Direct calculation of solid-liquid coexistence points of a binary mixture by thermodynamic integration

We present a new thermodynamic integration method that directly connects the liquid and the solid phases of a binary mixture by a reversible path. The states along the path are simulated in the isothermal-isobaric semigrand canonical ensemble, in which temperature, pressure, the total number of particles, and the fugacity fractions of the components are held fixed. The thermodynamic integration yields the chemical-potential difference between the two phases for one of the components and this information is then used to locate the solid-liquid coexistence points. The melting temperatures predicted by our method agree well with those predicted by the Gibbs-Duhem integration for a truncated and shifted Lennard-Jones system with a cutoff radius of 2.5sigma.     

A method for computing the solubility limit of solids: application to sodium chloride in water and alcohols

We present an adaptable method to compute the solubility limit of solids by molecular simulation, which avoids the difficulty of reference state calculations. In this way, the method is highly adaptable to molecules of complex topology. Results are shown for solubility calculations of sodium chloride in water and light alcohols at atmospheric conditions. The pseudosupercritical path integration method is used to calculate the free energy of the solid and gives results that are in good agreement with previous studies that reference the Einstein crystal. For the solution phase calculations, the self-adaptive Wang-Landau transition-matrix Monte Carlo method is used within the context of an expanded isothermal-isobaric ensemble. The method shows rapid convergence properties and the uncertainty in the calculated chemical potential was 1% or less for all cases. The present study underpredicts the solubility limit of sodium chloride in water, suggesting a shortcoming of the molecular models. Importantly, the proper trend for the chemical potential in various solvents was captured, suggesting that relative solubilities can be computed by the method.     

The thermodynamic characteristics of sublimation of fenamate molecular crystals

The temperature dependences of vapor pressure were determined by the transpiration method and the thermodynamic functions of sublimation were calculated for six molecular crystals from the group of nonsteroidal antiinflammatory drugs, for niflumic, flufenamic, tolfenamic, mefenamic, and N-phenylanthranylic acids and diphenylamine. The influence of substituents on the enthalpies of sublimation of compounds of this class was studied. A correlation was observed between the enthalpies of sublimation under standard conditions and the temperatures of fusion.     

Extended Veytsman statistics for the solid–fluid transition in the framework of lattice fluid

Lattice fluid can describe a vapor–liquid transition but not a solid–fluid transition. In this work, we propose a simple and analytic term which yields a solid–fluid transition when coupled with a lattice based equation of state (EOS). The proposed term is derived based on the two assumptions that (1) solid can be considered as highly associated phase affected by strong attractive force and (2) this force is distinct from the conventional attractive forces yielding a vapor–liquid transition. To formulate these assumptions, we extend Veytsman statistics by modifying its density dependency. The derived term was combined with a quasi-chemical nonrandom lattice fluid theory (QLF) developed by the authors. The combined model was found to require only two parameters besides 3 QLF parameters for physical properties calculation of three phases. When tested against equilibrium properties of 8 components, the combined model was found to closely reproduce melting pressure, sublimation pressure, and vapor pressure, but underestimate solid density as well as heat of melting at the triple point temperature. It was found that the present approach can yield a solid–liquid transition at all temperatures.     

Joint processing of experimental data on melting,evaporation, and sublimation processes

A technique and computational program for estimating thermodynamic parameters are developed for the joint processing of experimental data on the saturated vapor pressure in melting, evaporation, and sublimation processes. Computation is based on the equality of pressures over the solid and liquid phases at a melting temperature. The efficiency of the proposed technique is demonstrated by processing experimental data on the phase transitions of Sc(thd)₃.     

Path integral molecular dynamics methods: Application to neon

Feynman's path integral formulation of quantum statistical mechanics, which has commonly been applied be Monte Carlo methods, is now also implemented by traditional molecular dynamics simulations of the microcanonical ensemble and in the Nosé-Hoover method simulating the isothermal-isobaric ensemble. In this article these two methods are applied to solid and liquid neon, in which quantum effects are not negligible. The validity of the procedure is shown by comparison with Monte Carlo and Brownian Dynamics computer simulations and with experiment. © 1995 by John Wiley & Sons, Inc.     

Phase diagrams of crystalline adducts containing two volatile components

The phase relationships in binary systems forming a crystalline addition compound are obtained by means of classical thermodynamic arguments for the case in which both components are volatile. This approach can be applied to inclusion compounds and to other low-stability addition compounds existing only in the solid phase. The results are consistent with those already known for clathrates containing a volatile guest and a non-volatile host, and for symmetric systems, such as racemic compounds. The temperature range in which the adduct undergoes a congruent sublimation depends on the ratio of the vapor pressures of the two components. A relation has been found to exist between the properties of the pure components, the melting behavior and the enthalpy of formation of the adduct.     

Fluorene: An extended experimental thermodynamic study

This work reports new experimental thermodynamic results on fluorene. Vapor pressures of both crystalline and liquid phases were measured using a pressure gauge (capacitance diaphragm manometer) and Knudsen effusion methods over a wide temperature range (292.20 to 412.16) K yielding accurate determination of enthalpy and entropy of sublimation and of vaporization. The enthalpy of sublimation was also determined using Calvet microcalorimetry. The enthalpy of fusion was derived from vapor pressure results and from d.s.c. experiments. Static bomb calorimetry was used to determine the enthalpy of combustion of fluorene from which the standard enthalpy of formation in the crystalline phase was calculated. The enthalpy of formation in the gaseous phase was calculated combining the result derived for the crystalline phase with the enthalpy of sublimation.     

Thermodynamic parameters of sublimation of calix[4]arenes

The temperature dependences of the vapor pressure of calix[4]arenes were determined by the Knudsen effusion method. Some calix[4]arenes can form congruently subliming intramolecular compounds with a solvent. The thermodynamic parameters of the sublimation of the compounds were calculated. Molecules of organic solvents incorporated in the cavity of calix[4]arenes stabilize the crystal lattice, increasing the enthalpy of sublimation. The electrostatic interactions presumably make a significant contribution to stabilization of the crystal lattice of stoichiometric complexes of calix[4]arenes with solvents.     

The phase diagram of water from quantum simulations

The phase diagram of water has been calculated from the TIP4PQ/2005 model, an empirical rigid non-polarisable model. The path integral Monte Carlo technique was used, permitting the incorporation of nuclear quantum effects. The coexistence lines were traced out using the Gibbs-Duhem integration method, once having calculated the free energies of the liquid and solid phases in the quantum limit, which were obtained via thermodynamic integration from the classical value by scaling the mass of the water molecule. The resulting phase diagram is qualitatively correct, being displaced to lower temperatures by 15-20 K. It is found that the influence of nuclear quantum effects is correlated to the tetrahedral order parameter.     

Determination of the melting point of hard spheres from direct coexistence simulation methods

We consider the computation of the coexistence pressure of the liquid-solid transition of a system of hard spheres from direct simulation of the inhomogeneous system formed from liquid and solid phases separated by an interface. Monte Carlo simulations of the interfacial system are performed in three different ensembles. In a first approach, a series of simulations is carried out in the isothermal-isobaric ensemble, where the solid is allowed to relax to its equilibrium crystalline structure, thus avoiding the appearance of artificial stress in the system. Here, the total volume of the system fluctuates due to changes in the three dimensions of the simulation box. In a second approach, we consider simulations of the inhomogeneous system in an isothermal-isobaric ensemble where the normal pressure, as well as the area of the (planar) fluid-solid interface, are kept constant. Now, the total volume of the system fluctuates due to changes in the longitudinal dimension of the simulation box. In both approaches, the coexistence pressure is estimated by monitoring the evolution of the density along several simulations carried out at different pressures. Both routes are seen to provide consistent values of the fluid-solid coexistence pressure, p=11.54(4)k(B)T/sigma(3), which indicates that the error introduced by the use of the standard constant-pressure ensemble for this particular problem is small, provided the systems are sufficiently large. An additional simulation of the interfacial system is conducted in a canonical ensemble where the dimensions of the simulation box are allowed to change subject to the constraint that the total volume is kept fixed. In this approach, the coexistence pressure corresponds to the normal component of the pressure tensor, which can be computed as an appropriate ensemble average in a single simulation. This route yields a value of p=11.54(4)k(B)T/sigma(3). We conclude that the results obtained for the coexistence pressure from direct simulations of the liquid and solid phases in coexistence using different ensembles are mutually consistent and are in excellent agreement with the values obtained from free energy calculations.     

Thermal properties of hafnium(IV) and zirconium(IV) β-diketonates

Five volatile hafnium(IV) and zirconium(IV) β-diketonates: hafnium(IV) acetylacetonate, hafnium(IV) trifluoroacetylacetonate, hafnium(IV) pivaloyltrifluoroacetonate, hafnium(IV) 2,2,6,6-tetramethylheptane-3,5-dionate and zirconium(IV) 2,2,6,6-tetramethylheptane-3,5-dionate were obtained, purified and identified. Thermal behavior of solid compounds was investigated by thermogravimetry (TG) and differential scanning calorimetry (DSC) in helium atmosphere and in vacuum. DSC method was also used for definition of thermodynamic characteristics of melting processes. Using the static method with quartz membrane zero-manometer and the flow method the temperature dependencies of saturated vapor pressure for hafnium(IV) complexes was obtained. The standard thermodynamic characteristics ΔH _T⁰ and ΔS _T⁰ of sublimation and evaporation processes were calculated from the temperature dependences of saturated vapor pressure.     

Thermodynamics of vaporization of gallium trichloride

The unsaturated and saturated pressures of gallium trichloride vapor were measured by the static method with membrane-gauge manometers in wide pressure (0.2–760 Torr) and temperature (313–1071 K) intervals. Scanning calorimetry was used to determine the thermodynamic characteristics of GaCl₃ fusion. The thermodynamic characteristics were obtained for sublimation, fusion, vaporization, and association in the vapor of GaCl₃ molecules. The enthalpies of formation and the absolute entropies of GaCl₃ in the liquid and gaseous phases and Ga₂Cl₆ in the gaseous phase were calculated using literature data. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 7, pp. 1266–1269, July, 2007.     

Some thermodynamic properties of benzocaine

The vaporization enthalpy of benzocaine, ethyl 4-aminobenzoate, has been evaluated using correlation gas chromatography at 298.15 K. The temperature dependence of retention time has also been used to evaluate the vapor pressure of the sub-cooled liquid from 298.15 K to the fusion temperature, 365.2 K, by correlation with the vapor pressures of the compounds used as standards. The vaporization enthalpy calculated from the vapor pressures of benzocaine at the melting point was combined with the experimental fusion enthalpy to evaluate the sublimation enthalpy at the fusion temperature. Application of the Clausius–Clapeyron equation together with the vapor pressure common to both phases permitted calculation of the vapor pressure of the solid at 298.15 K. Similar calculations were performed for two of the standards that were solids for comparisons with experimental data. Vaporization and sublimation enthalpies of (91.8 ± 4.2) and (112.9 ± 4.3) kJ mol^?1 are calculated for benzocaine at 298.15 K as are vapor pressures of 0.0083 and 0.0018 Pa for the sub-cooled liquid and crystalline material, respectively.     

Solid vapor pressure for five heavy PAHs via the Knudsen effusion method

Polycyclic aromatic hydrocarbons (PAHs) are compounds resulting from incomplete combustion and many fuel processing operations, and they are commonly found as subsurface environmental contaminants at sites of former manufactured gas plants. Knowledge of their vapor pressures is the key to predict their fate and transport in the environment. The present study involves five heavy PAHs, i.e. benzo[b]fluoranthene, benzo[k]fluoranthene, benzo[ghi]perylene, indeno[1,2,3-cd]pyrene, and dibenz[a,h]anthracene, which are all as priority pollutants classified by the US EPA. The vapor pressures of these heavy PAHs were measured by using Knudsen effusion method over the temperature range of 364 K to 454 K. The corresponding values of the enthalpy of sublimation were calculated from the Clausius-Clapeyron equation. The enthalpy of fusion for the 5 PAHs was also measured by using differential scanning calorimetry and used to convert earlier published sub-cooled liquid vapor pressure data to solid vapor pressure in order to compare with the present results. These adjusted values do not agree with the present measured actual solid vapor pressure values for these PAHs, but there is good agreement between present results and other earlier published sublimation data.     

A consistent estimation of sublimation pressures using a cubic equation of state and fusion properties

In many cases of industrial fluid–solid separation process design, a thermodynamic key parameter may be the sublimation pressure of pure components. A new trend in chemical applications is the use of supercritical solvents either in purifying operations on mixtures of complex pharmaceutical molecules or in stripping on polluted stuff. Measurements of very low sublimation pressures of heavy components are very difficult to perform although their values are of most importance in the process evaluation. Unfortunately, the prediction tools available in the literature for the estimation of sublimation pressures are poor. This paper deals with a consistent approach of sublimation pressure estimation, applicable to any pure material using on one hand easy measurements of normal fusion temperature and fusion enthalpy, and on the other hand vapor pressure data. The influence of all the uncertainties is discussed and the method is proposed as a new reference with emphasis on extrapolating reliably to very heavy compounds. By computing vapor liquid equilibrium using a cubic equation of state (EOS), the estimation of sublimation pressures is discussed in a new perspective.     

Metastable extension of the sublimation curve and the critical contact point

Molecular dynamics methods have been employed in order to calculate the (p,rho,T)-properties and the internal energy of gas and crystal phases in stable and metastable equilibrium coexistence states for a model system consisting of 2048 Lennard-Jones particles. Thermal and caloric equations of state and the spinodal curves of the vapor and crystal phases have been determined. A new algorithm for the computation of phase equilibrium curves is suggested. Employing this method, the sublimation curve and its metastable extension to temperatures above the triple point have been calculated. It is found that the crystal-gas phase equilibrium terminates on the spinodal of the superheated crystal. The point of contact of the sublimation line and the spinodal is a singular point of the thermodynamic surface of states of a simple system considered.     

Thermodynamic characteristics of phase conversion of structural isomers for volatile complex of ruthenium (III) trifluoroacetylacetonate

The comprehensive analysis of volatile β-diketonate compound—ruthenium(III) trifruoroacetylacetonate (Ru(tfac)₃)—was carried out. By means of flow method in quasi-equilibrium conditions and static method the temperature dependencies of saturated vapor pressure have been measured over solid and liquid cis- and trans-modifications of Ru(tfac)₃ and isomer mixture. The thermodynamic characteristics of sublimation, evaporation, melting, and phase conversion have been calculated for structural isomers. Also by differential-scanning calorimetry the temperature meanings and the thermodynamic characteristics of melting have been determined for individual isomers of Ru(tfac)₃ and their mixtures. By XRD the structures for cis- and trans-modifications have been determined. Both structures consist of neutral molecules arranged in pseudo layers.