Capillary Phase Transition Research Articles

Correlation effect between the capillary flow and evaporation rate of water in a 2-D photothermal membrane

To shed light on the correlation effect between the capillary flow and phase transition of water in photothermal evaporation, the non-equilibrium molecular dynamics (NEMD) simulations were employed to investigate the evaporation of water in Multilayered graphene oxide membranes. It was initially found that water molecules need to overcome strong energy barriers to migrate upward by layers before evaporation, with the energy barrier increasing with the reduction in nanogap, hydroxyl content, or increase in layer spacing of graphene sheets. The strong energy barrier accordingly results in dramatic sensible heat conversion and high evaporation temperature. It was shown that the enhanced temperature and hydrophilicity both weaken the hydrogen bond strength of water molecules confined in 2-dimensional channels, contributing to the reduced evaporation enthalpy. The preferential pathways in graphene channels or the weakened hydrogen bonds in hydroxyl-functionalized graphene of water molecules were found to be important influences on capillary flow energy consumption, leading to differences in evaporation energy supply. In combination with these effects, the evaporation rate could be increased by up to 2 folds and an interfacial enthalpy of evaporation below 1500 kJ kg−1 could be achieved by properly tuning the configuration and chemical properties of the graphene membrane. Our findings lay a theoretical foundation for providing a strategy to improve the interfacial evaporation performance in desalination.

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.

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.

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.

Preparation of Supported Ionic Liquid Membranes Using a Supercritical Fluid Deposition Method and Study of the Capillary Phase Transition of Ionic Liquids in Supercritical CO2

Supported ionic liquid membranes (SILMs) based on [EMIM][Ac] and γ-Al2O3 membranes were prepared using a supercritical fluid deposition (SCFD) method at 12 MPa and 50 °C. The influences of the preparation time, ionic liquid loading, and ethanol content on the performance of SILMs were studied. The CO2/N2 selectivity of the as-prepared SILMs reached the ideal selectivity of [EMIM][Ac]. When the ionic liquid (IL) was dissolved in a mixture of supercritical CO2 (scCO2) and ethanol, the IL easily diffused into the small pores in supports. Moreover, the dissolved IL could transition to the liquid phase in the small pores because of the capillary phase transition, leading to the selective filling of the meso- and micropores in the supports. The surface tension of the liquid phase and the ratio of the IL concentration to the saturation IL concentration were found to be the key factors influencing the capillary phase transition of the IL.

Molecular simulation of capillary phase transitions in flexible porous materials.

We used flat-histogram sampling Monte Carlo to study capillary phase transitions in deformable adsorbent materials. Specifically, we considered a pure adsorbate fluid below its bulk critical temperature within a slit pore of variable pore width. The instantaneous pore width is dictated by a number of factors, such as adsorbate loading, reservoir pressure, fluid-wall interaction, and bare adsorbent properties. In the slit pores studied here, the bare adsorbent free energy was assumed to be biparabolic, consisting of two preferential pore configurations, namely, the narrow pore and the large pore configurations. Four distinct phases could be found in the adsorption isotherms. We found a low-pressure phase transition, driven primarily by capillary condensation/evaporation and accompanied by adsorbent deformation in response. The deformation can be a relatively small contraction/expansion as seen in elastic materials, or a large-scale structural transformation of the adsorbent. We also found a high-pressure transition driven by excluded volume effects, which tends to expand the material and thus results in a large-scale structural transformation of the adsorbent. The adsorption isotherms and osmotic free energies can be rationalized by considering the relative free energy differences between the basins of the bare adsorbent free energy.

Use of the Grand Canonical Transition-Matrix Monte Carlo Method to Model Gas Adsorption in Porous Materials

We present grand canonical transition-matrix Monte Carlo (GC-TMMC) as an efficient method for simulating gas adsorption processes, with particular emphasis on subcritical gas adsorption in which capillary phase transitions are present. As in other applications of TMMC, the goal of the simulation is to compute a particle number probability distribution (PNPD), from which thermophysical properties of the system can be computed. The key advantage of GC-TMMC is that, by appropriate use of histogram reweighting, one can generate an entire adsorption isotherm, including those with hysteresis loops, from the PNPD generated by a single GC-TMMC simulation. We discuss how to determine various thermophysical properties of an adsorptive system from the PNPD, including the identification of capillary phases and capillary phase transitions, the equilibrium phase transition, other free energies, and the heat of adsorption. To demonstrate the utility of GC-TMMC for studies of adsorption, we apply the method to various sy...

Simulation of Capillary Effects and Phase Transition under Freezing and Thawing Load in Liquid and Gas Saturated Porous Media

AbstractIn this article, a quadruple macroscopic model for the simulation of freeze‐thaw cycles in liquid‐ and gas filled porous media is presented. Attention is paid to the description of capillary effects and phase transition. In effect, this model describes the following aspects: expansion of ice during freezing, liquid and gas pressure on the surrounding surfaces, capillary effects, temperature distribution, and the influence of filter velocities. The illustrated results of the numerical example show that the simplified model is capable of predicting physical and experimental observations. Besides the influence of heat of fusion, especially, capillary suction as well as frost suction in liquid‐ and gas filled porous media under cycling thermal loading will be presented. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Acute effect of trace component on capillary phase transition of n-alkanes

The significant influence of trace chain molecules on the capillary phase transition (CPT)of n-alkanes in porous carbon is investigated systematically for the first time using aclassical density functional theory (DFT). It is discovered that: (i) the CPT ofn-alkanes can be adjusted to occur at a much lower concentration than whenthe trace chain component is absent; (ii) potential parameters of the trace chainmolecule, and its concentration in the bulk, show their acute effects within aparticular range beyond which the modulation effect eventually becomes a bitconstant; (iii) an acute modulation effect can be induced only if the number ofsegments per trace chain molecule is larger than or equal to that of the segments peralkane considered. The present discoveries have implications for the separation andenrichment of low concentration components, and easy and precise control ofCPT.

Structure and phase behavior of a confined nanodroplet composed of the flexible chain molecules

A polymer density functional theory has been employed for investigating the structure and phase behaviors of the chain polymer, which is modelled as the tangentially connected sphere chain with an attractive interaction, inside the nanosized pores. The excess free energy of the chain polymer has been approximated as the modified fundamental measure-theory for the hard spheres, the Wertheim's first-order perturbation for the chain connectivity, and the mean-field approximation for the van der Waals contribution. For the value of the chemical potential corresponding to a stable liquid phase in the bulk system and a metastable vapor phase, the flexible chain molecules undergo the liquid-vapor transition as the pore size is reduced; the vapor is the stable phase at small volume, whereas the liquid is the stable phase at large volume. The wide liquid-vapor coexistence curve, which explains the wide range of metastable liquid-vapor states, is observed at low temperature. The increase of temperature and decrease of pore size result in a narrowing of liquid-vapor coexistence curves. The increase of chain length leads to a shift of the liquid-vapor coexistence curve towards lower values of chemical potential. The coexistence curves for the confined phase diagram are contained within the corresponding bulk liquid-vapor coexistence curve. The equilibrium capillary phase transition occurs at a higher chemical potential than in the bulk phase.

Studies of Capillary Phase Transitions of Methane in Metal−Organic Frameworks by Gauge Cell Monte Carlo Simulation

Capillary phase transitions of CH(4) confined in a series of metal-organic frameworks (MOFs) were investigated in this work using gauge cell Monte Carlo simulations. The results show that capillary phase transitions can occur in MOFs, and the effects of temperature, pore size, and adsorption energy are very significant. Furthermore, this work shows the confinement can induce a shift in critical point for fluids confined in MOFs, leading to a decrease in critical temperature and an increase in critical density. The critical point shift is more obvious for MOFs with small pore size and large adsorption energy.

A Density Functional Theory with a Mean-field Weight Function: Applications to Surface Tension, Adsorption, and Phase Transition of a Lennard-Jones Fluid in a Slit-like Pore

A new density functional theory (DFT) for an inhomogeneous 12-6 Lennard-Jones fluid is proposed based on the modified fundamental measure theory for repulsive interaction and a weighted density functional for attractive interaction. The Helmholtz free energy functional for the attractive part is constructed using the modified Benedict-Webb-Rubin equation of state with a mean-field weight function. Comparisons of the theoretical results with molecular simulation data suggest that the new DFT yields accurate bulk surface tension, density distributions, adsorption-desorption isotherms, pore pressures, and capillary phase transitions for the Lennard-Jones fluid confined in slitlike pores with different widths and solid-fluid interactions. The new DFT reproduces well the vapor-liquid critical temperatures of the confined Lennard-Jones fluid, whereas the mean-field theory always overestimates the critical temperatures. Because the new DFT is computationally as simple and efficient as the mean-field theory, it will provide a good reference for further development of a statistical-thermodynamic theory of complex fluid under both homogeneous and inhomogeneous conditions when disperse force has to be considered.

Simplified gauge-cell method and its application to the study of capillary phase transition of propane in carbon nanotubes

A modification of the gauge-cell method for Monte Carlo studies of phase equilibrium in nano-confined systems is presented and employed for studying the capillary phase transition of propane in single-walled carbon nanotubes as a function of tube diameter. It is shown that if an analytical equation of state for the vapor phase is known, the acceptance rule for the trial move of particle exchange can be modified to reference the bulk system through its chemical potential. Under these conditions, the simulation procedure is simplified and acquires many characteristics of a Monte Carlo simulation conducted in the grand canonical ensemble. It is also shown that the critical temperature can be estimated by interpolation of sub- and supercritical values of the slope of the inverse isotherm at the inflection point. To enhance the sampling of propane molecules in the hollow space of the nanotubes the configurational-bias scheme is employed. The simulation results show that the confinement of propane increases its critical density, reduces the critical temperature and narrows the binodal curve with decreasing tube diameter until the system approaches one-dimensional behavior.

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.

Density Functional Theory Study on the Structure and Capillary Phase Transition of a Polymer Melt in a Slitlike Pore: Effect of Attraction

A density functional theory is proposed to investigate the effects of polymer monomer-monomer and monomer-wall attractions on the density profile, chain configuration, and equilibrium capillary phase transition of a freely jointed multi-Yukawa fluid confined in a slitlike pore. The excess Helmholtz energy functional is constructed by using the modified fundamental measure theory, Wertheim's first-order thermodynamic perturbation theory, and Rosenfeld's perturbative method, in which the bulk radial distribution function and direct correlation function of hard-core multi-Yukawa monomers are obtained from the first-order mean spherical approximation. Comparisons of density profiles and bond orientation correlation functions of inhomogeneous chain fluids predicted from the present theory with the simulation data show that the present theory is very accurate, superior to the previous theory. The present theory predicts that the polymer monomer-monomer attraction lowers the strength of oscillations for density profiles and bond orientation correlation functions and makes the excess adsorption more negative. It is interesting to find that the equilibrium capillary phase transition of the polymeric fluid in the hard slitlike pore occurs at a higher chemical potential than in bulk condition, but as the attraction of the pore wall is increased sufficiently, the chemical potential for equilibrium capillary phase transition becomes lower than that for bulk vapor-liquid equilibrium.

Confined Water in Mesoporous MCM-41 and Nanoporous AlPO4-5: Structure and Dynamics

Confined water presents unusual properties in comparison with other sorbate species. First of all, the sorption isotherm is of type III, even in the microporous confinement range (O < 20 A). Whatever the pore diameter, water sorption phenomenon looks like the so-called capillary condensation phase transition. Our results clearly valid such an expected behaviour in the mesoporous confinement range (20 A < O < 40 A). The water confined phase is a liquid phase characterized by a short range order and a high translational molecular mobility. The confinement induces a strong displacement towards the low temperature of the water confined liquid solidification Tsol. (for instance, Tsol. = 230 K for D2O confined liquid in MCM-41 (O = 24 A). We have determined the structure of the water confined solid phase observed below Tsol.. It looks like those of the cubic ice structure affected by strong quasi-isotropic finite size effects induced by the confinement. Such a quasi-(1d) solid appears as a polycrystalline column rather than a single crystalline nanofiber. Concerning water confinement in the microporous range (as for example, AlPO4-5 zeolite (O = 7.3 A)), our results are more surprising. Type III sorption isotherm is the signature of a crystallization phenomenon at room temperature (T = 300 K). The confined water crystallizes in two helices that are commensurate with the AlPO4-5 micropore structure. The confined ice has a density of 1.2 g⋅ cm− 3.

Adsorption and phase transitions on nanoporous carbonaceous materials: insights from molecular simulations

Three different examples of adsorption and phase transitions on nanoporous carbonaceous materials are investigated using molecular simulations. In the first example, N2 adsorption on the surface of and within a C60 crystal is studied using the grand canonical Monte Carlo simulation. On the crystal surface, the predicted isotherm is of type II in good agreement with experiment, and N2 molecules are found to initially occupy the octahedral voids, then the tetrahedral voids, and finally on the top of the C60 molecules with increasing coverage. Within the crystal, the predicted isotherm is of type I, and N2 molecules intercalate the octahedral voids. In the second example, N2 adsorption on two types of carbon nanotube bundles is studied using the Gibbs ensemble Monte Carlo simulation to explore the role of the external surface of the nanotube bundle in the character of adsorption isotherm. The isotherm for an infinite bundle without an external surface is found to be of type I independent of temperature, while for a finite bundle with an external surface the isotherm changes from type II to I as temperature changes from subcritical to supercritical. In the third example, the capillary phase transitions of n-alkanes (from C1 to C8) in a carbon nanotube are studied using the gauge-cell Monte Carlo simulation implemented with the configurational-bias technique. At subcritical temperatures the isotherms exhibit sigmoid van der Waals loops, including stable, metastable, and unstable regions, and the coexisting vapor−liquid phases are determined from a Maxwell construction along the isotherms. The confinement of an n-alkane in a carbon nanotube decreases its critical temperature, increases its critical density, and narrows its binodal curve.

Capillary Phase Transitions of n-Alkanes in a Carbon Nanotube

The capillary phase transitions of n-alkanes confined in a carbon nanotube are simulated for the first time using the gauge-cell Monte Carlo method with the configurational-bias scheme. At a subcritical temperature, the coexisting vapor-liquid phases are determined from a Maxwell construction along the adsorption isotherm, which exhibits a sigmoid van der Waals loop, including stable, metastable, and unstable regions. The confinement of an n-alkane in a carbon nanotube decreases its critical temperature, increases its critical density, and narrows its binodal curve.

Study of Hexane Adsorption in Nanoporous MCM-41 Silica

We study here the adsorption of hexane on nanoporous MCM-41 silica at 303,313, and 323 K, for various pore diameters between 2.40 and 4.24 nm. Adsorption equilibria, measured thermogravimetrically, show that all the isotherms, that are somewhat akin to those of type V, exhibit remarkably sharp capillary adsorption phase transition steps and are reversible. The position of the phase transition step gradually shifts from low to high relative pressure with an increase in the temperature as well as the pore sizes. The isosteric heats of adsorption derived from the equilibrium information using the Clapeyron equation reveal a gradual decrease with increasing adsorbed amount because of the surface heterogeneity but approach a constant value near the phase transition. A decrease in the pore size results in an increase in the isosteric heat of adsorption because of the increased dispersion forces. A simple strategy, based on the Broekhoff and De Boer adsorption theory, successfully interprets the hexane adsorption isotherms for the different pore size MCM-41 samples. The parameters of an empirical expression, used to represent the potential of interaction between the adsorbate and adsorbent, are obtained by fitting the monolayer region prior to capillary condensation and the experimental phase transition simultaneously, for some pore sizes. Subsequently, the parameters are used to predict the adsorption isotherm on other pore size samples, which showed good agreement with experimental data.

Cancellation of vorticity in steady-state non-isentropic flows of complex fluids

In steady-state non-isentropic flows of perfect fluids there is always thermodynamic generation of vorticity when the difference between the product of the temperature with the gradient of the entropy and the gradient of total enthalpy is different from zero. We note that this property does not hold in general for complex fluids for which the prominent influence of the material substructure on the gross motion may cancel the thermodynamic vorticity. We indicate the explicit condition for this cancellation (topological transition from vortex sheet to shear flow) for general complex fluids described by coarse-grained order parameters and extended forms of Ginzburg-Landau energies. As a prominent sample case we treat first Korteweg's fluid, used commonly as a model of capillary motion or phase transitions characterized by diffused interfaces. Then we discuss general complex fluids. We show also that, when the entropy and the total enthalpy are constant throughout the flow, vorticity may be generated by the inhomogeneous character of the distribution of material substructures, and indicate the explicit condition for such a generation. We discuss also some aspects of unsteady motion and show that in two-dimensional flows of incompressible perfect complex fluids the vorticity is in general not conserved, due to a mechanism of transfer of energy between different levels.