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

Bulk supercooled water versus adsorbed films on silica surfaces: specific heat by Monte Carlo simulation

Between 150 and 230.6 K, bulk supercooled water freezes upon cooling, and amorphous ice crystallizes upon heating: bulk water thus exists only in its stable ice form. To circumvent this problem, experiments are generally performed on water adsorbed in SiO2 based porous systems. In this work, we take advantage of Monte Carlo simulations to explore this metastable supercooled region inaccessible to experiments. Using three rigid, non-polarizable water models, namely SPC, TIP4P and TIP4P/2005, we investigate the isobaric specific heat capacity (Cp), between 100 and 300 K, of bulk water and water films of few monolayers adsorbed on different SiO2 surfaces: a smooth surface, a non-hydroxylated (0001) surface of quartz, and a fully hydroxylated (001) surface of cristobalite. As Cp is directly related to the entropy fluctuations and we focus on low temperatures, the convergence of the Monte Carlo simulations is a critical point of this work. Also, due to the small mass of the hydrogen atoms, quantum corrections are taken into account, and lead to an excellent agreement of the simulated and experimental Cp values at low temperature (100 K region). Altogether, we conclude that, in bulk, Cp is shown to exhibit a broad peak around 225 K for the SPC and TIP4P models, and around 250 K for the TIP4P/2005 model, in qualitative agreement with the experimentally observed features in Cp measurements. For interfacial water, in all cases, the broad Cp peak disappears. This result, at odds with experimental observations, suggests that disorder and hydrogen bonding at the interface (not yet taken into account) have a fundamental role in confined water transitions.

Mesoscopic modeling of structural and thermodynamic properties of fluids confined by rough surfaces

Simulations show that the ordering of particles confined by rough surfaces induces a structural phase transition while the interfacial tension is insensitive to it.

Influence of system size on the properties of a fluid adsorbed in a nanopore: Physical manifestations and methodological consequences

Hysteresis and discontinuities in the isotherms of a fluid adsorbed in a nanopore in general hamper the determination of equilibrium thermodynamic properties, even in computer simulations. A way around this has been to consider both a reservoir of small size and a pore of small extent in order to restrict the fluctuations of density and approach a classical van der Waals loop. We assess this suggestion by thoroughly studying through Monte Carlo simulations and density functional theory the influence of system size on the equilibrium configurations of the adsorbed fluid and on the resulting isotherms. We stress the importance of pore-symmetry-breaking states that even for modest pore sizes lead to discontinuous isotherms and we discuss the physical relevance of these states and the methodological consequences for computing thermodynamic quantities.

Modeling micelle-templated mesoporous material SBA-15: atomistic model and gas adsorption studies

We report the development of a realistic molecular model for mesoporous silica SBA-15, which includes both the large cylindrical mesopores and the smaller micropores in the pore walls. The methodology for modeling the SBA-15 structure involves molecular and mesoscale simulations combined with geometrical interpolation techniques. First, a mesoscale model is prepared by mimicking the synthesis process using lattice Monte Carlo simulations. The main physical features of this mesoscale pore model are then carved out of an atomistic silica block; both the mesopores and the micropores are incorporated from the mimetic simulations. The calculated pore size distribution, surface area, and simulated TEM images of the model structure are in good agreement with those obtained from experimental samples of SBA-15. We then investigate the adsorption of argon in this structure using Grand Canonical Monte Carlo (GCMC) simulations. The adsorption results for our SBA-15 model are compared with those for a similar model that does not include the micropores; we also compare with results obtained in a regular cylindrical pore. The simulated adsorption isotherm for the SBA-15 model shows semiquantitative agreement with the experimental isotherm for a SBA-15 sample having a similar pore size. We observe that the presence of the micropores leads to increased adsorption at low pressure compared to the case of a model without micropores in the pore walls. At higher pressures, for all models, the filling proceeds via the monolayer-multilayer adsorption on the mesopore surface followed by capillary condensation, which is mainly controlled by the mesopore diameter and is not influenced by the presence of the micropores.

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.

Monte-Carlo multiscale simulation study of argon adsorption/desorption hysteresis in mesoporous heterogeneous tubular pores like MCM-41 or oxidized porous silicon

In a recent paper [J. Chem. Phys. 2007, 127, 154701] a multiscale approach was introduced which allowed calculation of adsorption/desorption hysteresis for fluid confined in a single mesoporous, heterogeneous tubular pore. The main interest in using such an approach is that it allows one to reconcile a molecular simulation approach generally limited to the nanometer scale (atomistic description of the confined fluid and pore roughness) with the much larger scale (micrometer) relevant to understand the complexity of adsorption/desorption hysteresis (the numerous metastable states in the hysteresis loop are a consequence of the large-scale disorder in the porous material). In this paper, this multiscale approach is used to study adsorption phenomena in mesoporous models made of a collection of disordered, noninterconnected tubular pores, as MCM-41 or porous silicon. A double distribution is introduced: one to characterize the disorder in a given pore, and the other to characterize the disorder between the pores. We consider two distribution shapes: Gaussian and uniform truncated and two cases of pores open at one or both ends. These models are expected to cover a wide variety of real materials made of independent pores, as MCM-41 and oxidized porous silicon. A large variety of hysteresis shapes is obtained, ranging from almost parallel adsorption/desorption branches typical of MCM-41 adsorption to triangular hysteresis typical of porous silicon. The structure of the metastable states inside the hysteresis (scanning adsorption/desorption curves) is also examined. The results are expected to be useful to experimentalists who want to infer pore structure and level of disorder from experimental adsorption/desorption experiments.

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.

Colloid-polymer mixtures in the presence of quenched disorder: a theoretical and computer simulation study

We use theory and computer simulation to study the structure and phase behavior of colloid-polymer mixtures in the presence of quenched disorder. The Asakura-Oosawa model (AO) (Asakura and Oosawa 1954 J. Chem. Phys. 22 1255) is used to describe the colloid-colloid, colloid-polymer, and polymer-polymer pair interactions. We then investigate the behavior of this model in the presence of frozen-in (quenched) obstacles. The obstacles will be placed according to two different scenarios, both of which are experimentally feasible. In the first scenario, polymers are distributed at positions drawn from an ideal gas configuration. In the second scenario, colloidal particles are distributed at positions drawn from an equilibrium hard sphere configuration. We investigate how the unmixing transition of the AO model is affected by the type of quenched disorder. The theoretical formalism is based on the replica method of Given and Stell (1994 Physica A 209 495). Our foremost aim is to test the accuracy of three common closures to the replica Ornstein-Zernike equations, namely the hypernetted chain, the Percus-Yevick, and the Martinov-Sarkisov equations. The accuracy is determined by comparison with grand canonical Monte Carlo simulations. We find that, for quenched polymer disorder, all three closures perform remarkably well. However, when quenched colloid disorder is considered, i.e. the second mentioned scenario, the predictions of all three closures worsen dramatically.

Thermodynamic pressure of simple fluids confined in cylindrical nanopores by isothermal-isobaric Monte Carlo: influence of fluid/substrate interactions

The thermodynamic pressure or grand potential density is calculated by isobaric-isothermal Monte Carlo algorithm for simple Lennard-Jones fluid confined in cylindrical pores presenting chemical heterogeneities along their axis. Heuristic arguments and simulation results show that the thermodynamic pressure of the confined fluid contains two contributions. The first term is the usual pressure of the bulk fluid for a density equal to the confined fluid density defined as the total number of confined particles divided by the accessible volume due to thermal agitation. A second term has to be added, which is empirically shown to be proportional to the fluid/wall interface area and almost constant along the adsorption and desorption branches. This interfacial contribution, calculated for various pore models, has small variations reminiscent of the fluid adsorption/desorption properties calculated in the various pores. In particular, it is shown that this interfacial quantity is maximum for a fluid/substrate interaction intensity of the same order as the fluid/fluid one, while the thermodynamic pressure at which rapid desorption occurs presents a minimum. Stronger or weaker fluid/wall affinity favors gas state nucleation on the desorption of confined fluids.

Surface excess free energy of simple fluids confined in cylindrical pores by isothermal-isobaric Monte Carlo: influence of pore size

Confined fluid properties are mainly determined by interfacial phenomena characterized by surface quantities. Based on a simple model of Lennard-Jones particles confined in a cylindrical pore, this study introduces a grand potential surface quantity to quantify the difference in the thermodynamic pressure between the bulk and the confined fluids. The usual surface tension gamma defined as this grand potential difference for the same chemical potential in both confined and bulk states is generally strongly dependent on both the chemical potential and temperature. It is proposed here to introduce another surface quantity zeta which measures the thermodynamic pressure difference between confined and bulk states for identical densities. It is shown that this quantity is much less dependent on confined fluid density or chemical potential. It is actually constant along the gas-like and liquid-like adsorption/desorption branches for an irreversible isotherm (hysteresis), with a different value for each branch. For reversible supercritical isotherms, zeta is shown to remain constant in the low and high density parts of the isotherm. This independence on chemical potential (or equivalently fluid density) is believed to be of great interest for practical applications when one desires to calculate thermodynamic quantities such as the usual surface tension gamma or the thermodynamic pressure of a confined fluid for any given chemical potential and temperature. Such calculations are required to determine fundamental properties such as metastability or coexistence. The effects of temperature, fluid/substrate interaction strength, and pore size are studied.

Influence of surface chemical heterogeneities on adsorption/desorption hysteresis and coexistence diagram of metastable states within cylindrical pores

Grand canonical Monte Carlo simulations are performed to determine the adsorption/desorption isotherms at different temperatures of a Lennard-Jones fluid confined within a simple model of cylindrical pores presenting chemical heterogeneities. A complex hysteresis loop is observed, showing hysteresis subloops (scanning curves). This is shown to be consistent with the existence of several metastable states (local minima in the system free energy). A recent extension to the Gibbs ensemble technique is then used to calculate the complete coexistence diagram of these local minima.

Capillary phase transitions of linear and branched alkanes in carbon nanotubes from molecular simulation

Capillary phase transitions of linear (from C(1) to C(12)) and branched (C(5) isomers) alkanes in single-walled carbon nanotubes have been investigated using the gauge-cell Monte Carlo simulation. The isotherm at a supercritical temperature increases monotonically with chemical potential and coincides with that from the traditional grand canonical Monte Carlo simulation, whereas the isotherm at a subcritical temperature exhibits a sigmoid van der Waals loop including stable, metastable, and unstable regions. Along this loop, the coexisting phases are determined using an Maxwell equal-area construction. A generic confinement effect is found that reduces the saturation chemical potential, lowers the critical temperature, increases the critical density, and shrinks the phase envelope. The effect is greater in a smaller diameter nanotube and is greater in a nanotube than in a nanoslit.