Experimental Study on Phase Transitions of Carbon Dioxide Confined in Nanopores: Evaporation, Melting, Sublimation, and Triple Point.

Capillary phase transitions (evaporation, melting, and sublimation) and the pore triple point of CO2 confined in MCM-41 mesoporous media with a pore diameter of 3.5 nm have been studied by using an isochoric heating procedure in a high-pressure low-temperature differential scanning calorimeter over a pressure range of 0.5-40.5 bar. The procedure is validated by the agreement between the measured conditions of bulk evaporation/sublimation and literature data. The main finding in this work is that the solid-to-fluid phase transitions of CO2 in MCM-41 shift to temperatures higher than those of the corresponding bulk phase transitions. It is also found that the formation of a solid phase of CO2 in MCM-41 does not require the presence of a liquid or solid in the bulk. The capillary-melting and capillary-evaporation curves approach each other as temperature decreases until they meet at the pore triple point. The effect of pressure on capillary melting temperature is significant at pressures close to the pore triple point. Furthermore, the capillary-melting curve approaches the bulk saturated vapor-pressure curve as temperature increases, thus hinting an agreement with the prediction by molecular dynamics simulation in the literature that the curves eventually intersect each other at a high temperature and pressure. Based on the measured capillary phase transitions, the pore triple-point temperature and pressure of nanoconfined CO2 are bracketed and found to be much lower than those of the bulk triple point.

Non-isoplethic measurement on the solid-liquid-vapor equilibrium of binary mixtures at cryogenic temperatures.

We measured the solid-liquid-vapor (SLV) equilibrium of binary mixtures during experiments that alternated between cooling the mixture and injecting the more-volatile component into the sample chamber; thus, the composition of the mixture changed (non-isoplethic) throughout the experiment. Four binary mixtures were used in the experiments to represent mixtures with miscible solid phases (N2/CO) and barely miscible solid solutions (N2/C2H6), as well as mixtures with intermediate solid miscibility (N2/CH4 and CO/CH4). We measured new SLV pressure data for the binary mixtures, except for N2/CH4, which are also available in the literature for verification in this work. While these mixtures are of great interest in planetary science and cryogenics, the resulting pressure data are also needed for modeling purposes. We found the results for N2/CH4 to be consistent with the literature. The resulting new SLV curve for CO/CH4 shows similarities to N2/CH4. Both have two density inversion points (bracketing the temperature range where the solid floats). This result is important for places such as Pluto, Triton, and Titan, where these mixtures exist in vapor, liquid, and solid phases. Based on our experiments, the presence of a eutectic is unlikely for the N2/CH4 and CO/CH4 systems. An azeotrope with or without a peritectic is likely, but further investigations are needed to confirm. The N2/CO system does not have a density inversion point, as the ice always sinks in its liquid. For N2/C2H6, new SLV pressure data were measured near each triple point of the pure components.

First-order and gradual phase transitions of ethane confined in MCM-41.

The first-order phase transition of ethane confined in MCM-41, i.e., capillary condensation, has been measured using an isochoric cooling procedure by differential scanning calorimetry (DSC) under conditions ranging from 206 K and 1.1 bar up to the pore critical point (PCP). The PCP has also been determined using the three-line method developed earlier based on the vanishing heat of phase transition. As in the bulk phase, no first-order phase transition can occur above the critical point, which also implies that vapor can transform into liquid gradually by following a path around the critical point through the supercritical region. For the first time, the gradual phase transition is demonstrated with ethane in MCM-41, which is achieved through a multistep process with paths proceeding around the PCP without crossing the capillary-condensation curve. The occurrence of the gradual phase transition in nanopores, thus the confined supercriticality, is confirmed while our consistent DSC measurements are also well demonstrated.

Phase Transition and Criticality of Methane Confined in Nanopores.

For the first time, the phase transition and criticality of methane confined in nanoporous media are measured. The measurement is performed by establishing an experimental setup utilizing a differential scanning calorimeter capable of operating under very low temperatures as well as high pressures to detect the capillary phase transition of methane inside nanopores. By performing experiments along isochoric cooling paths, both the capillary condensation and the bulk condensation of methane are detected. The pore critical point of nanoconfined methane is also determined and then used to derive the parameters of a previously developed self-consistent equation of state based on the generalized van der Waals partition function. Using these parameters, the equation of state can predict the capillary-condensation curves that agree well with the experimental data.

Prototype equation of state for phase transition of confined fluids based on the generalized van der Waals partition function.

A simple self-consistent prototype equation of state (EOS) based on the generalized van der Waals (vdW) partition function has been demonstrated to describe the phase transition of simple fluids in nanopores with uniform size. Different from those commonly presented in the literature, the new EOS does not need an auxiliary equation that is conventionally applied to provide the capillary pressure derived from surface tension. The encouraging performance of the EOS calls for further extension to applications with more complex fluids and porous media.

Isochoric measurement of the evaporation point of pure fluids in bulk and nanoporous media using differential scanning calorimetry.

As a continuation of recent series of work, a new approach applying an isochoric heating process using differential scanning calorimetry (DSC) is introduced to measure the evaporation point of pure fluids in both bulk phase and nanoporous media, as opposed to the previous approach of isochoric cooling to measure the condensation point [X. Qiu et al., Phys. Chem. Chem. Phys., 2018, 20, 26241-26248; X. Qiu et al., Phys. Chem. Chem. Phys., 2019, 21, 224-231]. Though these two approaches must arrive at the same phase-transition point for a specified density of bulk pure fluids, it is not necessarily true for confined fluids due to hysteresis in a temperature range sufficiently far below the bulk critical point. The isochoric heating process allows one to accurately measure the phase transition of non-volatile fluids that exist in liquid phase at relatively high temperatures. As the new approach operates without an inert gas, which substantially dissolves in the test sample at high pressures if the standard isobaric measurement ASTM E1782 is used, application to the high-pressure range is enabled with higher accuracy. This method can also be extended to confined systems, where the evaporation points of both bulk and confined fluids are successively measured in a single run of experiment. The results reveal that capillary evaporation, i.e., evaporation of fluids confined in nanoporous media, occurs at a higher temperature (isobarically), or at a lower pressure (isothermally), than that in bulk only after the liquid in bulk space is completely evaporated. The method introduced in this work paves a new way to study the condensation/evaporation hysteresis of confined fluids as well as the evaporation point of confined fluid mixtures.

Experimental Study on the Criticality of a Methane/Ethane Mixture Confined in Nanoporous Media.

For the first time, the critical region of a methane/ethane mixture confined in nanoporous media (SBA-15) is experimentally investigated using differential scanning calorimetry with an isochoric cooling procedure. The results reveal that the supercritical region of the confined fluid mixture exists at a lower pressure than its counterpart in the bulk space. The shift of the critical region is dependent on the pore size, which is similar to that of pure fluids [Tan et al., J. Phys. Chem. C, 2019, 123, 9824-9830]. Specifically, compared to that in bulk, the shift is greater for smaller pore size. The heat of capillary condensation of this mixture is also discussed. The findings in this work would shed some light on the understanding of confined phase behavior, especially criticality, in investigations toward more complex confined mixtures encountered in practical engineering application, for example, oil and gas recovery from unconventional reservoirs.

Simple and accurate isochoric differential scanning calorimetry measurements: phase transitions for pure fluids and mixtures in nanopores.

Various types of nanopores are encountered in many different engineering and science applications. Due to incomplete understanding of the phase behavior of fluids in nanosize confined space, the improvement of such applications has been largely based on experience and empirical approaches. Therefore, experimental studies on the phase behavior of confined fluids that are simple but accurate are still urgently needed. We recently developed a new isochoric procedure using a Differential Scanning Calorimeter (DSC) to measure the onset of vapor-liquid phase transitions, which has been successfully used in experiments measuring the vapor pressures of pure substances and the dew points of a bulk mixture in the absence of nanopores [Qiu et al., Phys. Chem. Chem. Phys., 2018, 20, 26241-26248]. It is the purpose of this work to extend the new method to confined fluids. To demonstrate the superior ability of the new method, we measure the capillary condensation of CO2 and the dew points of a binary methane/ethane gas mixture confined in SBA-15 with different pore diameters.

Novel isochoric measurement of the onset of vapor-liquid phase transition using differential scanning calorimetry.

A novel method for measuring the onset of vapor-liquid phase transition applying an isochoric procedure in a high-pressure micro differential scanning calorimeter is introduced for the first time. Isochoric dew-point measurement is used to measure vapor pressures of CO2 at different boiling temperatures and dew points of a methane/ethane gas mixture at different pressures or temperatures. The isochoric two-phase bubble-point measurement, similar to the isobaric method, is also demonstrated to measure vapor pressures of methanol at different boiling temperatures. All results are in agreement with the literature data. The isochoric method is found to be superior to the widely used isobaric method. It can be used to measure the onset of vapor-liquid phase transition for a wide range of substances and mixtures, including the ones for which the isobaric method is inapplicable, and it eliminates difficulties usually encountered in the isobaric method. The proposed method along with the findings of this study can pave the way for experimental measurements of phase equilibria in more complex systems.

Phenomenological Study of Confined Criticality: Insights from the Capillary Condensation of Propane, n-Butane, and n-Pentane in Nanopores.

We use the comparison of experimentally measured isotherms for propane, n-butane, and n-pentane in 2.90, 4.19, and 8.08 nm MCM-41 to show that the current model for the progression of capillary condensation may not hold true for chain molecules, such as normal alkanes. Until now, the capillary condensation of gases in unconnected, uniformly sized and shaped nanopores has been shown to progress in two distinct stages before ending in supercriticality of the confined fluid. First, at relatively low temperatures in isothermal measurements, the phase change is accompanied by hysteresis of adsorption and desorption. Second, as temperature increases, the hysteresis critical temperature is surpassed, and the phase change occurs reversibly. Although propane followed this progression, we observed a new progression for n-butane and n-pentane, in which hysteresis continues into the supercritical region of the confined fluid. We attribute this behavior to the molecular chain lengths of the adsorbates. Through further comparison of the adsorption, desorption, and critical properties of the adsorbates, we discovered new pressure phenomena of the confined supercritical fluids.

Capillary Condensation of Binary and Ternary Mixtures of n-Pentane-Isopentane-CO2 in Nanopores: An Experimental Study on the Effects of Composition and Equilibrium.

Confinement in nanopores can significantly impact the chemical and physical behavior of fluids. While some quantitative understanding is available for how pure fluids behave in nanopores, there is little such insight for mixtures. This study aims to shed light on how nanoporosity impacts the phase behavior and composition of confined mixtures through comparison of the effects of static and dynamic equilibrium on experimentally measured isotherms and chromatographic analysis of the experimental fluids. To this end, a novel gravimetric apparatus is introduced and validated. Unlike apparatuses that have been previously used to study the confinement-induced phase behavior of fluids, this apparatus employs a gravimetric technique capable of discerning phase transitions in a wide variety of nanoporous media under both static and dynamic conditions. The apparatus was successfully validated against data in the literature for pure carbon dioxide and n-pentane. Then, isotherms were generated for binary mixtures of carbon dioxide and n-pentane using static and flow-through methods. Finally, two ternary mixtures of carbon dioxide, n-pentane, and isopentane were measured using the static method. While the equilibrium time was found important for determination of confined phase transitions, flow rate in the dynamic method was not found to affect the confined phase behavior. For all measurements, the results indicate qualitative transferability of the bulk phase behavior to the confined fluid.

Retrograde behavior revisited: implications for confined fluid phase equilibria in nanopores.

Many fluid mixtures exhibit retrograde behavior, including those that define natural gases. While the behavior is well understood for mixtures in bulk, it is not so in nanosize porous space that dominates shale formations in unconventional reservoirs. The lack of experimental data creates the need for modeling works to make estimates as good as possible due to immediate needs in gas recovery. However, such efforts have been straying without firm guidance from systematic studies over what we have known so far. This article is intended to present the results of such a study that would incite further investigations in this area of research. Revisiting the retrograde behavior in the bulk is appropriate to start with, followed by a short review of what we know about fluids confined in nanosize pores. Based on this information, implications for the behavior of confined mixtures in the retrograde region can be inferred. The implied features that have been supported by experimental evidence are the locations of the confined dew point and bubble point at low temperatures, which are both at pressures lower than their bulk counterparts. Another feature found in this study is completely new, and therefore still open for further investigation. We reveal that the dew-point and bubble-point curves of confined mixtures end at moderate pressures on a multiphase curve, beyond which equilibrium occurs among the bulk and confined phases. The well-known points in the bulk retrograde region, i.e. the critical point and cricondenbar, are consequently absent in confined mixtures.

Heat of capillary condensation in nanopores: new insights from the equation of state.

Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) coupled with the Young-Laplace equation is a recently developed equation of state (EOS) that successfully presents not only the capillary condensation but also the pore critical phenomena. The development of this new EOS allows further investigation of the heats involved in condensation. Compared to the conventional approaches, the EOS calculations present the temperature-dependent behavior of the heat of capillary condensation as well as that of the contributing effects. The confinement effect was found to be the strongest at the pore critical point. Therefore, contrary to the bulk heat condensation that vanishes at the critical point, the heat of capillary condensation in small pores shows a minimum and then increases with temperature when approaching the pore critical temperature. Strong support for the existence of the pore critical point is also discussed as the volume expansivity of the condensed phase in confinement was found to increase dramatically near the pore critical temperature. At high reduced temperatures, the Clausius-Clapeyron equation was found to apply better for confined fluids than it does for bulk fluids.

Accurate Monte Carlo simulations on FCC and HCP Lennard-Jones solids at very low temperatures and high reduced densities up to 1.30.

Canonical Monte Carlo simulations on face-centered cubic (FCC) and hexagonal closed packed (HCP) Lennard-Jones (LJ) solids are conducted at very low temperatures (0.10 ≤ T(∗) ≤ 1.20) and high densities (0.96 ≤ ρ(∗) ≤ 1.30). A simple and robust method is introduced to determine whether or not the cutoff distance used in the simulation is large enough to provide accurate thermodynamic properties, which enables us to distinguish the properties of FCC from that of HCP LJ solids with confidence, despite their close similarities. Free-energy expressions derived from the simulation results are also proposed, not only to describe the properties of those individual structures but also the FCC-liquid, FCC-vapor, and FCC-HCP solid phase equilibria.

Statistical associating fluid theory coupled with restrictive primitive model extended to bivalent ions. SAFT2: 2. Brine/seawater properties predicted.

Statistical associating fluid theory coupled with restricted primitive model (SAFT2) represents the properties of aqueous multiple-salt solutions, such as brine/seawater. The osmotic coefficients, densities, and vapor pressures are predicted without any additional parameters using the salt hydrated diameters obtained for single-salt solutions. For a given ion composition of brine, the predicted vapor pressure, osmotic coefficient, activity of water, and density are found to agree with the experimental data.

Statistical associating fluid theory coupled with restrictive primitive model extended to bivalent ions. SAFT2: 1. Single salt + water solutions.

Statistical associating fluid theory coupled with the restricted primitive model is extended to multivalent ions by relaxing the range of the square-well width parameter, which leads to a new dispersion term approximation and calls for a new set of salt and ion parameters. This new approximation, referred to as SAFT2, requires a single set of parameters derived from the salt (mean ionic) activity coefficients and liquid densities of single-salt solutions for five cations (Li(+), Na(+), K(+), Ca(2+), Mg(2+)), six anions (Cl(-), Br(-), I(-), NO(3)(-), SO(4)(-2), HCO(3)(-)), and 24 salts. These parameters, in turn, are shown to predict the osmotic coefficients for single salt + water solutions.