work for interactions of fluids with complex pore systems. The monolithic sample and a powder sample were characterized by small-angle neutron scattering data.

Phase coexistence in heterogeneous porous media: A new extension to Gibbs ensemble Monte Carlo simulation method

The effect of confinement on phase behavior of simple fluids is still an area of intensive research. In between experiment and theory, molecular simulation is a powerful tool to study the effect of confinement in realistic porous materials, containing some disorder. Previous simulation works aiming at establishing the phase diagram of a confined Lennard-Jones-type fluid, concentrated on simple pore geometries (slits or cylinders). The development of the Gibbs ensemble Monte Carlo technique by Panagiotopoulos [Mol. Phys. 61, 813 (1987)], greatly favored the study of such simple geometries for two reasons. First, the technique is very efficient to calculate the phase diagram, since each run (at a given temperature) converges directly to an equilibrium between a gaslike and a liquidlike phase. Second, due to volume exchange procedure between the two phases, at least one invariant direction of space is required for applicability of this method, which is the case for slits or cylinders. Generally, the introduction of some disorder in such simple pores breaks the initial invariance in one of the space directions and prevents to work in the Gibbs ensemble. The simulation techniques for such disordered systems are numerous (grand canonical Monte Carlo, molecular dynamics, histogram reweighting, N-P-T+test method, Gibbs-Duhem integration procedure, etc.). However, the Gibbs ensemble technique, which gives directly the coexistence between phases, was never generalized to such systems. In this work, we focus on two weakly disordered pores for which a modified Gibbs ensemble Monte Carlo technique can be applied. One of the pores is geometrically undulated, whereas the second is cylindrical but presents a chemical variation which gives rise to a modulation of the wall potential. In the first case almost no change in the phase diagram is observed, whereas in the second strong modifications are reported.

Application of the Bethe-Peierls approximation to a lattice-gas model of adsorption on mesoporous materials

We calculate adsorption and desorption isotherms in models of several classes of porous materials using a lattice-gas model solved in the Bethe-Peierls (quasichemical) approximation. Isotherms and fluid density profiles from the Bethe-Peierls and Bragg-Williams approximations are compared with grand-canonical Monte Carlo simulation results. The Bethe-Peierls approximation produces both more accurate adsorption and desorption isotherms and more realistic fluid density profiles than the Bragg-Williams approximation. Details of the application of the Bethe-Peierls approximation applied to a three-dimensionally inhomogeneous system are given. We show that the numerical solution of this theory can be accomplished using a self-consistent iterator very similar to that currently used in studies employing the Bragg-Williams approximation. This iterative scheme is substantially more efficient than the numerical optimization method used in many previous studies of lattice-gas models in the quasichemical approximation. We find that use of the Bethe-Peierls approximation is only slightly more computationally demanding than the Bragg-Williams approximation, and thus recommend it for use in future work on this class of models.

Dynamic aspects of mercury porosimetry: a lattice model study

Grand canonical Monte Carlo simulations using both Glauber dynamics and Kawasaki dynamics have been carried out for a recently developed lattice model of a nonwetting fluid confined in a porous material. The calculations are aimed at investigating the molecular scale mechanisms leading to mercury retention encountered during mercury porosimetry experiments. We first describe a set of simulations on slit and ink-bottle pores. We have studied the influence of the pore width parameter on the intrusion/extrusion curve shapes and investigated the corresponding mechanisms. Entrapment appears during Kawasaki dynamics simulations of extrusion performed on ink-bottle pores when the system is studied for short relaxation times. We then consider the more realistic and complex case of a Vycor glass building on recent work on the dynamics of adsorption of wetting fluids (Woo, H. J.; Monson, P. A. Phys. Rev. E 2003, 67, 041207). Our results suggest that mercury entrapment is caused by a decrease in the rate of mass transfer associated with the fragmentation of the liquid during extrusion.