Capillary condensation in disordered porous materials: hysteresis versus equilibrium behavior

The spectrum of experimentally accessible states for melting and freezing transitions in mesoporous materials

Structural disorder in mesoporous solids gives rise to complex phase behavior for materials confined within their pore spaces. As a result, a wide spectrum of possible phase configurations associated with spatial distributions of thermodynamic phases throughout the pore networks can be realized in experiments. Despite their importance, quantifying these states remains largely unaddressed. By considering solid-liquid equilibria as a representative example and using a simple random network model, we investigate the spectrum of such states accessible in real experiments and relate this spectrum to the structural characteristics of porous solids. We classify these states by their free energies and demonstrate how network effects break degeneracies for specific phase compositions and temperatures. Furthermore, we identify the experimental conditions that delineate boundary free energy states, differentiating accessible from inaccessible states. The insights from this study on solid-liquid equilibria are also equally applicable to gas-liquid equilibria in confined spaces and contribute to a deeper understanding of relaxation dynamics associated with hysteresis.

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.

Water Condensation in the Nanoscale Pores of Pt/C Catalyst Particles and Its Impact on Catalyst Utilization: A Simulation Based on a Reconstructed Structure from Nanoimaging

In polymer electrolyte membrane fuel cells, carbon-supported platinum (Pt/C) catalyst particles require sufficient water condensation within the nanoscale pores to effectively utilize the interior Pt catalysts. Since experimental visualizations with nanoscale precision of this phenomenon are not yet possible, we utilized a Pt/C catalyst particle reconstructed from segmented nanoimaging of a catalyst powder, which served as the computational domain for lattice density functional theory (LDFT) simulation of water condensation. Paired with experimental water uptake data, LDFT successfully simulated high-resolution water condensation, capturing both thin-film and capillary water condensation phenomena. Using a simple proton movement method within the water network, we reproduced the Pt utilization data from a CO stripping experiment. Our findings highlight that at low relative humidity (RH), Pt utilization is influenced by thin water film formations, mainly dictated by the wettability properties of surfaces within primary pores and the Pt/C catalyst particle's exterior. Conversely, at high RH, Pt utilization is attributed to capillary water condensation in medium-to-large sized pores. This approach contributes a qualitative and quantitative discussion on hypotheses regarding the mechanism of Pt utilization, supporting recent studies (e.g., Girod, R.; Nat. Catal. 2023, 6, (5), 383-391).

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.

Stability of nanoparticle laden aerosol liquid droplets

We develop a model for the thermodynamics and evaporation dynamics of aerosol droplets of a liquid, such as water, surrounded by gas. When the temperature and the chemical potential (or equivalently the humidity) are such that the vapor phase is in the thermodynamic equilibrium state, then, of course, droplets of the pure liquid evaporate over a relatively short time. However, if the droplets also contain nanoparticles or any other non-volatile solute, then the droplets can become thermodynamically stable. We show that the equilibrium droplet size depends strongly on the amount and solubility of the nanoparticles within, i.e., on the nature of the particle interactions with the liquid and, of course, also on the vapor temperature and chemical potential. We develop a simple thermodynamic model for such droplets and compare predictions with results from a lattice density functional theory that takes as input the same particle interaction properties, finding very good agreement. We also use dynamical density functional theory to study the evaporation/condensation dynamics of liquid from/to droplets as they equilibrate with the vapor, thereby demonstrating droplet stability.

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.

Inverse transitions and disappearance of the λ-line in the asymmetric random-field Ising and Blume-Capel models

We report on reentrance in the random-field Ising and Blume-Capel models, induced by an asymmetric bimodal random-field distribution. The conventional continuous line of transitions between the paramagnetic and ferromagnetic phases, the λ-line, is wiped away by the asymmetry. The phase diagram, then, consists of only first-order transition lines that always end at ordered critical points. We find that, while for symmetric random-field distributions there is no reentrance, the asymmetry in the random-field results in a range of temperatures for which magnetization shows reentrance. While this does not give rise to an inverse transition in the Ising model, for the Blume-Capel model, however, there is a line of first-order inverse phase transitions that ends at an inverse-ordered critical point. We show that the location of the inverse transitions can be inferred from the ground-state phase diagram of the model.

Single-Collision Statistics Reveal a Global Mechanism Driven by Sample History for Contact Electrification in Granular Media

Models for same-material contact electrification in granular media often rely on a local charge-driving parameter whose spatial variations lead to a stochastic origin for charge exchange. Measuring the charge transfer from individual granular spheres after contacts with substrates of the same material, we find instead a "global" charging behavior, coherent over the sample's whole surface. Cleaning and baking samples fully resets charging magnitude and direction, which indicates the underlying global parameter is not intrinsic to the material, but acquired from its history. Charging behavior is randomly and irreversibly affected by changes in relative humidity, hinting at a mechanism where adsorbates, in particular, water, are fundamental to the charge-transfer process.

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.

Connecting dynamic pore filling mechanisms with equilibrium and out of equilibrium configurations of fluids in nanopores

In the present study, using dynamic mean field theory complemented by grand canonical molecular dynamics simulations, we investigate the extent to which the density distributions encountered during the dynamics of capillary condensation are related to those distributions at equilibrium or metastable equilibrium in a system at fixed average density (canonical ensemble). We find that the states encountered can be categorized as out of equilibrium or quasi-equilibrium based on the magnitude of the driving force for mass transfer. More specifically, in open-ended slit pores, pore filling via double bridging is an out of equilibrium process, induced by the dynamics of the system, while pore filling by single bridge formation is connected to a series of configurations that are equilibrium configurations in the canonical ensemble and that cannot be observed experimentally by a standard adsorption process, corresponding to the grand canonical ensemble. Likewise, in closed cap slits, the formation of a liquid bridge near the pore opening and its subsequent growth while the initially detached meniscus from the capped end remains immobilized are out of equilibrium processes that occur at large driving forces. On the other hand, at small driving forces, there is a continuous acceleration of the detached meniscus from the capped end, which is associated with complete reversibility in the limit of an infinitesimally small driving force.

Machine-Learned Free Energy Surfaces for Capillary Condensation and Evaporation in Mesopores

Using molecular simulations, we study the processes of capillary condensation and capillary evaporation in model mesopores. To determine the phase transition pathway, as well as the corresponding free energy profile, we carry out enhanced sampling molecular simulations using entropy as a reaction coordinate to map the onset of order during the condensation process and of disorder during the evaporation process. The structural analysis shows the role played by intermediate states, characterized by the onset of capillary liquid bridges and bubbles. We also analyze the dependence of the free energy barrier on the pore width. Furthermore, we propose a method to build a machine learning model for the prediction of the free energy surfaces underlying capillary phase transition processes in mesopores.

Models of adsorption-induced deformation: ordered materials and beyond

Adsorption-induced deformation is a change in geometrical dimensions of an adsorbent material caused by gas or liquid adsorption on its surface. This phenomenon is universal and sensitive to adsorbent properties, which makes its prediction a challenging task. However, the pure academic interest is complemented by its importance in a number of engineering applications with porous materials characterization among them. Similar to classical adsorption-based characterization methods, the deformation-based ones rely on the quality of the underlying theoretical framework. This fact stimulates the recent development of qualitative and quantitative models toward the more detailed description of a solid material, e.g. account of non-convex and corrugated pores, calculations of adsorption stress in realistic three-dimension solid structures, the extension of the existing models to new geometries, etc. The present review focuses on the theoretical description of adsorption-induced deformation in micro and mesoporous materials. We are aiming to cover recent theoretical works describing the deformation of both ordered and disordered porous bodies.

Thermodynamics of fluctuations based on time-and-space averages

We develop nonequilibrium theory by using averages in time and space as a generalized way to upscale thermodynamics in nonergodic systems. The approach offers a classical perspective on the energy dynamics in fluctuating systems. The rate of entropy production is shown to be explicitly scale dependent when considered in this context. We show that while any stationary process can be represented as having zero entropy production, second law constraints due to the Clausius theorem are preserved due to the fact that heat and work are related based on conservation of energy. As a demonstration, we consider the energy dynamics for the Carnot cycle and for Maxwell's demon. We then consider nonstationary processes, applying time-and-space averages to characterize nonergodic effects in heterogeneous systems where energy barriers such as compositional gradients are present. We show that the derived theory can be used to understand the origins of anomalous diffusion phenomena in systems where Fick's law applies at small length scales, but not at large length scales. We further characterize fluctuations in capillary-dominated systems, which are nonstationary due to the irreversibility of cooperative events.

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.

The Effect of Topology on Phase Behavior under Confinement

This work studies how morphology (i.e., the shape of a structure) and topology (i.e., how different structures are connected) influence wall adsorption and capillary condensation under tight confinement. Numerical simulations based on classical density functional theory (cDFT) are run for a wide variety of geometries using both hard-sphere and Lennard-Jones fluids. These cDFT computations are compared to results obtained using the Minkowski functionals. It is found that the Minkowski functionals can provide a good description of the behavior of Lennard-Jones fluids down to small system sizes. In addition, through decomposition of the free energy, the Minkowski functionals provide a good framework to better understand what are the dominant contributions to the phase behavior of a system. Lastly, while studying the phase envelope shift as a function of the Minkowski functionals it is found that topology has a different effect depending on whether the phase transition under consideration is a continuous or a discrete (first-order) transition.

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 Confinement on Capillary Phase Transition in Granular Aggregates

Using a 3D mean-field lattice-gas model, we analyze the effect of confinement on the nature of capillary phase transition in granular aggregates with varying disorder and their inverse porous structures obtained by interchanging particles and pores. Surprisingly, the confinement effects are found to be much less pronounced in granular aggregates as opposed to porous structures. We show that this discrepancy can be understood in terms of the surface-surface correlation length with a connected path through the fluid domain, suggesting that this length captures the true degree of confinement. We also find that the liquid-gas phase transition in these porous materials is of second order nature near capillary critical temperature, which is shown to represent a true critical temperature, i.e., independent of the degree of disorder and the nature of the solid matrix, discrete or continuous. The critical exponents estimated here from finite-size scaling analysis suggest that this transition belongs to the 3D random field Ising model universality class as hypothesized by F. Brochard and P.G. de Gennes, with the underlying random fields induced by local disorder in fluid-solid interactions.

A novel application of nanoporous gold to humidity sensing: a framework for a general volatile compound sensor

Volatile organic compounds (VOC) are ubiquitous in industrial applications creating a pressing desire for novel transduction pathways to build a broad family of new gas sensors. Nanoporous gold (NPG) is a material with a vast range of untapped potential applications; offering a high surface area found generally in nanomaterials, while also being comparatively simple to fabricate. NPG based sensors can also leverage the unique physics of gold at the nanoscale. In this work, we leverage the multiple unique nanoscale phenomena associated with NPG to demonstrate two novel transduction mechanisms to sense humidity, a model compound. Through direct electrical measurements of NPG, we were able to sense changes in the electronic properties of NPG induced by ambient humidity. We propose two novel transduction mechanisms: chemoresistive changes induced by surface adsorption and electrochemical capacitive changes induced by the electric double layer to detect humidity. To our knowledge this is the first reported application of both these mechanisms for sensing any volatile compounds utilizing NPG.

Reminiscent capillarity in subnanopores

Fluids in large and small pores display different behaviors with a crossover described through the concept of critical capillarity. Here we report experimental and simulation data for various siliceous zeolites and adsorbates that show unexpected reminiscent capillarity for such nanoporous materials. For pore sizes D exceeding the fluid molecule size, the filling pressures p are found to follow a generic behavior k_BT ln p ∼ γ/ρD where γ and ρ are the fluid surface tension and density. This result is rationalized by showing that the filling chemical potential for such ultra-small pores is the sum of an adsorption energy and a capillary energy that remains meaningful even for severe confinements. A phenomenological model, based on Derjaguin’s formalism to bridge macroscopic and molecular theories for condensation in porous materials, is developed to account for the behavior of fluids confined down to the molecular scale from simple parameters.

Confined fluids in porous media exhibit different behaviors in large and small pores, the crossover between the two regimes being not well understood. Here the authors show, by experiments and simulations, that capillarity is reminiscent even for very small pore diameters, providing a unified picture.

Multiscale poromechanics of wet cement paste

Capillary effects, such as imbibition drying cycles, impact the mechanics of granular systems over time. A multiscale poromechanics framework was applied to cement paste, which is the most common building material, experiencing broad humidity variations over the lifetime of infrastructure. First, the liquid density distribution at intermediate to high relative humidity is obtained using a lattice gas density functional method together with a realistic nanogranular model of cement hydrates. The calculated adsorption/desorption isotherms and pore size distributions are discussed and compare well with nitrogen and water experiments. The standard method for pore size distribution determination from desorption data is evaluated. Second, the integration of the Korteweg liquid stress field around each cement hydrate particle provided the capillary forces at the nanoscale. The cement mesoscale structure was relaxed under the action of the capillary forces. Local irreversible deformations of the cement nanograins assembly were identified due to liquid-solid interactions. The spatial correlations of the nonaffine displacements extend to a few tens of nanometers. Third, the Love-Weber method provided the homogenized liquid stress at the micrometer scale. The homogenization length coincided with the spatial correlation length of nonaffine displacements. Our results on the solid response to capillary stress field suggest that the micrometer-scale texture is not affected by mild drying, while nanoscale irreversible deformations still occur. These results pave the way for understanding capillary phenomena-induced stresses in heterogeneous porous media ranging from construction materials to hydrogels and living systems.

On Condensation and Evaporation Mechanisms in Disordered Porous Materials

Sorption isotherm measurement is a standard method for characterizing porous materials. However, such isotherms are generally hysteretic, differing between condensation and evaporation. Quantitative measurement of pore diameter distributions requires proper identification of the mechanisms at play, a topic which has been and remains the subject of intensive studies. In this paper, we compare high-precision measurements of condensation and evaporation of helium in Vycor, a prototypical disordered porous glass, to a model incorporating mechanisms on the single pore level through a semimacroscopic description and collective effects through lattice simulations. Our experiment determines both the average of the fluid density through volumetric measurements and its spatial fluctuations through light scattering. We show that the model consistently accounts for the temperature dependence of the isotherm shape and of the optical signal over a wide temperature range as well as for the existence of thermally activated relaxation effects. This demonstrates that the evaporation mechanism evolves from pure invasion percolation from the sample's surfaces at the lowest temperature to percolation from bulk cavitated sites at larger temperatures. The model also shows that the experimental lack of optical signals during condensation does not imply that condensation is unaffected by network effects. In fact, these effects are strong enough to make most pores to fill at their equilibrium pressure, a situation deeply contrasting the behavior for isolated pores. This implies that, for disordered porous materials, the classical Barrett-Joyner-Halenda approach, when applied to the condensation branch using an extended version of the Kelvin equation, should properly measure the true pore diameter distribution. Our experimental results support this conclusion.

Capillary Stress and Structural Relaxation in Moist Granular Materials

A numerical and theoretical framework to address the poromechanical effect of capillary stress in complex mesoporous materials is proposed and exemplified for water sorption in cement. We first predict the capillary condensation/evaporation isotherm using lattice-gas simulations in a realistic nanogranular cement model. A phase-field model to calculate moisture-induced capillary stress is then introduced and applied to cement at different water contents. We show that capillary stress is an effective mechanism for eigenstress relaxation in granular heterogeneous porous media, which contributes to the durability of cement.

Multi- and instabilities in gas partitioning between nanoporous materials and rubber balloons

In the two-balloon experiment, two rubber balloons are connected and allowed to exchange gas. Owing to the non-monotonic relationship between the radius of the balloon and the pressure of gas inside it, the two-balloon system presents multi- and in-stabilities. Herein, we consider a two-adsorbent system, where two different adsorbents are allowed to exchange gas. We show that, for rigid adsorbents, the thermodynamic equilibrium state is unique. Then, we consider an adsorbent-balloon system, where an adsorbent exchanges gas with a rubber balloon. This system can exhibit multiple states at thermodynamic equilibrium- two (meta)stable and one unstable. The size of the balloon, pressure of gas in the balloon, and partitioning of gas between the adsorbent and the balloon differ among the equilibrium states. Temperature changes and the addition/removal of gas into/from the adsorbent-balloon system can induce catastrophe bifurcations and show hysteresis. Furthermore, the adsorbent-balloon system exhibits a critical temperature where, when approached from below, the discrepancy of balloon size between the two (meta)stable states decreases and, beyond, bistability is impossible. Practically, our findings preclude multiple partitions of adsorbed gas in rigid, mixed-linker or stratified metal-organic frameworks and may inspire new soft actuator and sensor designs.

Morphology of Fluids Confined in Physically Reconstructed Mesoporous Silica: Experiment and Mean Field Density Functional Theory

Three-dimensional physical reconstruction of the random mesopore network in a hierarchically structured, macroporous-mesoporous silica monolith via electron tomography has been used to generate a lattice model of amorphous, mesoporous silica. This geometrical model has subsequently been employed in mean field density functional theory (MFDFT) calculations of adsorption and desorption. Comparison of the results with experimental sorption isotherms for nitrogen at 77 K shows a good qualitative agreement, with both experiment and theory producing isotherms characterized by type H2 hysteresis. In addition to the isotherms, MFDFT provides the three-dimensional density distribution for the fluid in the porous material for each state studied. We use this information to map the phase distribution in the mesopore network in the hysteresis region. Phase distributions on the desorption boundary curve are compared to those on the adsorption boundary curve for both fixed pressure and fixed density, revealing insights into the relationship between phase distribution and hysteresis.

A comparison of dynamic mean field theory and grand canonical molecular dynamics for the dynamics of pore filling and capillary condensation of fluids in mesopores

We use results from grand canonical molecular dynamics (GCMD) to test the predictions from dynamic mean field theory (DMFT) for the pore filling and capillary condensation mechanisms of a fluid confined in slit shaped mesopores. The theory predicts that capillary condensation occurs by a nucleation process in which a liquid bridge forms between the two walls, and the pore is filled via the growth of this bridge. For longer pores, multiple bridging is seen. These mechanisms are confirmed by the molecular dynamics simulations. The primary difference between the theory and simulations lies in the role of fluctuations. DMFT predicts a single nucleation time and location, while in GCMD (and in nature) a distribution of nucleation times and locations is seen.

Image-based modeling of gas adsorption and deformation in porous media

Understanding adsorption of CO₂ in porous formations is crucial to its sequestration in geological formations. We describe a model for adsorption of CO₂ and the deformation that it induces in a sandstone formation over wide ranges of temperature and pressure. The model couples the thermodynamics of sorption with elastic deformation of the solid. Finite-element computations are then used in order to compute CO₂ adsorption isotherms along with the induced strain in the formation. We also compute the Darcy permeability of the porous medium using the lattice-Boltzmann method. All the computations are carried out with a three-dimensional image of a core sample from Mt. Simon sandstone, the target porous formation for a pilot CO₂ sequestration project that is currently being carried out by Illinois State Geological Survey. Thus, no assumptions are made regarding the shape and sizes of the pore throats and pore bodies. The computed CO₂ sorption isotherm at 195 K is in excellent agreement with our experimental data. The computed permeability is also in good agreement with the measurement. As a further test we also compute the sorption isotherm of N₂ in the same formation at 77.3 K, and show that it is also in good agreement with our experimental data. The model is capable of predicting adsorption of CO₂ (or any other gas for that matter) in porous formations at high pressures and temperatures. Thus, it is used to study the effect of hydrostatic pressure on adsorption and deformation of the porous formation under various conditions. We find that the effect of the confining pressure is more prominent at higher temperatures. Also computed is the depth-dependence of the capacity of the formation for CO₂ adsorption, along with the induced volumetric strain.

Vapor-liquid phase behavior of a size-asymmetric model of ionic fluids confined in a disordered matrix: The collective-variables-based approach

We develop a theory based on the method of collective variables to study the vapor-liquid equilibrium of asymmetric ionic fluids confined in a disordered porous matrix. The approach allows us to formulate the perturbation theory using an extension of the scaled particle theory for a description of a reference system presented as a two-component hard-sphere fluid confined in a hard-sphere matrix. Treating an ionic fluid as a size- and charge-asymmetric primitive model (PM) we derive an explicit expression for the relevant chemical potential of a confined ionic system which takes into account the third-order correlations between ions. Using this expression, the phase diagrams for a size-asymmetric PM are calculated for different matrix porosities as well as for different sizes of matrix and fluid particles. It is observed that general trends of the coexistence curves with the matrix porosity are similar to those of simple fluids under disordered confinement, i.e., the coexistence region gets narrower with a decrease of porosity and, simultaneously, the reduced critical temperature T_{c}^{*} and the critical density ρ_{i,c}^{*} become lower. At the same time, our results suggest that an increase in size asymmetry of oppositely charged ions considerably affects the vapor-liquid diagrams leading to a faster decrease of T_{c}^{*} and ρ_{i,c}^{*} and even to a disappearance of the phase transition, especially for the case of small matrix particles.

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.

Quasi-Two-Dimensional Phase Transition of Methane Adsorbed in Cylindrical Silica Mesopores

Using Monte Carlo and molecular dynamics simulations, we examine the adsorption of methane in cylindrical silica mesopores in an effort to understand a possible phase transition of adsorbed methane in MCM-41 and SBA-15 silica that was previously identified by an unexpected increase in the adsorbed fluid density following capillary condensation, as measured by small-angle neutron scattering (SANS) [Chiang, W-S., et al., Langmuir 2016, 32, 8849]. Our initial simulation results identify a roughly 10 % increase in the density of the liquidlike adsorbed phase for either an isotherm with increasing pressure or an isobar with decreasing temperature and that this densification is associated with a local maximum in the isosteric enthalpy of adsorption. Subsequent analysis of the simulated fluid, via computation of bond-orientational order parameters of specific annular layers of the adsorbed fluid, showed that the layers undergo an ordering transition from a disordered, amorphous state to one with two-dimensional hexagonal structure. Furthermore, this two-dimensional restructuring of the fluid occurs at the same thermodynamic state points as the aforementioned densification and local maximum in the isosteric enthalpy of adsorption. We thus conclude that the densification of the fluid is the result of structural reorganization, which is signaled by the maximum in the isosteric enthalpy. Owing to the qualitative similarity of the structural transitions in the simulated and experimental methane fluids, we propose this hexagonal reorganization as a plausible explanation of the densification observed in SANS measurements. Lastly, we speculate how this structural transition may impact the transport properties of the adsorbed fluid.

Phase transitions in disordered mesoporous solids

Fluids confined in mesoporous solids exhibit a wide range of physical behavior including rich phase equilibria. While a notable progress in their understanding has been achieved for fluids in materials with geometrically ordered pore systems, mesoporous solids with complex pore geometries still remain a topic of active research. In this work we study phase transitions occurring in statistically disordered linear chains of pores with different pore sizes. By considering, quite generally, two phase change mechanisms, nucleation and phase growth, occurring simultaneously we obtain the boundary transitions and the scanning curves resulting upon reversing the sign of the evolution of the chemical potential at different points along the main transition branches. The results obtained are found to reproduces the key experimental observations, including the emergence of hysteresis and the scanning behavior. By deriving the serial pore model isotherm we suggest a robust framework for reliable structural analysis of disordered mesoporous solids.

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.

Hysteresis of liquid adsorption in porous media by coarse-grained Monte Carlo with direct experimental validation

The effects of path-dependent wetting and drying manifest themselves in many types of physical systems, including nanomaterials, biological systems, and porous media such as soil. It is desirable to better understand how these hysteretic macroscopic properties result from a complex interplay between gasses, liquids, and solids at the pore scale. Coarse-Grained Monte Carlo (CGMC) is an appealing approach to model these phenomena in complex pore spaces, including ones determined experimentally. We present two-dimensional CGMC simulations of wetting and drying in two systems with pore spaces determined by sections from micro X-ray computed tomography: a system of randomly distributed spheres and a system of Ottawa sand. Results for the phase distribution, water uptake, and matric suction when corrected for extending to three dimensions show excellent agreement with experimental measurements on the same systems. This supports the hypothesis that CGMC can generate metastable configurations representative of experimental hysteresis and can also be used to predict hysteretic constitutive properties of particular experimental systems, given pore space images.

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.

Adsorption on ordered and disordered duplex layers of porous anodic alumina

We have carried out systematic experiments and numerical simulations of the adsorption on porous anodic aluminum oxide (AAO) duplex layers presenting either an ordered or a disordered interconnecting interface between the large (cavity) and small (constriction) sections of the structured pores. Selective blocking of the pore openings resulted in three different pore topologies: open structured pores, funnel pores, and ink-bottle pores. In the case of the structured pores having an ordered interface, the adsorption isotherms present a rich phenomenology characterized by the presence of two steps in the condensation branch and the opening of one (two) hysteresis loops during evaporation for the ink-bottle (open and funnel) pores. The isotherms can be obtained by summing the isotherms measured on uniform pores having the dimensions of the constrictions or of the cavities. The numerical analysis of the three different pore topologies indicates that the shape of the junction between the two pore sections is only important for the adsorption branch. In particular, a conic junction which resembles that of the AAO pores represents the experimental isotherms for the open and funnel pores better, but the shape of the junction in the ink bottle pores does not matter. The isotherms for the duplex layers with a disordered interface display the same general features found for the ordered duplex layers. In both cases, the adsorption branches coincide and have two steps which are shifted to lower relative pressures compared to those for the ordered duplex. Furthermore, the desorption branches comprise hysteresis loops much wider than those of the ordered duplex layers. Overall, this study highlights the important role played by morphologies where there are interconnections between large and small pores.

Theoretical model for fluid-solid coupling in porous materials

This paper introduces a unifying theory for describing complex behavior for porous materials. The key ingredients are the stored energy in solid-fluid interaction as well as the solid-solid and fluid-fluid interactions. A finite element formulation is employed which naturally accounts for the pore-pore network effects and is easily applicable to most pore geometries such as cellular solids and foams. The interactions, built in at the finite element level, give rise to the mechanical response of the macroscopic material unit. Through numerical studies, we show that there is strong coupling between fluid and solid that induces complex mechanical response, i.e., hysteresis and anisotropy. It is demonstrated that hysteresis arises directly from the fluid-solid coupling. We term this type of hysteresis emergent hysteresis.

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.

Unexpected sorption-induced deformation of nanoporous glass: evidence for spatial rearrangement of adsorbed argon

Sorption of substances in pores generally results in a deformation of the porous matrix. The clarification of this effect is of particular importance for the recovery of methane and the geological storage of CO2. As a model system, we study the macroscopic deformation of nanoporous Vycor glass during the sorption of argon using capacitative measurements of the length change of the sample. Upon desorption we observe an unpredicted sharp contraction and re-expansion peak, which contains information on the draining mechanism of the porous sample. We have modified the theoretical model by Gor and Neimark1 to predict the sorption-induced deformation of (partly) filled porous samples. In this analysis, the contraction is attributed to a metastable or nonequilibrium configuration where a thin surface layer on the pore walls coexists with capillary bridges. Alternatively, pore blocking and cavitation during the draining of the polydisperse pore network can be at the origin of the deformation peak. The results are a substantial step toward a correlation between the spatial configuration of adsorbate, its interaction with the host material, and the resulting deformation.

Condensation of helium in aerogel and athermal dynamics of the random-field Ising model

High resolution measurements reveal that condensation isotherms of (4)He in high porosity silica aerogel become discontinuous below a critical temperature. We show that this behavior does not correspond to an equilibrium phase transition modified by the disorder induced by the aerogel structure, but to the disorder-driven critical point predicted for the athermal out-of-equilibrium dynamics of the random-field Ising model. Our results evidence the key role of nonequilibrium effects in the phase transitions of disordered systems.

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.