Temperature-independent Binary Interaction Parameter Research Articles

Modelling polylactide/water/dioxane systems for TIPS scaffold fabrication

The representation of liquid–liquid equilibria (LLE) in ternary systems composed by water, 1,4-dioxane and different grades of poly(lactic acid) (PDLLA and PLLA), has been addressed through the PC-SAFT equation of state (EoS), in which the scheme of induced association is used to represent the interaction between solvent (dioxane) and non-solvent (water). The model parameters devoted to the description of pure component properties, as well as those pertinent to the representation of thermodynamic behaviour of solvent/non-solvent mixtures, were tuned on the basis of specific pressure–volume–temperature (PVT) data for the corresponding systems. Only the binary parameters for polymer–solvent and polymer/non-solvent pairs were adjusted to obtain a useful representation of experimental LLE data for the ternary systems. A suitable description of the thermodynamic properties of ternary mixtures was obtained using temperature-independent binary interaction parameters in the range 25–80°C, and the consistency of the approach in the entire composition range was verified against experimental solubility data specifically measured for the polymer/non-solvent pair. The model shows good ability in the description of the thermodynamic properties of the system and it represents a reliable tool for the prediction of LLE also at conditions different from those considered for its set-up. This approach thus represents a useful designing tool for processes, such as thermally induced phase separation (TIPS), used in the preparation of microporous polymeric scaffolds.

Permeability, diffusivity and solubility of carbon dioxide in fluoropolymers: an experimental and modeling study

Carbon dioxide has successfully been used as an alternative refrigerant in many applications, replacing chlorofluoro- and hydrofluorocarbons (CFCs and HFCs), due to its negligible ozone depletion and significantly lower global warming potential. However, the use of carbon dioxide as a refrigerant requires a refrigeration cycle with greater extremes of pressure, placing greater demands on the plant’s seals and packings. The integrity of the refrigeration system (it should release as little refrigerant as possible to the atmosphere) depends crucially on the material used for the seals and packings. Using a high-pressure permeation cell, the permeability and diffusivity of carbon dioxide were measured in several polymers used as packing and sealing materials. These were the fluoropolymers PTFE, FKM and TFM, both pure and containing glass, graphite, Ekonol and polysulfone as additives. The solubility coefficient of carbon dioxide in these polymers was then obtained as the ratio of the measured permeability and diffusivity data. Measurements were carried out over a pressure range of 45–50 bar and a temperature range of 40–80 °C. The solubility of carbon dioxide in the polymers is then modeled with the Simplified Perturbed Chain – Statistical Associating Fluid Theory (sPC-SAFT) equation of state. Pure component parameters were determined using an extrapolation method based on the lower molecular weight monomer and available density data for the polymers. In the case of copolymers, mixing rules were used to determine parameters. Carbon dioxide solubility can be accurately correlated to the measured data with the sPC-SAFT equation of state using a temperature–independent binary interaction parameter.

High-pressure gas solubility in multicomponent solvent systems for hydroformylation. Part II: Syngas solubility

High-pressure solubility of syngas with a molar ratio of hydrogen (H2) and carbon monoxide (CO) of 1:1 was investigated in various solvents like n-decane, dimethylformamide (DMF), 1-dodecene and n-dodecanal as well as in mixtures of n-decane and DMF and in a mixture of 1-dodecene, n-dodecanal, n-decane and DMF at temperatures between 302K and 367K and at pressures of up to 14MPa. Moreover, the H2 solubility in 1-dodecene and n-dodecanal was measured in the same pressure and temperature range. The solubility measurements were performed in a high-pressure volume-variable view cell using a visual synthetic method. For modeling and prediction of the gas solubility (H2, CO, and syngas (H2/CO)) in the considered solvents, the Perturbed Chain Statistical Associating Fluid Theory (PC-SAFT) was used. The systems containing one gas (H2 or CO) and one solvent were modeled accurately by applying temperature-independent binary interaction parameters (kij's). These kij's were used to predict the syngas solubility in pure solvents and their mixtures without further adjustments. The kij between H2 and CO was always set to zero. The results showed that PC-SAFT is able to predict the syngas solubility in pure solvents with an average relative deviation of 3.1–12.0%. Syngas solubility in the n-decane/DMF mixture was predicted with a deviation of 7.2%.

High-pressure gas solubility in multicomponent solvent systems for hydroformylation. Part I: Carbon monoxide solubility

High-pressure gas-solubility data of carbon monoxide (CO) in various solvents like n-hexane, propylene carbonate, dimethylformamide, 1-dodecene, n-dodecanal and n/iso-tridecanal was measured for temperatures between 295K and 364K and pressures up to 17MPa. The experiments were performed in a high-pressure variable-volume view cell applying the synthetic method. The binary systems investigated were correlated using the perturbed chain statistical associating fluid theory (PC-SAFT). A temperature-independent binary interaction parameter kij was fitted to solubility data. Based on this, to CO solubility in mixtures of n-dodecanal and 1-dodecene with various molar compositions of the two liquids (3:1, 1:1, 1:3) were predicted. CO-solubility measurements for these systems confirmed that PC-SAFT is able to accurately predict the ternary data based on the knowledge of the binary subsystems, only.

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.

High-pressure gas–liquid equilibrium of the system carbon dioxide–β-caryophyllene at 50 and 70 °C

New experimental data of high-pressure gas–liquid equilibrium for the system carbon dioxide–β-caryophyllene are provided. The equilibrium measurements were carried out at 50 and 70 °C, for pressures which are particularly relevant in the context of the supercritical deterpenation of lemon essential oil (from 8.8 to 15.6 MPa). Both the liquid and the gas equilibrium composition were measured. The experiments were carried out using a two-chamber gas-phase recirculation apparatus of 340 cm 3. The experimental results agree well with the few experimental data available in the literature and extend the experimental knowledge on this system. The measured data were satisfactorily correlated by means of the Peng–Robinson equation of state, expressing the mixture parameters with the van der Waals mixing rules corrected by two temperature-independent binary interaction parameters.

Water solubility of drug-like molecules with the cubic-plus-association equation of state

Although of extreme importance for evaluating the effective therapeutic action, aqueous solubility data involving drug-like molecules are scarce. Thermodynamic models can be used to estimate these solubilities, and different models, namely activity coefficient models, have been applied for that purpose. Still, these frequently cannot describe with accuracy broad temperature and pressure ranges, various solvent compositions or multifunctional molecules. Despite the success of the cubic-plus-association (CPA) equation of state (EoS) in modeling complex systems, it has never been used for modeling the phase equilibria of drug-like molecules, explicitly accounting for the number and nature of associating sites. In this work, aqueous solubilities of different complex solutes, like acetamide, acetanilide, acetylsalicylic acid, adipic acid, ascorbic acid, bisphenol A, camphor, dibenzofuran, hexachlorobenzene, hydroquinone, ibuprofen, nicotinic acid, paracetamol, piperazine, stearic acid, sorbitol, terephthalic acid and vanillin are estimated in a wide temperature range with the CPA EoS. Generally, the modeling results are within the experimental uncertainties using a single temperature independent binary interaction parameter, or a solvation parameter for some non-associating solutes. Globally, an average absolute deviation of 39% was obtained.

Vapor−Liquid Equilibria of Acid Gas−Aqueous Ethanolamine Solutions Using the PC-SAFT Equation of State

Using the perturbed-chain statistical associating fluid theory (PC-SAFT), the vapor pressure, saturated liquid density, and heat of vaporization for monoethanolamine (MEA), diethanolamine (DEA), and methyldiethanolamine (MDEA) were calculated. PC-SAFT accurately described the properties of the pure ethanolamines along the coexistence curve. Then, the vapor−liquid equilibria (VLE) of the aqueous ethanolamine solutions were calculated by temperature-independent binary interaction parameters. Using the binary interaction parameters for the systems DEA + water, DEA + methanol, and methanol + water, the VLE of the ternary system DEA + water + methanol was predicted. The results indicated that PC-SAFT successfully described the equilibrium properties of the aqueous ethanolamine solutions. Finally, the solubilities of carbon dioxide and hydrogen sulfide in the aqueous ethanolamine solutions were predicted and compared to the experimental data. While no adjustable parameters were used, PC-SAFT reasonably describe...

Equation-of-state modeling of mixtures with ionic liquids

A non-electrolyte equation-of-state model was used to describe the phase behavior of binary systems containing alkyl-methyimidazolium bis(trifluoromethyl-sulfonyl)imide ionic liquids. A methodology is suggested for modeling this phase behavior by using the Non-Random Hydrogen-Bonding (NRHB) model. According to this methodology, the scaling constants of the ionic liquid are calculated using limited available experimental data on liquid densities and Hansen's solubility parameters, while all electrostatic interactions (polar, hydrogen bonding and ionic) are treated as strong specific interactions. Using the aforementioned methodology, the model is applied to describe the vapor-liquid and the liquid-liquid equilibria in mixtures of ionic liquids with various polar or quadrupolar solvents at low and high pressures. In all cases, one temperature-independent binary interaction parameter was used. Accurate correlations were obtained for the majority of the systems, both, for vapor-liquid and liquid-liquid equilibria.

Representation of Phase Behavior of Ionic Liquids Using the Equation of State for Square-well Chain Fluids with Variable Range

An equation of state (EOS) for square-well chain fluids with variable range (SWCF-VR) developed based on statistical mechanics for chemical association was employed for the calculations of pressure-volume-temperature ( pVT) and phase equilibrium of pure ionic liquids (ILs) and their mixtures. The new molecular parameters for 23 ILs were obtained by fitting their experimental density data over a wide temperature and pressure ranges. The molecular parameters of ILs composed of homologous organic cation and an identical anion such as [C x mim][NTf 2] are good linear with respect to their molecular weight, indicating that the molecular parameters of homologous substances, subsequently pVT and vapor-liquid equilibria vapor-liquid equilibria (VLE) can be predicted using the generalized parameter when no experimental data were available. The new set of parameters were satisfactorily used for calculations of the property of solvent and ILs mixture and the solubility of gas in various ILs at low pressure only using one temperature-independent binary interaction parameter.

Liquid Viscosities of Cyclohexane, Cyclohexane + Tetradecane, and Cyclohexane + Benzene from (313 to 393) K and Pressures Up to 60 MPa

Liquid viscosities of pure cyclohexane and of the cyclohexane + tetradecane and cyclohexane + benzene systems at four different compositions were measured using a rolling-ball viscometer from (313.2 to 393.2) K and pressures up to 60 MPa with an estimated experimental uncertainty in the measured viscosity data of 2 %. A comparison between our measured viscosities and those reported by others authors for cyclohexane was established with the hard-sphere scheme given by Assael et al. [Int. J. Thermophys. 1992, 13, 269−281]. The comparison showed an average relative deviation of 2.3 %. The measured mixture viscosity data were regressed with the correlations of Grunberg−Nissan (GN) and Katti−Chaudhri (KC), and a liquid viscosity model based on Eyring’s theory coupled with a cubic equation of state (ET-EoS), all of them using a single temperature-independent binary interaction parameter to describe the whole η, T, p, x surface of study. Results of the representation with the GN, KC, and ET-EoS viscosity models ...

Equation of state for square-well chain molecules with variable range II. Extension to mixtures

An equation of state (EOS) developed in our previous work for square-well chain molecules with variable range is further extended to the mixtures of non-associating fluids. The volumetric properties of binary mixtures for small molecules as well as polymer blends can well be predicted without using adjustable parameter. With one temperature-independent binary interaction parameter, satisfactory correlations for experimental vapor–liquid equilibria (VLE) data of binary normal fluid mixtures at low and elevated pressures are obtained. In addition, VLE of n-alkane mixtures and nitrogen + n-alkane mixtures at high pressures are well predicted using this EOS. The phase behavior calculations on polymer mixture solutions are also investigated using one-fluid mixing rule. The equilibrium pressure and solubility of gas in polymer are evaluated with a single adjustable parameter and good results are obtained. The calculated results for gas + polymer systems are compared with those from other equations of state.

Modeling the Phase Behavior in Mixtures of Pharmaceuticals with Liquid or Supercritical Solvents

The concept of solubility parameter, which is widely used for the screening of solvents in pharmaceutical applications, is combined with a thermodynamic theory that is able to model systems with large deviations from ideal behavior. The nonrandom hydrogen-bonding (NRHB) theory is applied to model the phase behavior of mixtures of six pharmaceuticals (i.e., ibuprofen, ketoprofen, naproxen, benzoic acid, methyl paraben, and ethyl paraben). The pure fluid parameters of the studied pharmaceuticals were estimated using limited available experimental (or predicted) data on sublimation pressures, liquid densities, and Hansen's solubility parameters. The complex hydrogen-bonding behavior was explicitly accounted for, while the corresponding parameters were adopted from simpler molecules of similar chemical structure or/and fitted to the aforementioned pure fluid properties. In this way, the solubility of the studied pharmaceuticals in liquid solvents was calculated. The average root-mean-square deviation between experimental and calculated solubilities is 0.190 and 0.037 in log(10) units for prediction (calculations without a binary interaction parameter adjustment) and for correlation (calculations using one binary interaction parameter fitted to experimental data), respectively. In addition, using one temperature-independent binary interaction parameter the phase behavior of pharmaceuticals in supercritical CO(2) and ethane was satisfactorily correlated. Finally, preliminary encouraging results are shown concerning two ternary mixtures where the model is able to predict accurately the solubility of pharmaceuticals in mixed solvents based on interaction parameters fitted to corresponding single solvent data.

Modeling the vapor–liquid equilibria of polymer–solvent mixtures: Systems with complex hydrogen bonding behavior

The vapor–liquid equilibria of binary polymer–solvent systems was modeled using the Non-Random Hydrogen Bonding (NRHB) model. Mixtures of poly(ethylene glycol), poly(propylene glycol), poly(vinyl alcohol) and poly(vinyl acetate) with various solvents were investigated, while emphasis was put on hydrogen bonding systems, in which functional groups of the polymer chain can self-associate or cross-associate with the solvent molecules. Effort has been made to explicitly account for all hydrogen bonding interactions. The results reveal that the NRHB model offers a flexible approach to account for various self- or cross-associating interactions. In most cases model's predictions (using no binary interaction parameter k ij = 0) and model's correlations (using one temperature independent binary interaction parameter, k ij ≠ 0) are in satisfactory agreement with the experimental data, despite the complexity of the examined systems.

Liquid Viscosities of the Ternary System Benzene + Cyclohexane + n-Tetradecane from (313 to 393) K and Pressures up to 60 MPa

Liquid viscosities of eight mixtures for the ternary system benzene + cyclohexane + n-tetradecane were experimentally measured using a rolling-ball viscometer from (313.2 to 393.2) K and at pressures up to 60 MPa. We performed the modeling of the measured mixture viscosity data (256 points) by applying the Grunberg−Nissan (GN) and Katti−Chaudhri (KC) correlations and a liquid viscosity model based on Eyring’s theory coupled to a cubic equation of state (ET-EoS) by using a single temperature-independent binary interaction parameter for the benzene + n-tetradecane, benzene + cyclohexane, and cyclohexane + n-tetradecane systems. Results of the modeling process yielded an average absolute deviation of (4.9, 5.3, and 6.7) % for the GN, KC, and ET-EoS viscosity models, respectively, which show that the GN model is superior to the KC and ET-EoS models in predicting the whole viscosity−temperature−pressure−composition surface of the ternary system studied.

Liquid viscosities of benzene, n-tetradecane, and benzene + n-tetradecane from 313 to 393 K and pressures up to 60 MPa: Experiment and modeling

In this work, kinematic viscosities of benzene, n-tetradecane, and of the mixture benzene + n-tetradecane at four different compositions were measured using a rolling-ball viscometer from 313.2 to 393.2 K and pressures up to 60 MPa. Kinematic viscosities were converted to dynamic viscosities through the use of a density Tait-like equation for pure components and a single density mixing rule for the mixtures. A comparison between our measured viscosities and those reported by other authors for benzene and n-tetradecane was established with the correlation given by Assael et al. [M.J. Assael, J.H. Dymond, M. Papadaki, P.M. Patterson, Correlation and prediction of dense fluid transport coefficients. I. n-alkanes, Int. J. Thermophys. 13 (1992) 269–281]. The comparison showed an average absolute deviation of 1.5% for benzene and 2.7% for n-tetradecane. The measured mixture viscosity data were modeled with a proposed liquid viscosity model based on the Eyring's theory coupled with a cubic equation of state and using a single temperature-independent binary interaction parameter to describe the whole η − T − p − x surface of study. Results of the modeling effort yielded an average absolute deviation of 2.0%, which is within the experimental uncertainty.

Modeling vapor–liquid equilibria of ethanol + 1,1,1,2,3,3,3-heptafluoropropane binary mixtures using PC-SAFT

One objective of the Third Industrial Fluid-Properties Simulation Challenge was the extrapolation of mixture phase equilibrium information obtained from one isotherm to other temperatures. In this work, we present modeling results for the vapor–liquid equilibrium of the ethanol/1,1,1,2,3,3,3-heptafluoropropane (HFC-227ea) mixture obtained with the PC-SAFT equation of state. The required pure-component parameters were determined by fitting pure-component vapor pressures and liquid density data. To get a quantitative description of the mixture, a temperature-independent binary interaction parameter was adjusted to experimental bubble-point data at 283.17 K. Using these parameters, bubble-point pressures at T = 343.13 K were predicted for different concentrations.

Vapor–liquid equilibria for the ternary mixture of carbon dioxide + 1-propanol + propyl acetate at elevated pressures

Vapor–liquid equilibrium (VLE) data for the ternary mixture of carbon dioxide, 1-propanol and propyl acetate were measured in this study at 308.2, 313.2, and 318.2 K, and at pressures ranging from 4 to 10 MPa. A static type phase equilibrium apparatus with visual sapphire windows was used in the experimental measurements. New VLE data for CO 2 in the mixed solvent were presented. These ternary VLE data at elevated pressures were also correlated using either the modified Soave–Redlich–Kwong or Peng–Robinson equation of state (EOS), and by employing either the van der Waals one-fluid or Huron–Vidal mixing model. Satisfactory correlation results from both EOS models are reported with temperature-independent binary interaction parameters. It is observed that at 318.2 K and 10 MPa, 1-propanol may probably be separated from propyl acetate into the vapor phase at the entire concentration range in the presence of high pressure CO 2.

Vapor−Liquid and Vapor−Liquid−Liquid Equilibria of Carbon Dioxide/n-Perfluoroalkane/n-Alkane Ternary Mixtures

Perfluoroalkanes have numerous applications (e.g., in the medical field and the chemical industry), and their high affinity for carbon dioxide makes them attractive as surfactants and cosolvents. Although research in this area has grown in the past few years, very little phase-equilibrium data is available in the open literature for these systems. In this work, we present, for the first time, predictions of vapor-liquid and vapor-liquid-liquid equilibria of binary and ternary systems of carbon dioxide/n-perfluoroalkane/n-alkane. Our results are based on the SAFT-VR EOS (statistical associating fluid theory of variable range, equation of state), and we study the influence of temperature, pressure, composition, and chain length on the phase diagram. The predicted phase diagrams are based on temperature-independent binary interaction parameters, and no ternary parameters are introduced. Comparisons to the available experimental and molecular simulation data show that the predicted diagrams should provide a good representation of the phase equilibria.

Liquid–liquid equilibria of a hydrofluoroether + water + ethanol system

The ability to manipulate the liquid–liquid equilibria (LLE) of a commercially available hydrofluoroether (HFE-7100 ®, an approximately equimolar mixture of the isomers methoxy-nonafluoroisobutane and methoxy-nonafluorobutane) + water with the addition of ethanol, which is mutually miscible with both solvents, was examined. LLE data were determined at 298, 308 and 323 K for the system of HFE-7100 ®+water+ethanol. The UNIQUAC and NRTL excess Gibbs energy models were able to adequately represent the type I phase behavior observed over this temperature range. The goodness of the fit of each model was compared for temperature-dependent and temperature-independent binary interaction parameters.