Classical and recent free-volume models for polymer solutions: A comparative evaluation

In this work, two “classical” (UNIFAC-FV, Entropic-FV) and two “recent” free-volume (FV) models (Kannan-FV, Freed-FV) are comparatively evaluated for polymer–solvent vapor–liquid equilibria including both aqueous and non-aqueous solutions. Moreover, some further developments are presented here to improve the performance of a recent model, the so-called Freed-FV. First, we propose a modification of the Freed-FV model accounting for the anomalous free-volume behavior of aqueous systems (unlike the other solvents, water has a lower free-volume percentage than polymers). The results predicted by the modified Freed-FV model for athermal and non-athermal polymer systems are compared to other “recent” and “classical” FV models, indicating an improvement for the modified Freed-FV model for aqueous polymer solutions. Second, for the original Freed-FV model, new UNIFAC group energy parameters are regressed for aqueous and alcohol solutions, based on the physical values of the van der Waals volume and surface areas for both FV-combinatorial and residual contributions. The prediction results of both “recent” and “classical” FV models using the new regressed energy parameters are significantly better, compared to using the classical UNIFAC parameters, for VLE of aqueous and alcohol polymer systems.     

Effect of temperature on acid–base equilibria in separation techniques. A review

Studies on the theoretical principles of acid–base equilibria are reviewed and the influence of temperature on secondary chemical equilibria within the context of separation techniques, in water and also in aqueous-organic solvent mixtures, is discussed. In order to define the relationships between the retention in liquid chromatography or the migration velocity in capillary electrophoresis and temperature, the main properties of acid–base equilibria have to be taken into account for both, the analytes and the conjugate pairs chosen to control the solution pH. The focus of this review is based on liquid–liquid extraction (LLE), liquid chromatography (LC) and capillary electrophoresis (CE), with emphasis on the use of temperature as a useful variable to modify selectivity on a predictable basis. Simpli?ed models were evaluated to achieve practical optimizations involving pH and temperature (in LLE and CE) as well as solvent composition in reversed-phase LC.     

Correlation of thermodynamic modeling and molecular simulations for liquid-liquid equilibrium of ternary polymer mixtures based on a phenomenological scaling method

In our previous study [S.Y. Oh, Y.C. Bae, J. Phys. Chem. B 114 (2010) 8948-8953], we presented a new method to predict liquid-liquid equilibria in ternary simple liquid mixtures by using a combination of a thermodynamic model and molecular simulations. As a continuation of that effort, we extend our previously developed method to ternary polymer systems. In the simulations, we used the dummy atoms to calculate the pair interaction energy values between the polymer segments and the solvent molecules. Furthermore, a thermodynamic model scaling concept is introduced to consider the chain length dependence of the energy parameters. This method was applied to ternary mixtures incorporating low to high molecular weight polymers. The method presented here well described the experimental observations using one or no adjustable parameters.     

Modelling of high-pressure phase equilibria using the Sako–Wu–Prausnitz equation of state: II. Vapour–liquid equilibria and liquid–liquid equilibria in polyolefin systems

Phase equilibria in binary and ternary polyolefin systems are calculated using the cubic equation of state proposed by Sako–Wu–Prausnitz (SWP). Calculations were done for high-pressure phase equilibria in ethylene/polyethylene (LDPE) systems and for liquid–liquid equilibria (LLE) in systems containing either high-density polyethylene or poly(ethylene-co-propylene). The calculations for the copolymer/solvent systems are compared with those using the SAFT EOS. The two equations of state can describe UCST, LCST as well as U-LCST behaviour with similar accuracy. Whereas, the binary interaction parameter is temperature-independent for SAFT, it is found to be a function of temperature for the SWP model. Moreover, the influence of an inert gas on the LCST of the polyethylene/hexane system is investigated using the SWP EOS. The polydispersity of the different polyethylenes is considered in the phase equilibrium calculations using pseudocomponents chosen by the moments of the experimental molecular weight distributions.     

Alkylsulfate-based ionic liquids to separate azeotropic mixtures

The knowledge of liquid–liquid equilibria (LLE) of the ternary systems (hexane or heptane + ethanol + 1-ethyl-3-methylimidazolium ethylsulfate (EMIM EtSO₄)) is essential for the separation of alkanes from their azeotropic mixtures with ethanol. The experimental LLE have been determined at 298.15 K and atmospheric pressure. Experimental LLE are correlated using NRTL equation. The solvent capacity of the IL is compared with others aiming to analyze the efficiency of these molten salts used as entrainers. The extraction processes with this IL are simulated using conventional software. A comparison of the alkylsulfate-based IL's ability for the extraction process, determined from the simulation results, is enclosed.     

Prediction of vapor–liquid and liquid–liquid equilibria for polymer systems: Comparison of activity coefficient models

A large number of equations of state and activity coefficient models capable of describing phase equilibria in polymer solutions are available today, but only a few of these models have been applied to different systems. It is therefore useful to investigate the performance of existing thermodynamic models for complex polymer solutions which have not yet been widely studied. The present work studies the application of several activity coefficient models [P.J. Flory, Principles of Polymer Chemistry, Cornell University Press, New York, NY, 1953; T. Oishi, J.M. Prausnitz, Estimation of solvent activities in polymer solutions using a group-contribution method, Ind. Eng. Chem. Process Design Dev. 17 (1978) 333; H.S. Elbro, A. Fredenslund, P. Rasmussen, A new simple equation for the prediction of solvent activities in polymer solutions, Macromolecules 23 (1990) 4707; G.M. Kontogeorgis, A. Fredenslund, D. Tassios, Simple activity coefficient model for the prediction of solvent activities in polymer solutions, Ind. Eng. Chem. Res. 32 (1993) 362; C. Chen, A segment-based local composition model for the Gibbs energy of polymer solutions, Fluid Phase Equilib. 83 (1993) 301; A. Vetere, Rules for predicting vapor–liquid equilibria of amorphous polymer solutions using a modified Flory–Huggins equation, Fluid Phase Equilib. 97 (1994) 43; C. Qian, S.J. Mumby, B.E. Eichinger, Phase diagrams of binary polymer solutions and blends, Macromolecules 24 (1991) 1655; Y.C. Bae, J.J. Shim, D.S. Soane, J.M. Prausnitz, Representation of vapor–liquid and liquid–liquid equilibria for binary systems containing polymers: applicability of an extended Flory–Huggins equation, J. Appl. Polym. Sci. 47 (1993) 1193; G. Bogdanic, J. Vidal, A segmental interaction model for liquid–liquid equilibrium calculations for polymer solutions, Fluid Phase Equilibria 173 (2000) 241] and activity coefficient from equations of state [F. Chen, A. Fredenslund, P. Rasmussen, Group-contribution Flory equation of state for vapor–liquid equilibria en mixtures with polymers, Ind. Eng. Chem. Res. 29 (1990) 875; M.S. High, R.P. Danner, Application of the group contribution lattice—fluids EOS to polymer solutions, AIChE J. 36 (1990) 1625]. The evaluation of these models was carried out both at infinite dilution and at finite concentrations and the results compared to experimental data. Furthermore, liquid–liquid equilibrium predictions for binary polymer solutions using six activity coefficient models are compared in this work. The parameters were estimated for all the models to achieve the best possible representation of the reported experimental equilibrium behavior.     

Bubble points of hydrogen chloride–water–isopropanol and hydrogen chloride–water–isopropanol–benzene systems and liquid–liquid equilibria of hydrogen chloride–water–benzene and hydrogen chloride–water–isopropanol–benzene systems

Bubble points of the HCl–water–isopropanol and the HCl–water–isopropanol–benzene systems and liquid–liquid equilibria (LLE) of the HCl–water–benzene and the HCl–water– isopropanol–benzene systems were measured at 25–85°C and 30–70°C, respectively. The electrolyte nonrandom two-liquid model proposed by Chen et al. [C.-C. Chen, H.I. Britt, J.F. Boston, L.B. Evans, AIChE J. 28 (1982) 588–596] can satisfactorily correlate bubble points and liquid–liquid equilibria of the present mixed-solvent electrolyte systems over the entire range of temperature and concentrations using only binary adjustable parameters.     

Liquid–liquid equilibrium in ternary ionic liquid systems by UNIFAC: New volume,surface area and interaction parameters. Part I

Ternary liquid–liquid equilibria (LLE) data in systems involving ionic liquids has been investigated by several years, mainly due to the innovative role of ionic liquids as extraction solvents. The thermodynamic modeling of these systems has been performed almost invariably with the well-known NRTL model. In recent years, the UNIQUAC model has also been used, with structural parameters for ionic liquids determined either by empirical correlations or, more recently, through quantum mechanics calculations. In this work, the structural group volume and area parameters for the group-contribution UNIFAC method have been calculated for six ionic liquids following the quantum mechanics approach. The Density Functional Theory (DFT) was used to optimize the molecular geometry and the Polarizable Continuum Method (PCM) was used to calculate the area and volume. The obtained parameters were used to correlate LLE data for twenty-four ternary systems, totalizing 169 tie-lines. New interaction parameters were also estimated between the solvent and ionic liquid functional groups. The results are very satisfactory, with root mean square deviations between experimental and calculated compositions about 1.6%.     

A simplified approach to vapor–liquid equilibria calculations with the group-contribution lattice-fluid equation of state

Equations of state that are based on the lattice-statistics approach use Guggenheim's quasi-chemical approximation to describe the non-randomness in the mixture due to the energetic interactions between the molecules. For ternary and higher-component systems the non-randomness expression is complex and requires an iterative calculation procedure. We have shown that the non-randomness parameters play a negligible role in the application of the GCLF-EoS model (based on the Panayiotou–Vera EoS) for predicting vapor–liquid equilibria. Omission of the non-randomness parameters from such calculations can significantly improve the computation efficiency. Binary, ternary, and quaternary vapor–liquid equilibria predictions were made including polystyrene, polyvinyl acetate, polyethylene, and polypropylene in polar and non-polar solvents to test the theory.     

Liquid + liquid equilibria for the quaternary systems of (water + acetic acid + mixed solvent) at 298.2 K and atmospheric pressure

Liquid–liquid equilibrium (LLE) data for the quaternary systems of [water + acetic acid + mixed solvent (dipropyl ether + diisopropyl ether)] were measured at 298.2 K and atmospheric pressure, using various compositions of mixed solvent. Binodal curves and tie-lines for the quaternary systems have been determined in order to investigate the effect of solvent mixture, dipropyl ether (DPE) and diisopropyl ether (IPE), on extracting acetic acid from aqueous solution. A comparison of the extracting capabilities of the mixed solvents was made with respect to distribution coefficients, separation factors, and solvent free selectivity bases. Reliability of the data was confirmed by using the Othmer–Tobias and Hand plots. The tie-lines were also correlated using the UNIFAC model. The average root-mean-square deviations between the observed and calculated mass fractions for the studied systems were in the range of 10–14%.     

The new experimental data and a new thermodynamic model based on group contribution for correlation liquid–liquid equilibria in aqueous two-phase systems of PEG and (K2HPO4 or Na2SO4)

The new experimental data of liquid–liquid equilibria for aqueous two-phase systems PEG–K₂HPO₄–water and PEG–Na₂SO₄–water are presented. The effects of pH and molecular weight of polyethylene glycol were investigated and the tie lines with binodal curves for both systems are shown. A new thermodynamic model based on group contribution has been proposed for studying the phase behavior of aqueous two-phase polymer–salt systems. The assumptions of NRTL-NRF model and the activity coefficient equation of UNIQUAC-NRF model have been used for the groups. In this new model, UNIFAC-NRF, the nonrandom state of groups were selected as a reference state. The binary interaction parameters were adjusted using the data of binary salt–water systems and the ternary systems were correlated with only six binary adjustable parameters. The Debye–Huckel equation based on Fowller–Guggenheim equation was used to calculate the long range electrostatic interaction of the ions. The UNIFAC-NRF model was applied to correlate the experimental data of aqueous two-phase systems: PEG–K₂HPO₄–water and PEG–Na₂SO₄–water for two different molecular weight of PEG at different pH. The results of the new model showed that it can be used to correlate the LLE in aqueous solution of polymer–salt very well.     

Liquid–liquid equilibria for {hexane + benzene + 1-ethyl-3-methylimidazolium ethylsulfate} at (298.2, 313.2 and 328.2) K

Liquid–liquid equilibria (LLE) for the ternary system {hexane + benzene + 1-ethyl-3-methylimidazolium ethylsulfate ([emim]C₂H₅SO₄)} have been measured at the temperatures (298.2, 313.2 and 328.2) K and atmospheric pressure. The reliability of the experimental data was tested using the Othmer–Tobias correlation. For the extractive effectiveness of the solvent, the distribution ratio and separation factor curves were plotted and compared with those of sulfolane. In addition, the LLE data were also correlated with UNIQUAC and NRTL models in a satisfactory manner.     

Application of the Perturbed-Chain SAFT equation of state to polar systems

The Perturbed-Chain SAFT (PC-SAFT) equation of state is applied to pure polar substances as well as to vapor–liquid and liquid–liquid equilibria of binary mixtures containing polar low-molecular substances and polar co-polymers. For these components, the polar version of the PC-SAFT model requires four pure-component parameters as well as the functional-group dipole moment. For each binary system, only one temperature-independent binary interaction k_ij is needed. Simple mixing and combining rules are adopted for mixtures with more than one polar component without using an additional binary interaction parameter. The ability of the model to accurately describe azeotropic and non-azeotropic vapor–liquid equilibria at low and at high pressures, as well as liquid–liquid equilibria is demonstrated for various systems containing polar components. Solvent systems like acetone–alkane mixtures and co-polymer systems like poly(ethylene-co-vinyl acetate)/solvent are discussed. The results for the low-molecular systems also show the predictive capabilities of the extended PC-SAFT model.     

An activity coefficient model for predicting salt effects on vapor–liquid equilibria of mixed solvent systems

In the present study, an activity coefficient model, based on the concept of local volume fractions and the Gibbs–Helmholtz relation, has been developed. Some modifications were made from Tan–Wilson model (1987) and TK–Wilson model (1975) to represent activity coefficients in mixed solvent–electrolyte systems. The proposed model contains two groups of binary interaction parameters. One group for solvent–solvent interaction parameters corresponds to that given by the TK–Wilson model (1975) in salt-free systems. The other group of salt–solvent interaction parameters can be calculated either from vapor pressure or bubble temperature data in binary salt–solvent systems. It is shown that the present model can also be used to describe liquid–liquid equilibria. No ternary parameter is required to predict the salt effects on the vapor–liquid equilibria (VLE) of mixed solvent systems. By examining 643 sets of VLE data, the calculated results show that the prediction by the present model is as good as that by the Tan–Wilson model (1987), with an overall mean deviation of vapor phase composition of 1.76% and that of the bubble temperature of 0.74 K.     

Liquid-liquid equilibrium in ternary ionic liquid systems by UNIFAC: New volume, surface area and interaction parameters. Part II

Ionic liquids are potential solvents for liquid extraction processes; thermodynamic modeling of liquid-liquid equilibrium (LLE) data is essential for the optimization and operation of these processes. Therefore, ternary LLE data in systems involving ionic liquids have been investigated by several years. In most of the cases, the thermodynamic modeling of these systems has been made using the NRTL model; in some cases, the UNIQUAC model has also been used. The structural parameters of UNIQUAC for ionic liquids have been determined either by empirical correlations or, more recently, through quantum mechanics calculation. This work is a continuation of a recent paper, in which the structural group volume and area parameters for the group-contribution UNIFAC method have been calculated for five ionic liquids following the quantum mechanics approach. In order to optimize the molecular geometry and to calculate the area and volume, the Density Functional Theory (DFT) and the Polarizable Continuum Method (PCM) were used, respectively. The obtained parameters were used to correlate LLE data for fifteen ternary systems, totalizing 155 tie-lines. New interaction parameters were also estimated between the solvent and the ionic liquid functional groups. The results are very satisfactory, with root mean square deviations 0.0037 between experimental and calculated equilibrium mole fractions.     

Liquid–liquid equilibrium data for binary perfluoroalkane (C6 and C8) + n-alkane systems

This study aims to make detailed measurements of the solubility data for perfluoroalkane + n-alkane systems. Using a laser-scattering technique developed in our laboratory, we determined the liquid–liquid equilibria (LLE) for three binary mixtures: perfluorohexane + n-hexane, perfluorohexane + n-octane, and perfluorooctane + n-octane. The experimental LLE data were represented by the NRTL equation. In addition, the activity coefficients obtained from the experimental LLE data were compared with those obtained from the vapor–liquid equilibrium (VLE) data.     

(Liquid + liquid) equilibria of binary polymer solutions using a free-volume UNIQUAC-NRF model

In this work, a modified free-volume (FV) model based on the UNIQUAC-Nonrandom factor (UNIQUAC-NRF) model developed by Haghtalab and Asadollahi was proposed. While the combinatorial part of the proposed model for activity coefficient takes the same form as that of the entropic free-volume (entropic-FV) model, the residual part is similar to that of the UNIQUAC-NRF model. The proposed model, i.e., the FV-UNIQUAC-NRF model overcomes the main shortcoming of the original UNIQUAC-NRF model in predicting the lower critical solution temperature (LCST) for polymer solutions. The appearance of the LCST is believed to be attributed to the existence of the free volume differences between polymer and solvent molecules. Thus, the models without considering such differences fail to predict the LCST behavior of polymer solutions. The proposed model was applied to correlate the experimental data of (liquid + liquid) equilibria (LLE) for a number of binary polymer solutions at various temperatures. The values for the binary characteristic energy parameters for the proposed model and the FV-UNIQUAC model along with their average relative deviations from the experimental data were reported. It should be stated that the binary polymer solutions studied in this work were considered as monodisperse. The results obtained from the FV-UNIQUAC-NRF model were compared with those obtained from the FV-UNIQUAC model. The results of the proposed model show that the FV-UNIQUAC-NRF model can accurately correlate the experimental data for LLE of polymer solutions studied in this work. Also the error produced from the FV-UNIQUAC-NRF model show the slightly better accuracy in comparison with that from the FV-UNIQUAC model. The clear advantage of the proposed model, contrary to the original UNIQUAC-NRF model, is its capability in predicting the LCST for binary polymer solutions.     

Group contribution method for the swelling behavior of thermo‐responsive hydrogels

A group contribution method is introduced to describe the swelling behavior of thermo‐sensitive hydrogel systems. The accuracy of group contribution calculations is strongly dependent on the choice of thermodynamic model. Therefore, we revise the modified double lattice (MDL) model and develop a new expression for the interaction energy parameter using the association theory of Sanchez to take into account complex polymer/solvent mixing. The net Helmholtz energy for a hydrogel is established by combining the revised MDL model and modified Flory–Rehner elastic model. Group parameters are generated by fitting to experimental swelling data from both homopolymer and copolymer gel systems. The effect of salt on the volume phase transition is modeled by introducing an additional salt‐specific parameter to investigate various stimuli‐response swelling behavior. Calculated swelling equilibria using the new group contribution method shows excellent agreement with experimental data and various stimuli‐response volume phase transitions. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017 , 55, 455–463