Liquid-vapor Coexistence Research Articles

Exploring the Thermodynamics and Dynamics of CO2 Using Rigid Models

Understanding the behavior of carbon dioxide (CO2) under varying thermodynamic conditions is essential for optimizing processes such as Carbon Capture and Storage (CCS) and supercritical fluid extraction. This study employs molecular dynamics (MD) simulations with the EPM2 and TraPPE-small force fields to examine CO2 phase behavior, structural characteristics, and transport properties across a temperature range of 228–500 K and pressures from 1 to 150 atm. Our findings indicate a good agreement between simulated and experimental liquid–vapor coexistence curves, validating the capability of both force fields to model CO2 accurately in a wide range of thermodynamical conditions. Radial distribution functions (RDFs) reveal distinct interaction patterns in liquid and supercritical phases, while mean squared displacement (MSD) analyses show diffusivity increasing from 5.2×10−9 m2/s at 300 K to 1.8×10−8 m2/s at 500 K. Additionally, response functions such as the heat capacity effectively capture phase transitions. These findings provide quantitative insights into CO2 phase behavior and transport properties, enhancing the predictive reliability of simulations for CCS and related industrial technologies. This work bridges gaps in the CO2 modeling literature and highlights the potential of MD simulations in advancing sustainable applications.

Vapour-liquid equilibrium and low-temperature liquid-crystal phase diagram of discotic colloids

Discotic colloids give rise to a paradigmatic family of liquid crystals with sound applications in Materials Science. In this paper, Monte Carlo simulations are employed to characterise the low-temperature liquid crystal phase diagram and the vapour-liquid coexistence of discotic colloids interacting via a Kihara potential. Discoidal particles with thickness-diameter aspect ratios L ∗ ≡ L / D = 0.5 , 0.3, 0.2 and 0.1 are considered. For the less anisotropic particles ( L ∗ ≥ 0.2 ), coexistence of a vapour phase with the isotropic fluid and with the columnar liquid crystal phase is observed. As the particle anisotropy increases, the vapour-liquid coexistence shifts to lower temperatures and its density range diminishes, eventually merging with coexistences involving the liquid crystal phases. The L ∗ = 0.1 fluid displays a rich sequence of mesophases, including a nematic phase and a novel lamellar phase in which particles arrange in layers perpendicular to the nematic director.

Emergence of social phases in human movement.

Recent empirical studies have found different thermodynamic phases for collective motion in animals. However, such a thermodynamic description of human movement remains unclear. Existing studies of traffic and pedestrian flows have primarily focused on relatively high-speed mobility data, revealing only a fluidlike phase. This focus is partly because the parameter space of low-speed movement, which is governed predominantly by pairwise social interaction, remains largely uncharted. Here, we used ultrawideband radio frequency identification (UWB-RFID) technology to collect high-resolution spatiotemporal data on movements in four different classroom and playground settings. We observed two unique social phases in children's movements: a gaslike phase of free movement and a liquid-vapor coexistence phase characterized by the formation of small social groups. We also developed a simple statistical physics model that can reproduce different empirically observed phases. The proposed UWB-RFID technology can also be used to study the dynamics of active matter systems, including animal behavior, coordinating robotic swarms, and monitoring human interactions within complex systems, potentially benefiting future research in social physics.

Extension of the SpK atomic physics code to generate global equation of state data

Global microphysics models are required for the modelling of high-energy-density physics (HEDP) experiments, the improvement of which are critical to the path to inertial fusion energy. This work presents further developments to the atomic and microphysics code, SpK, part of the numerical modelling suite of Imperial College London and First Light Fusion. We extend the capabilities of SpK to allow the calculation of the equation of state (EoS). The detailed configuration accounting calculations are interpolated into finite-temperature Thomas–Fermi calculations at high coupling to form the electronic component of the model. The Cowan model provides the ionic contribution, modified to approximate the physics of diatomic molecular dissociation. By utilising bonding corrections and performing a Maxwell construction, SpK captures the EoS from states ranging from the zero-pressure solid, through the liquid–vapour coexistence region and into plasma states. This global approach offers the benefit of capturing electronic shell structure over large regions of parameter space, building highly-resolved tables in minutes on a simple desktop. We present shock Hugoniot and off-Hugoniot calculations for a number of materials, comparing SpK to other models and experimental data. We also apply EoS and opacity data generated by SpK in integrated simulations of indirectly-driven capsule implosions, highlighting physical sensitivities to the choice of EoS models.

Thermodynamically consistent phase field model for liquid-gas phase transition with soluble surfactant

Despite the enormous potential in facilitating natural development and migration of interfaces during multiphase simulation, the phase-field method remains restricted to low-density ratios, owing to inherent thermodynamic inconsistency, especially for multiphase flow systems with surfactants. The present paper first constructs a liquid-vapor phase transition phase-field model with soluble surfactants using the second law of thermodynamics as the original model. Then, a simplified liquid-vapor phase transition model with soluble surfactants that satisfies thermodynamic consistency is proposed to simulate pool boiling at higher-density ratio. A novel numerical algorithm for the simplified model that satisfies semi-discrete thermodynamic consistency is also developed. Compared with the original model, the thermodynamically consistent characteristics of the simplified numerical model proposed in this paper can significantly reduce the spurious velocity on the interface of a static droplet and thus enable the numerical model to simulate liquid-vapor transition at higher liquid/vapor density ratios. Vapor-liquid coexistence, Laplace's law, and multiple bubble coalescence are used to validate the accuracies and effectiveness of the mathematical model and numerical algorithm. The liquid/vapor density ratio can reach 6776:1 under saturation temperature 0.3Tc (Tc is the critical temperature). The approach is then used to model pool boiling at a low saturation temperature (0.5Tc) with and without soluble surfactants, significantly lower than reported in comparable literature. The results demonstrate that surfactants significantly influence the dynamics of bubbles, and a critical concentration can be identified. In addition, soluble surfactants can also suppress coalescence between adjacent bubbles and prevent the formation of larger bubbles during pool boiling.

Predicting phase coexistence and adsorption isotherms of classical and quantum fluids using the microcanonical-ensemble perturbation theory (MEPT)

The Microcanonical-Ensemble Perturbation Theory (MEPT) of Sastre et al. (2018) [7] has been extended to study the vapor-liquid phase coexistence of binary and ternary mixtures of fluids. The attractive interactions between chains of molecules are represented as monomer segments interacting via a square-well pair potential. Calculations for the thermodynamic properties and phase behavior of square-well monomer chains are considered and compared with experimental data. Molecular parameters have been obtained to model the phase behavior of real fluids such as n-alkanes (from C1 to C12), nitrogen, perfluoromethane, carbon dioxide, i-butane, i-pentane, neon, and hydrogen. Furthermore, the capability of the MEPT approach in predicting critical and azeotropic lines of binary and ternary mixtures is explored. The results demonstrate that the MEPT approach provides a robust description of the phase behavior of mixtures containing chains of fluids. Additionally, we have integrated the MEPT approach with the two-dimensional Statistical Associating Fluid Theory for fluids interacting via variable range potentials (SAFT-VR-2D) to investigate the effect of quantum contributions on both phase behavior and adsorption. Remarkable improvements are observed when both higher order perturbation terms of the Helmholtz free energy and quantum contributions are included in the predictions of the phase behavior of quantum fluids such as neon and hydrogen. In all cases, the theoretical results exhibit favorable comparisons with experimental data in a wide range of compositions, pressures, and temperatures.

The ion-activated attractive patchy particle model and its application to the liquid-vapor phase transitions.

Patchy particles are an intriguing subject of study and indeed a model system in the field of soft matter physics. In recent years, patchy particle models have been applied to describe a wide variety of systems, including colloidal crystals, macromolecular interactions, liquid crystals, and nanoparticle assemblies. Given the importance of the topic, rationalizing and capturing the basic features of these models is crucial to their correct application in specific systems. In this study, we extend the ion-activated attractive patchy particles model previously employed to elucidate the phase behavior of protein solutions in the presence of trivalent salts. Our extension incorporates the effect of repulsion between unoccupied and occupied binding sites, depicted as patches. Furthermore, we examine the influence of model parameters on the liquid-vapor coexistence region within the phase diagram, employing numerical methods. A deeper understanding of this model will facilitate a better comprehension of the effects observed in experiments.

Thermodynamic and transport properties of triangular-well fluids from molecular dynamics

Thermodynamic and transport properties of particles interacting via the triangular-well potential in the range of 1.4 ≤ λ ≤ 2.6 have been studied using perturbation theory and Molecular Dynamics simulations. We present thermodynamic properties such as vapour-liquid coexistence, vapour pressures, and density for different values of the attractive range potential. Good agreement is observed between the theoretical approach and computer simulations in a wide range of densities, temperatures, and pressures. Additionally, we show Molecular Dynamic simulation results of transport properties such as the self-diffusion coefficient as a function of both density and temperature. Finally, thermodynamic and transport properties of real fluids like oxygen, methane, hydrogen sulfide, and fluoromethane have been predicted using both approaches. Results of vapour-liquid coexistence, vapour pressures, and critical points were in excellent agreement with experimental data. The coupling of perturbation theory, Molecular Dynamics simulations, and the triangular-well pair potential offers a versatile and efficient method to explore various real fluid systems, which would include associating fluids, complex molecular liquids, and colloidal systems. This approach can advance our understanding of these systems using a simple approach and to contribute the development of more accurate and predictive models.

Unmasking quantum effects in the surface thermodynamics of fluid nanodrops.

The focus of our study is an in-depth investigation of the quantum effects associated with the surface tension and other thermodynamic properties of nanoscopic liquid drops. The behavior of drops of quantum Lennard-Jones fluids is investigated with path-integral Monte Carlo simulations, and the test-area method is used to determine the surface tension of the spherical vapor-liquid interface. As the thermal de Broglie wavelength, λB, becomes more significant, the average density of the liquid drop decreases, with the drop becoming mechanically unstable at large wavelengths. As a consequence, the surface tension is found to decrease monotonically with λB, vanishing altogether for dominant quantum interactions. Quantum effects can be significant, leading to values that are notably lower than the classical thermodynamic limit, particularly for smaller drops. For planar interfaces (with infinite periodicity in the direction parallel to the interface), quantum effects are much less significant with the same values of λB but are, nevertheless, consequential for values representative of hydrogen or helium-4 at low temperatures corresponding to vapor-liquid coexistence. Large quantum effects are found for small drops of molecules with quantum interactions corresponding to water, ethane, methanol, and carbon dioxide, even at ambient conditions. The notable decrease in the density and tension has important consequences in reducing the Gibbs free-energy barrier of a nucleating cluster, enhancing the nucleation kinetics of liquid drops and of bubble formation. This implies that drops would form at a much greater rate than is predicted by classical nucleation theory.

Using the Zeno line to assess and refine molecular models.

The Zeno line is the locus of points on the temperature-density plane where the compressibility factor of the fluid is equal to one. It has been observed to be straight for a broad variety of real fluids, although the underlying reasons for this are still unclear. In this work, a detailed study of the Zeno line and its relation to the vapor-liquid coexistence curve is performed for two simple model pair-potential fluids: attractive square-well fluids with varying well-widths λ and Mie n-6 fluids with different repulsive exponents n. Interestingly, the Zeno lines of these fluids are curved, regardless of the value of λ or n. We find that for square-well fluids, λ ≈ 1.8 presents a Zeno line, which is the most linear over the largest temperature range. For Mie n-6 fluids, we find that the straightest Zeno line occurs for n between 8 and 10. Additionally, the square-well and Mie fluids with the straightest Zeno line showed the closest quantitative agreement with the vapor-liquid coexistence curve for experimental fluids that follow the principle of corresponding states (e.g., argon, xenon, krypton, methane, nitrogen, and oxygen). These results suggest that the Zeno line can provide a useful additional feature, in complement to other properties, such as the phase envelope, to evaluate molecular models.

Bubble-water/catalyst triphase interface microenvironment accelerates photocatalytic OER via optimizing semi-hydrophobic OH radical

Photocatalytic water splitting (PWS) as the holy grail reaction for solar-to-chemical energy conversion is challenged by sluggish oxygen evolution reaction (OER) at water/catalyst interface. Experimental evidence interestingly shows that temperature can significantly accelerate OER, but the atomic-level mechanism remains elusive in both experiment and theory. In contrast to the traditional Arrhenius-type temperature dependence, we quantitatively prove for the first time that the temperature-induced interface microenvironment variation, particularly the formation of bubble-water/TiO2(110) triphase interface, has a drastic influence on optimizing the OER kinetics. We demonstrate that liquid-vapor coexistence state creates a disordered and loose hydrogen-bond network while preserving the proton transfer channel, which greatly facilitates the formation of semi-hydrophobic •OH radical and O-O coupling, thereby accelerating OER. Furthermore, we propose that adding a hydrophobic substance onto TiO2(110) can manipulate the local microenvironment to enhance OER without additional thermal energy input. This result could open new possibilities for PWS catalyst design.

Structure of liquid-vapor interfaces: Perspectives from liquid state theory, large-scale simulations, and potential grazing-incidence x-ray diffraction.

Grazing-incidence x-ray diffraction (GIXRD) is a scattering technique that allows one to characterize the structure of fluid interfaces down to the molecular scale, including the measurement of surface tension and interface roughness. However, the corresponding standard data analysis at nonzero wave numbers has been criticized as to be inconclusive because the scattering intensity is polluted by the unavoidable scattering from the bulk. Here, we overcome this ambiguity by proposing a physically consistent model of the bulk contribution based on a minimal set of assumptions of experimental relevance. To this end, we derive an explicit integral expression for the background scattering, which can be determined numerically from the static structure factors of the coexisting bulk phases as independent input. Concerning the interpretation of GIXRD data inferred from computer simulations, we extend the model to account also for the finite sizes of the bulk phases, which are unavoidable in simulations. The corresponding leading-order correction beyond the dominant contribution to the scattered intensity is revealed by asymptotic analysis, which is characterized by the competition between the linear system size and the x-ray penetration depth in the case of simulations. Specifically, we have calculated the expected GIXRD intensity for scattering at the planar liquid-vapor interface of Lennard-Jones fluids with truncated pair interactions via extensive, high-precision computer simulations. The reported data cover interfacial and bulk properties of fluid states along the whole liquid-vapor coexistence line. A sensitivity analysis shows that our findings are robust with respect to the detailed definition of the mean interface position. We conclude that previous claims of an enhanced surface tension at mesoscopic scales are amenable to unambiguous tests via scattering experiments.

Liquid-Vapor Coexistence and Spontaneous Evaporation at Atmospheric Pressure of Common Rigid Three-Point Water Models in Molecular Simulations.

Molecular dynamics (MD) simulations are widely used to investigate molecular systems at atomic resolution including biomolecular structures, drug-receptor interactions, and novel materials. Frequently, MD simulations are performed in an aqueous solution with explicit models of water molecules. Commonly, such models are parameterized to reproduce the liquid phase of water under ambient conditions. However, often, simulations at significantly higher temperatures are also of interest. Hence, it is important to investigate the equilibrium of the liquid and vapor phases of molecular models of water at elevated temperatures. Here, we evaluate the behavior of 11 common rigid three-point water models over a wide range of temperatures. From liquid-vapor coexistence simulations, we estimated the critical points and studied the spontaneous evaporation of these water models. Moreover, we investigated the influence of the system size, choice of the pressure-coupling algorithm, and rate of heating on the process and compared them with the experimental data. We found that modern rigid three-point water models reproduce the critical point surprisingly well. Furthermore, we discovered that the critical temperature correlates with the quadrupole moment of the respective water model. This indicates that the spatial arrangement of the partial charges is important for reproducing the liquid-vapor phase transition. Our findings may guide the selection of water models for simulations conducted at high temperatures.

The Influence of Wettability Effect and Adsorption Thickness on Nanoconfined Methane Phase Behavior: Vapor-Liquid Co-Existence Curves and Phase Diagrams

Research interest in the behavior of methane inside nanopores has been growing, driven by the substantial geological reserves of shale gas and coalbed methane. The phase diagram of methane in nanopores differs significantly from its bulk state, influencing its existing form and pertinent physical properties—such as density and viscosity—at specific pressures and temperatures. Currently, there is a lack of effort to understand the nanoconfinement effect on the methane phase diagram; this is a crucial issue that needs urgent attention before delving into other aspects of nanoconfined methane behavior. In this study, we establish a fully coupled model to predict the methane phase diagram across various scales. The model is based on vapor-liquid fugacity equilibrium, considering the shift in critical pressure and temperature induced by pore size shrinkage and adsorption-phase thickness. Notably, our proposed model incorporates the often-overlooked factor of capillary pressure, which is greatly amplified by nanoscale pore size and the presence of the adsorption phase. Additionally, we investigated the impact of surface wettability, correlated to capillary pressure and the shift in critical properties, on the methane phase diagram. Our results indicate that (a) as pore size decreases, the methane phase diagram becomes more vertical, suggesting a transition from a gaseous to a liquid state for some methane molecules, which is contrary to the conventional phase diagram; (b) enhancing surface wettability results in a more vertical phase diagram, with the minimum temperature corresponding to 0 MPa pressure on the phase diagram, increasing by as much as 87.3%; (c) the influence of capillary pressure on the phase diagram is more pronounced under strong wettability conditions compared to weak wettability, and the impact from the shift in critical properties can be neglected when the pore size exceeds 50 nm.

Estimation of the Compressibility Factor of Nanoconfined Alkanes along Vapor–Liquid Coexistence

Estimation of the Compressibility Factor of Nanoconfined Alkanes along Vapor–Liquid Coexistence

Electrothermal instability in different modes of underwater electrical wire explosion

Electrothermal instability and its effect on the uniformity of discharge channels during underwater electrical wire explosions at different energy deposition rates have been investigated. According to the liquid–vapor transition mechanism, we classified underwater electrical explosion into “phase explosion mode” and “supercritical mode.” Two sets of experiments corresponding to the two modes were conducted, and the exploding wires were observed by a shadow imaging system. Results showed that a bamboo-shaped discharge channel was formed in the phase explosion mode, whereas the discharge channel in the supercritical mode was a uniform cylinder. Self-consistent magnetohydrodynamic simulation results indicated that exploding wires transfer into liquid–vapor coexistence phase in the phase explosion mode, accompanied by a rapid increase in the density perturbation and the formation of bamboo-shaped structures. Moreover, a small perturbation model was derived to analyze the electrothermal instability in different thermodynamic states. It was indicated that the density perturbation is easier to grow in the liquid–vapor coexistence state than the supercritical state, which provides a theoretical explanation for the differences between the two electrical explosion modes.

The Rapid Boiling of Thin Liquid Films with Different Thicknesses on Nanochannel Copper Plates: A Molecular Dynamics Study

Boiling heat transfer on nanostructured surfaces presents great potential in cooling highly integrated microelectronic devices. Analysis of the factors affecting boiling heat transfer included the analysis of nanostructure and wettability, indicating that consideration of the influence of working liquid quantity is essential in finite spaces. Rapid boiling water films with various thicknesses placed on the same nanochannel copper plate were studied via molecular dynamics (MD) simulations. The simulation results reveal that the potential energy difference in the vapor–liquid coexisting region on the nanochannels was lower for thicker films, and the evaporation rate was lower. The effect of water film thickness on boiling heat transfer is closely related to the potential energy difference in the vapor–liquid coexisting region on the nanochannels. The heat transfer effect was the worst in case 1, where the water thickness was lower than the height of the nanochannels. This is because there is no guaranteed liquid replenishment at the nucleation points, although the potential energy difference was greatest in the vapor–liquid coexistence zone of case 1. Evaporation was the greatest in case 2, where the water film just covered the nanochannels because of the larger potential energy difference and sufficient liquid water replenishment. This study is of great significance for the analysis of the vapor–liquid flow mechanisms of micro/nanostructured surfaces and the improved design of thermal management equipment of micro/nano devices.

Attractive Solution of Binary Bose Mixtures: Liquid-Vapor Coexistence and Critical Point.

We study the thermodynamic behavior of attractive binary Bose mixtures using exact path-integral MonteCarlo methods. Our focus is on the regime of interspecies interactions where the ground state is in a self-bound liquid phase, stabilized by beyond mean-field effects. We calculate the isothermal curves in the pressure vs density plane for different values of the attraction strength and establish the extent of the coexistence region between liquid and vapor using the Maxwell construction. Notably, within the coexistence region, Bose-Einstein condensation occurs in a discontinuous way as the density jumps from the normal gas to the superfluid liquid phase. Furthermore, we determine the critical point where the line of first-order transition ends and investigate the behavior of the density discontinuity in its vicinity. We also point out that the density discontinuity at the transition could be observed in experiments of mixtures in traps.

Assessment of the pseudopotential lattice-Boltzmann method for modeling multiphase fuel droplets

An improved pseudopotential lattice–Boltzmann model was proposed for simulating multiphase flow dynamics to describe fuel droplets, and its thermodynamic consistency was tested against the Peng–Robinson equation of state. The studied liquid fuels included paraffinic hydrocarbons with a different number of carbon atoms (C[Formula: see text]–C[Formula: see text]), methanol (CH[Formula: see text]OH), hydrogen (H[Formula: see text]), ammonia (NH[Formula: see text]), and water (H[Formula: see text]O). To improve accuracy and reduce the magnitude of the spurious currents, the multi-relaxation times collision operator was implemented and the forcing term was computed using the hybrid pseudopotential interaction force with an eighth-order isotropic degree. The pseudopotential lattice–Boltzmann model accurately predicted the equilibrium densities and captured satisfactorily the thermodynamic vapor-liquid coexistence curve given by the analytical solution of the Peng–Robinson equation of state for acentric factors ranging from [Formula: see text]0.22 to 0.56, keeping the maximum average error for the liquid and vapor branches below 0.8% and 3.7%, respectively. Nevertheless, Peng–Robinson was found to be insufficiently accurate to replicate the actual thermodynamic state, especially for H[Formula: see text]O and CH[Formula: see text]OH, for which the results strongly deviated from the experimental vapor-liquid equilibrium densities and reached average errors for the vapor phase of nearly 28%. Furthermore, the surface tension ([Formula: see text]) was retrieved using the multiphase pseudopotential lattice–Boltzmann results and served to verify the thermodynamic consistency of the pseudopotential lattice–Boltzmann with respect to the parachor model. Lastly, the pseudopotential lattice–Boltzmann model was also shown to predict accurately the transient behavior of oscillating droplets. Overall, the enhanced model satisfactorily predicted the properties and behavior of the substances for a wide range of conditions.

Neural Network Water Model Based on the MB-Pol Many-Body Potential.

The MB-pol many-body potential accurately predicts many properties of water, including cluster, liquid phase, and vapor-liquid equilibrium properties, but its high computational cost can make applying it in large-scale simulations quite challenging. In order to address this limitation, we developed a "deep potential" neural network (DPMD) model based on the MB-pol potential for water. We find that a DPMD model trained on mostly liquid configurations yields a good description of the bulk liquid phase but severely underpredicts vapor-liquid coexistence densities. By contrast, adding cluster configurations to the neural network training set leads to a good agreement for the vapor coexistence densities. Liquid phase densities under supercooled conditions are also represented well, even though they were not included in the training set. These results confirm that neural network models can combine accuracy and transferability if sufficient attention is given to the construction of a representative training set for the target system.