Sublimation Pressure Research Articles

Correlating and predicting the solubilities of structurally similar organic solid compounds in supercritical CO2 using the compressed gas model and the reference solubilites

In this paper, the solubilities of some structurally similar organic solid compounds namely 9,10-anthraquinone derivatives, thioxanthone derivatives, pyrazolones and steroids were correlated and predicted using the compressed gas model combined with the Carnahan–Starling–van der Waals equation of state (CS–VDW EoS) and the Peng–Robinson equation of state (PR EoS), respectively. To avoid using the sublimation pressure of the solute and reduce the applied pressure range of the corresponding equation of state, a solubility datum was used as the reference solubility in the compressed gas model. By introducing the reference solubility, the simple van der Waals one-parameter (VDW1) mixing rules can be used for the supercritical solutions and the calculated solubilities are not sensitive to the binary parameter in the compressed gas model. So in solubility prediction, the binary parameter in the compressed gas model can be set constant for a series structurally similar organic compound. The prediction results showed that the compressed gas model combined with the CS–VDW EoS–VDW1 provide better prediction (average absolute relative deviations, AARD=18.41%) for the compounds with similar structure and without intermolecular hydrogen bond. For the compounds with larger structural differences, the compressed gas model combined with the PR EoS–VDW1 is recommended. However, for the compounds with intermolecular hydrogen bond, neither of the two EoS can provide satisfactory prediction results.

Solubility and Solubility Modeling of Polycyclic Aromatic Hydrocarbons in Subcritical Water

A static analytical equilibrium method was used to measure the binary and ternary solubilities of anthracene and p-terphenyl in subcritical water between 393 and 473 K and at 50 and 150 bar. Temperature was found to have the most significant effect on the solubility of polycyclic aromatic hydrocarbons (PAHs) in subcritical water. The effect of pressure, and the combined effect of temperature and pressure on solubility were found to be insignificant, particularly when the range of pressure considered is relatively small. The solubilities of PAHs were found to be governed primarily by sublimation pressure, and only secondarily by the dielectric constant of water. The Peng–Robinson equation of state was used to correlate the aqueous solubilities of PAHs under subcritical conditions, with good agreement between experimental and calculated values obtained for binary systems.

Correlation and Prediction of the Solubility of Solid Solutes in Chemically Diverse Supercritical Fluids Based on the Expanded Liquid Theory

For the proper design of any extraction procedure based on supercritical solvents, it is essential to have a sound knowledge of the solubility data of different compounds and the accurate way to represent it. The solute’s solubility in a supercritical solvent is dependent on the solute, the solvent, and the operating conditions (temperature and pressure). Developing a comprehensive experimental data set is an onerous task and time consuming and, thus, the incentive to develop predictive tools is substantial. In this paper, a technique is presented and tested to correlate and predict solute’s solubility in different supercritical fluids with a methodology based on the expanded liquid theory, in which the solid-fluid equilibrium is modeled using the local composition model of UNIQUAC in which the interaction parameters are related to the solvent reduced density with empiric equations. The most advantages of this model include: it does not require the knowledge of critical properties and sublimation pressure of solid solutes and does take into account the binary interaction between solid solute and solvent. The evaluation of the proposed model capabilities is done by testing it on a large data base consisting of experimental solubility data taken from literature of 33 binary systems solid-SC fluid. The results obtained for both correlation and prediction show good agreement with the experimental data used. For the comparison we have considered some literature models that account for effect of the system conditions (temperature and pressure) in addition to the sublimation pressure of the solute through their introduction of the enhancement factor and a model based on a modified Peng-Robinson equation of state.

Correlating and predicting the solubilities of polycyclic aromatic hydrocarbons in supercritical fluids using the compressed gas model and the reference solubilities

The solubilities of some polycyclic aromatic hydrocarbons (PAHs) in supercritical fluids were correlated and predicted using the compressed gas model and the reference solubilities. By introducing the reference solubilities, the compressed gas models combined with Peng–Robinson equation of state, Carnahan–Starling–van der Waals hard sphere equation of state and van der Waals one-parameter mixing rules can yield the overall averages of the average absolute relative deviations (AARDs) of 7.45% and 8.16% in solubility correlation for PAHs in supercritical fluids, respectively, which are much less than the values obtained using the compressed gas model combined with the corresponding equation of state and the sublimation pressures of the solutes. By introducing the reference solubilities, the calculated solubilities are not sensitive to the binary interaction parameters and the solubilities of PAHs in the corresponding supercritical fluid can be predicted with a specific binary interaction parameter. When using reference solubilities in the compressed gas model, the two equations of state provide comparable average AARDs in solubility prediction for PAHs in supercritical fluids, which are 14.00% and 14.19%, respectively. The introduction of reference solubilities into the compressed gas model provides a feasible and simple solubility prediction method for the compounds in supercritical fluids without using their sublimation pressures. Moreover, combined with the reference solubilities and the compressed gas model, the hard sphere equation of state provides a more simple method to predict the solubilities of solutes in supercritical fluids with only their solid molar volumes.

On the Way to Determination of the Vapor-Pressure Curve of Pure Water

The determination of the physical properties of pure water, especially the vapor-pressure curve of water, is one of the major issues identified by the Consultative Committee for Thermometry of the International Committee for Weights and Measures (CIPM) to improve the accuracy of the national references in humidity. At the present time the saturation-pressure data, corresponding to ice or liquid-vapor equilibrium, at low temperature are scarce and unreliable. This study presents new measurements of vapor and sublimation pressures of, respectively, water and ice, using a static apparatus. Prior to saturation-pressure measurements, the temperature and pressure sensors of the static apparatus were calibrated against reference gauges in use at the LNE-CETIAT laboratories. The effect of thermal transpiration has been studied. The explored temperature range lies between 250 K and 374 K, and the pressure range between 70 Pa and 10(5) Pa. An automatic data acquisition program was developed to monitor the pressure and temperature. The obtained results have been compared with available literature data. The preliminary uncertainty budget took into account several components: pressure measurements, temperature measurements, and environmental error sources such as thermal transpiration and hydrostatic correction.

A new and effective Bin–Monte Carlo scheme to study vapour–liquid equilibria and vapour–solid equilibria

A new scheme for Monte Carlo simulation, Bin-CMC, that was introduced recently by Fan et al. (C. Fan, D.D. Do, D. Nicholson, J. Phys. Chem. B, 115 (2011) 10509–10517), is applied to study: (1) vapour–liquid equilibria and (2) vapour–solid equilibria. Using bins in the simulation, we are able to sample space very efficiently, with larger displacements of particles in regions where densities are low and smaller displacements in regions where densities are very high. Furthermore, by exchanging particles between bins within the simulation box, we can take full advantage of the creation/destruction feature of a grand canonical simulation (built within a canonical ensemble) which enables the system to achieve equilibrium more rapidly. To illustrate the application of the new technique, we simulate the phase equilibria of argon, nitrogen, and carbon dioxide to obtain thermodynamic properties of the fluid phases including: saturation densities of the gas and condensed phases, the saturation vapour or sublimation pressure, the enthalpy of vapourization or sublimation, and the surface tension at the interface. The new scheme is superior to the Gibbs ensemble Monte Carlo (GEMC) method because the latter suffers from the extremely low probability of exchanging particles when one box is very dense, which makes it unsuitable for the study of vapour–solid equilibria and of vapour–liquid equilibria at low temperatures.

Thermodynamics and kinetics of nucleation of a spherical gas bubble inside an elastoplastic material due to sublimation

General thermodynamic and kinetic approaches for sublimation inside an elastoplastic material developed in Levitas (2012) are applied to the problem of a nucleation of a spherical gas bubble inside an infinite elastoplastic sphere. A large-strain solution of the mechanical problem on a spherical void formation is generalized for the case with internal pressure and surface tension. Nucleation via homogeneous transformation in the nucleus of a fixed mass and nucleation via continuous interface propagation are studied in detail. For both paths, the explicit expressions for the thermodynamic driving forces and activation energies are derived. Using a kinetic nucleation criterion, the kinetic relationships between tensile sublimation pressure and temperature are derived. For both transformation paths, three different regions are present on the kinetic temperature-stress curve. For small stresses, elastic deformation of a sphere takes place, and the results for both paths coincide. For large stresses, nucleus size is equal to the minimum radius for which one still can distinguish between solid and gas, and for the intermediate stresses the radius of the critical nucleus maximizes the activation energy. For all cases with plastic expansion, nucleation via homogeneous transformation is more probable for small stresses and significantly more probable for large stresses. However, such a homogeneously transformed nucleus cannot grow. It is necessary to slightly increase temperature or tensile pressure (to a value well below that for nucleation via interface propagation) to cause growth. Below some critical temperature θin, while the nucleus cannot grow because of solid–gas transformation, it expands like a balloon due to loss of mechanical stability. To our knowledge, this is the only known example of transformation of a subcritical nucleus into a supercritical one due to mechanical instability. The thermodynamics and the kinetics of evaporation are considered as well, and similar mechanical instability is found. Also, homogeneously transformed nucleus, while it starts to shrink, does not completely disappear; it represents a metastable rather than a critical nucleus. All of these results do not have counterparts in nucleation in elastic materials.

Equation of State for Solid Carbon Dioxide Based on the Gibbs Free Energy

In this work a fundamental equation of state explicit in the Gibbs free energy was established, which was fitted to experimental data (heat capacity, molar volume, expansion coefficient, and compressibility) of solid carbon dioxide. Almost all of the data that the equation was fitted to are represented within the experimental uncertainty given by the authors. However, only very limited data for the thermodynamic properties of solid carbon dioxide are available. The new equation behaves physically reasonably within its range of validity. Sublimation and melting pressures of dry ice are predicted accurately using Gibbs energies calculated from the new dry ice equation and from the fundamental equation by Span and Wagner for the fluid phase (J. Phys. Chem. Data1996, 25, 1509–1596). The results agree with those of the reference equations for sublimation and melting pressure published by Span and Wagner mostly within the uncertainty given for these equations. The resulting sublimation and melting pressures are...

Determining Sublimation Pressure of Ibuprofen from Solubility Data in Supercritical Carbon Dioxide

Solvent effects in the calculation of the sublimation pressure of pure ibuprofen using high pressure solubility data are discussed. The solubility of ibuprofen in supercritical carbon dioxide was measured using a dynamic apparatus in the pressure between 80 and 130 bar and at three temperatures, 308.15, 313.15 and 318.15 K. With this experimental region, the mole fraction of ibuprofen in fluid phase was in the range from 0.015 × 10-3 - 3.261 × 10-3. The sublimation pressure PSub of the solid drug is considered as a parameter to be determined by regression analysis of experimental solubility data (TPy), using four equations of state along with two mixing rules. The equations of state are Redlich-Kwong (RK), Soave-Redlich-Kwong (SRK), Peng-Robinson (PR) and Pazuki and some others. Mixing rules are van der Waals-1 parameter (vdW1) and van der Waals-2 parameter (vdW2). Correlations were compared and discussed on the basis of the employed equations-of-state, mixing/combining rules, the results show that the determination of sublimation pressure using high pressure solubility data is reliable and all systems lead to very good fit results, with almost identical values of AARD (Changing from 4.71% to 17.98%).

Measurement and Modeling of Acridine Solubility in Supercritical Carbon Dioxide

Supercritical carbon dioxide has gained increasing attention in food and pharmaceutical processing owing to the fact that it is environmentally inexpensive, not flammable, essentially non-toxic, and it has a convenient critical point. Also, it has been attracting much attention in many fields, such as extraction of sensitive materials and pharmaceutical processing and polymerization processes. For designing these processes, solubility data of solute in SCCO2 are needed as the fundamental knowledge. And the correlation and extension of existing equilibrium data is an important step in the application and development of such processes. Acridine is a raw material used for the production of dyes and some valuable drugs and its derivatives have antiseptic properties like Proflavine. In this research, the solubility of Acridine in supercritical carbon dioxide was measured at temperatures of 313, 323 and 333 K and in the pressure range of 120 to 350 bar using static method. The crossover pressure of Acridine was observed at about 150 bar. The experimental data were correlated using Peng- Robinson (PR) and Soave- Redlich- Kwong (SRK) equations of state (EOS) and van der Waals mixing rule with one (vdW 1) and two adjustable parameters (vdW 2) and Huron-Vidal mixing rules. For applying the Huron-Vidal mixing rule, NRTL activity coefficient model was used. The binary interaction parameters of the studied models were reported. The results of average absolute relative deviations (AARD) illustrated good accuracy of the studied models. Furtheremore, the modeling has been done with and without considering the sublimation pressure of the solid (Acridine) as an additional adjustable parameter. It can be concluded when sublimation pressure is considered as adjustable parameter, the AARD results of the studied models significantly decrease. Also, the estimated values of sublimation pressure of Acridine were reported at different temperatures. The results also showed that, among the studied models, PR- HV model with adjusted Psub has the minimum AARD (2.47 %).

New Equations for the Sublimation Pressure and Melting Pressure of H2O Ice Ih

New reference equations, adopted by the International Association for the Properties of Water and Steam (IAPWS), are presented for the sublimation pressure and melting pressure of ice Ih as a function of temperature. These equations are based on input values derived from the phase-equilibrium condition between the IAPWS-95 scientific standard for thermodynamic properties of fluid H2O and the equation of state of H2O ice Ih adopted by IAPWS in 2006, making them thermodynamically consistent with the bulk-phase properties. Compared to the previous IAPWS formulations, which were empirical fits to experimental data, the new equations have significantly less uncertainty. The sublimation-pressure equation covers the temperature range from 50 K to the vapor–liquid–solid triple point at 273.16 K. The ice Ih melting-pressure equation describes the entire melting curve from 273.16 K to the ice Ih–ice III–liquid triple point at 251.165 K. For completeness, we also give the IAPWS melting-pressure equation for ice III, which is slightly adjusted to agree with the ice Ih melting-pressure equation at the corresponding triple point, and the unchanged IAPWS melting-pressure equations for ice V, ice VI, and ice VII.

Measurement and correlation of the solubility of juglone in supercritical carbon dioxide

Juglone (5-hydroxy-1,4-naphthoquinone) is an allelopathic compound predominantly abundant in the roots, leaves, bark and wood of Juglans sp. (walnut). Juglone presents cytotoxic properties as well as antibacterial, antiviral and antifungal activities. The selective extraction of this compound using supercritical fluids (SCF) may present clear advantages over conventional extraction methods, particularly if cosmetic, pharmaceutical or food applications are envisaged. However, the optimization of any high pressure extraction process requires the knowledge of the solubility of the target compounds to be extracted. In this work we report the experimental measurement and correlation of the equilibrium solubility of juglone in scCO 2. Results were obtained using a static analytical method at 308.2 K, 318.2 K and 328.2 K, and in a pressure range from 9.2 up to 24.4 MPa. Experimental equilibrium solubility was found to be between 2.0 × 10 −5 and 1.6 × 10 −3 (in terms of juglone mole fraction). Experimental data were correlated with three density-based models (Chrastil, Bartle and Méndez-Santiago–Teja models) and with the Peng-Robinson cubic equation of state (PR-EOS), using the conventional van der Waals mixing and combining rules. Juglone critical and thermophysical properties were estimated by different methods available in the literature and the influence of these estimation methods on its properties (namely on sublimation pressure) was discussed in terms of the final PR-EOS correlation results accuracy. The best obtained average absolute relative deviations (AARD) were 5.5% and 4.1%, for semi-empirical models and for the PR-EOS, respectively.

Estimating fusion properties for functionalised acids

Abstract. Multicomponent organic aerosol (OA) is likely to be liquid, or partially liquid. Hence, to describe the partitioning of these components, their liquid vapour pressure is desired. Functionalised acids (e.g. diacids) can be a significant part of OA. But often measurements are available only for solid state vapour pressure, which can differ by orders of magnitude from their liquid counterparts. To convert such a sublimation pressure to a subcooled liquid vapour pressure, fusion properties (two out of these three quantities: fusion enthalpy, fusion entropy, fusion temperature) are required. Unfortunately, experimental knowledge of fusion properties is sometimes missing in part or completely, hence an estimation method is required. Several fusion data estimation methods are tested here against experimental data of functionalised acids, and a simple estimation method is developed, specifically for this family of compounds, with a significantly smaller estimation error than the literature methods.

Measurement and Modeling of CO2 Frost Points in the CO2–Methane Systems

Technology is being developed to separate carbon dioxide (CO2) from natural gas by frosting CO2 out from the mixture. Vapor–solid phase equilibrium data in the CO2–methane systems are important in developing such processes. In this work, new experimental data are reported for the frost points in the CO2–methane systems for a wide range of CO2 range concentration (i.e., CO2 mole fraction 0.108 to 0.542). The Soave–Redlich–Kwong (SRK) equation of state (EoS) is employed to calculate the fugacity of the fluid phase. The CO2 solid-forming conditions are modeled by a solid fugacity model based on the sublimation pressure of pure CO2. The thermodynamic model was used to predict the CO2 frost points in the presence of methane. Predictions of the developed model are validated against independent experimental data and the data generated in this work. A good agreement between predictions and experimental data is observed, supporting the reliability of the developed model.

ThermoData Engine (TDE): Software Implementation of the Dynamic Data Evaluation Concept. 6. Dynamic Web-Based Data Dissemination through the NIST Web Thermo Tables

ThermoData Engine (TDE) is the first full-scale software implementation of the dynamic data evaluation concept, as reported recently in this journal. In the present paper, we describe the development of a World Wide Web-based interface to TDE evaluations of pure compound properties, including critical properties, phase boundary equilibria (vapor pressures, sublimation pressures, and crystal-liquid boundary pressures), densities, energetic properties, and transport properties. This includes development of a system for caching evaluation results to maintain high availability and an advanced window-in-window interface that leverages modern Web-browser technologies. Challenges associated with bringing the principal advantages of the TDE technology to the Web are described, as are compromises to maintain general access and speed of interaction while remaining true to the tenets of dynamic data evaluation. Future extensions of the interface and associated Web-services are outlined.

Gas-solid phase calculations of binary mixtures using optimization of evolutionary algorithms

A comparison between different modern populations based optimization methods applied to the gas-solid phase calculations is presented. Simulations are carried out in twelve binary mixtures containing supercritical carbon dioxide. Particle swarm optimization (PSO) and genetic algorithm (GA) are used to calculate interaction parameters, solubility, and sublimation pressure on these mixtures using the Peng-Robinson equation of state with the Wong-Sandler mixing rules. Comparing PSO with GA shows that the performance of PSO is better than that of GA and that it is a preferable method to optimize parameters of the gas-solid equilibrium.

On the use of semiempirical models of (solid + supercritical fluid) systems to determine solid sublimation properties

Experimental solubility data of solid–supercritical fluids have significantly increased in the last few years, and semiempirical models are emerging as one of the best choices to fit this type of data. This work establishes a methodology to calculate sublimation pressures using this type of equations. It requires the use of Bartle’s equation to model equilibria data solid–supercritical fluids with the aim of determining the vaporization enthalpy of the compound. Using this method, low deviations were obtained by calculating sublimation pressures and sublimation enthalpies. The values of the sublimation pressures were subsequently used to successfully model different multiphasic equilibria, as solid–supercritical fluids and solid–solvent–supercritical fluids with the Peng–Robinson equation of state (without considering the sublimation pressure as an adjustable parameter). On the other hand, the sublimation pressures were also used to calculate solid sublimation properties and acetaminophen solvation properties in some solvents. Also, solubility data solid–supercritical fluids from 62 pharmaceuticals were fitted with different semiempirical equations (Chrastil, Kumar-Johnston and Bartle models) in order to present the values of solvation enthalpies in sc-CO 2 and vaporization enthalpies for these compounds. All of these results highlight that semiempirical models can be used for any other purpose as well as modeling (solid + supercritical fluids) equilibria.

New Knudsen effusion apparatus with simultaneous gravimetric and quartz crystal microbalance mass loss detection

A new Knudsen effusion apparatus, enabling simultaneous gravimetric and quartz crystal microbalance mass loss detection, is described. This device allows the measurement of vapour pressures of small sample mass (50 to 100) mg over a wide temperature range (350 to 650) K using very short effusion time intervals. The performance of the apparatus was checked by measuring the vapour pressures of anthracene, benzanthrone, and 1,3,5-triphenylbenzene, between (0.1 and 1) Pa, over temperature intervals of 20 K. The derived standard molar enthalpies of sublimation and vapour pressures are in excellent agreement with the mean of the available literature values and with the recommended values. The new working methodology and design of this apparatus allows the measurement of high quality vapour pressure data due to: accurate temperature measurement and control; improvement in vacuum thermal contact between the effusion cell and the oven metal block; optimisation of the quartz crystal sensor head microbalance position; efficient temperature control of the quartz crystal microbalance head; accurate measurement of the resonance crystal frequency using an impedance circuit analyser methodology.

TEOS-10: A New International Oceanographic Standard for Seawater, Ice, Fluid Water, and Humid Air

Very accurate empirical thermodynamic potential functions are available for fluid water, ice, seawater, and humid air covering wide ranges of temperature and pressure conditions, including those of the terrestrial hydrosphere and atmosphere. These potential functions are formulated as international standards endorsed by the International Association for the Properties of Water and Steam (IAPWS). A related seawater standard referred to as the International Thermodynamic Equation of Seawater 2010 (TEOS-10) was adopted in 2009 by UNESCO for oceanography. Here, the formulations available from TEOS-10 for the description of the vapor pressure of ice and for thermodynamic properties of humid air, in particular, the relative humidity, are reviewed. It is concluded that the IAPWS formulation for the sublimation pressure is superior in uncertainty and range of validity over other available correlation equations, and that relative fugacity is a physically reasonable generalization of relative humidity for the case of non-ideal gases or equilibria with moist substances.

A comparison between models based on equations of state and density-based models for describing the solubility of solutes in CO 2

The poor dissolution behaviour of solid drugs in biological environment leads to a low bioavailability. However, the dissolution rate of such drugs can be enhanced dramatically by reduction of the particle size. At present, supercritical fluid based particle size reduction processes are gaining in importance in pharmaceutical technology. For the design of such particle formation processes and the determination of their best operating conditions the knowledge of phase equilibrium and solute solubility in a supercritical fluid is essential. Today, models based on equations of state, together with different mixing rules, are most widely used to correlate and predict the solubility in supercritical fluids. Therefore the accurate knowledge of the required solute data, such as critical parameters, acentric factor, solid molar volume, and sublimation pressure of the solutes is essential. However, the common, non-equation of state based group-contribution methods are mostly empirical and often lead to inconsistent and unreliable results. Thus, due to the lack of information on these data, density-based models are often used for the correlation of experimental solubility data. In this investigation, the solubility of Salicylic acid, of S-Naproxen, of RS-Ibuprofen and of Phytosterol in CO 2 is correlated by different methods: two methods for the pressure–solubility correlation and two methods for the density–solubility correlation. In addition, the influence of solute data predicted by different group-contribution methods is investigated. With the exception of S-Naproxen all systems investigated can be modelled sufficient well with a non-cubic equation of state while a cubic equation of state gives less accurate results. In addition, it is shown that for the solutes investigated, the equation of state based method is very sensitive to the values of the sublimation pressure.