Phase behavior and dynamics of fluids in mesoporous glasses

Gas Sorption Characterization of Porous Materials Employing a Statistical Theory for Bethe Lattices

In the present work, a recently developed statistical theory for adsorption and desorption processes in mesoporous solids, modeled by random Bethe lattices, has been applied to obtain pore size distributions and interpore connectivity from sorption isotherms in real random porous materials, employing a robust and validated methodology. Using the experimental adsorption-desorption N2 isotherms at 77.4 K on Vycor glass, a porous material with random pore structure, we demonstrate the solution of the inverse problem resulting in extracted pore size distribution and interpore connectivity, notably different from the predictions of earlier theories. The results presented are corroborated by the analysis of 3D digital images of reconstructed Vycor porous glass, showing excellent agreement between the predictions of geometric analysis and the new statistical theory.

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.

On the role of history-dependent adsorbate distribution and metastable states in switchable mesoporous metal-organic frameworks

A unique feature of metal-organic frameworks (MOFs) in contrast to rigid nanoporous materials is their structural switchabilty offering a wide range of functionality for sustainable energy storage, separation and sensing applications. This has initiated a series of experimental and theoretical studies predominantly aiming at understanding the thermodynamic conditions to transform and release gas, but the nature of sorption-induced switching transitions remains poorly understood. Here we report experimental evidence for fluid metastability and history-dependent states during sorption triggering the structural change of the framework and leading to the counterintuitive phenomenon of negative gas adsorption (NGA) in flexible MOFs. Preparation of two isoreticular MOFs differing by structural flexibility and performing direct in situ diffusion studies aided by in situ X-ray diffraction, scanning electron microscopy and computational modelling, allowed assessment of n-butane molecular dynamics, phase state, and the framework response to obtain a microscopic picture for each step of the sorption process.

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.

Impact of Geometrical Disorder on Phase Equilibria of Fluids and Solids Confined in Mesoporous Materials

Porous solids used in practical applications often possess structural disorder over broad length scales. This disorder strongly affects different properties of the substances confined in their pore spaces. Quantifying structural disorder and correlating it with the physical properties of confined matter is thus a necessary step toward the rational use of porous solids in practical applications and process optimization. The present work focuses on recent advances made in the understanding of correlations between the phase state and geometric disorder in nanoporous solids. We overview the recently developed statistical theory for phase transitions in a minimalistic model of disordered pore networks: linear chains of pores with statistical disorder. By correlating its predictions with various experimental observations, we show that this model gives notable insight into collective phenomena in phase-transition processes in disordered materials and is capable of explaining self-consistently the majority of the experimental results obtained for gas-liquid and solid-liquid equilibria in mesoporous solids. The potentials of the theory for improving the gas sorption and thermoporometry characterization of porous materials are discussed.

Effect of capillary condensation on gas transport properties in porous media

We investigate the effect of capillary condensation on gas diffusivity in porous media composed of randomly packed spheres with moderate wettability. To simulate capillary phenomena at the pore scale while retaining complex pore networks of the porous media, we employ density functional theory (DFT) for coarse-grained lattice gas models. The lattice DFT simulations reveal that capillary condensations preferentially occur at confined pores surrounded by solid walls, leading to the occlusion of narrow pores. Consequently, the characteristic lengths of the partially wet structures are larger than those of the corresponding dry structures with the same porosities. Subsequent gas diffusion simulations exploiting the mean-square displacement method indicate that while the effective diffusion coefficients significantly decrease in the presence of partially condensed liquids, they are larger than those in the dry structures with the same porosities. Moreover, we find that the ratio of the porosity to the tortuosity factor, which is a crucial parameter that determines an effective diffusion coefficient, can be reasonably related to the porosity even for the partially wet porous media.

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.

Carbon nanoparticle-modified multi-wall carbon nanotubes with fast adsorption kinetics for water treatment

Carbon nanoparticle-modified multi-wall carbon nanotubes were prepared using a dehydration of carbohydrate compound method. The structural change was characterized by transmission electron microscopy, Raman spectroscopy, and Brunauer, Emmett and Teller measurement. Fast adsorption kinetics was observed for multi-wall carbon nanotubes with modification, as demonstrated by the adsorption of the model compound methylene blue. This work provides a novel facile engineering strategy to equip multi-wall carbon nanotubes with fast adsorption kinetics, which is promising for efficient water purification.

Phase separation dynamics of polydisperse colloids: a mean-field lattice-gas theory

Strong theoretical evidence shows that dense colloidal mixtures phase-separate in two stages and the denser phase contains long-lived composition heterogeneities.

Anomalously slow relaxation of interacting liquid nanoclusters confined in a porous medium

Anomalously slow relaxation of clusters of a liquid confined in a disordered system of pores has been studied for the (water-L23 nanoporous medium) system. The evolution of the system of confined liquid clusters consists of a fast formation stage followed by slow relaxation of the system and its decay. The characteristic time for the formation of the initial state is τ(p)∼10 s after the reduction of excess pressure after complete filling. Anomalously slow relaxation has been observed for times of 10(1)-10(5) s, and decay has been observed at times of >10(5) s. The time dependence of the volume fraction θ of pores filled with the confined liquid is described by a power law θ∼t(-α) with the exponent α<0.15. The exponent α and temperature dependence α(T) are qualitatively described theoretically for the case of a slightly polydisperse medium in a mean-field approximation with the inclusion of the interaction of liquid clusters and averaging over various degenerate local configurations of clusters. In this approximation, slow relaxation is represented as a continuous transition through a sequence of metastable states of the system of clusters with a decreasing barrier.

Modeling the influence of side stream and ink bottle structures on adsorption/desorption dynamics of fluids in long pores

We apply dynamic mean field theory to study relaxation dynamics for lattice models of fluids confined in linear pores with side streams and with ink bottle structures. Our results show several mechanisms for how the pore structure affects the dynamics, and these are amplified in longer pores. An important conclusion of this work is that features such as side streams and ink bottle segments can substantially slow the equilibration of fluids confined in long pore systems where the pore lengths can be more than 100 micrometers, such as in porous silicon. This may make it difficult to properly equilibrate these systems for states close to those where the pores should be completely filled with liquids. The presence of trapped bubbles in the system may change the desorption characteristics of the system and the shape of the hysteresis loops.

Pyrrolic nitrogen-doped carbon nanotubes: physicochemical properties, interactions with Pd and their role in the selective hydrogenation of nitrobenzophenone

The selective synthesis of pyrrolic N-CNTs, which promote the catalytic activity, and selectivity of PdN/CNTs used to hydrogenate nitrobenzophenone.

Condensation of droplets on nanopillared hydrophobic substrates

Using the constrained lattice density functional theory, we investigated the mechanism of droplet condensation, including droplet nucleation and growth, on nanopillared substrates. We find that similar to a macroscopic droplet on such a substrate, the critical nucleus also exhibits either the Wenzel or Cassie wetting state, depending on both the pillar height and the interpillar spacing. Our calculations show that there exists a critical value of the interpillar spacing, above which the critical nucleus is always in the Wenzel state and the pillared substrate always promotes the nucleation as compared to the smooth substrate, regardless of the pillar height. Below the critical interpillar spacing, however, the pillars always inhibit the nucleation, and the wetting state of the critical nucleus depends on the pillar height. Furthermore, our results demonstrate that the wetting state of the critical nuclei is not necessarily the wetting state of the formed microdroplets: droplets originated from the critical nuclei in the Wenzel state may change into the Cassie state spontaneously during the droplet growth process if the pillar height is greater than a critical value.

Filling dynamics of closed end nanocapillaries

We have studied the filling dynamics of model capillaries using dynamic mean field theory for a confined lattice gas and Kawasaki dynamics simulations. We have found two different scenarios for filling of capped nanocapillaries from the vapor phase. As compared to channels with macroscopic width, in which the filling process occurs by the detachment of the meniscus from the cap, in mesoscopic channels there is an alternative mechanism associated with the spontaneous condensation of the liquid close to the pore opening and its subsequent growth toward the closed pore end. We show that these two scenarios have totally different filling dynamics, providing an additional mechanism for slow capillary condensation kinetics in nanoscopic objects.

Dynamic mean field theory for lattice gas models of fluid mixtures confined in mesoporous materials

We present the extension of dynamic mean field theory (DMFT) for fluids in porous materials (Monson, P. A. J. Chem. Phys. 2008, 128, 084701) to the case of mixtures. The theory can be used to describe the relaxation processes in the approach to equilibrium or metastable equilibrium states for fluids in pores after a change in the bulk pressure or composition. It is especially useful for studying systems where there are capillary condensation or evaporation transitions. Nucleation processes associated with these transitions are emergent features of the theory and can be visualized via the time dependence of the density distribution and composition distribution in the system. For mixtures an important component of the dynamics is relaxation of the composition distribution in the system, especially in the neighborhood of vapor-liquid interfaces. We consider two different types of mixtures, modeling hydrocarbon adsorption in carbon-like slit pores. We first present results on bulk phase equilibria of the mixtures and then the equilibrium (stable/metastable) behavior of these mixtures in a finite slit pore and an inkbottle pore. We then use DMFT to describe the evolution of the density and composition in the pore in the approach to equilibrium after changing the state of the bulk fluid via composition or pressure changes.

Kinetics of the dispersion transition and nonergodicity of a system consisting of a disordered porous medium and a nonwetting liquid

An approach has been proposed for the description of the dispersion transition of a nonwetting liquid in confinement. This approach describes intrusion and extrusion processes for the ground state of a disordered porous medium, which is characterized by the formation of a fractal percolation cluster. The observed transition of the system of liquid nanoclusters in confinement to a metastable state in a narrow range of degrees of filling and temperatures has been explained by the appearance of a potential barrier owing to fluctuations of the collective "multiparticle interaction" of liquid nanoclusters in neighboring pores of different sizes on the shell of the fractal percolation cluster of filled pores. The energy of the metastable state forms a potential relief in the space of the porous medium with many maxima and minima. The volume of the dispersed liquid in the metastable state has been calculated within the analytical percolation theory for the ground state with the infinite percolation cluster. The extrusion-time distribution function of pores has been calculated. It has been found that the volume of the nonwetting liquid remaining in the porous medium decreases with time according to a power law. Relaxation in the system under study is a multistep process involving discontinuous equilibrium and overcoming of many local maxima of the potential relief. The formation of the metastable state of the trapped nonwetting liquid has been attributed to the nonergodicity of the disordered porous medium. The model reproduces the observed dependence of the volume of the dispersed liquid both on the degree of filling and on the temperature.

Diffusion Study by IR Micro-Imaging of Molecular Uptake and Release on Mesoporous Zeolites of Structure Type CHA and LTA

The presence of mesopores in the interior of microporous particles may significantly improve their transport properties. Complementing previous macroscopic transient sorption experiments and pulsed field gradient NMR self-diffusion studies with such materials, the present study is dedicated to an in-depth study of molecular uptake and release on the individual particles of mesoporous zeolitic specimens, notably with samples of the narrow-pore structure types, CHA and LTA. The investigations are focused on determining the time constants and functional dependences of uptake and release. They include a systematic variation of the architecture of the mesopores and of the guest molecules under study as well as a comparison of transient uptake with blocked and un-blocked mesopores. In addition to accelerating intracrystalline mass transfer, transport enhancement by mesopores is found to be, possibly, also caused by a reduction of transport resistances on the particle surfaces.

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.

Spontaneous imbibition in disordered porous solids: a theoretical study of helium in silica aerogels

We present a theoretical study of spontaneous imbibition of liquid (4)He in silica aerogels focusing on the effect of porosity on the fluid dynamical behavior. We adopt a coarse-grained three-dimensional lattice-gas description like in previous studies of gas adsorption and capillary condensation and use a dynamical mean-field theory, assuming that capillary disorder predominates over permeability disorder as in recent phase-field models of spontaneous imbibition. Our results reveal a remarkable connection between imbibition and adsorption as also suggested by recent experiments. The imbibition front is always preceded by a precursor film, and the classical Lucas-Washburn √t scaling law is generally recovered, although some deviations may exist at large porosity. Moreover, the interface roughening is modified by wetting and confinement effects. Our results suggest that the interpretation of the recent experiments should be revised.

Molecular simulation of water confined in nanoporous silica

This paper reports on a molecular simulation study of the thermodynamics, structure and dynamics of water confined at ambient temperature in hydroxylated silica nanopores of a width H = 10 and 20 Å. The adsorption isotherms for water in these nanopores resemble those observed for experimental samples; the adsorbed amount increases continuously in the multilayer adsorption regime until a jump occurs due to capillary condensation of the fluid within the pore. Strong layering of water in the vicinity of the silica surfaces is observed as marked density oscillations are observed up to 8 Å from the surface in the density profiles for confined water. Our results indicate that water molecules within the first adsorbed layer tend to adopt a H-down orientation with respect to the silica substrate. For all pore sizes and adsorbed amounts, the self-diffusivity of confined water is lower than the bulk, due to the hydrophilic interaction between the water molecules and the hydroxylated silica surface. Our results also suggest that the self-diffusivity of confined water is sensitive to the adsorbed amount.

Molecular simulation of nitrogen adsorption in nanoporous silica

This article reports on a molecular simulation study of nitrogen adsorption and condensation at 77 K in atomistic silica cylindrical nanopores (MCM-41). Two models are considered for the nitrogen molecule and its interaction with the silica substrate. In the "pea" model, the nitrogen molecule is described as a single Lennard-Jones sphere and only Lennard-Jones interactions between the nitrogen molecule and the oxygens atoms of the silica substrate are taken into account. In the "bean" model (TraPPE force field), the nitrogen molecule is composed of two Lennard-Jones sites and a linear array of three charges on the atomic positions and at the center of the nitrogen-nitrogen bond. In the bean model, the interactions between the sites on the nitrogen molecule and the Si, O, and H atoms of the substrate are the sum of the Coulombic and dispersion interactions with a repulsive short-range contribution. The data obtained with the pea and bean models in silica nanopores conform to the typical behavior observed in the experiments for adsorption/condensation in cylindrical MCM-41 nanopores; the adsorbed amount increases continuously in the multilayer adsorption regime until an irreversible jump occurs because of capillary condensation and evaporation of the fluid within the pore. Our results suggest that the pea model can be used for characterization purposes where one is interested in capturing the global experimental behavior upon adsorption and desorption in silica nanopores. However, the bean model is more suitable to investigating the details of the interaction with the surface because this model, which accounts for the partial charges located on the nitrogen atoms of the molecule (quadrupole), allows a description of the specific interactions between this adsorbate and silica surfaces (silanol groups and siloxane bridges) or grafted silica surfaces. In particular, the bean model provides a more realistic picture of nitrogen adsorption in the vicinity of silica surfaces or confined in silica nanopores, where the isosteric heat of adsorption curves show that the nitrogen molecule in this model is sensitive to the surface heterogeneity.

Investigating cluster formation in adsorption of CO2, CH4, and Ar in zeolites and metal organic frameworks at subcritical temperatures

The critical temperatures, T(c), of CO(2), CH(4), and Ar are 304 K, 191 K, and 151 K, respectively. This paper highlights some unusual characteristics of adsorption and diffusion of these molecules in microporous structures such as zeolites and metal organic frameworks at temperatures T < T(c). Published experimental adsorption data for T < T(c) show that the isotherms invariably display stepped characteristics. The inverse thermodynamic factor 1/Gamma(i) identical with d ln c(i)/d ln f(i) exceeds unity for a range of fugacities f(i) and molar concentrations c(i) within the pore corresponding to the steep portion of the isotherm. With the aid of Monte Carlo simulations of isotherms for different temperatures T < T(c) in a variety of zeolites (AFI, MTW, FAU, NaY, MFI, and MOR), metal-organic frameworks (IRMOF-1, CuBTC, MIL-47 (V), and MIL-53 (Cr)), and covalent-organic frameworks (COF-102, and COF-108), we investigate the conditions required for 1/Gamma(i) > 1. For each of the three species investigated, data on pore concentrations c(i) at any given temperature below T(c) fall within the binodal region for the bulk fluid phase. We present evidence to suggest that, in the concentration ranges for which 1/Gamma(i) > 1, clustering of molecules occurs. The extent of clustering is enhanced as T falls increasingly below T(c). Furthermore, molecular dynamics simulations of diffusion demonstrate that the concentration dependence of the diffusivities is markedly influenced in the regions where 1/Gamma(i) > 1. In regions where molecular clustering occurs, the Fick diffusivity shows, in some cases, a decreasing trend with concentration.

Microscopic theory of hysteretic hydrogen adsorption in nanoporous materials

Understanding gas adsorption confined in nanoscale pores is a fundamental issue with broad applications in catalysis and gas storage. Recently, hysteretic H(2) adsorption was observed in several nanoporous metal-organic frameworks (MOFs). Here, using first-principles calculations and simulated adsorption/desorption isotherms, we present a microscopic theory of the enhanced adsorption hysteresis of H(2) molecules using the MOF Co(1,4-benzenedipyrazolate) [Co(BDP)] as a model system. Using activated H(2) diffusion along the small-pore channels as a dominant equilibration process, we demonstrate that the system shows hysteretic H(2) adsorption under changes of external pressure. For a small increase of temperature, the pressure width of the hysteresis, as well as the adsorption/desorption pressure, dramatically increases. The sensitivity of gas adsorption to temperature changes is explained by the simple thermodynamics of the gas reservoir. Detailed analysis of transient adsorption dynamics reveals that the hysteretic H(2) adsorption is an intrinsic adsorption characteristic in the diffusion-controlled small-pore systems.

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.

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.

Understanding capillary condensation and hysteresis in porous silicon: network effects within independent pores

The ability to exert a significant degree of pore structure control in porous silicon materials has made them attractive materials for the experimental investigation of the relationship between pore structure, capillary condensation, and hysteresis phenomena. Using both experimental measurements and a lattice gas model in mean field theory, we have investigated the role of pore size inhomogeneities and surface roughness on capillary condensation of N2 at 77K in porous silicon with linear pores. Our results resolve some puzzling features of earlier experimental work. We find that this material has more in common with disordered materials such as Vycor glass than the idealized smooth-walled cylindrical pores discussed in the classical adsorption literature. We provide strong evidence that this behavior comes from the complexity of the processes within independent linear pores, arising from the pore size inhomogeneities along the pore axis, rather than from cooperative effects between different pores.

Contact angles, pore condensation, and hysteresis: insights from a simple molecular model

We discuss the thermodynamics of adsorption of fluids in pores when the solid-fluid interactions lead to partial wetting of the pore walls, a situation encountered, for example, in water adsorption in porous carbons. Our discussion is based on calculations for a lattice gas model of a fluid in a slit pore treated via mean field density functional theory (MFDFT). We calculate contact angles for pore walls as a function of solid-fluid interaction parameter, alpha, in the model, using Young's equation and the interfacial tensions calculated in MFDFT. We consider adsorption and desorption in both infinite pores and in finite length pores in contact with the bulk. In the latter case, contact with the bulk can promote evaporation or condensation, thereby dramatically reducing the width of hysteresis loops. We show how the observed behavior changes with alpha. By using a value of alpha that yields a contact angle of about 85 degrees and maintaining the bulk fluid in a supersaturated vapor state on adsorption, we find an adsorption/desorption isotherm qualitatively similar to those for graphitized carbon black where pore condensation occurs at supersaturated bulk vapor states in the spaces between the primary particles of the adsorbent.

Adsorption of simple fluid on silica surface and nanopore: effect of surface chemistry and pore shape

This paper reports a molecular simulation study on the adsorption of simple fluids (argon at 77 K) on hydroxylated silica surfaces and nanopores. The effect of surface chemistry is addressed by considering substrates with either partially or fully hydroxylated surfaces. We also investigate the effect of pore shape on adsorption and capillary condensation by comparing the results for cylindrical and hexagonal nanopores having equivalent sections (i.e., equal section areas). Due to the increase in the polarity of the surface with the density of OH groups, the adsorbed amounts for fully hydroxylated surfaces are found to be larger than those for partially hydroxylated surfaces. Both the adsorption isotherms for the cylindrical and hexagonal pores conform to the typical behavior observed in the experiments for adsorption/condensation in cylindrical nanopores MCM-41. Capillary condensation occurs through an irreversible discontinuous transition between the partially filled and the completely filled configurations, while evaporation occurs through the displacement at equilibrium of a hemispherical meniscus along the pore axis. Our data are also used to discuss the effect of surface chemistry and pore shape on the BET method. The BET surface for fully hydroxylated surfaces is much larger (by 10-20%) than the true geometrical surface. In contrast, the BET surface significantly underestimates the true surface when partially hydroxylated surfaces are considered. These results suggest that the surface chemistry and the choice of the system adsorbate/adsorbent is crucial in determining the surface area of solids using the BET method.

Probing memory effects in confined fluids via diffusion measurements

Confinement of fluids in porous materials is widely exploited in a variety of technologies, including chemical conversion by heterogeneous catalysis and adsorption separations. Important fundamental phenomena associated with many-molecule interactions occur in such systems, including a remarkably long "memory" of the past when the actual amount of molecules in the pores dramatically depends on the history of how the external conditions have been changed. We demonstrate that the intrinsic diffusivity as measured by NMR serves as an excellent probe of the history-dependent states of the confined fluid. A remarkable feature of our results are differences in diffusivity between out-of-equilibrium states with the same density within the hysteresis loop. This reflects different spatial distributions of the confined fluid that accompany the arrested equilibration of the system in this region.

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.

Dynamical aspects of the adsorption hysteresis phenomenon

Equilibrium and nonequilibrium transport properties of adsorbates in mesoporous Vycor porous glass have been experimentally studied using nuclear magnetic resonance techniques. With the known geometrical characteristics of porous glass and with measured self-diffusivities, transient sorption curves have been quantitatively compared to those predicted within a Fick's law model. This model correctly describes data outside a hysteresis region. In contrast, in the hysteresis region, a two-step mechanism of density relaxation is required to explain the behavior. These two mechanisms are identified as diffusion at early stages and activated density redistribution at later stages of adsorption. The latter mechanism, being intrinsically slow in nature, is anticipated to prevent the system from reaching equilibrium.