Solid-liquid Coexistence Curve Research Articles

Estimation of solid-liquid coexistence curve for coarse-grained water models through reliable free energy method

The anomalies properties of water have been interpreted theoretically using several all-atom and coarse-grained water models. Here we use a robust and traditional free energy approach to develop the solid-liquid coexistence curve for water using coarse-grained monatomic mW and machine-learned bond order potential (ML-BOP) water models. We employ the pseudo-supercritical thermodynamic path in combining multiple histogram reweighting (MHR) and Gibbs-Duhem integration. The ML-BOP model has a broad density-temperature hysteresis loop and shows lower maximum and minimum densities as compared to the mW model. The computed excess Helmholtz free energy and the Gibbs free energy at the approximate melting temperature are higher for the ML-BOP model in comparison with the mW model. The pressure dependence fusion curve for both water models aligns with the literature. This analysis indicates that the free energy method accurately captures the solid-liquid transformation and the thermodynamic melting point of water.

Predicting Melt Curves of Energetic Materials Using Molecular Models

AbstractIn this work, the solid–liquid coexistence curves of classical fully flexible atomistic models of α‐RDX and β‐HMX were calculated using thermodynamically rigorous methodologies that identify where the free energy difference between the phases is zero. The free energy difference between each phase at a given state point was computed using the pseudosupercritical path (PSCP) method, and Gibbs–Helmholtz integration was used to evaluate the solid–liquid free energy difference as a function of temperature. This procedure was repeated for several pressures to determine points along the coexistence curve, which were then fit to the Simon–Glatzel functional form. While effective, this method is computationally expensive. An alternative approach is to compute the melting point at a single pressure via the PSCP method, and then use the Gibbs–Duhem integration technique to trace out the coexistence curve in a more computationally economical manner. Both approaches were used to determine the coexistence curve of α‐RDX. The Gibbs–Duhem integration method was shown to generate a melt curve that is in good agreement with the PSCP‐derived melt curve, while only costing ∼10 % of the computational resources used for the PSCP method. For α‐RDX, the predicted melting temperature increases significantly more for a given increase in pressure when compared to available experimental data.

Thermodynamics of carbon dioxide mixtures at cryogenic conditions

Carbon capture and sequestration / utilization using cryogenic conditions have found attention due to lower energy penalty compared to other separation methods. In cryogenic processes, carbon dioxide is likely to desublimate from a vapor phase or freezes out from a liquid phase. This study deals with phase equilibrium calculations where solid carbon dioxide forms in the presence of vapor phase (SLV), liquid phase (SLE), or both (SLVE). Two of the successful solid fugacity models are used with predictive cubic equations of state (EOSs) in calculating the phase equilibrium of carbon dioxide mixtures. The advantages and limitations of the models are discussed. In addition, a new fugacity model which describes solid carbon dioxide along solid–liquid coexistence curve is developed. This model remedies the previous models and is used from low to very high pressure. This model reduces to an analytical expression for describing carbon dioxide melting curve. When coupled with the predictive cubic EOSs, this model satisfactorily describes the SVE, SLE, and SVLE of carbon dioxide mixtures.

Pressure-energy correlations in liquids. V. Isomorphs in generalized Lennard-Jones systems

This series of papers is devoted to identifying and explaining the properties of strongly correlating liquids, i.e., liquids with more than 90% correlation between their virial W and potential energy U fluctuations in the NVT ensemble. Paper IV [N. Gnan et al., J. Chem. Phys. 131, 234504 (2009)] showed that strongly correlating liquids have "isomorphs," which are curves in the phase diagram along which structure, dynamics, and some thermodynamic properties are invariant in reduced units. In the present paper, using the fact that reduced-unit radial distribution functions are isomorph invariant, we derive an expression for the shapes of isomorphs in the WU phase diagram of generalized Lennard-Jones systems of one or more types of particles. The isomorph shape depends only on the Lennard-Jones exponents; thus all isomorphs of standard Lennard-Jones systems (with exponents 12 and 6) can be scaled onto a single curve. Two applications are given. One tests the prediction that the solid-liquid coexistence curve follows an isomorph by comparing to recent simulations by Ahmed and Sadus [J. Chem. Phys. 131, 174504 (2009)]. Excellent agreement is found on the liquid side of the coexistence curve, whereas the agreement is less convincing on the solid side. A second application is the derivation of an approximate equation of state for generalized Lennard-Jones systems by combining the isomorph theory with the Rosenfeld-Tarazona expression for the temperature dependence of the potential energy on isochores. It is shown that the new equation of state agrees well with simulations.

Modeling the Dissociation Conditions of Salt Hydrates and Gas Semiclathrate Hydrates: Application to Lithium Bromide, Hydrogen Iodide, and Tetra-n-butylammonium Bromide + Carbon Dioxide Systems

A thermodynamic approach is proposed to determine the dissociation conditions of salt hydrates and semiclathrate hydrates. The thermodynamic properties of the liquid phase are described with the SAFT-VRE equation of state, and the solid-liquid equilibria are solved by applying the Gibbs energy minimization criterion under stoichiometric constraints. The methodology is applied to water + halide salt systems, and an excellent description of the solid-liquid coexistence curves is obtained. The approach is extended to the water + tetra-n-butylammonium bromide (TBAB) binary mixture, and an accurate representation of the solid-liquid coexistence curves and dissociation enthalpies is obtained. The van der Waals-Platteeuw (vdW-P) theory combined with the new model for salt hydrates is used to determine the dissociation temperatures of semiclathrate hydrates of TBAB + carbon dioxide. A good description of the dissociation pressures of CO(2) semiclathrate hydrates is obtained over wide temperature, pressure, and TBAB composition ranges (AAD = 10.5%). For high TBAB weight fractions the new model predicts a change of hydrate structure from type A to type B as the partial pressure of CO(2) is increased. The model can also capture a change of behavior with respect to TBAB concentration, which has been observed experimentally: an increase of the TBAB weight fraction leads to a stabilization of the gas semiclathrate hydrate at low initial TBAB concentrations below the stoichiometric composition but leads to a destabilization of the hydrate at TBAB concentrations above the stoichiometric composition.

The Nonequilibrium Phase and Glass Transition Behavior of β-Lactoglobulin

Concentrated solutions of bovine β-lactoglobulin were studied using osmotic stress and rheological techniques. At pH 6.0 and 8.0, the osmotic pressure was largely independent of NaCl concentration and could be described by a hard sphere equation of state. At pH 5.1, close to the isoelectric point, the osmotic pressure was lower at the lower NaCl concentrations (0 mM, 100 mM) and was fitted by an adhesive hard sphere model. Liquid-liquid phase separation was observed at pH 5.1 at ionic strengths of 13 mM and below. Comparison of the liquid-liquid and literature solid-liquid coexistence curves showed these solutions to be supersaturated and the phase separation to be nonequilibrium in nature. In steady shear, the zero shear viscosity of concentrated solutions at pH 5.1 was observed at shear rates above 50 s −1. With increasing concentration, the solution viscosity showed a progressive increase, a behavior interpreted as the approach to a colloidlike glass transition at ∼60% w/w. In oscillatory shear experiments, the storage modulus crossed the loss modulus at concentrations of 54% w/w, an indication of the approaching glass transition. Comparison of the viscous behavior with predictions from the Krieger-Dougherty equation indicates the hydrodynamic size of the protein decreases with increasing concentration, resulting in a slower approach to the glass transition than a hard sphere system.

Solid–liquid phase equilibria in binary (1-octanol + n-alkane) mixtures under high-pressure : Part 2. (1-Octanol + n-octane, n-dodecane) systems

The solid–liquid phase equilibria (SLE) of the (1-octanol+ n-alkane) systems have been investigated at temperatures from 263 to 293 K and pressures up to 200 MPa by the visual observation with a high-pressure optical vessel. In this work, (1-octanol+ n-octane or n-dodecane) systems are discussed. The uncertainties of the measurements of temperature, pressure, and composition are within ±0.1 K, ±0.5 MPa, and ±0.001 mole fraction, respectively. The solid–liquid coexistence curve and the eutectic point are found to increase to higher temperatures monotonically with increasing pressure in these systems. A new correlation method in order to represent the SLE curves under high-pressure was proposed based on the general solubility equation of a solid in a liquid at atmospheric pressure.

Solid–liquid phase equilibria in binary (1-octanol + n-alkane) mixtures under high pressure : Part 1. (1-Octanol + n-tetradecane or n-hexadecane) systems

The solid–liquid phase equilibria (SLE) of the (1-octanol+ n-alkane) systems have been investigated at temperatures from 268 to 333 K and pressures up to 220 MPa by the visual observation with a high-pressure optical vessel. In this work, (1-octanol+ n-tetradecane) and (1-octanol+ n-hexadecane) systems are discussed. The uncertainties of the measurements of temperature, pressure, and composition are within ±0.1 K, ±0.5 MPa, and ±0.001 mole fraction, respectively. The solid–liquid coexistence curve and the eutectic point are found to increase to higher temperatures monotonically with increasing pressure in these systems. In order to describe the pressure ( P), temperature ( T), composition ( x) relation of the SLE, a new simple equation with two exponents g and h has been proposed as follow: T= B( P)+ C( P) x g + D( P) x h where B, C, and D are pressure-dependent coefficients and are expressed by the polynomials of pressure. It is found that the SLE diagrams of these two systems under high pressure can be correlated successfully by this equation.

Solid-liquid phase equilibria in binary (benzene, cyclohexane + n-tetradecane, n-hexadecane) systems at temperatures 230–323 K and pressures up to 120 MPa

The solid-liquid phase behavior has been measured for the binary systems (C 6H 6 + n-C 14H 30), (C 6H 6 + n-C 16H 34), (C 6H 12 + n-C 14H 30), and (C 6H 12 + n-C 16H 34) at temperatures from 230 to 323 K and pressures up to 120 MPa by the visual observation of the phase transition using a high-pressure optical vessel with the aid of a video microscope. The uncertainties in measurements of temperature, pressure, and composition are within 0.1 K, 0.5 MPa and 0.001 mole fraction, respectively. The solid-liquid equilibrium (SLE) diagrams of the investigated systems consist of two liquidus curves intersecting at the eutectic point. Two components in each system have immiscibility in the solid phase, while they are completely miscible in the liquid phase. The solid-liquid coexistence curve and the eutectic point are found to increase to higher temperatures monotonically with increasing pressure in each system. The SLE diagrams at atmospheric pressure could be predicted successfully by the UNIFAC estimation method.

The role of attractive forces in determining the thermodynamic properties of two-dimensional Lennard-Jones fluids

Computer simulations were performed to obtain the radial distribution function for two-dimensional Lennard-Jones fluids over a wide range of densities and temperatures and for different contributions of the attractive forces. The repulsive and attractive intermolecular forces are separated following the Weeks-Chandler-Andersen perturbation theory. The influence of the attractive forces on the potential and internal energies, pressure, Helmholtz free energy and chemical potential was then analysed. These results will be used in later studies of the influence of these forces on the vapour-liquid and solid-liquid coexistence curves, and on theoretical adsorption isotherms.

Thermodynamic behaviour of liquid p-xylene near freezing

Experimental pρT measurements and derived thermodynamic properties of p-xylene (1,4-dimethylbenzene) have been obtained with an expansion technique for temperatures between 288 and 303 K and pressures up to 43 MPa, or freezing pressure when lower. The solid-liquid coexistence curve of this compound was also measured up to 40 MPa. The experimental results have been correlated in terms of a recently derived equation of state, which is introduced here and has been used to calculate the isothermal compressibility, κT, and the thermal expansion coefficient, αp, as functions of pressure and temperature. The equation of state depends only on six parameters, all of which are physically meaningful. Comparisons of several properties show good agreement with literature values.

Effect of pressure on the solid-liquid phase equilibria in (water + sodium sulfate) system

The effect of pressure on the phase diagram of (H 2O + Na 2SO 4) system has been investigated at temperatures from 263 to 343 K and pressures up to 500 MPa. This system forms an intermolecular compound Na 2SO 4·10H 2O. The sodium sulfate decahydrate has an incongruent melting point at 305.5 K at atmospheric pressure. The present study was undertaken to obtain extensive and accurate data concerning the effect of pressure on two kinds of solid-liquid phase equilibria, namely, the solubility curve and the incon-gruent melting point (peritectic point) of Na 2SO 4·10H 2O. The solid-liquid equilibrium measurements were performed by the direct visual observation of the crystal growth and disappearance using a high-pressure optical vessel. The uncertainties in measurements of temperature, pressure, and composition are within 0.1 K, 0.5 MPa and 0.001 mole fraction, respectively. It was found that both the solubility curve and the incongruent melting temperature of Na 2SO 4·10H 2O decrease with increasing pressure. The solid-liquid coexistence curves were correlated by an empirical equation.

Experimental and theoretical studies of the equation of state of liquid 2-butyne from 248 to 293 K and pressures up to 104 MPa

The expansion method has been used to measure the density of liquid 2-butyne, from 248 to 293 K and pressures up to 104 MPa. The solid-liquid coexistence curve up to 100 MPa has also been determined. The experimental results have been fitted to the Strobridge equation of state, which has been used to estimate several propertie of compresed liquid. The abilities of other semitheoretical and theoretical equations of state to predict the density and thermodynamic properties have been examined and discussed

Computer simulation of solid-liquid coexistence in binary hard sphere mixtures

We present the results of a computer simulation study of the solid-liquid coexistence of a binary hard sphere mixture for diameter ratios in the range 0.85 ~< ct ~< 1.00. For the solid phase we only consider substitutionally disordered FCC and HCP crystals. For 0-9425 < ct < 100 we find a solid-liquid coexistence curve of the 'spindle' type. For ct = 0-9425 this becomes an azeotropic and for ct = 0-875 a eutectic diagram. We compare these results with the predictions of the density functional theory of Barrat, Baus and Hansen. We observe that the density functional theory accurately predicts the point where the spindle diagram transforms into an azeotrope. However, the density functional theory differs from the simulation results on a number of counts. The greatest differences between computer simulations and theory are that the changeover from an azeotropic to a eutectic diagram is found to occur at c~ = 0-875, rather than at the predicted value of ct = 0.92, that the density difference between the solid and the liquid at liquid-solid coexistence is found to have a minimum as a function of the mole fraction of the large spheres, while density functional theory predicts a maximum, and finally that the solubility of large spheres in a solid mixture of small spheres is much larger than predicted.

Effect of pressure on the solid-liquid phase equilibria of (carbon tetrachloride + p-xylene) and (carbon tetrachloride+benzene) systems

Solid-liquid phase equilibria of the carbon tetrachloride + p-xylene and the carbon tetrachloride+benzene systems have been investigated at temperatures from 278 to 323 K and pressures up to 500 MPa using a high-pressure optical vessel. The uncertainties in the measurements of temperature, pressure, and composition are within ±0.1 K, ±0.5 MPa, and ±0.001 mole fraction, respectively. In the former system, which has an intermolecular compound with a congruent melting point, the freezing temperature at a constant composition increases monotonously with increasing pressure. The two eutectic points of this system shift to higher temperatures and richer compositions of the compound with increasing pressure. In the latter system, which has two intermolecular compounds with incongruent melting points, the one compound disappears under the present experimental conditions and the incongruent melting point of the other compound changes to the congruent melting point under high pressures. The solid-liquid coexistence curves of these systems can be correlated satisfactorily by the equation previously proposed.

Solid-liquid phase equilibria of benzene + 2-methyl-2-propanol system under high pressures

Solid-liquid phase equilibria of the benzene + 2-methyl-2-propanol system have been investigated at temperatures from 278 to 323 K and pressures up to 300 MPa using a high-pressure optical vessel. The uncertainties of the measurements of temperature, pressure and composition are within ±0.1 K, ±0.5 MPa, and ±0.001 mole fraction, respectively. The freezing pressure at a constant composition increases monotonously with pressure. The eutectic point shifts to a higher temperature and benzene-rich composition with increasing pressure. In order to describe the pressure-temperature-composition relation of high-pressure solid-liquid phase equilibria, a new simple equation has been proposed as follows: $$In x_i (P,T) = - \frac{1}{{RT}}\{ C(T)[P - B(T)] + D(T)[P^2 - B(T)^2 ]\} $$ where B, C, and D are the temperature-dependent coefficients and are expressed by the polynomials of reciprocal of temperature. It is found that the solid-liquid coexistence curves of both eutectic systems and solid-solution systems can be correlated satisfactorily by this equation.

Solid-liquid phase equilibria of benzene + cyclohexane system under high pressures

Solid-liquid phase equilibria of the benzene + cyclohexane system have been investigated experimentally at temperatures from 278 to 323 K and pressures up to 500 MPa using a newly designed optical vessel. The uncertainties of the measurements of temperature, pressure, and composition are within ±0.1 K, ±0.5 MPa, and ±0.001 mole fraction, respectively. The solid-liquid equilibrium pressure at a constant composition increases almost linearly with increasin temperature. The eutectic point shifts to a higher temperature and to a benzenerich composition with increasing pressure. This trend is found to agree with the direction predicted by the van Laar equation. The solid-liquid coexistence curves can be expressed by the Wilson equation with a mean deviation of 0.007 and a maximum deviation of 0.029 in mole fraction.

Developments in the hard sphere model for self-diffusion and shear viscosity

Abstract Examination of shear viscosity (η) and self-diffusion coefficient ( D ) data for liquid methane, together with equivalent hard sphere diameters (σ ϱ ) derived from liquid densities along the solid-liquid coexistence curve, is used to show that the Stokes-Einstein equation in the hydrodynamic slip limit is obeyed only at very high densities. The product D ησ ϱ / kT differs significantly both at low and at very high densities from values obtained from molecular dynamics (MD) simulations of a hard sphere fluid. Values of η/η E (η E = Enskog dense fluid viscosity) for methane, used in place of those from MD simulations, gave the expected values of A η (translational-rotational coupling factor) for nitrogen ( A η > 1), and (within the uncertainty of the experimental data on which the calculation is based) for the liquefied rare gases ( A η = 1) at temperatures within 20–25% of the critical temperatures. Apparent departures from smooth hard sphere behaviour, of the liquefied rare gases at temperatures approaching the triple points, are accounted for by the assumption of less dense packing in the liquids at low solid-liquid transition temperatures than for a hard sphere fluid.

3He nuclear magnetic relaxation in solid helium near its melting temperature

From the NMR measurement, the correlation time of the motion of a 3He spin via vacancies was found to be a constant along the solid-liquid coexistence curve. This implies that the ratio of the formation energy of a vacancy to the melting temperature is a constant within 1%, whose absolute value was 10.8 ± 1.0.