Thermodynamic Characterization of Fluids Confined in Heterogeneous Pores by Monte Carlo Simulations in the Grand Canonical and the Isobaric−Isothermal Ensembles

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.

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.

A density functional theory for Lennard-Jones fluids in cylindrical pores and its applications to adsorption of nitrogen on MCM-41 materials

A density functional theory (DFT) constructed from the modified fundamental-measure theory and the modified Benedict-Webb-Rubin equation of state is presented. The Helmholtz free energy functional due to attractive interaction is expressed as a functional of attractive weighted-density in which the weight function is a mean-field-like type. An obvious advantage of the present theory is that it reproduces accurate bulk properties such as chemical potential, bulk pressure, vapor-liquid interfacial tension, and so forth when compared with molecular simulations and experiments with the same set of molecular parameters. Capabilities of the present DFT are demonstrated by its applicability to adsorption of argon and nitrogen on, respectively, a model cylindrical pore and mesoporous MCM-41 materials. Comparison of the theoretical results of argon in the model cylindrical pore with those from the newly published molecular simulations indicates that the present DFT predicts accurate average densities in the pore, slightly overestimates the pore pressure, and correctly describes the effect of the fluid-pore wall interaction on average densities and pressures in the pore. Application to adsorption of nitrogen on MCM-41 at 77.4 K shows that the present DFT predicts density profiles and adsorption isotherms in good agreement with those from molecular simulations and experiments. In contrast, the hysteresis loop of adsorption calculated from the mean-field theory shifts toward the low pressure region because a low bulk saturated pressure is produced from the mean-field equation of state. The present DFT offers a good way to describe the adsorption isotherms of porous materials as a function of temperature and pressure.

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.

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.