Unveiling the Molecular Origin of Vapor-Liquid Phase Transition of Bulk and Confined Fluids

At temperatures below the critical temperature, discontinuities in the isotherms are one critical issue in the design and construction of separation units, affecting the level of confidence for a prediction of vapor–liquid equilibriums and phase transitions. In this work, we study the molecular mechanisms of fluids that involve the vapor–liquid phase transition in bulk and confinement, utilizing grand canonical (GCE) and meso-canonical (MCE) ensembles of the Monte Carlo simulation. Different geometries of the mesopores, including slit, cylindrical, and spherical, were studied. During phase transitions, condensation/evaporation hysteretic isotherms can be detected by GCE simulation, whereas employing MCE simulation allows us to investigate van der Waals (vdW) loop with a vapor spinodal point, intermediate states, and a liquid spinodal point in the isotherms. Depending on the system, the size of the simulation box, and the MCE method, we are able to identify three distinct groups of vdW-type isotherms for the first time: (1) a smooth S-shaped loop, (2) a stepwise S-shaped loop, and (3) a stepwise S-shaped loop with just a vertical segment. The first isotherm type is noticed in the bulk and pores having small box sizes, in which vapor and liquid phases are close and not clearly identified. The second and the third types occurred in the bulk, cylindrical, and slit mesopores with sufficiently large spaces, where vapor and liquid phases are distinctly separated. Results from our studies provide an insight analysis into vapor–liquid phase transitions, elucidating the effect of the confinement of fluid behaviors in a visual manner.     

Thermodynamics and phase transitions in a fluid confined by a harmonic trap

We study a fluid of interacting atoms confined by a three-dimensional anisotropic harmonic potential, similar to those produced by the magnetic traps used to confine cold atoms. We show that instead of the usual thermodynamic variables pressure and volume, no longer existing in this case, there appear "new" variables: the volume is replaced by (the inverse cube of) the geometric average of the oscillator frequencies of the trap, and the hydrostatic pressure is replaced by an intensive variable, conjugate to the previous one, and responsible for the mechanical equilibrium of the fluid in the trap. We discuss the origin and physical meaning of these new variables. With the aid of molecular dynamics simulations we show the emergence of novel liquid, vapor and solid-like phases in a classical fluid. In particular, we calculate the liquid-vapor-like coexistence curve and show evidence for the appearance of a critical point. These phase transitions should be observable in fluids of not-so-cold alkaline atoms.     

Interfacial phase transitions in conducting fluids

We present a review, largely based on recent experimental work of our group, on phase transitions at interfaces of fluid metals, alloys and ionic liquids. After a brief analysis of possible experimental errors and limitations of surface sensitive methods, we first deal with first-order wetting transitions at the liquid/vapour and liquid/wall interface in systems such as Ga-based alloys, K-KCl melts, and fluid Hg. The following chapter refers to surface freezing or surface induced crystallization in different metal alloys. The respective surface phase diagrams are discussed in comparison with their bulk counterpart. In the last part we present very recent investigations of ionic liquid interfaces, including order-disorder transitions at the liquid/vapour interface and examples of two-dimensional phase transitions at the electrified ionic liquid/metal interface. Finally, a simple electrowetting experiment with an ionic liquid droplet under vacuum is described which gives new insight into the contact angle saturation problem. The article ends up with a few perspective remarks on open problems and potential impact of interfacial phenomena on applied research.     

Measuring coexisting densities from a two-phase molecular dynamics simulation by voronoi tessellations

A new algorithm is presented that allows for the determination of bulk liquid and vapor densities from a two-phase Molecular Dynamics (2phiMD) simulation. This new method does not use any arbitrary cutoffs for phase definitions; rather it uses single-phase simulations as a self-consistency check. The method does not use any spatial bins for generating histograms of local properties, thereby avoiding the statistical issues associated with bins. Finally, it allows one to approach very close to the critical point. The new method utilizes Voronoi tessellations to determine the molecular volume of every point at every instance in a molecular dynamics simulation. Since the molecular volume is calculated throughout the simulation, statistical parameters such as the average molecular volume and average molecular variance are easy to obtain. To define the phases, the normalized variance of the molecular volume from 1phiMD and 2phiMD is used as a self-consistency check. The new method gives new insight into the nature of the near-subcritical fluid. The critical properties from this analysis are T(c) = 1.293 and rho(c) = 0.313. Direct simulation of the two-phase system was performed up to a temperature of 1.292. The results show excellent agreement to experimental results and Gibbs Ensemble Monte Carlo for coexisting densities. We see that well below the critical temperature, some particles are neither liquid nor vapor. These interfacial particles are primarily, but not exclusively, concentrated at the bulk interface. However, as we approach the critical point, some particles are considered both liquid and vapor. These interfacial particles are distributed through the system.     

A corresponding states treatment of the liquid–vapor saturation line

In this work we analyze correlations for the maxima of products of some liquid–vapor saturation properties. These points define new characteristic properties of each fluid that are shown to exhibit linear correlations with the critical properties. We also demonstrate that some of these properties are well correlated with the acentric factor. An application is made to predict the properties of two new low global warming potential (GWP) refrigerants.     

Topological ferroelectric bistability in a polarization-modulated orthogonal smectic liquid crystal

We report a bent-core liquid crystal (LC) compound exhibiting two fluid smectic phases in which two-dimensional, polar, orthorhombic layers order into three-dimensional ferroelectric states. The lower-temperature phase has a uniform polarization field which responds in an analog fashion to applied electric field. The higher-temperature phase is a new smectic state with periodic undulation of the polarization, structurally modulated layers, and a bistable response to applied electric field which originates in the periodically splay-modulated bulk of the LC rather than by surface stabilization at the cell boundaries.     

Parachors of liquid/vapor systems: A set of critical amplitudes

In light of the available experimental data and of our current understanding of liquid–vapor critical phenomena, we examine the values of the parachors and of the parachor exponent, which are commonly used to estimate surface tension from the density difference between coexisting liquid and vapor phases. This is a controversial issue, as values for the parachor exponent ranging from 3.5 to 4 have been proposed in the literature. The parachor exponent and parachors can be viewed as a critical exponent and critical amplitudes, respectively. The Ising value, equal to 3.88, should be observed for the exponent “close enough” to the liquid/vapor critical point, i.e., for “low enough” tensions and densities. However, a review of experimental data for several fluids suggests an effective value in the range of 3.6, in line with the effective values observed for the exponents that describe the vanishing of the density difference and capillary length with the distance to the critical temperature. In fact, the asymptotic Ising regime is not reached experimentally, as confirmed by an estimation of the parachors very near the critical point. Those (Ising) parachors can be inferred from other critical amplitudes corresponding to bulk properties by using two-scale factor universality. Their values exceed those deduced from off-critical tension and density data by more than 10%, corresponding to surface tension differences larger than 50%. We argue that effective parachors (i.e., corresponding to an exponent in the range of 3.6) can be utilized in combination with two-scale-factor universality for determining the critical behavior of fluid systems in an extended range around their liquid/vapor critical point.     

Melting behavior of an idealized membrane model

The melting behavior of an idealized model giving rise to two-dimensional (2D) structures at low temperature and low density is investigated by Monte Carlo simulations. The system is made of particles carrying a spin of constant length and variable orientation, whose potential energy is the sum of a repulsive spherical pair interaction, and of a spin-spin contribution, reminiscent of but essentially different from the electrostatic dipole-dipole interaction. The simulation results show that the model phase diagram is determined by the interplay of a ferro- to paraelectric transition in the spin part and of the solid to fluid transition found in simple pair-potential models. The 2D solid melts into a three-dimensional (3D) fluid when the spin-spin interaction is weak. Strong spin-spin interactions give rise to two transitions, the first one corresponding to the melting of the 2D solid into a 2D fluid, and the second one corresponding to the crossover from a 2D to a 3D fluid. The fluid phase stable in between these two transitions provides a model for the liquid state arising in organic and biological membranes across their main transition.     

添加剂对LiBr溶液吸收蒸汽过程中的强化机理

The surface tensions of aqueous lithium bromide（LiBr）with additive（2-ethyl-1-hexanol and 1-Octanol）have been measured by using a Wihelmy plate method,and the enhancement effect of the additives on the absorption of steam into aqueous LiBr in a static pool has been studied by a real-time type laser holographic visualization method. The experimental results show that both of liquid additive and vapor additive can decrease the surface tensions of aqueous LiBr significantly,vapor additive not only can trigger the Marangoni convection at the absorption interface just like the liquid additive,but can bring about better enhancement effect on the absorption performance than that liquid additive can. The enhancement mechanism of additive on absorption has been concluded that both liquid additive and vapor additive can be adsorbed by aqueous LiBr at the liquid-vapor-interface from the liquid side and the vapor side respectively,which result in surface tension gradient,and then cause Marangoni convection at the interface which enhances the heat and mass transfer performance during the absorption process.     

Nucleation and cavitation of spherical, cylindrical, and slablike droplets and bubbles in small systems

Computer simulations are employed to obtain subcritical isotherms of small finite sized systems inside the coexistence region. For all temperatures considered, ranging from the triple point up to the critical point, the isotherms gradually developed a sequence of sharp discontinuities as the system size increased from approximately 8 to approximately 21 molecular diameters. For the smallest system sizes, and more so close to the critical point, the isotherms appeared smooth, resembling the continuous van der Waals loop obtained from extrapolation of an analytic equation of state outside the coexistence region. As the system size was increased, isotherms in the chemical potential-density plane developed first two, then four, and finally six discontinuities. Visual inspection of selected snapshots revealed that the observed discontinuities are related to structural transitions between droplets (on the vapor side) and bubbles (on the liquid side) of spherical, cylindrical, and tetragonal shapes. A capillary drop model was developed to qualitatively rationalize these observations. Analytic results were obtained and found to be in full agreement with the computer simulation results. The analysis shows that the shape of the subcritical isotherms is dictated by a single characteristic volume (or length scale), which depends on the surface tension, compressibility, and coexistence densities. For small reduced system volumes, the model predicts that a homogeneous fluid is stable across the whole coexistence region, thus explaining the continuous van der Waals isotherms observed in the simulations. When the liquid and vapor free energies are described by means of an accurate mean-field equation of state and surface tensions from simulation are employed, the capillary model is found to describe the simulated isotherms accurately, especially for large systems (i.e., larger than about 15 molecular diameters) at low temperature (lower than about 0.85 times the critical temperature). This implies that the Laplace pressure differences can be predicted for drops as small as five molecular diameters, and as few as about 500 molecules. The theoretical study also shows that the extrema or apparent spinodal points of the finite size loops are more closely related to (finite system size) bubble and dew points than to classical spinodals. Our results are of relevance to phase transitions in nanopores and show that first order corrections to nucleation energies in finite closed systems are power laws of the inverse volume.     

Phase behavior of density-dependent pair potentials

Phase diagram is calculated by a recently proposed third-order thermodynamic perturbation theory (TPT) for fluid phase and a recently proposed first-order TPT for solid phases; the underlying interparticle potential consists of a hard sphere repulsion and a perturbation tail of an attractive inverse power law type or Yukawa type whose range varies with bulk densities. It is found that besides usual phase transitions associated with density-independent potentials, the density dependence of the perturbation tail evokes some additional novel phase transitions including isostructural solid-solid transition and liquid-liquid transition. Novel triple points are also exhibited which includes stable fluid (vapor or liquid)-face-centered cubic(fcc)-fcc and liquid-liquid-fcc, metastable liquid-body-centered cubic(bcc)-bcc. It also is found that the phase diagram sensitively depends on the density dependence and the concrete mathematical form of the underlying potentials. Some of the disclosed novel transitions has been observed experimentally in complex fluids and molecular liquids, while others still remain to be experimentally verified.     

Two-dimensional supercritical behavior of an ethanol monolayer: a molecular dynamics study

The two-dimensional (2D) supercritical behavior of an ethanol monolayer formed at the vapor/liquid interface of an ethanol solution has been investigated by a molecular dynamics (MD) calculations with a combination of the OPLS-UA and SPC/E potential models. A 100 A thick slab of ethanol solution was placed at the volume center of the rectangular unit cell by 10 A thick nonabsorbate water surfaces. With such an initial configuration, five independent 15 ns NVT constant MD calculations were carried out under 298.15 K, in which the initial ethanol mole fraction of the bulk solution layer was set to 0.010, 0.022, 0.045, 0.10, and 0.20, respectively. The 2D radial distribution function (rdf) of an adsorbed ethanol molecule showed that the ethanol monolayer could be regarded as a 2D fluid where the adsorbed ethanol molecule had an effective 2D diameter of 4.65 A. On the basis of the 2D rdf result, 2D cluster analysis was carried out from the perspective of the percolation theory. It is confirmed that the critical area occupation probability density, the critical exponents, and the fractal dimension of both nonpercolating and percolating clusters satisfied their nature of universality. Therefore, we concluded that an ethanol monolayer formed at the vapor/liquid interface of ethanol solution behaves as a 2D supercritical fluid at 298.15 K.     

Long-range Lennard-Jones and electrostatic interactions in interfaces: application of the isotropic periodic sum method

Molecular dynamics (MD) simulations of heptane/vapor, hexadecane/vapor, water/vapor, hexadecane/water, and dipalmitoylphosphatidylcholine (DPPC) bilayers and monolayers are analyzed to determine the accuracy of treating long-range interactions in interfaces with the isotropic periodic sum (IPS) method. The method and cutoff (rc) dependences of surface tensions, density profiles, water dipole orientation, and electrostatic potential profiles are used as metrics. The water/vapor, heptane/vapor, and hexadecane/vapor interfaces are accurately and efficiently calculated with 2D IPS (rc=10 A). It is demonstrated that 3D IPS is not practical for any of the interfacial systems studied. However, the hybrid method PME/IPS [Particle Mesh Ewald for electrostatics and 3D IPS for Lennard-Jones (LJ) interactions] provides an efficient way to include both types of long-range forces in simulations of large liquid/vacuum and all liquid/liquid interfaces, including lipid monolayers and bilayers. A previously published pressure-based long-range LJ correction yields results similar to those of PME/IPS for liquid/liquid interfaces. The contributions to surface tension of LJ terms arising from interactions beyond 10 A range from 13 dyn/cm for the hexadecane/vapor interface to approximately 3 dyn/cm for hexadecane/water and DPPC bilayers and monolayers. Surface tensions of alkane/vapor, hexadecane/water, and DPPC monolayers based on the CHARMM lipid force fields agree very well with experiment, whereas surface tensions of the TIP3P and TIP4P-Ew water models underestimate experiment by 16 and 11 dyn/cm, respectively. Dipole potential drops (DeltaPsi) are less sensitive to long-range LJ interactions than surface tensions. However, DeltaPsi for the DPPC bilayer (845+/-3 mV proceeding from water to lipid) and water (547+/-2 mV for TIP4P-Ew and 521+/-3 mV for TIP3P) overestimate experiment by factors of 3 and 5, respectively, and represent expected deficiencies in nonpolarizable force fields.     

Capillary condensation in cylindrical pores: Monte Carlo study of the interplay of surface and finite size effects

When a fluid that undergoes a vapor to liquid transition in the bulk is confined to a long cylindrical pore, the phase transition is shifted (mostly due to surface effects at the walls of the pore) and rounded (due to finite size effects). The nature of the phase coexistence at the transition depends on the length of the pore: for very long pores, the system is axially homogeneous at low temperatures. At the chemical potential where the transition takes place, fluctuations occur between vapor- and liquidlike states of the cylinder as a whole. At somewhat higher temperatures (but still far below bulk criticality), the system at phase coexistence is in an axially inhomogeneous multidomain state, where long cylindrical liquid- and vaporlike domains alternate. Using Monte Carlo simulations for the Ising/lattice gas model and the Asakura-Oosawa model of colloid-polymer mixtures, the transition between these two different scenarios is characterized. It is shown that the density distribution changes gradually from a double-peak structure to a triple-peak shape, and the correlation length in the axial direction (measuring the equilibrium domain length) becomes much smaller than the cylinder length. The (rounded) transition to the disordered phase of the fluid occurs when the axial correlation length has decreased to a value comparable to the cylinder diameter. It is also suggested that adsorption hysteresis vanishes when the transition from the simple domain state to the multidomain state of the cylindrical pore occurs. We predict that the difference between the pore critical temperature and the hysteresis critical temperature should increase logarithmically with the length of the pore.     

Liquid–liquid crystalline phase separation in biomolecular solutions

Liquid–liquid phase separation (LLPS) and liquid crystalline (LC) ordering are ubiquitous phenomena in nature, in a variety of biomolecular solutions. Here, we review instances in DNA, nanocellulose, and other systems, where they occur together, leading to the formation of liquid–liquid crystalline phase separation (LLCPS), and we highlight analogies, differences, recent advances, and open questions. Remarkably, the intrinsic fluid yet ordered nature of LC, combined with the spatial confinement induced by LLPS, leads to peculiar biomolecular compartments suitable for a broad range of applications, ranging from material science to synthetic biology. We argue that tools from the LC field help to address still unexplained processes such as the onset of phase transitions in intracellular biomolecular condensates.     

Free-energy landscape of nucleation with an intermediate metastable phase studied using capillarity approximation

Capillarity approximation is used to study the free-energy landscape of nucleation when an intermediate metastable phase exists. The critical nucleus that corresponds to the saddle point of the free-energy landscape as well as the whole free-energy landscape can be studied using this capillarity approximation, and various scenarios of nucleation and growth can be elucidated. In this study, we consider a model in which a stable solid phase nucleates within a metastable vapor phase when an intermediate metastable liquid phase exists. We predict that a composite critical nucleus that consists of a solid core and a liquid wetting layer as well as pure liquid and pure solid critical nuclei can exist depending not only on the supersaturation of the liquid phase relative to that of the vapor phase but also on the wetting behavior of the liquid surrounding the solid. The existence of liquid critical nucleus indicates that the phase transformation from metastable vapor to stable solid occurs via the intermediate metastable liquid phase, which is quite similar to the scenario of nucleation observed in proteins and colloidal systems. By studying the minimum-free-energy path on the free-energy landscape, we can study the evolution of the composition of solid and liquid within nuclei which is not limited to the critical nucleus.     

Vapor-liquid equilibrium of ethanol by molecular dynamics simulation and Voronoi tessellation

Explicit atom simulations of ethanol were performed by molecular dynamics using the OPLS-AA potential. The phase densities were determined self-consistently by comparing the distribution of Voronoi volumes from two-phase and single-phase simulations. This is the first demonstration of the use of Voronoi tessellation in two-phase molecular dynamics simulation of polyatomic fluids. This technique removes all arbitrary determination of the phase diagram by using single-phase simulations to self-consistently validate the probability distribution of Voronoi volumes of the liquid and vapor phases extracted from the two-phase molecular dynamics simulations. Properties from the two phase simulations include critical temperature, critical density, critical pressure, phase diagram, surface tension, and molecule orientation at the interface. The simulations were performed from 375 to 472 K. Also investigated were the vapor pressure and hydrogen bonding along the two phase envelope. The phase envelope agrees extremely well with literature values from GEMC at lower temperatures. The combined use of two-phase molecular dynamics simulation and Voronoi tessellation allows us to extend the phase diagram toward the critical point.     

Measurements of tension (<Emphasis Type="Italic">P</Emphasis> &lt; 0) in a metastable aqueous 2<Emphasis Type="Italic">m</Emphasis> Na<Subscript>2</Subscript>WO<Subscript>4</Subscript>–CsCl solution

The negative pressure (tension) was measured by Raman spectroscopy in an aqueous 2m Na₂WO₄–CsCl solution during a metastable-to-stable state transition. Phase transitions were observed optically in synthetic fluid inclusions in a single quartz crystal. In the metastable liquid phase, the vapor phase nucleation pressure at 48°C is ?105 ± 5 MPa. Water equation of state (IAPWS-95) predicts the nucleation pressure for this density to be approximately ?160 MPa.     

Constrained fluid lambda-integration: constructing a reversible thermodynamic path between the solid and liquid state

A novel lambda-integration path is proposed for calculating the Gibbs free energy difference between any arbitrary solid and liquid state needed for the location of melting lines. This technique involves reversibly forcing a liquid state to a solid state across the phase transition along a nonphysical path, thermodynamically coupling the two states directly. The process eliminates the need for coupling to idealized reference states as is presently performed and hence simplifies the location of phase transitions for computer simulation systems. More specifically the path involves a three stage process, whereby, initially a liquid state is transformed to a weakly attractive fluid using linear lambda-integration scaling of the intermolecular potential. In the second stage, the resulting fluid is then constrained to the required solid configurational phase space via the insertion of a periodic lattice of 3D Gaussian wells. The final stage involves reversing to full strength the main intermolecular potential while gradually turning off the constraining 3D Gaussian lattice finally resulting in a stable (or metastable) solid state. Each stage was found to be completely reversible and the resulting change in free energy was thermodynamically integrable. The methodology is demonstrated and validated by calculating solid-liquid coexistence points using the new technique and comparing to those in present literature for the truncated and shifted Lennard-Jones system. The results are found to be in good agreement. The new method is not limited to melting phase transitions and is readily applicable to any simulation methodology, simulation cell size and/or intermolecular potential including ab initio methods.     

Saturated vapor pressure in the thallium-cadmium system

Component vapor pressures in the thallium-cadmium system determined by the method of boiling points (isothermal variant) and the flow method were used to calculate the thermodynamic characteristics of the vapor and condensed phases in the region of the existence of liquid solutions. The temperature-concentration dependences of the thermodynamic values were determined. The phase diagram was augmented by liquid-vapor phase transitions at atmospheric pressure and in a vacuum (100 and 10 Pa) with the determination of the boundaries for the coexistence region of the liquid and vapor phases.