Liquid Density Data Research Articles

Comments and Additional Work on “High-Pressure Volumetric Properties of Imidazolium-Based Ionic Liquids: Effect of the Anion”

This works follows a publication of our group in J. Chem. Eng. Data2007, 52, 2204–2211 presenting high temperature and pressure density data for five imidazolium-based ionic liquids. At this period, very few ionic liquid density data were available in the literature, especially at high pressure, and the uncertainty of published results was calculated with respect to the literature data available for three of the five ionic liquids studied. Since 2007, the ionic liquid density databank has largely increased. In this work, a comparison of our published data in J. Chem. Eng. Data2007, 52, 2204–2211, with more than 1800 high pressure data coming from the literature up to December 2011 is presented to assess the uncertainty of our published values. The claimed uncertainty is close to 0.31 % for all IL density data sets except in the case of the [C1C2Im][EtSO4], where the uncertainty is up to 1.1 %. Reported data in J. Chem. Eng. Data2007, 52, 2204–2211, for this particular ionic liquid cannot be used as a refe...

Volume-translated Peng–Robinson equation of state for saturated and single-phase liquid densities

Cubic equations of state (CEOS) are widely used for process design calculations and reservoir simulations in the oil and gas industry. However, most CEOS yield poor predictions of liquid densities. To remedy this problem, several volume-translation approaches have been presented in the literature. Currently, most of these approaches yield predictions that appear reasonable only in the saturated or the single-phase region. In this work, a volume-translation method is presented that is applicable to both saturated and single-phase regions. The method contains only one fluid-specific parameter, which has been generalized in terms of readily available molecular properties such as critical compressibility factor, acentric factor and dipole moment. Three specific cases were considered ranging from simple linear correlations to non-linear neural networks for generalizing the fluid-specific parameter. The neural network models require 3–6 molecular properties for the selected fluid (in addition to the usual critical temperature, critical pressure and acentric factor).For model development and generalization, a database of highly accurate data for liquid densities was compiled. The database contains 65 pure fluids involving several classes of chemical compounds that vary widely in terms of their molecular size, shape, chain-length, asymmetry and polarity. The model was developed based on these 65 fluids, and an additional 20 fluids were used for validating the generalized model.Results indicate that the volume-translation method developed in this work is capable of precise representations of saturated liquid density data for the fluids in the database. Specifically, an overall average absolute percentage deviation (%AAD) of 0.6 was obtained for 65 fluids, including more than 12,000 data points. The model was then generalized, and the generalization predicted the same data set with a %AAD of 0.8. Further, the generalized model was validated by predicting saturated liquid densities of 20 compounds not used in model development. For these 20 fluids, the method provided generalized predictions with 1.0%AAD. Further, the volume-translation approach was also extended to predict liquid densities in the single-phase region. Of the fluids tested, the generalized model provided predictions with 1.8%AAD. Thus, this approach was capable of producing accurate predictions for both saturated and compressed liquid densities of diverse classes of molecules.

Thermodynamic Modeling of Aqueous Ionic Liquid Solutions Using PC-SAFT Equation of State

In this work, an equation of state has been utilized for thermodynamic modeling of aqueous ionic liquid (IL) solutions. The proposed equation of state is a combination of perturbed chain statistical associating fluid theory (PC-SAFT) equation of state and mean spherical approximation (MSA) term. In this model, the ion-based approach has been used to adjust the model parameters. The ion parameters have been estimated through simultaneous fitting to experimental mean ionic activity coefficient and liquid density data of strong electrolytes. Using adjusted ion parameters, osmotic coefficients, mean ionic activity coefficients, liquid densities, apparent molar volume, and water activity of several ILs, assumed as chainlike electrolytes, have been calculated. Results show that PC-SAFT, in combination with the MSA term has acceptable accuracy for prediction of density, apparent molar volume, and activity coefficient of ILs. The average deviations of predicted mean ionic activity coefficients, liquid densities, water activity, and apparent molar volume are 6.43, 0.86, 0.033, and 8.20%, respectively.

Equation of state modelling of systems with ionic liquids: Literature review and application with the Cubic Plus Association (CPA) model

For the last decade ionic liquids have been regarded as compounds of interest by the academic and industrial communities. These compounds present several advantages when compared to other typical solvents. However, because of their novelty, a deep understanding of their phase behaviour and their interactions with other components is still needed. In this work, we made a review of literature studies on modelling systems with ionic liquids using equation of state models. Furthermore, we applied the Cubic Plus Association (CPA) equation of state to describe the phase behaviour of two ionic liquids, 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ([C2mim][NTf2]) and 1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ([C4mim][NTf2]). The first step was to study an adequate approach for the determination of pure component parameters for the ionic liquids. The parameters were obtained by fitting the predictions of the model to experimental vapour pressure and liquid density data. The parameters provide a good description of both experimental vapour pressures and liquid density, with maximum percentage deviations of respectively 8.9 and 1.3% for [C2mim][NTf2] and 5.7 and 0.5% for [C4mim][NTf2]. Different sets of pure component parameters for each ionic liquid were considered and their suitability to describe the behaviour of ionic liquids was evaluated by modelling the vapour–liquid equilibria (VLE) of mixtures with CO2 and the liquid–liquid equilibria (LLE) with water. The results for VLE proved to be very good in the range of pressures studied when using one temperature-independent binary interaction parameter, with percentage deviations in pressure between 8 and 13% for [C2mim][NTf2] and around 12% for [C4mim][NTf2]. For the LLE of ionic liquids with water a temperature-independent binary interaction parameter was also used, but the results do not describe the experimental data as well as with the VLE, with percentage deviations ranging from 4 to 100%. However, for some of the sets of pure component parameters a good description of the experimental data is obtained and work is in progress for improving the modelling of LLE with the CPA equation of state.

Modeling the phase equilibria of a H2O–CO2 mixture with PC-SAFT and tPC-PSAFT equations of state

Water–carbon dioxide binary mixtures are important for a number of industrial and environmental applications. Accurate modeling of the thermodynamic properties is a challenging task due to the highly non-ideal intermolecular interactions. In this work, two models based on the Statistical Associating Fluid Theory (SAFT) are used to correlate reliable experimental vapor–liquid equilibria (VLE) and liquid–liquid equilibria (LLE) data in the temperature range 298–533 K. CO2 is modeled as a non-associating or associating component within the Perturbed Chain-SAFT (PC-SAFT) and as a quadrupolar component within the truncated PC-Polar SAFT (tPC-PSAFT). It is shown that PC-SAFT with explicit account of H2O–CO2 cross-association and tPC-PSAFT with explicit account of CO2 quadrupolar interactions are the most accurate of the models examined. Saturated liquid mixture density data are accurately predicted by the two models.

Fluid phase behavior from molecular simulation: Hydrazine, Monomethylhydrazine, Dimethylhydrazine and binary mixtures containing these compounds

New molecular models for Hydrazine and its two most important methylized derivatives (Monomethylhydrazine and Dimethylhydrazine) are proposed to study the fluid phase behavior of these hazardous compounds. A parameterization of the classical molecular interaction models is carried out by using quantum chemical calculations and subsequent fitting to experimental vapor pressure and saturated liquid density data. To validate the molecular models, vapor–liquid equilibria for the pure hydrazines and binary hydrazine mixtures with Water and Ammonia are calculated and compared with the available experimental data. In addition, the Henry's law constant for the physical solubility of Argon, Nitrogen and Carbon Monoxide in liquid Hydrazine, Monomethylhydrazine and Dimethylhydrazine is computed. In general, the simulation results are in very good agreement with the experimental data.

An Equation of State for Fluoroethane (R161)

Fluoroethane (R161, C2H5F, 353-36-6) is a potential alternative refrigerant with excellent cycle performance, with zero ozone-depletion potential and low global warming potential. In this study, the thermodynamic property formulation for fluoroethane has been developed with the use of available experimental thermodynamic property data. In determining the equation of state, multiproperty fitting methods were used including single-phase pressure–density–temperature (pρT), vapor pressure, and saturated liquid-density data. The equation of state has been developed to conform to the Maxwell criterion for two-phase liquid–vapor equilibrium states, and is valid for temperatures from 130 K to 450 K, and pressures to 5 MPa. The extrapolation behavior of the equation of state at high temperatures and high pressures is reasonable. As there are very few compressed liquid-density experimental data published, the uncertainties in density of the equation of state are estimated to be 2.0 % in the compressed-liquid region and 0.5 % in the gas and supercritical regions. Uncertainties in vapor pressure are 0.5 % above 200 K and increase at lower temperatures. The uncertainties for all properties are higher in the critical region, except vapor pressure. Detailed comparisons between experimental and calculated data have been performed in this study.

Temperature dependence of the surface tension and 0.1 MPa density for 1-Cn-3-methylimidazolium tris(pentafluoroethyl)trifluorophosphate with n = 2, 4, and 6

Experimental air–liquid interfacial tension data and density data are presented for three 1-Cn-3-methylimidazolium tris(pentafluoroethyl)trifluorophosphates (FAP), [CnMIM][(C2F5)3PF3], with n=2, 4, and 6, measured at atmospheric pressure in the temperature range from 267K to 360K using the Krűss K100MK2 tensiometer. The accuracy of the surface tension measurements was checked by employing the Wilhelmy plate and the du Noüy ring methods in parallel. The combined standard uncertainty associated with the Wilhelmy plate method is estimated to be ±0.1mN·m−1. The density data were obtained using buoyancy method with an estimated standard uncertainty less then ±0.4kg·m−3 (3·10−4ϱ). The chloride anions decrease the density of the tris(pentafluoroethyl)trifluorophosphates of interest up to six times more effectively than they decrease the density of the imidazolium based tetrafluoroborates. A QSPR analysis of the surface tension of imidazolium based ionic liquids with BF4, TFA, DCA, FAP, NTf2, and PF6 anions indicates, that the FAP ionic liquids fit well into the analyzed group of imidazolium based ionic liquids while those having hexafluorophosphate anion show anomalously high deviations of the experimental surface tension from the values predicted by the QSPR model.

Solubility of Aliphatic Hydrocarbons in Piperidinium Ionic Liquids: Measurements and Modeling in Terms of Perturbed-Chain Statistical Associating Fluid Theory and Nonrandom Hydrogen-Bonding Theory

Ionic liquids (ILs) reveal many unique properties which make them very interesting for applications in modern "green" technologies. For that reason, detailed knowledge about correlations between the ions' structure, their combinations, and the bulk properties is of great importance. That knowledge can be accessed by reliable measurements and modeling of systems with ILs in terms of various theoretical approaches. In this paper we report new experimental results on liquid-liquid equilibrium (LLE) measurements of 10 binary systems composed of piperidinium ILs [namely, 1-propyl-1-methylpiperidinium bis(trifluoromethylsulfonyl)imide and 1-butyl-1-methylpiperidinium bis(trifluoromethylsulfonyl)imide] and aliphatic hydrocarbons (n-hexane, n-heptane, n-octane, cyclohexane, and cycloheptane). Moreover, new results on liquid density of pure 1-butyl-1-methylpiperidinium bis(trifluoromethylsulfonyl)imide are presented. Upper critical solution temperature type of phase behavior for all studied systems was observed. Decrease of solubility of n-alkane with an increase of its alkyl chain length and increase of solubility when changing linear into cyclic structure of hydrocarbon were detected. LLE modeling of investigated systems was performed in terms of two modern theories, namely, perturbed-chain statistical associating fluid theory (PC-SAFT) and nonrandom hydrogen-bonding theory (NRHB). Pure fluid parameters of the models were obtained from fitting of experimental liquid density and solubility parameter data at ambient pressure and tested against high pressure densities. Then literature values of activity coefficients of n-alkanes and cycloalkanes at infinitely diluted mixtures with ILs were used to optimize binary interaction parameters of the models. Finally, the LLE phase diagrams were calculated with average absolute relative deviations of 4.1% and 3.4% of the IL mole fraction for PC-SAFT and NRHB, respectively. The PC-SAFT and NRHB models were both able to capture phase behavior in a qualitative manner. Both models predict the order in which solubility of hydrocarbon in the IL increases, including the effects of chain length of n-alkane as well as chain length of alkyl substituent in piperidinium cation. Moreover, predicted solubility of cycloalkanes is also higher than that of respective n-alkanes. Our results suggest that the presented approach of PC-SAFT and NRHB modeling can be successfully applied to cross-associating systems as well. In summary, we have shown that relatively good results can be obtained for such complex systems by using quite simple molecular models and combining rules. To the best of our knowledge, this is the very first paper in which such equation-of-state modeling has been adopted for systems with ILs.

THERMOPHYSICAL PROPERTIES OF ASSOCIATING FLUIDS IN NATURAL GAS INDUSTRY USING PC-SAFT EQUATION OF STATE

The perturbed-chain statistical associating fluid theory (PC-SAFT) is employed to calculate the thermophysical properties of some associating fluids that are widely used in the natural gas industry. Methanol, alkanolamines, and glycols are considered in this work. The alkanolamines include monoethanolamine (MEA), diethanolamine (DEA), and methyldiethanolamine (MDEA). Two new modified associating schemes are introduced to describe the alkanolamine associating behavior. The glycols considered in this work are monoethylene glycol (MEG), diethylene glycol (DEG), and triethylene glycol (TEG). The pure component parameters of these associating fluids are determined using vapor pressure and saturated liquid density data. The heats of vaporization and heat capacities of these compounds are then predicted. Sound velocities and Joule-Thomson coefficients are additionally predicted for methanol. The results indicate that PC-SAFT is accurate for correlating the vapor pressure and liquid density of methanol, the glycols, and alkanolamines. PC-SAFT is also accurate in predicting the Joule-Thomson coefficients and sound velocities of methanol. Although PC-SAFT is not accurate enough for predicting the thermal properties (heat capacities and heats of vaporization) of MEG and TEG, it reasonably describes the thermal properties of MEA, DEA, MDEA, and DEG.

SAFT-γ Force Field for the Simulation of Molecular Fluids. 1. A Single-Site Coarse Grained Model of Carbon Dioxide

An application of the "top-down" concept for the development of accurate coarse-grained intermolecular potentials of complex fluids is presented. With the more common "bottom-up" procedure, coarse-grained models are constructed from a suitable simplification of a detailed atomistic representation, and small adjustments to the intermolecular parameters are made by comparison with limited experimental data where necessary. In contrast, in the top-down approach, a molecular-based equation of state is used to obtain an effective coarse-grained intermolecular potential that reproduces the macroscopic experimental thermophysical properties over a wide range of conditions. These coarse-grained intermolecular potentials can then be used in conventional molecular simulation to obtain properties (such as structure or dynamics) that are not directly accessible from the equation of state or at extreme conditions where the theory is expected to fail. To demonstrate our procedure, a coarse-grained model for carbon dioxide (CO(2)) is obtained from a recent implementation of the statistical associating fluid theory of variable range (SAFT-VR) employing a Mie (generalized Lennard-Jones) potential; the parameters of this single-site Mie model of CO(2) are estimated by optimizing the equation of state's description of the experimental vapor-pressure and saturated liquid density data. This approach is only viable because of the excellent agreement of the SAFT-VR Mie EoS with simulation data. Our single-site SAFT-γ coarse-grained model for CO(2) is used in Monte Carlo molecular simulation to assess the adequacy of the description of the fluid-phase behavior and properties that were not used to develop the potential model such as the enthalpy of vaporization, interfacial tension, density profiles, supercritical densities, and second-derivative thermodynamic properties (thermal expansivity, isothermal compressibility, heat capacity, Joule-Thompson coefficient, and speed of sound). The accuracy of the description with the single-site SAFT-γ model of CO(2) is found to be of similar quality to that of more sophisticated intermolecular potentials such as a six-site (three LJ centers and three charged sites) all-atom model. The SAFT-γ top-down approach to coarse-graining resolves a key challenge with coarse-graining techniques: the provision of a direct robust link between the microscopic and macroscopic scales.

Temperature Dependence of the Surface Tension and Density at 0.1 MPa for 1-Ethyl- and 1-Butyl-3-methylimidazolium Dicyanamide

Experimental air–liquid interfacial tension data and density data are presented for two ionic liquids with the 1-Cn-3-methylimidazolium cation, n = 2 and 4, and the dicyanamide anion. The measurements were performed at atmospheric pressure in the temperature range from (278 to 356) K using the Krüss K100MK2 tensiometer. The accuracy of the surface tension measurements was confirmed by employing the Wilhelmy plate and the du Noüy ring methods in parallel. The combined expanded uncertainty at 0.95 confidence level associated with the Wilhelmy plate method is estimated to be 0.1 mN·m–1. The density data were obtained using a buoyancy method with an estimated expanded uncertainty at 0.95 confidence level of 3·10–4ρ. An analysis of the experimental density data, using a group contribution model, performed for eight ionic liquids with the 1-Cn-3-methylimidazolium cation (n = 2, 4, 6) and tetrafluoroborate and trifluoromethanesulfonate and the dicyanamide anion indicates that the uncertainty arising from impurities present in the sample is dominant. The upper-bound estimate for the overall expanded uncertainty (k = 2) in the density measurements including the uncertainty stemming from impurities in the sample is equal to ± 0.002ρ. The model is capable of providing predictions for pure imidazolium-based ionic liquids with [BF4], [CF3SO3], and [N(CN)2] anions.

Determining Force Field Parameters Using a Physically Based Equation of State

Force field parameters used in classical molecular simulations can be estimated from quantum mechanical calculations or spectroscopic measurements. This especially applies to bonded interactions such as bond-stretching, bond-bending, and torsional interactions. However, it is difficult and computational expensive to obtain accurate parameters describing the nonbonded van der Waals interactions from quantum mechanics. In many studies, these parameters are adjusted to reproduce experimental data, such as vapor-liquid equilibria (VLE) data. Adjusting these force field parameters to VLE data is currently a cumbersome and computationally expensive task. The reason is that the result of a calculation of the vapor-liquid equilibria depends on the van der Waals interactions of all atom types in the system, therefore requiring many time-consuming iterations. In this work, we use an analytical equation of state, the perturbed chain statistical associating fluid theory (PC-SAFT), to predict the results of molecular simulations for VLE. The analytical PC-SAFT equation of state is used to approximate the objective function f(p) as a function of the array of force field parameters p. The objective function is here for example defined as the deviations of vapor pressure, enthalpy of vaporization and liquid density data, with respect to experimental data. The parameters are optimized using the analytical PC-SAFT equation of state, which is orders of magnitude quicker to calculate than molecular simulation. The solution is an excellent approximation of the real objective function, so that the resulting method requires only very few molecular simulation runs to converge. The method is here illustrated by optimizing transferable Lennard-Jones parameters for the n-alkane series. Optimizing four force field parameters p = (ε(CH(2))(CH(2)), ε(CH(3))(CH(3)), σ(CH(2))(CH(2)), σ(CH(3))(CH(3))) we obtain excellent agreement of coexisting densities, vapor pressure and caloric properties within only 2 -3 molecular simulation runs.

Solvent Swelling Extent of Permian-Aged Vitrinite- and Inertinite-Rich Coals: Experiments and Modeling Using the Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT)

The perturbed-chain statistical associating fluid theory (PC-SAFT) was used to predict the solvent swelling extent of vitrinite- and inertinite-rich coals. These two maceral different coals yet similar in rank and carbon content were modeled as a mixture of pseudo-components according to molecular-weight fractions (obtained from laser desorption–ionization time-of-flight mass spectrometry). The pure-component parameters for the solvents used for solvent swelling (pyridine, N-methylpyrrolidone, and the binary mixture of carbon disulfide and N-methylpyrrolidone) were determined by simultaneous fitting to experimental vapor pressure and liquid density data. The predicted swelling trends obtained from the PC-SAFT were comparable to experimental swelling extents. This approach may be a promising tool for solvent–coal interaction predictions.

Comparison between Dicationic and Monocationic Ionic Liquids: Liquid Density, Thermal Properties, Surface Tension, and Shear Viscosity

We report the data of liquid density, thermal properties including glass transition temperature, melting point, and decomposition temperature, surface tension, and shear viscosity for imidazolium-based dicationic ionic liquids with the anions of bis(trifluoromethylsulfonyl)amide, bis(pentafluoroethylsulfonyl)amide, tetrafluoroborate, and nitrate. To find the unique and general features of the dicationic ionic liquids, data of their corresponding monocationic ionic liquids are also summarized. The results of the dicationic ionic liquids showed that the density was high; the glass transition temperature and melting point were high, and they were thermally stable. Also the surface tension was large, and the shear viscosity was high in comparison with the reference monocationic ionic liquids. The data of the physical properties including liquid density, surface tension, and shear viscosity of the ionic liquids were also compared with that of alkanediols and alkyl alcohols to find the alkyene-linker and alkyl-...

A modified Peng–Robinson equation of state for phase equilibrium calculation of liquefied, synthetic natural gas, and gas condensate mixtures

AbstractA modified Peng–Robinson equation of state, MPR2 EOS, is introduced by incorporating a new alpha function and a temperature dependent function for covolume, b. The modified cubic EOS has three input per each substance: critical temperature, critical pressure, and acentric factor. The coefficients of temperature dependence of the alpha and beta functions, relating to the parameters a and b of the new cubic EOS, are obtained by simultaneous fitting of saturated experimental vapour pressure and liquid density data for several pure components. The percent absolute average deviation (AAD%) of 1.38, 4.80 and 2.89 are obtained to correlation of the saturation vapour pressure, liquid density and vapour volume, respectively. Also the ADD% of 2.575 is computed for prediction of saturation enthalpy of vapourisation of the pure compounds. For calculation of phase equilibrium of mixture, the modified PR EOS is used for prediction of liquid density of the LNG mixtures. Also the new EOS is applied for construction of the phase envelop of synthetic natural gas, SNG, mixtures and calculation vapour–liquid equilibria of gas condensates. The results demonstrate that the new MPR2 EOS can be used for calculation of vapour–liquid equilibrium of pure components and mixtures with good accuracy.

Extending the GC-SAFT-VR approach to associating functional groups: Alcohols, aldehydes, amines and carboxylic acids

The statistical associating fluid theory is a widely used molecular-based equation of state that has been successfully applied to study a broad range of fluid systems. It provides a framework in which the effects of molecular shape and interactions on the thermodynamics and phase behavior of fluids can be separated and quantified. In the original approach, molecules were modeled as chains composed of identical segments; the heterogeneity of molecules in terms of structure and functional groups was described implicitly through effective parameters. To overcome this limitation, in recent works [Peng et al. Fluid Phase Equilib. 227(2), 131 (2009); Ind. Eng. Chem. Res. 49(3), 1378 (2010)] the GC-SAFT-VR approach has been developed to extend the theory to model chains composed of segments of different size and/or energy of interaction and enable the development of a group-contribution approach within the SAFT-VR framework in which molecular heterogeneity and connectivity is explicitly accounted for. The parameters for several key functional groups (CH 3, CH 2, CH, CH 2 CH, C O, C 6H 5, esters, ethers, cis-alkenes and trans-alkenes groups) were determined by fitting to experimental vapor pressure and saturated liquid density data for a number of small molecules containing the functional groups of interest and transferability of the parameters tested by comparing the theoretical predictions with experimental data for pure fluids not included in the fitting process and binary mixtures of both simple fluids and the VLE and LLE of small molecules in polymer systems. In this work, we further extend the applicability of the GC-SAFT-VR approach through the study of the vapor–liquid phase behavior of associating systems, such as linear and branched alcohols, primary and secondary amines, aldehydes, and carboxylic acids, and their mixtures. In the study of these new molecules several new functional groups (OH (linear and branched), HC O, NH 2, NH and C OOH) are defined and their molecular parameters characterized. The transferability of the parameters is again tested by comparing the theoretical predictions with experimental data for pure fluids and binary mixtures not included in the fitting process. The GC-SAFT-VR approach is found to predict the phase behavior of the systems studied in most cases in good agreement with experimental data and accurately captures the effects of changes in structure and molecular composition on phase behavior.

Effect of structuring on the density of the liquid in colloidal capillary porous bodies

A method has been developed for calculating the density of the liquid in peat being dried, and liquid density data have been obtained for the first time for peat specimens differing in dispersity and for different drying temperatures. These data are at variance with the tabulated data for the corresponding structuring periods. Unprocessed and slightly processed peat specimens are characterized by smaller density values. High densities are observed for profoundly processed peat. The liquid density as a function of temperature passes through a maximum. At temperatures above the hydrogen bonding manifestation limit, the interaction between elements of the wet peat body is mainly due to the molecular van der Waals forces. The porosity of peat varies with temperature in both structuring periods. There is a discrepancy between the density data obtained using the conventional approach and those obtained by the method suggested here. The data coincide only for the first structuring period, when the moisture content is fairly high, because of the insignificant structuring effect of the solid phase.

Solid–liquid equilibrium using the SAFT-VR equation of state: Solubility of naphthalene and acetic acid in binary mixtures and calculation of phase diagrams

A solid–liquid equilibrium (SLE) thermodynamic model based on the SAFT-VR equation of state (EOS) is presented. The model allows for the calculation of solid–liquid phase equilibria in binary mixtures at atmospheric pressure. The fluid (liquid) phase is treated with the SAFT-VR approach, where molecules are modelled as associating chains of tangentially bonded spherical segments interacting via square-well potentials of variable range. The equilibrium between the liquid and solid phase is treated following a standard thermodynamic method that requires the experimental temperature and enthalpy of fusion of the solute. The model is used to calculate the solubilities of naphthalene and acetic acid in common associating and non-associating organic solvents and to determine the solid–liquid phase behaviour of binary mixtures with simple eutectics. The SAFT-VR pure component model parameters are determined by comparison to experimental vapour pressure and saturated liquid density data with the choice of association models according to the nature of the molecule; in addition, an unlike adjustable parameter ( k ij ) is used to model the solutions. The solubility data of naphthalene and acetic acid in both associating and non-associating solvents are reproduced essentially within the accuracy of the experimental measurements. The phase boundaries and the position of the eutectic points in the binary mixtures considered are, in most cases, reproduced with the accuracy commensurate with the industrial applications. Overall, the results presented show that the SAFT-VR EOS can be used with confidence for the prediction of the SLE of binary systems at atmospheric pressure.

A Novel Theory for Predicting Critical Constants and the α Function for Pure Polymers

The cubic equation of state (CEoS) requires critical temperature (Tc), critical pressure (Pc), and the alpha (α) function for all components including polymers before it can be used for the prediction of phase behavior and thermodynamic properties for the system. For nonpolymers or conventional components, Tc, Pc, and α usually are available in databanks. However, this is not the case for polymers since their critical point is not measurable and they lack vapor pressures for the derivation of the α function. As a result, the task of finding CEoS critical constants as well as the α function for polymers becomes extremely challenging in the case of polymeric systems. A rigorous theory requiring only the liquid density data of the pure polymer is successfully developed in this work for the accurate prediction of the critical temperature, the critical pressure, and the α function for the pure polymer for use in all types of cubic equations of state. The proposed theory extends the application of cubic equations of state to polymer systems in a very simple fashion.