Perturbed-chain Statistical Associating Fluid Theory Research Articles

Thermodynamic properties of selenoether-functionalized ionic liquids and their use for the synthesis of zinc selenide nanoparticles.

Three selenoether-functionalized ionic liquids (ILs) of N-[(phenylseleno)methylene]pyridinium (1), N-(methyl)- (2) and N-(butyl)-N'-[(phenylseleno)methylene]imidazolium (3) with bis(trifluoromethanesulfonyl)imide anions ([NTf2]) were prepared from pyridine, N-methylimidazole and N-butylimidazole with in situ obtained phenylselenomethyl chloride, followed by ion exchange to give the desired compounds. The crystal structures of the bromide and tetraphenylborate salts of the above cations (1-Br, 2-BPh4 and 3-BPh4) confirm the formation of the desired cations and indicate a multitude of different supramolecular interactions besides the dominating Coulomb interactions between the cations and anions. The vaporization enthalpies of the synthesized [NTf2]-containing ILs were determined by means of a quartz-crystal microbalance method (QCM) and their densities were measured with an oscillating U-tube. These thermodynamic data have been used to develop a method for assessment of miscibility of conventional solvents in the selenium-containing ILs by using Hildebrandt solubility parameters, as well as for modeling with the electrolyte perturbed-chain statistical associating fluid theory (ePC-SAFT) method. Furthermore, structure-property relations between selenoether-functionalized and similarly shaped corresponding aryl-substituted imidazolium- and pyridinium-based ILs were analyzed and showed that the contribution of the selenium moiety to the enthalpy of vaporization of an IL is equal to the contribution of a methylene (CH2) group. An incremental approach to predict vaporization enthalpies of ILs by a group contribution method has been developed. The reaction of these ILs with zinc acetate dihydrate under microwave irradiation led to ZnSe nanoparticles of an average diameter between 4 and 10 nm, depending on the reaction conditions.

Density and Compressibility of Multicomponent n-Alkane Mixtures up to 463 K and 140 MPa

Density measurements of two ternary alkane mixtures (methane/n-butane/n-decane and methane/n-butane/n-dodecane) and two multicomponent mixtures composed of methane/n-butane/n-octane/n-dodecane/n-hexadecane/n-eicosane were performed in the temperature range from (278.15 to 463.15) K and pressures up to 140 MPa. The isothermal compressibility values of these mixtures were obtained by differentiation from a Tait-type fitting of experimental densities as a function of temperature and pressure. Excess volume of the studied mixtures was also determined. Four different equations of state, that is, Soave–Redlich–Kwong (SRK), Peng–Robinson (PR), Perturbed Chain Statistical Associating Fluid Theory (PC-SAFT), and Soave-Benedict-Webb-Rubin (Soave-BWR) were used for predicting the experimental density values as well as the excess volumes.

Physical stability of API/polymer-blend amorphous solid dispersions

The preparation of amorphous solid dispersions (ASDs) is a well-established strategy for formulating active pharmaceutical ingredients by embedding them in excipients, usually amorphous polymers. Different polymers can be combined for designing ASDs with desired properties like an optimized dissolution behavior. One important criterion for the development of ASD compositions is the physical stability. In this work, the physical stability of API/polymer-blend ASDs was investigated by thermodynamic modeling and stability studies. Amorphous naproxen (NAP) and acetaminophen (APAP) were embedded in blends of hydroxypropyl methylcellulose acetate succinate (HPMCAS) and either poly(vinylpyrrolidone) (PVP) or poly(vinylpyrrolidone-co-vinyl acetate) (PVPVA64). Parameters for modeling the API solubility in the blends and the glass-transition temperature curves of the water-free systems with Perturbed-Chain Statistical Associating Fluid Theory and Kwei equation, respectively, were correlated to experimental data. The phase behavior for standardized storage conditions (0%, 60% and 75% relative humidity (RH)) was predicted and compared to six months-long stability studies. According to modeling and experimental results, the physical stability was reduced with increasing HPMCAS content and increasing RH. This trend was observed for all investigated systems, with both APIs (NAP and APAP) and both polymer blends (PVP/HPMCAS and PVPVA64/HPMCAS). PC-SAFT and the Kwei equation turned out to be suitable tools for modeling and predicting the physical stability of the investigated API/polymer-blends ASDs.

Measuring and Predicting the Extraction Behavior of Biogenic Formic Acid in Biphasic Aqueous/Organic Reaction Mixtures.

The distribution coefficients and selectivities required for extraction purposes were predicted with a thermodynamic equation of state for the ternary system formic acid/water/extraction solvent. These predictions were validated with experimental data from the literature and experimental data from the oxidation of biomass to formic acid process measured in this work. Extraction solvents discussed in this work are 1-butanol, 1-pentanol, 1-hexanol, 1-heptanol, 1-octanol, 1-decanol, ethyl n-butyl ether, diisopropyl ether, di-n-butyl ether, benzyl formate, and heptyl formate. The considered temperature ranged from 273 to 363 K under atmospheric pressure. Perturbed-chain statistical associating fluid theory (PC-SAFT) was used for prediction purposes applying an approach as simple as possible and as complex as necessary to achieve trustworthy data for selecting the best extraction solvent. Using PC-SAFT allowed identifying 1-hexanol as the most promising solvent out of the 11 extraction agents. The predicted data were in good agreement with the experimental distribution coefficients and the selectivities, which are very sensitive to experimental uncertainties.

Phase equilibrium of PVAc + CO2 binary systems and PVAc + CO2 + ethanol ternary systems

The cloud point and bubble point isopleths were measured for poly(vinyl acetate) (PVAc) + CO2 binary systems and PVAc + CO2 + ethanol ternary systems using a supercritical CO2 phase equilibrium apparatus. A transition point measurement device was designed to accurately determine the cloud point pressures by measuring the resistance variation of a photoresistor. The effects of the temperature, pressure, components, and polymer molecular weight on the phase behavior of these binary and ternary systems were investigated. We found that the transition point pressure increased with increasing temperature and molecular weight of PVAc, the cloud point isopleths for the PVAc + CO2 binary systems are upper critical solution pressure (UCSP) type, the cloud point pressures moved downwards with the addition of ethanol to PVAc + CO2, and the cloud point pressures decreased with increasing PVAc + ethanol concentration at a fixed mass ratio of 1:7. The perturbed-chain statistical associating fluid theory equation of state (PC-SAFT EOS) was used to investigate the phase behavior of these binary and ternary systems by adjusting the binary interaction parameter, kij. The modeling shows a very good agreement with the experimental data.

Measurement and Modeling the Excess Molar Volumes and Refractive Index Deviations of Binary Mixtures of 2-Propanol, 2-Butanol and 2-Pentanol with N-Propylamine

The densities, ρ, and refractive indices, n D, of 2-alkanols (C3–C5) with N-propylamine have been measured for the whole range of composition at temperatures from (298.15–328.15) K at 10 K intervals and ambient pressure of 81.5 kPa, using an Anton Paar DMA 4500 oscillating tube densimeter and an Anton Paar Abbemat 500 automatic refractometer. From the experimental data, excess molar volumes \( V_{\text{m}}^{\text{E}} \) partial molar volumes \( \bar{V}_{i} \) apparent molar volumes V ϕi and refractive index deviations Δn D the binary systems consisting of N-propylamine + 2-alkanols (2-propanol, 2-butanol, 2-pentanol) were calculated and \( V_{\text{m}}^{\text{E}} \) and Δn D values were correlated with the Redlich–Kister polynomial. The effect of temperature and the chain length of the alcohol on the excess molar volumes and refractive index deviations are discussed in terms of molecular interaction between unlike molecules. The excess molar volumes are negative and refractive index deviations are positive over the entire composition range, which indicates strong hydrogen bonding between molecules of the mixtures. A comparative study has been made of the refractive indices obtained experimentally and those calculated by means of the Lorentz–Lorenz, Weiner and Arago–Biot relations. The perturbed chain statistical associating fluid theory (PC-SAFT), simplified PC-SAFT and Prigogine–Flory–Patterson theory were also applied to correlate and predict the density and excess molar volumes of the mixtures.

The friction theory for modeling the viscosities of deep eutectic solvents using the CPA and PC-SAFT equations of state

Deep Eutectic Solvents (DESs), as recently introduced green solvents, are interesting for different fields and applications. Most of the known DESs have high viscosities, which change dramatically with temperature. Therefore, the viscosity of a DES is most often one of the vital physical properties which must be known accurately. Because of the strong non-ideal interactions between the constituents, as well as the dramatic changes of DES viscosity with temperature, modeling and predicting the viscosities of DESs over wide ranges of temperatures is very challenging. In this study, a viscosity approach is used and implemented into two advanced association equations of state for different families of deep eutectic solvents. The cubic plus association (CPA) and the perturbed chain-statistical associating fluid theory (PC-SAFT) equations of state (EoSs), which are two powerful models to handle associating compounds, have been coupled with the friction theory, which is itself among the successful theoretical viscosity models of literature. Twenty-seven different types of DESs, for which density and viscosity data are available in open literature, were considered. A large density databank, consisting of 590 density data over wide ranges of temperatures and pressures, together with a large viscosity databank covering 253 viscosity data over wide ranges of temperatures at atmospheric pressure were collected. The resulting friction theory models with the CPA and PC-SAFT EoSs were checked against experimental data and their deviations were found to be the same and equal to 4.4%. Such accuracy showed the promising capability of both models. By changing the hydrogen bond donor types for a fixed hydrogen bond acceptor, the accuracies of the models were also shown to be good with respect to experimental values. In addition, both models perfectly followed the trends of changing ratios of hydrogen bond donors to hydrogen bond acceptors. The viscosity-temperature trend of the different DESs was also successfully modeled.

New Two-Dimensional Particle-Scale Model To Simulate Asphaltene Deposition in Wellbores and Pipelines

A new two-dimensional dynamic model was developed to simulate asphaltene precipitation, aggregation, and deposition at isothermal and non-isothermal conditions. The perturbed-chain statistical associating fluid theory equation of state was used to model the asphaltene precipitation. Also, novel kinetic models were used to account for the aggregation and deposition of asphaltene particles. The effect of the aggregate size on the rate of aggregation and deposition was studied, and it was concluded that the rate of asphaltene deposition increases, while the concentration of nanoaggregates increases in the well column. The tendency of smaller aggregates to deposit on the surface could be explained as a result of the increase in the diffusion coefficient of asphaltene aggregates. The results obtained from the new model for the rate and amount of asphaltene deposition were compared to the experimental data reported in the literature. It was shown that the results of the new simulation were in good agreement wit...

Asphaltene precipitation modeling with PR and PC-SAFT equations of state based on normal alkanes titration data in a Multisolid approach

Reservoir fluid Asphaltenes show different precipitation behavior during titration with different normal paraffins, reminding a polydisperse nature. In this respect, the precipitated Asphaltene is increased with decreasing the solvent carbon number. Titration experimental data can be used to improve the precipitation model flexibility. In this study, an improved thermodynamic model is developed to calculate the Asphaltene precipitation conditions. The main focus of this work is on the maximum use of experimental data to increase the accuracy of Asphaltene precipitation calculation using perturbed chain statistical associating fluid theory (PC-SAFT) and Peng-Robinson (PR) equations of state (EOS) (including volume shift) in a Multisolid framework. To do so, at first, PR and PC-SAFT Asphaltene parameters are regressed to bubble point pressure, precipitation onset pressure and the amount of precipitated Asphaltene using the published experimental data on titration of dead oil using normal pentane as a solvent in atmospheric conditions. Afterwards, to follow the polydisperse behavior, the Asphaltene component is divided into three pseudo-components based on the precipitating solvents and the calculations are repeated to adjust the parameters of the EOSs of the new Asphaltene parts. Finally, the results for monodisperse and polydisperse Asphaltene are compared with experimental date of two types of Mexican crude oil samples from reliable published literature and the modeling results with statistical associating fluid theory for the potentials of variable attractive range (SAFT-VR) used by Buenrostro-Gonzalez et al. [1]. The maximum and minimum deviations from the experimental data to calculate the weight percent of the precipitated Asphaltene after dilution are obtained by PR EOS for monodisperse and by PC-SAFT EOS for polydisperse Asphaltene. For one of the oil samples the maximum and minimum mean percent deviation by PR and PC-SAFT EOSs are 9.1079 and 1.7279, respectively, while for the other oil sample they are 3.6674 and 1.0845, respectively.

Impact of Polymer Type and Relative Humidity on the Long-Term Physical Stability of Amorphous Solid Dispersions.

The purpose of this work is to compare the long-term physical stability of amorphous solid dispersion (ASD) formulations based on three different commercially used excipients, namely, poly(vinylpyrrolidone) K25 (PVP), poly(vinylpyrrolidone-co-vinyl acetate) (PVPVA64), and hydroxypropyl methylcellulose acetate succinate 126G (HPMCAS), at standardized ICH storage conditions, 25 °C/0% relative humidity (RH), 25 °C/60% RH, and 40 °C/75% RH. Acetaminophen (APAP) and naproxen (NAP) were used as active pharmaceutical ingredients (APIs). 18 month long stability studies of these formulations were analyzed and compared with the API/polymer phase diagrams, which were modeled and predicted by applying the Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) and the Gordon-Taylor or Kwei equation. The study showed that, at dry storage, the solubility of the APIs in the polymers and the kinetic stabilizing ability of the polymers increase in the following order: HPMCAS < PVPVA64 < PVP. RH significantly reduces the kinetic stabilization as well as NAP solubility in the polymers, while the impact on APAP solubility is small. The impact of RH on the stability increases with increasing hydrophilicity of the pure polymers (HPMCAS < PVPVA64 < PVP). The experimental stability results were in very good agreement with predictions confirming that PC-SAFT and the Kwei equation are suitable predictive tools for determining appropriate ASD compositions and storage conditions to ensure long-term physical stability.

Binary Vapor–Liquid Equilibrium Data for Perfluorooctane with Light Gases (Oxygen, Nitrogen, and Methane)

Experimental vapor–liquid equilibrium data are reported for the binary systems of perfluorooctane + either oxygen, nitrogen, or methane. Isothermal measurements were performed within the temperature range of 293.21 to 353.23 K, and at pressures up to 21 MPa, using two apparatuses; one based on the “static-analytic” method and the other on the “static-synthetic” method. The experimental data were correlated using the perturbed-chain statistical associating fluid theory equation of state. The model provides a satisfactory representation of the experimental data within the measured temperature range.

Viscosity modeling of water + alkanediols mixtures

In this study, both theoretical and empirical viscosity models were evaluated for binary associating liquid mixtures of water+1,2-ethanediol, 1,3-propanediol, 1,4-butanediol, and 1,5-pentanediol. The interaction between molecules in the mixtures was analyzed using the calculation of excess energy of flow obtained from Eyring's absolute rate theory. Free volume (FV) viscosity model was coupled with Peng-Robinson (PR) and perturbed-chain statistical associating fluid theory (PC-SAFT) equation of states (EoS); friction theory (FT) was coupled with PR EoS; no significant difference was observed in the modeling results using different EoS. A new mixing rule was found to improve the modeling results of FT coupled with the PR EoS for the binary mixtures studied. The empirical models correlated viscosity of aqueous diol systems well with average absolute percent deviation (AAD%) <1.

Prediction of dew points and liquid dropouts of gas condensate mixtures

Thermodynamic modeling of reservoir fluids behavior is of great importance for the oil and gas industry. For design and safe operation purposes, it is necessary to have an accurate, simple and robust model for the prediction of the phase equilibrium of reservoir fluids. In this work, the UMR-PRU model is applied in the prediction of dew points and liquid dropouts of gas condensate mixtures, and is compared with the widely used cubic equations of state Soave-Redlich-Kwong (SRK) and Peng-Robinson (PR) as well as the non-cubic Perturbed Chain Statistical Associating Fluid Theory (PC-SAFT) equation of state. The evaluation of the models was based both on synthetic and real gas condensate mixtures. For real gas condensates, a characterization method for the C7+ fraction based on the one proposed by Pedersen is developed for UMR-PRU. The results reveal that UMR-PRU is a sufficiently accurate model for dew point and liquid dropout predictions of gas condensates.

Thermodynamic properties and sPC-SAFT modeling of 2-ethoxyethanol, 2-propoxyethanol and 2-butoxyethanol from T = (293.15–413.15) K and pressure up to 30 MPa

New experimental PρT data of three glycols ethers, namely, 2-ethoxyethanol, 2-propoxyethanol and 2-butoxyethanol were measured in a wide range of temperatures (293.15–413.15) K and pressures (0.1–30) MPa with a vibrating-tube densimeter. The experimental PρT data were correlated with the modified Tait equation. The study is completed with modeling in terms of the simplified perturbed-chain statistical associating fluid theory (sPC-SAFT) equation of state. The pure compound parameters of the sPC-SAFT equation are generally determined by fitting the equation to experimental saturated vapor pressure and liquid density data. In this work, by simultaneously minimizing the total objective function of temperature, pressure and density new correlation were developed to estimate the sPC-SAFT equation parameters with two association scheme for three glycols ethers including, 2-ethoxyethanol, 2-propoxyethanol and 2-butoxyethanol by using PρT data and with a fitting AAD% of 0.17 on average. The validity of the parameters and the employed association scheme were tested by the evaluation of densities and derivative properties such as isobaric thermal expansion coefficients, αP, isothermal compressibility, κΤ, isobaric heat capacities, CP, and speed of sound, u. All correlated/predicted results were compared with the modified Tait equation and experimental literature data. The obtained results showed that the sPC-SAFT equation of state, along with the proposed correlations, presents good results for modeling these glycols ethers.

Thermodynamic prediction of the solvent effect on a transesterification reaction

This work focuses on the thermodynamic prediction of solvent effects on the transesterification of butyl acetate with ethanol to butanol and ethyl acetate in the solvent heptane at 293.15 K and 303.15 K. Both, the reaction equilibrium and the reaction kinetics have been investigated experimentally by Schmidt et al. (1999). They found that the solvent heptane does not affect the reaction equilibrium but significantly influences the reaction kinetics. They described the solvent effect on the reaction kinetics by empirically correlating the experimentally-observed apparent rate constants with the dielectric constants of the different reaction mixtures.In this work we re-evaluated the experimental data and now present a thermodynamic approach to consistently predict the solvent effect on both, the reaction equilibrium and the reaction kinetics. Accounting for the activity coefficients of the reactants/products obtained from the Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) allowed for considering the interactions of the reactants/products among themselves and also with the solvent heptane. Accounting for those, it is shown that the solvent effect on the reaction equilibrium as well as on the reaction rate can even be predicted in very good agreement with the experimental data.

Predictions of homogeneous nucleation rates for n-alkanes accounting for the diffuse phase interface and capillary waves.

Homogeneous droplet nucleation has been studied for almost a century but has not yet been fully understood. In this work, we used the density gradient theory (DGT) and considered the influence of capillary waves (CWs) on the predicted size-dependent surface tensions and nucleation rates for selected n-alkanes. The DGT model was completed by an equation of state (EoS) based on the perturbed-chain statistical associating fluid theory and compared to the classical nucleation theory and the Peng-Robinson EoS. It was found that the critical clusters are practically free of CWs because they are so small that even the smallest wavelengths of CWs do not fit into their finite dimensions. The CWs contribute to the entropy of the system and thus decrease the surface tension. A correction for the effect of CWs on the surface tension is presented. The effect of the different EoSs is relatively small because by a fortuitous coincidence their predictions are similar in the relevant range of critical cluster sizes. The difference of the DGT predictions to the classical nucleation theory computations is important but not decisive. Of the effects investigated, the most pronounced is the suppression of CWs which causes a sizable decrease of the predicted nucleation rates. The major difference between experimental nucleation rate data and theoretical predictions remains in the temperature dependence. For normal alkanes, this discrepancy is much stronger than observed, e.g., for water. Theoretical corrections developed here have a minor influence on the temperature dependency. We provide empirical equations correcting the predicted nucleation rates to values comparable with experiments.

Solubility of Carbon Dioxide in Poly(oxymethylene) Dimethyl Ethers

Experimental data on the solubility of carbon dioxide (CO2) in poly(oxymethylene) dimethyl ethers (CH3O(CH2O)nCH3, OMEn) are presented for OME2, OME3, and OME4. The total pressure was measured as a function of the liquid phase composition at 313.15 and 353.15 K for pressures up to 4.3 MPa in a high-pressure view-cell. Henry’s law constants of CO2 in OME2, OME3, and OME4 are determined. They are similar for all studied OME and depend strongly on the temperature. The experimental data are modeled by the original perturbed-chain statistical associating fluid theory equation of state. As a basis, pure component models for OME were developed based on literature data on the liquid density and vapor pressure. The solubility of CO2 in OME is successfully described using a group contribution scheme. The results show that OME are interesting candidates as physical absorbents for CO2.

Vapour–liquid interfacial properties of n-alkanes

The vapour–liquid interfacial properties of linear alkanes (n-hexane, n-heptane, n-octane, n-nonane, and n-decane) were studied via the square gradient theory (SGT) and by molecular dynamics (MD) simulations. The objectives were the determination of interfacial density profiles, surface tensions, molecular orientations, and conformations via order parameters and radii of gyration, the self-diffusion coefficients and free energy profiles. The Soave-Redlich-Kwong (SRK) and Perturbed-Chain SAFT (PC-SAFT) equations of state (EoSs) were combined with SGT to correlate experimental surface tensions and to predict density profiles. SGT-EoSs and MD interfacial density profiles and interface thicknesses are very similar, especially at low reduced temperatures. MD simulations revealed that not only does the density change throughout the interface but also the average molecular orientation and conformation change. The interface can be roughly divided into three main regions: around the Gibbs dividing surface the molecules, on average, lie at the interface; and in the two regions close to the bulk phases they favour a non-parallel orientation. With respect to the self-diffusion coefficients, three different zones were also observed: close to the bulk phases, the diffusivity is a nonlinear function of the local density, whereas in the middle zone it is linear and coincides with the quasi-linear portion of the density profile. Free energy profiles were obtained via umbrella sampling technique, showing an increase of energy at the interfacial region. These profiles show a similar behaviour as the density profiles.

Characterization and Modeling of the Liquid Phase of Deep Eutectic Solvents Based on Fatty Acids/Alcohols and Choline Chloride

The solid–liquid equilibria phase diagrams of eight eutectic systems formed by choline chloride and fatty acids, or fatty alcohols, were measured to characterize the nonideality of the liquid phase of these systems, commonly reported in the literature as examples of type III deep eutectic solvents (DESs), and to evaluate the best modeling approaches to their description. Most of these systems are shown to present only slight deviations from ideal behavior, resulting from a fine balance of the hydrogen bonding between the hydroxyl/carboxylic groups with the chloride anion and the interactions present in the pure compounds. The phase diagrams measured were modeled with an associative equation of state (EoS) and a gE model. As an EoS, the perturbed-chain statistical associating fluid theory (PC-SAFT) was used, and this model was able to accurately describe the experimental data and to provide reliable estimates of the eutectic points using just a single binary temperature-dependent interaction parameter that often correlates with the acid/alcohol chain length. The performance of PC-SAFT was further compared with the gE model, a non-random two-liquid model (NRTL), and was found to provide a better description of the experimental data, especially for the more nonideal systems. Ultimately, the data gathered, and the molecular modeling, allowed the discussion of the behavior of fatty acids or fatty alcohols as hydrogen bond donors in choline chloride-based DESs.

Isothermal Vapor–Liquid Equilibria for Binary Mixtures of Methyl Nonafluorobutyl Ether + Acetone, Cyclopentyl Methyl Ether, Ethyl Acetate, n-Heptane, Methanol, and Toluene

Measurements of vapor–liquid equilibrium data in binary systems methyl nonafluorobutyl ether + solvent (acetone, cyclopentyl methyl ether, ethyl acetate, n-heptane, methanol, and toluene) were carried out at constant temperature (328.15 or 318.15 K) by means of a vapor–liquid equilibrium circulation still. In the most cases, the acquired data satisfied thermodynamic consistency tests. The obtained vapor–liquid equilibrium data were (successfully) correlated by two principally different thermodynamic models: the nonrandom two-liquid equation for the excess Gibbs energy, and the perturbed-chain statistical associating fluid theory equation of state. The latter model was tested also for its predictive capabilities and was found not to be suitable for reliable predictions in the studied binary systems, although it may correctly predict the azeotropic behavior of some systems.