Perturbed-chain Statistical Associating Fluid Theory Parameters Research Articles

Predicting Solvation Free Energies from the Minnesota Solvation Database Using Classical Density Functional Theory Based on the PC-SAFT Equation of State.

We critically assess the capabilities of classical density functional theory (DFT) based on the perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state to predict the solvation free energies of small molecules in various hydrocarbon solvents. We compare DFT results with experimental data from the Minnesota solvation database and utilize statistical methods to analyze the accuracy of our approach, as well as its weaknesses. The mean absolute error of the solvation free energies is 3.7 kJ mol-1 for n-alkane solvents, ranging from pentane to hexadecane, with 473 solute-solvent systems. For solvents consisting of cyclic hydrocarbons (cyclohexane, benzene, toluene, and ethylbenzene) with 245 solute-solvent systems, we report a slightly larger mean absolute error of 4.2 kJ mol-1. We identify three possible sources of errors: (i) the neglect of solute-solvent and solvent-solvent Coulomb interactions, which limits the applicability of PC-SAFT DFT to nonpolar and weakly polar molecules; (ii) the solute's Lennard-Jones parameters supplied by the general AMBER force field, which are not parametrized toward solvation free energies; and (iii) the application of the Lorentz-Berthelot combining rules to the dispersive interactions between a segment of the PC-SAFT solvent and a Lennard-Jones interaction site of the solute. The approach is more accurate than standard implementations of phenomenological models in common chemistry software packages, which exhibit mean absolute errors larger than 9.12 kJ mol-1, even though newer phenomenological models achieve a mean absolute error of about 2 kJ mol-1. PC-SAFT DFT is more computationally efficient than state of the art explicit molecular simulations in combination with free energy perturbation methods. It is predictive with respect to solvation free energies, i.e., the input for the model is the (element-specific) molecular force field, the solute configuration from molecular dynamics simulations, and the (substance-specific) PC-SAFT parameters. The PC-SAFT parametrization uses pure-component data and does not require experimental solvation free energies. The PC-SAFT equation of state, without applying a DFT formalism, can also be used to calculate solvation free energies, provided that the PC-SAFT parameters for the solute are available. A large number of substances was recently parametrized by members of our group (Esper, T.; Bauer, G.; Rehner, P.; Gross, J. Ind. Eng. Chem. Res. 2023, 62), which enables a comparison to the DFT approach for 103 substances. Accurate results are obtained from the PC-SAFT equation of state with an MAE below 2.51 kJ mol-1. The DFT approach does not require PC-SAFT parameters for the solute and can be applied to all solutes that can be represented by the molecular force field.

Can Pure Predictions of Activity Coefficients from PC-SAFT Assist Drug-Polymer Compatibility Screening?

The bioavailability of poorly water-soluble active pharmaceutical ingredients (APIs) can be improved via the formulation of an amorphous solid dispersion (ASD), where the API is incorporated into a suitable polymeric carrier. Optimal carriers that exhibit good compatibility (i.e., solubility and miscibility) with given APIs are typically identified through experimental means, which are routinely labor- and cost-inefficient. Therefore, the perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state, a popular thermodynamic model in pharmaceutical applications, is examined in terms of its performance regarding the computational pure prediction of API-polymer compatibility based on activity coefficients (API fusion properties were taken from experiments) without any binary interaction parameters fitted to API-polymer experimental data (that is, kij = 0 in all cases). This kind of prediction does not need any experimental binary information and has been underreported in the literature so far, as the routine modeling strategy used in the majority of the existing PC-SAFT applications to ASDs comprised the use of nonzero kij values. The predictive performance of PC-SAFT was systematically and thoroughly evaluated against reliable experimental data for almost 40 API-polymer combinations. We also examined the effect of different sets of PC-SAFT parameters for APIs on compatibility predictions. Quantitatively, the total average error calculated over all systems was approximately 50% in the weight fraction solubility of APIs in polymers, regardless of the specific API parametrization. The magnitude of the error for individual systems was found to vary significantly from one system to another. Interestingly, the poorest results were obtained for systems with self-associating polymers such as poly(vinyl alcohol). Such polymers can form intramolecular hydrogen bonds, which are not accounted for in the PC-SAFT variant routinely applied to ASDs (i.e., that used in this work). However, the qualitative ranking of polymers with respect to their compatibility with a given API was reasonably predicted in many cases. It was also predicted correctly that some polymers always have better compatibility with the APIs than others. Finally, possible future routes to improve the cost-performance ratio of PC-SAFT in terms of parametrization are discussed.

Modeling cobalt (III) acetylacetonate and iron (III) acetylacetonate solubilities in supercritical CO2 with PC-SAFT based on experimentally-determined solid–liquid equilibria in organic solvents

A methodology to model the solubilities of metal complexes in supercritical CO2 is indispensable for effectively designing the supercritical CO2-based deposition method. Herein, the solubility of two metal acetylacetonates (acac), Co(acac)3 and Fe(acac)3, in supercritical CO2 was modeled based on the perturbed-chain statistical associating fluid theory (PC-SAFT) and experimentally-determined solid–liquid equilibria in organic solvents. This modeling approach is more predictive than conventional cubic-type equations of state or semi-empirical correlation models. The pure-component parameters of PC-SAFT for metal acetylacetonates are obtained by fitting the obtained solubility data to four typical organic solvents (toluene, acetone, 2-butanone, and ethyl acetate). By applying these PC-SAFT parameters, the model satisfactorily reproduced the solubilities of the metal complexes in supercritical CO2, particularly under low-temperature conditions even with the kij (binary interaction parameter) set to 0 in the combining rule. The isobaric solubilities can also be described by PC-SAFT by generalizing the temperature dependence of kij.

Predicting PC-SAFT pure-component parameters by machine learning using a molecular fingerprint as key input

In this work, a machine learning (ML)-approach was developed to predict pure-component parameters for the Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) for non-associating molecules using a deep neural network. Extended-connectivity fingerprints (ECFP) were used as key inputs for the neural network to achieve flexible and easily available non-experimental representations of a chemical molecule. A detailed analysis of bit collisions during the ECFP generation was performed to obtain the optimal ECFP initial bit lengths creating possible inputs for neural networks to be trained. Three ECFP initial bit lengths (210, 212, 214) were used to train three neural networks. The results show that the neural networks using ECFP initial bit lengths of 212 and 214 achieve high prediction accuracy (AARD < 5 %) for original (literature) PC-SAFT pure-component parameters. Moreover, correlations for homologous series of PC-SAFT pure-component parameters were adapted by the neural networks trained. Further validation was performed comparing calculations of physical properties (vapor pressure, saturation liquid density) using ML-predicted PC-SAFT pure-component parameters to experimental data. Being a predictive ML-approach, the neural networks of this work can be used in early process synthesis to obtain PC-SAFT pure-component parameters without experimental data.

Estimating the solubility of salsalate in supercritical CO2 via PC-SAFT modeling using its experimental solubility data in organic solvents

In this work, a methodology was studied for estimating the solubility of salsalate, an active pharmaceutical ingredient of non-steroidal anti-inflammatory drugs, in supercritical CO2 (scCO2) using the experimental data of its solubility in organic solvents and perturbed-chain statistical associating fluid theory (PC-SAFT)-based modeling. This type of modeling is more predictive than conventional semi-empirical correlation models and cubic-type equations of state. The PC-SAFT pure-component parameters of salsalate were determined by fitting its solubility data in organic solvents, which were newly measured in this work. The PC-SAFT parameters obtained thus were then applied to estimate the solubility of salsalate in scCO2. This approach can adequately reproduce the experimental values of the isothermal and isobaric solubilities of salsalate in scCO2 over a wide range of temperatures and pressures even when the binary interaction parameter (kij) is set to zero.

Investigation of carbon dioxide solubility in various families of deep eutectic solvents by the PC-SAFT EoS

Having been introduced in 2003, Deep Eutectic Solvents (DESs) make up a most recent category of green solvents. Due to their unique characteristics, and also their tunable physical properties, DESs have shown high potentials for use in various applications. One of the investigated applications is CO2 absorption. The thermodynamic modeling of CO2 solubility in DESs has been pursued by a number of researchers to estimate the capacity and capability of DESs for such tasks. Among the advanced equations of state (EoSs), the Perturbed Chain-Statistical Associating Fluid Theory (PC-SAFT) is a well-known EoS. In this study, the performance of the PC-SAFT EoS for estimating CO2 solubility in various DESs, within wide ranges of temperatures and pressures, was investigated. A large data bank, including 2542 CO2 solubility data in 109 various-natured DESs was developed and used for this study. This is currently the most comprehensive study in the open literature on CO2 solubility in DESs using an EoS. For modeling, the DES was considered as a pseudo-component with a 2B association scheme. CO2 was considered as both an inert and a 2B-component and the results of each association scheme were compared. Considering the very challenging task of modeling a complex hydrogen bonding mixture with gases, the results of AARD% being lower than 10% for both of the investigated association schemes of CO2, showed that PC-SAFT is a suitable model for estimating CO2 solubilities in various DESs. Also, by proposing generalized correlations to predict the PC-SAFT parameters, covering different families of DESs, the developed model provides a global technique to estimate CO2 solubilities in new and upcoming DESs, avoiding the necessity of further experimental work. This can be most valuable for screening and feasibility studies to select potential DESs from the innumerable options available.

Modeling the Vapor-Liquid equilibria of binary and ternary systems comprising associating and non-Associating compounds by using Perturbed-Chain Statistical association fluid Theory. Part I

Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) was implemented for modeling the vapor–liquid equilibrium of binary and ternary systems of carbon dioxide (CO2) + fatty oil, CO2 + ionic liquids (IL), CO2 + perfluoroalkanes, CO2 + HFE-449mec-f, CO2 + water + IL, CO2 + thiophene, and alcohols + thiophene at temperatures between 298.15 and 543.15 K and at pressures up to 200 bar. ILs studied in this work contain 1-octyl-3-methylimidazolium hexafluorophosphate [OMIM][PF6] and N-methyl-2-hydroxyethylammonium propionate [m-2HEA][Pr]. The PC-SAFT pure-component parameters were fitted to the experimental density and vapor pressure data of pure-components. For ILs, only liquid density data were used to obtain pure-IL PC-SAFT parameters, because of the negligible values of the vapor pressure of ILs. Temperature-dependent binary interaction parameters of the binary and ternary systems were fitted to vapor–liquid equilibrium data taken from experimental literature data. These parameters were then used to describe the VLE of other binary and ternary systems. Correlation results of the PC-SAFT were found to be in qualitative agreement with the available experimental data and improved the modeling accuracy of past models in the literature. The overall value of the absolute average relative deviation in pressure (ARDP) and vapor-phase mole fraction (ARDy) of 12.05% and 6.13%, respectively, reveals the goodness of the developed models for modeling the phase behavior of other associating or non-associating mixtures with the same parameters reported in this work.

An effective asphaltene precipitation modeling approach using PC-SAFT with detailed fluid descriptions for gas injection conditions

Fluid characterization plays a prominent role in identifying the properties of the crude oil, particularly the equilibrium conditions. It gains more importance, especially in problematic crudes that, for instance, contain precipitating constituents, like Asphaltene. Aside from the pressure depletion, enhanced Asphaltene precipitation during the miscible gas injection causes many problems to the production system. Therefore, the employed characterization procedure must be able to predict the Asphaltene instability conditions effectively. Recently a class of solution techniques using the perturbed chain statistical associating fluid theory (PC-SAFT) and dealing with Asphaltene phase as a liquid-like phase have gained attractions in literature. However, such techniques could not consider the effect of the injected gas composition and structure, because they lumped all the heavy gas components in a single pseudo-component. Hence, in this study, a detailed characterization method is proposed that can account for the heavier gas components. The modeling approach in this work, assumes the liquid-like Asphaltene framework and PC-SAFT for phase behavior calculations. In this work, the three PC-SAFT parameters for Asphaltene and Aromatic + Resin are simultaneously regressed with gas injection, to match the saturation and Asphaltene onset pressures with experimental data. The outcomes of this study are compared with the experimental data and previous characterization models. The results prove the ability of the detailed characterization approach for predicting the bubble point and Asphaltene onset pressures. It not only leads to lower estimation errors in most cases but also can capture the actual trend of bubble and Asphaltene onset curves, which makes it even more reliable for the prediction of instability conditions.

Physical stability of hydroxypropyl methylcellulose-based amorphous solid dispersions: Experimental and computational study.

The preparation of an amorphous solid dispersion (ASD) is a promising strategy for improving the poor oral bioavailability of many active pharmaceutical ingredients (APIs). However, poor predictability of ASD long-term physical stability remains a prevalent problem. The purpose of this study was to evaluate and compare the predictive performance of selected models concerning solid-liquid equilibrium (SLE) curve and glass-transition temperature (Tg) line modeling of ibuprofen (IBU) in cellulosic polymers (i.e., hydroxypropyl methylcellulose (HPMC) and hydroxypropyl methylcellulose acetate succinate (HPMCAS)). For SLE curve modeling, an empiricalanalyticalapproach(Kyeremateng et al., 2014)and the Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) equation of state (EOS) were chosen. Due to the unavailability of PC-SAFT parameters for both polymers, an approximation procedure for parametrization was applied. The Gordon-Taylor equation and Kwei equation were considered for Tg line determination. The impact of various computational set-ups (e.g., model parametrization or extrapolation length) on IBU solubility prediction at storage conditions was thoroughly investigated, assessed and confronted with the results from an 18-month physical stability study. IBU developed stable 20wt% API content ASDs with both HPMC and HPMCAS.The extrapolation behavior and subsequent ASD thermodynamic stability prediction at storage conditions deduced from the aforementioned models weresignificantly different. Overall, the PC-SAFT EOS predicted higher IBU solubility in both polymers and, thus, a lower recrystallization tendency when compared to the empirical analytical approach. At higherIBU concentrations, liquid-liquid demixing inIBU-polymer systems was predicted by the PC-SAFT EOS, which was in qualitative disagreement with experimental observation.

Evaluation and improvement of the predictive capabilities of PC-SAFT for the liquid–liquid phase boundaries in the solution polymerisation process

A systematic investigation was undertaken to determine the predictive capabilities of the perturbed-chain statistical associating fluid theory (PC-SAFT) when modelling (solvent + linear low-density polyethylene) phase behaviour. Two different branching concepts were compared [Gross et al. Ind. Eng. Chem. Res. 42, 1266; Dominik & Chapman, Polymer 38, 10836], and the advantages of group-contribution method (GCM)-estimated binary interaction parameters (BIPs) [Peters et al. Fluid Phase Equilib. 358, 137] were evaluated. Dominik and Chapman's branching concept leads to slightly better predictions than that of Gross et al., and slight improvements are obtained when using GCM-estimated BIPs. A simplified BIP-estimation method was proposed for Dominik and Chapman's concept; this method reparameterises their branching concept and uses a quantitative structure–property relationship to estimate LLDPE–solvent BIPs using only pure-component PC-SAFT parameters. The modification leads to a slight increase in predictive capacity of solution process systems, and simpler correlation of multicomponent systems.

Predicting the solubilities of metal acetylacetonates in supercritical CO2: Thermodynamic approach using PC-SAFT

Solubilities of metal precursors in supercritical carbon dioxide (scCO2) are needed to effectively design the scCO2-based deposition method. Herein, a method for predicting the solubilities of metal acetylacetonate (acac) precursors in scCO2 was developed using the perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state. Three PC-SAFT pure-component parameters viz., the segment diameter, segment number, and dispersion energy, for two metal acetylacetonates (Cr(acac)3 and Cu(acac)2) were determined by adjusting their values to the measured solubilities in organic solvents. The PC-SAFT parameters of Cr(acac)3 and Cu(acac)2 were then applied to predict the experimentally determined metal precursor solubilities in scCO2 from the literature. The PC-SAFT predictions accurately described the experimental solubilities in scCO2 over a wide range of pressures and temperatures even if the binary interaction parameter kij was set to 0. The isobaric solubilities in scCO2 were also calculated with the generalized kij values, which provided a successful PC-SAFT description.

Solubility of Pharmaceutical Ingredients in Natural Edible Oils.

Natural edible oils (NEOs) are common excipients for lipid-based formulations. Many of them are complex mixtures comprising hundreds of different triglycerides (TGs). One major challenge in developing lipid-based formulations is the variety in NEO compositions affecting the solubility of active pharmaceutical ingredients. In this work, solubilities of indomethacin (IND), ibuprofen (IBU), and fenofibrate (FFB) in soybean oil and in coconut oil were measured via differential scanning calorimetry, high-performance liquid chromatography, and Raman spectroscopy. Furthermore, this work proposes an approach that mimics NEOs using one key TG and models the API solubilities in these NEOs based on perturbed-chain statistical associating fluid theory (PC-SAFT). Key TGs were determined using the 1,2,3-random hypothesis, and PC-SAFT parameters were estimated via a group-contribution method. Using the proposed approach, the solubility of IBU and FFB was modeled in soybean oil and coconut oil. Furthermore, the solubilities of five more APIs (IND, cinnarizine, naproxen, griseofulvin, and felodipine) were modeled in soybean oil. All modeling results were found in very good agreement with the experimental data. The influence of different NEO kinds on API solubility was examined by comparing FFB and IBU solubilities in soybean oil and refined coconut oil. PC-SAFT was thus found to allow assessing the batch-to-batch consistency of NEO batches in silico.

Interfacial structure and differential capacitance of ionic liquid/graphite interface: A perturbed-chain SAFT density functional theory study

The perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state (EoS) was combined with the electrostatic free energy from the mean spherical approximation (MSA) theory, and applied to represent densities of pure imidazolium ionic liquids (ILs) with anion [BF4]−. The PC-SAFT parameters of cations were linearized with their molar mass and obtained by simultaneously fitting the model predictions to experimental densities of some ILs. The PC-SAFT-MSA model provides accurate correlations and predictions of densities comparing with experimental data. Then a classical density functional theory (DFT) was developed based on PC-SAFT-MSA. The DFT model was applied to explore the structure and differential capacitance of the electrical double layer (EDL) in ILs on graphite. The model predicts similar density profiles for both cation and anion on a neutral surface, and layered structure with alternating layers of cations and anions on a charged surface. The charge inversion phenomena were also studied based on ion distributions. We further studied the effects of the alkyl chain length, temperature and non-electrostatic solid-fluid interactions on the differential capacitance of the EDL. The model provides bell-shaped differential capacitance curves. The peak positions of differential capacitance curves shift toward positive potentials as ions size asymmetry increases in agreement with previous experiments and simulations studies. The maximum capacitance decreases with increasing alkyl chain length as well as increasing temperature.

The role of molecular interactions on Michaelis constants of α-chymotrypsin catalyzed peptide hydrolyses

In this work, the effects of co-solvent and pressure on Michaelis constants at ambient temperature were analyzed for the enzymatic peptide hydrolyses of L-phenylalanine-p-nitroanilide (HPNA) and of N-succinyl-L-phenylalanine-p-nitroanilide (SPNA). These two substrates resemble each other in their molecular structure. That is, at the position of SPNA’s succinyl-group (S), HPNA possesses a hydrogen atom (H). Two co-solvents were considered: trimethylamine N-oxide and dimethyl sulfoxide. The thermodynamic model Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) was used to predict the activity of HPNA and SPNA under different reaction conditions regarding solvent composition and pressure. The PC-SAFT parameters (pure-component parameters and one binary parameter between substrate and solvent) were fitted to solubility data of HPNA in different solvents (water, ethanol, ethyl acetate, dimethyl sulfoxide), which were measured in this work at 30 °C and 1 bar. The resulting PC-SAFT predicted Michaelis constants were validated by experimental literature data. Results show that pressure decreased the Michaelis constants of both reactions, HPNA hydrolysis and SPNA hydrolysis. In spite of that, co-solvent effects on the Michaelis constants were predicted to be contrary for the two hydrolysis reactions. For the hydrolysis of HPNA, the co-solvents under investigation decreased the Michaelis constant while the co-solvents increased the Michaelis constant for the hydrolysis of SPNA. These PC-SAFT predictions were in qualitative agreement with the experimental literature data. This shows that molecular interactions are the key to understand the effects of co-solvents on Michaelis constants for the considered reactions. Applying the thermodynamic model PC-SAFT allowed predicting the observed combined effects of co-solvent and pressure on enzymatic reaction kinetics, which opens the door for solvent design of enzymatic reactions in the future.

Experimental High-Temperature, High-Pressure Density Measurement and Perturbed-Chain Statistical Associating Fluid Theory Modeling of Dimethyl Sulfoxide, Isoamyl Acetate, and Benzyl Alcohol

Experimental high-temperature, high-pressure (HTHP) density of three solvents including dimethyl sulfoxide, benzyl alcohol, and isoamyl acetate was measured at temperatures of 293.15–473.15 K and pressures up to 35–37.5 MPa. The density was measured with an Anton Paar density meter (DMA HP) at 20 K and 2.5 MPa intervals. The calibration fluids were water and benzene. The combined expanded uncertainty of density taking into account the device specification and the impurities of the materials was 1 kg·m–3 (0.95 level of confidence). The experimental density data were correlated with the Tait and new modified Tait equations. The thermal expansion coefficient (αp) and isothermal compressibility (κT) were calculated with the new modified Tait equations. Moreover, the perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state was used to model the density data at HTHP. In most cases, the PC-SAFT parameters are obtained from saturated vapor pressure and liquid phase density; however, these ...

Vapor Liquid Equilibria of 1-Ethyl-3-methylimidazolium Triflate (C2mimTfO) and n-Alkyl Alcohol Mixtures.

The isobaric vapor liquid equilibria (VLE) of different binary mixtures of the ionic liquid (IL) 1-ethyl-3-methylimidazolium trifluoromethanesulfonate (C2mimTfO) with the n-alkyl alcohols, methanol, ethanol, propan-1-ol, and butan-1-ol, are studied at the pressures of p = 500, 700, and 1000 mbar, covering a composition range 0.25-0.35 ≤ x(solvent) ≤ 1.0. Complementarily, the experimental results are compared with calculations by the perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state (EoS). For deriving suitable PC-SAFT parameters, experimental liquid densities were determined for the neat IL C2mimTfO and its longer homologues, 1-butyl-3-methylimidazolium trifluoromethanesulfonate (C4mimTfO) and 1-hexyl-3-methylimidazolium trifluoromethanesulfonate (C6mimTfO), in a temperature range of 288.15 K ≤ T ≤ 363.15 K (C2mimTfO) and 293.15 K ≤ T ≤ 363.15 K (C4mimTfO and C6mimTfO), respectively. The PC-SAFT EoS is found to be suitable for describing the VLEs under study with good accuracy (AARDVLE ≤ 0.4%).

Thermodynamic Properties of Amines under High Temperature and Pressure: Experimental Results Correlating with a New Modified Tait-like Equation and PC-SAFT

New experimental densities for diethylamine (DEA), dibutylamine (DBA), and tributylamine (TBA) at 11 isotherms in the range of 293.15–473.15 K and 18 isobars up to 37.5 MPa are reported. PρT measurements (176 experimental data points) have been performed using a high-pressure vibrating-tube densimeter. These data were correlated with a new modified Tait-like equation considering standard deviations of less than 2 × 10–4 g·cm–3, and then isothermal compressibility (κT) and thermal expansion coefficient (αP) were calculated. This study is supported by the results of modeling using the perturbed-chain statistical associating fluid theory (PC-SAFT). The parameters of PC-SAFT equation of state (EoS), for pure solvents, were rigorously determined by fitting the equation to the liquid PρT experimental data. In this study, the correlations, which are based on minimizing the total objective functions (density, pressure, and temperature) simultaneously, were developed to estimate the PC-SAFT parameters. The model r...

Assessment of carbon dioxide solubility in ionic liquid/toluene/water systems by extended PR and PC-SAFT EOSs: Carbon capture implication

Recently, there has been a growing interest in CO2 capture using ionic liquids (ILs). To determine the CO2 absorption potential of ILs and their selectivity in the presence of other gaseous components in the mixture, the solubility of ILs at various operating conditions and the influence of impurities/additives such as water and toluene should be evaluated. Carbon capture capacity of the ILs can be examined using various methods such as experiments, thermodynamic approaches including Equations of State (EOSs), and molecular-based modeling. In this research work, the extended Peng–Robinson (PR) and Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) EOSs are utilized to assess the solubility and selectivity of CO2 in ILs through comparing the modeling results with experimental data. PC-SAFT and PR parameters are determined by employing the experimental density data. Modeling results reveal that the solubility values estimated by the PC-SAFT due to considering the association effects have a lower deviation (or a better performance) than PR EOS based on the magnitudes of Absolute Average Deviation (AAD %). The AAD (%) for [bmim][BF4], [bmim][PF6], [bmim][Tf2N], [hmim][Tf2N], [hmim][FAP], and [hmim][FAP] are calculated using PR EOS and PC-SAFT EOS, which are 2–5.7% and 3–7.5%, respectively. Furthermore, ternary systems of CO2 + ILs + water and CO2 + ILs + toluene are modeled to determine the effect of water and toluene on the gas solubility in ILs and viscosity of ILs with PC-SAFT EOS. Based on the results, low concentrations of water (0.1 wt%) have a negligible influence on the CO2 solubility in ILs. However, with increasing the water concentration, the solubility of water reduces significantly. On the other hand, the viscosity of ILs is reduced with increasing the water concentration. Viscosity reduction in the hydrophilic ILs is significant. It seems promising to add water up to 10 wt% to hydrophilic ILs, since a decrease in the viscosity to an amount close to the viscosity of water and a decrease in solubility by 9% are experienced. Finally, the selectivity of [hmim][Tf2N] in separation of CO2 from mixtures containing H2S, SO2, CH4, and H2 are reported. Based on the results, [hmim][Tf2N] is not appropriate for separation of CO2 from streams with a high concentration of H2S and SO2 gases.

Vapor-liquid equilibrium of metal dialkyldithiophosphates: An analysis with the statistical associating fluid theory

The vapor pressure osmometry (VPO) of metal dialkyldithiophospate (MDDPs) association in simple hydrocarbon solvents [1] has been analyzed using the Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) [2]. From this analysis, we obtain a fluid-state free energy theory of MDDPs, including zinc dialkyldithiophosphates (ZnDDPs), an important class of multifunctional lubricant additives present in most automotive and commercial vehicle formulations marketed worldwide [3]. As expected, the PC-SAFT parameters of the MDDP compounds are found to vary smoothly with molecular size, metal atom type (Zn, Cd, Hg, Pb), and alkyl chain structure. Analysis of benzene/MDDP VPO isotherms with PC-SAFT suggests that selected MDDP compounds cross-associate with benzene.

Measuring and modeling thermodynamic properties of aqueous lysozyme and BSA solutions

A novel approach towards modeling proteins in aqueous solutions by applying perturbed-chain statistical associating fluid theory (PC-SAFT) is proposed in this work. Lysozyme and bovine serum albumin (BSA) were chosen as model proteins due to a vast database available in literature. However, the huge majority of these literature data had been measured at certain ionic strengths, which is disadvantageous in order to derive pure-component parameters for proteins. Thus, in a first step within this work osmotic coefficients of dialyzed lysozyme and of dialyzed BSA in pure water were measured at 298.15 K. The data were very different for dialyzed and non-dialyzed solutions and further showed a strong dependence on pH and ionic strength. In a second step, the pure-component parameters of lysozyme and BSA were adjusted to the measured osmotic coefficients and to solution densities of dialyzed lysozyme or dialyzed BSA. PC-SAFT explicitly takes into account the complex association behavior between protein and water as well as among the proteins. Therefore, the number of protein association sites of one protein was determined from the sum of association sites of the single amino-acid constituents of a protein available from previous work (Ind. Eng. Chem. Res 50 (2011) 141–151). Similarly, the two PC-SAFT parameters “segment number” and “segment diameter” of a protein were summed or averaged from the single amino-acid constituents. This approach allowed modeling densities and osmotic coefficients of protein solutions with reasonable accuracy compared to experimental data.