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

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.

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.

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.

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.

Lower closure point of adsorption hysteresis in ordered mesoporous silicas

To examine the nature of the lower closure point of adsorption hysteresis in ordered mesoporous silicas, we measured the temperature dependence of the adsorption-desorption isotherm of nitrogen for three kinds of ordered silicas with cagelike pores and three kinds of ordered silicas with cylindrical pores. The lower closure point pressure of nitrogen in the cagelike pores with sufficiently small necks, that is, the cavitation pressure of a confined liquid, did not depend appreciably on the cage size in the temperature region far away from a hysteresis critical temperature (Tch) but its cage-size dependence was noticeable in the vicinity of Tch. The lower closure point in the cylindrical pores depended on the pore size, and its thermal behavior was totally different from that in the cagelike pores. Nevertheless, the hysteresis critical points of nitrogen in the ordered mesoporous silicas, which are defined as a threshold of temperatures (Tch) and pressure above which reversible capillary condensation takes place in a given size and shape of pores, fell on a common line in a temperature-pressure diagram regardless of the pore geometries. We consider this finding as evidence that capillary evaporation in the cylindrical pores follows a cavitation process in the vicinity of Tch in the same way as that in the cagelike pores and also that the low limit of the hysteresis loop that has been long recognized since 1965 is due to the occurrence of a vapor bubble in a stretched metastable liquid confined to the pores with decreasing pressure (cavitation).

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.

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.