Liquid-vapor Coexistence Region Research Articles

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.

Fluid-fluid phase transitions in a chiral molecular model.

Molecular chirality is a fundamental phenomenon, underlying both life as we know it and industrial pharmaceutical syntheses. Understanding the symmetry breaking phase transitions exhibited by many chiral molecular substances provides basic insights for topics ranging from the origin of life to the rational design of drug manufacturing processes. In this work, we have performed molecular dynamics simulations to investigate the fluid-fluid phase transitions of a flexible three-dimensional four-site chiral molecular model developed by Latinwo et al. [J. Chem. Phys. 145, 154503 (2016)] and Petsev et al. [J. Chem. Phys. 155, 084105 (2021)]. By introducing a bias favoring local homochiral vs heterochiral interactions, the system exhibits a phase transition from a single achiral phase to a single chiral phase that undergoes infrequent interconversion between the two thermodynamically identical chiral states: the L-rich and D-rich phases. According to the phase rule, this reactive binary system has two independent degrees of freedom and exhibits a density-dependent critical locus. Below the liquid-liquid critical locus, there exists a first-order vapor-liquid coexistence region with a single independent degree of freedom. Our results provide basic thermodynamic and kinetic insights for understanding many-body chiral symmetry breaking phenomena.

Breakdown of the law of rectilinear diameter and related surprises in the liquid-vapor coexistence in systems of patchy particles.

The phase diagram of molecular or colloidal systems depends strongly on the range and angular dependence of the interactions between the constituent particles. For instance, it is well known that the critical density of particles with "patchy" interactions shifts to lower values as the number of patches is decreased [see Bianchi et al. Phys. Rev. Lett. 97, 168301 (2006)]. Here, we present simulations that show that the phase behavior of patchy particles is even more interesting than had been appreciated. In particular, we find that, upon cooling below the critical point, the width of the liquid-vapor coexistence region of a system of particles with tetrahedrally arranged patches first increases, then decreases, and finally increases again. In other words, this system exhibits a doubly re-entrant liquid-vapor transition. As a consequence, the system exhibits a very large deviation from the law of rectilinear diameter, which assumes that the critical density can be obtained by linear extrapolation of the averages of the densities of the coexisting liquid and vapor phases. We argue that the unusual behavior of this system has the same origin as the density maximum in liquid water and is not captured by the Wertheim theory. The Wertheim theory also cannot account for our observation that the phase diagram of particles with three patches depends strongly on the geometrical distribution of the patches and on the degree to which their position on the particle surface is rigidly constrained. However, the phase diagram is less sensitive to small angular spreads in the patch locations. We argue that the phase behavior reported in this paper should be observable in experiments on patchy colloids and may be relevant for the liquid-liquid equilibrium in solutions of properly functionalized dendrimers.

Generalized coupling parameter expansion: Application to square well and Lennard-Jones fluids

The coupling parameter expansion in thermodynamic perturbation theory of simple fluids is generalized to include the derivatives of bridge function with respect to coupling parameter. We applied seventh order version of the theory to Square-Well (SW) and Lennard-Jones (LJ) fluids using Sarkisov Bridge function. In both cases, the theory reproduced the radial distribution functions obtained from integral equation theory (IET) and simulations with good accuracy. Also, the method worked inside the liquid-vapor coexistence region where the IETs are known to fail. In the case of SW fluids, the use of Carnahan-Starling expression for Helmholtz free energy density of Hard-Sphere reference system has improved the liquid-vapor phase diagram (LVPD) over that obtained from IET with the same bridge function. The derivatives of the bridge function are seen to have significant effect on the liquid part of the LVPD. For extremely narrow SW fluids, we found that the third order theory is more accurate than the higher order versions. However, considering the convergence of the perturbation series, we concluded that the accuracy of the third order version is a spurious result. We also obtained the surface tension for SW fluids of various ranges. Results of present theory and simulations are in good agreement. In the case of LJ fluids, the equation of state obtained from the present method matched with that obtained from IET with negligible deviation. We also obtained LVPD of LJ fluid from virial and energy routes and found that there is slight inconsistency between the two routes. The applications lead to the following conclusions. In cases where reference system properties are known accurately, the present method gives results which are very much improved over those obtained from the IET with the same bridge function. In cases where reference system data is not available, the method serves as an alternative way of solving the Ornstein-Zernike equation with a given closure relation with the advantage that solution can be obtained throughout the phase diagram with a proper choice of the reference system.

Isomorphism in Fluid Phase Diagrams: Kulinskii Transformations Related to the Acentric Factor

For a wide class of molecular fluids, the temperature–density phase diagrams exhibit two prominent generic properties: a nearly linear locus, termed the Zeno line, along which the compressibility factor, Z = P/ρRT = 1 (same as an ideal gas), and the widely arching border of the vapor–liquid coexistence region, termed the binodal curve, with gas and liquid branches meeting at the critical point. The Zeno and binodal loci have been known for more than a century, yet only during the past two decades were striking empirical correlations between them recognized. Recently, Kulinskii introduced a remarkably simple projective transformation, wherein the linearity of the Zeno line and its relation to the binodal curve are geometrical consequences of an approximate isomorphism of the fluid with a venerable theoretical model, the lattice gas (equivalent to the Ising spin model). Here we show the Kulinskii transformation is significantly improved in accuracy and scope by using as input, in place of the lattice gas, t...

Testing the recent charge-on-spring type polarizable water models. II. Vapor-liquid equilibrium

We studied the vapor-liquid coexistence region of seven molecular models of water. All models use the charge-on-spring (COS) method to express polarization. The studied models were the COS∕G2, COS∕G3 [H. Yu and W. F. van Gunsteren, J. Chem. Phys. 121, 9549 (2004)], the SWM4-DP [G. Lamoureux, A. D. MacKerell, Jr., and B. Roux, J. Chem. Phys. 119, 5185 (2003)], the SWM4-NDP [G. Lamoureux, E. Harder, I. V. Vorobyov, B. Roux, and A. D. MacKerell, Jr., Chem. Phys. Lett. 418, 245 (2006)], and three versions of our model, the BKd1, BKd2, and BKd3. The BKd1 is the original Gaussian model [P. T. Kiss, M. Darvas, A. Baranyai, and P. Jedlovszky, J. Chem. Phys. 136, 114706 (2012)] with constant polarization and with a simple exponential repulsion. The BKd2 applies field-dependent polarizability [A. Baranyai and P. T. Kiss, J. Chem. Phys. 135, 234110 (2011)], while the BKd3 model has variable size to approximate the temperature-density (T-ρ) curve of water [P. T. Kiss and A. Baranyai, J. Chem. Phys. 137, 194102 (2012)]. We calculated the second virial coefficient, the heat of vaporization, equilibrium vapor pressure, the vapor-liquid coexistence curve, and the surface tension in terms of the temperature. We determined and compared the critical temperatures, densities, and pressures of the models. We concluded that the high temperature slope of the (T-ρ) curve accurately predicts the critical temperature. We found that Gaussian charge distributions have clear advantages over the point charges describing the critical region. It is impossible to describe the vapor-liquid coexistence properties consistently with nonpolarizable models, even if their critical temperature is correct.

Role of electronic-excitation effects in the melting and ablation of laser-excited silicon

We present a model of laser–solid interactions in silicon based on a previously-developed interatomic potential for silicon where the parameters describing the interactions depend on the temperature of the electronic subsystem Te, which is directly related to the density of electron–hole pairs and hence the number of broken covalent bonds. For 25fs pulses, a wide range of fluence values are simulated resulting in heterogeneous melting, homogeneous melting, and ablation. The results presented here demonstrate that phase transitions can usually be described by ordinary thermal processes even when the electronic temperature Te is much greater than the lattice temperature TL during the transition. However, the evolution of the system and details of the phase transitions depend strongly on Te and corresponding density of broken bonds. Homogeneous melting appears to be an ordinary thermal phase transition, but occurring over very fast time scales (1–5ps) before TL reaches the ordinary melting temperature of silicon. For high enough laser fluence, homogeneous melting is followed by rapid expansion of the superheated liquid and ablation. Rapid expansion of the superheated liquid occurs partly due to high pressures generated by a high density of broken bonds. As a result of rapid expansion of the superheated liquid, the system is readily driven into the liquid–vapor coexistence region which initiates phase explosion. These results strongly indicate that phase explosion, generally thought of as an ordinary thermal process, can occur even under strong nonequilibrium conditions when Te≫TL. Thus, the results both for melting and ablation processes suggest that for many cases there is no clear separation between thermal and nonthermal processes. Instead, ordinary thermal mechanisms are found to apply when Te≫TL, with the high density of broken bonds playing an important role in the detailed evolution of the system.

A star-function based density functional study of the adsorption of Lennard-Jones fluid near its supercritical states

The goal of this paper is to show that the wetting behavior of simple fluids on a repulsive solid surface – especially the “drying” phenomenon – is closely related to the proximity of the supercritical state of the bulk fluids to their vapor–liquid coexistence region. We propose here a new DFT (the star-function based density functional theory, s-DFT) that is based on the functional Taylor expansion of the intrinsic free energy F[ ρ] and the singlet direct correlation C w ( 1 ) ( r ) to arrive at closed-form expressions for both quantities without truncations or approximations. The two formulas are mutually consistent because of the introduction of a star function S w that has been shown to be the functional primitive of the bridge function B w , i.e. δ S w * / δ ρ = B w (L.L. Lee, J. Chem. Phys. 97 (1992) 8606 [34]). The new formulation is applied to the Lennard-Jones molecules adsorbed on a planar hard wall (LJ/HW). We carried out new Monte Carlo simulations for this system. Since the s-DFT uses a bridge function B w , we demonstrate (i) the existence of a set of data (inverted from the MC information) that can perform as the bridge function and reproduce accurately the density profiles ρ w ( 1 ) ( r ) ; (ii) this set of data can be “fitted” by a function-form with acronym ZSEP; finally (iii) ZSEP expresses the bridge function B w in terms of a new renormalized basis function γ H , i.e. B w ( γ H ) . The existence of a bridge function dispels some of the misconceptions that the bridge-function based formulations did not describe the “drying” behavior. We also show that for the high density case ZSEP equation can qualify as a “closure relation”, but seems to deteriorate for the two low-density supercritical states that are close to the bulk saturated liquid phase boundaries.

Effect of the interfacial area on the equilibrium properties of Lennard-Jones fluid

The influence of the system size on the interfacial and equilibrium properties of the Lennard-Jones fluid obtained using the inhomogeneous Monte Carlo simulations is studied for temperatures covering the vapor-liquid coexistence region. The values of the surface tension, coexistence densities, as well as the pressure of saturated vapor are affected by the varying area of the interface. Moreover the loss of isotropy of the fluid structure is observed as a consequence of using the periodic boundary conditions in molecular simulations. The equilibrium properties are evaluated also in simulation boxes of the shape of hexangular prism and compared to the results of simulations performed in the commonly used quadrangular parallelepiped. Both sets seem to be affected by the finite-size effects in similar extent.

The thermodynamic properties of liquid and vapor in the cadmium-thallium-lead system

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

Compressed CO 2 antisolvent precipitation of lysozyme

The precipitation of proteins using compressed CO 2 as antisolvent in the precipitation with a compressed antisolvent (PCA) process has been investigated for lysozyme in its DMSO solution. In the vapor liquid coexistence region of the solvent–antisolvent mixture, particles between 100 and 200 nm were obtained, whereas at supercritical and liquid conditions studied in the 25–40 ° C and 100–150 bar ranges, particle sizes were reproducibly below 100 nm. No effect on particle size was observed for variations of the CO 2 and solutions flow rates between 40 and 120 g/min, and between 0.4 and 2 ml/min, respectively. Phase behavior experiments indicate that protein precipitation results from a metastable liquid–liquid phase separation, with the protein rich phase remaining trapped in a gel-like state. Moreover, we suggest that due to the high CO 2 concentrations involved in PCA, phase separation takes place by spinodal decomposition. The proposed precipitation mechanism is not limited to the PCA process, but can be extended also to results obtained for the precipitation of lysozyme using the gas antisolvent (GAS) process.

Preparation of Nano- and Micrometric Ceftazidime Particles with Supercritical Anti-Solvent Technique

Nano- and microparticles of ceftazidime were prepared via a supercritical antisolvent (SAS) process. The influences of various processing parameters on the characteristics of the resultant particles were investigated. The experimental results revealed that the product's morphology closely correlated with the phase behavior of the mixtures in the precipitator during particle formation stage. Networked nanospheroids with narrow particle size distribution were produced when the precipitation was operated in either the compressed liquid region or in the supercritical region. However, the particulate products became less uniform as the precipitation was implemented near the critical region. While microspheroids were obtained as the precipitation was conducted in the superheated vapor region, dense films together with microparticles were formed in the vapor-liquid coexistence region. The untreated ceftazidime and the SAS precipitated samples were characterized with wide-angle X-ray scattering (WAXS), a differential scanning calorimeter (DSC), a thermogravimetric analyzer (TGA), and Fourier transform infrared spectrophotometry (FTIR). The analysis results indicated that the SAS-processed particles were amorphous and the water content was markedly reduced. Moreover, the molecular structure was still retained after the SAS processing.

Role of phase behavior in micronization of lysozyme via a supercritical anti-solvent process

Abstract Ultra-fine particles of protein lysozyme were prepared with a supercritical anti-solvent (SAS) apparatus by using dimethyl sulfoxide (DMSO) as solvent and carbon dioxide as anti-solvent. The influences of various experimental factors on the morphology and the mean size of particulate products were investigated. As evidenced from the experimental results, phase behavior of the mixtures in precipitator during the particle formation stage played a crucial role in the SAS processes. Uniform networked nano-particles were obtained when the precipitations were conducted in the supercritical region of carbon dioxide + DMSO mixture. Several different types of morphologies were produced simultaneously as the precipitations were operated near the critical region. Spherical micron-scale clusters were formed in the superheated vapor region, while submicron-particles were aggregated as dense cake when lysozyme precipitated in the vapor–liquid coexistence region. The wide angle X-ray scattering (WAXS) patterns indicated that both the raw lysozyme and the processed particulate samples were amorphous. The differential scanning calorimeter (DSC) thermograms showed that the dehydration peak was disappeared after SAS treatment. Moreover, the networked primary particles could be disintegrated and dispersed well in water through ultrasonication, which were confirmed by analysis with dynamic laser scattering (DLS). A continuous stirred tank reactor (CSTR) model was used to calculate the dynamic composition variations of the mixtures in precipitator during the particle formation period.

The influence of phase behavior on the morphology of protein α-chymotrypsin prepared via a supercritical anti-solvent process

Ultra-fine particles of α-chymotrypsin were produced with a supercritical anti-solvent (SAS) technique by using dimethyl sulfoxide (DMSO) as a solvent and carbon dioxide as an anti-solvent. According to the vapor-liquid equilibrium (VLE) phase diagram of DMSO + carbon dioxide, the precipitation experiments have been conducted in different phase regions, including supercritical, superheated vapor, and vapor–liquid phase coexistence zones. It was found that the phase behavior of the mixtures during precipitation governed the product's morphology. Uniform networked nano-particles were obtained as the precipitation was implemented in the supercritical region. The uniformity of the resulting products became worse when the particles were precipitated around the critical region. Irregular micro-scale aggregated particles were formed in the superheated region, while both dense cake and spherical clusters were produced in the vapor–liquid coexistence region. A continuous stirred tank reactor (CSTR) model was applied to calculate the dynamic composition variations of mixtures in precipitator during the particle formation process. The crystalline and thermal property of the original and the SAS processed samples were analyzed by a wide-angle X-ray scattering (WAXS), a differential scanning calorimeter (DSC) and a thermogravimetric analyzer (TGA), respectively. No significant changes were found after SAS treatment. Besides, the biological activity of the SAS processed α-chymotrypsin was retained in a range of 30–75% of the original protein.

Structure and thermodynamics of discrete potential fluids in the OZ–HMSA formalism

We study the structural and thermodynamic properties of three discrete potentialfluids: the square well (SW), the square well–barrier (SWB), and the squarewell–barrier–well (SWBW) fluids by means of the Ornstein–Zernike (OZ) integralequation and the HMSA (hybrid mean spherical approximation) closure relation.The radial distribution functions, structure factors, and pressure of the systemsare calculated as a function of the strength of the attractive and repulsive partsof the potential in an extended range of densities, mainly covering the range0.1 ≤ ρ* ≤ 0.9. We find that far away from the liquid–vapour coexistence region the HMSA theory is anaccurate approach that compares well with Monte Carlo simulations. We also find that when theattractive parts of the potential dominate over the repulsive part the structure factor at lowq values shows a considerable increase, which suggests the formation of large-scale domainsthat locally exhibit fluid-like structure.

Vapour-liquid equilibria of the two- and three-dimensional monoatomic classical fluids interacting via double Yukawa potential

We have carried out Monte Carlo simulations in Gibbs ensemble for two-and three-dimensional double Yukawa fluid. We have compared liquid-vapour equilibrium curve with that of Lennard-Jones, when parameters occurring in double Yukawa potential are chosen to fit Lennard-Jones potential. The results are in good agreement. The role of repulsive and attractive contributions for the potential on the liquid-vapour coexistence region as well as on critical temperature and critical density has been studied. The critical temperature is found to be more sensitive than the critical density to the variation in repulsive and attractive parts of the potential. Also, the range of the attractive interaction directly influences range of the liquid vapour coexistence region. It has been found that smaller the values of the attractive parameter, larger is the coexistence region.

Nanoparticles formation for metallocene catalyzed cyclic olefin copolymer via a continuous supercritical anti-solvent process

Nanoparticles of the metallocene catalyzed cyclic olefin copolymer (mCOC) were prepared with a lab scale continuous supercritical anti-solvent (SAS) apparatus. Several experimental parameters were investigated to explore their influences on the morphology and the mean size of the products. These parameters included the character of carbon dioxide injector, precipitation pressure and temperature, anti-solvent density, the polymer concentration, the flow rate of feed, and the nature of organic solvents. The phase states of the mixtures of solvent + anti-solvent in precipitation stage may govern the mean size of the resulting particles. Nanoparticles of mCOC were obtained in the homogeneous compressed liquid or supercritical region, while sub-micrometric particles were formed in the vapor–liquid coexistence region. The morphology of precipitates was also significantly changed, turning from spherical nanoparticles to microfibrils, as the polymer concentration of feed was increased from 2 to 4 wt.%. Under 15 MPa and 306.2 K, the mean size of the resultant primary mCOC particles as small as 39 nm with a standard deviation of about 6 nm could be produced. The residual solvent was about 1.6 wt.% in the sample after SAS processing by analyzing with a thermogravimetric analyzer (TGA), and the particle samples exhibited sub-glass transition behavior according to the thermal histograms of differential scanning calorimeter (DSC).

Improved equation of state of metals in the liquid-vapor region

The existing “quotidian equation state” model, based on Thomas-Fermi theory, is modified so as to improve the low density region of phase diagram of metals. A scheme for estimating the critical parameters of liquid-vapor phase transition is proposed. The new model reproduces experimental critical isotherms to a good degree of accuracy. Furthermore, the proposed model is validated with thermodynamic data in the liquid-vapor co-existence region, including results on isobaric expansion as well as released isentropes.

Ultra-fine particles formation of C.I. Pigment Green 36 in different phase regions via a supercritical anti-solvent process

Ultra-fine particles of C.I. Pigment Green 36 were prepared using a continuous supercritical anti-solvent (SAS) apparatus employing quinoline as solvent and supercritical carbon dioxide as anti-solvent. A series of precipitation experiments were conducted at different temperatures, pressures, and flow rates of pigment solution. The vapor–liquid phase boundaries of carbon dioxide + quinoline mixtures were also measured with a volume-variable phase equilibrium analyzer at temperatures from 308.2 K to 328.2 K. Mapping the estimated composition of mixtures in a model CSTR (continuously stirred tank reactor) precipitator at the end of injection of pigment solution onto the phase diagram found that the morphology of prepared particles was mainly governed by the phase behavior of anti-solvent + solvent mixtures. Nano-particles were obtained as the precipitation loci were manipulated within either supercritical or superheated vapor region through the SAS process, whereas micro-metric aggregated ball-like particles were produced as the precipitation loci passed by the vapor–liquid coexistence region.

Continuous phase transition and negative specific heat in finite nuclei

The liquid-gas phase transition in finite nuclei is studied in a heated liquid-drop model where the nuclear drop is assumed to be in thermodynamic equilibrium with its own evaporated nucleonic vapor, conserving the total baryon number and isospin of the system. It is found that in the liquid-vapor coexistence region the pressure is not a constant on an isotherm, indicating that the transition is continuous. At constant pressure, the caloric curve shows some anomalies; namely, the systems studied exhibit negative heat capacity in a small temperature domain. The dependence of this specific feature on the mass and isospin of the nucleus, Coulomb interaction, and the chosen pressure is studied. The effects of the presence of clusters in the vapor phase on specific heat have also been explored.