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.     

Liquid-liquid equilibria of polymer solutions: Applicability of extended Redlich-Kister expansion

We developed a simple and improved expression for the Helmholtz energy of mixing which uses a Taylor series of an exponential function based on extending the Redlich-Kister expansion. This model incorporates the chain-length dependence of polymers and specific interactions such as hydrogen bonds. The proposed model can accurately predict most phase diagrams of various binary polymer solutions including upper critical solution temperature (UCST), lower critical solution temperature (LSCT), both UCST and LCST, and closed miscibility loops. Our model fits experimental data of the complex phase behavior of polymer solutions well.     

Residence time model for assessing liquid-liquid extraction systems

A model based on the residence time of solvent in the extraction system may be used to describe the dynamic operation of a continuous liquid-liquid extractor. It is proposed that optimum performance occurs when the extract exiting from the contactor is near equilibrium with the solution being extracted. This approach was tested on two commercially available continuous extraction systems. The difference in their performance was found to be related to the level of agitation of the two contactor vessels: the stirred system was approximately six times more efficient than the simple column continuous extractor. The stirred system achieved a near equilibrium analyte distribution between the solvent and sample and could be described accurately in terms of residence time theory. This was in marked contrast to its unmixed counterpart where the analyte distribution between solvent and sample reached 14% of its equilibrium value during its residence in the contactor. The effect of dead volume of solvent within the extraction assembly on the extraction rate was also apparent; its main effect was to delay the extraction process.     

Molecular thermodynamics approach for polymer-polymer miscibility

We extended the previous lattice model for polymer solution systems to binary polymer blend systems. Based on Müller’s Monte-Carlo simulation data for symmetric system (r₁ = 32 and r₂ = 32), the energy of mixing is correlated as a function of temperature and composition using an empirical expression. In addition, we introduce new universal functions which reflect the characteristics of polymer-polymer miscibility behaviors. In associated blend systems, specific interactions between polymer segments are considered by using a secondary lattice. Using only one or two adjustable parameters, the proposed model satisfactory correlates the experimental data of real polymer blend systems with greater accuracy than those of other models.     

Influence of temperature on the (liquid + liquid) equilibria of {methanol + benzene + hexane} ternary system

In order to show the influence of temperature on the liquid-liquid equilibria (LLE) of {methanol (1) + benzene (2) + hexane (3)} ternary system, equilibrium data at T = (278.15, 283.15, and 293.15) K are reported. The effect of the temperature on liquid-liquid equilibrium is determined and discussed. Ternary system is available from the literature at T = 298 K. All chemicals were quantified by gas chromatography using a thermal conductivity detector. The solubility data for methanol + hexane and the upper critical temperature (UCST) at 308.3 K was reported. The tie line data for the ternary system were satisfactorily correlated by the Othmer and Tobias method, and the plait point coordinates for the three temperatures were estimated. Experimental data for the ternary system are compared with values calculated by the NRTL and UNIQUAC equations, and predicted by means of the UNIFAC group contribution method. It is found that the UNIQUAC and NRTL models provide similar good correlations of the equilibrium data at these three temperatures. Finally, the UNIFAC model predicts an immiscibility region larger than the experimental observed. Distribution coefficients were also analysed through distribution curves.     

Correlation of liquid-liquid equilibria in aqueous and organic systems using a modified Wilson model

A modified Wilson model is extended to involve three ternary parameters per ternary to allow the model to represent ternary liquid-liquid equilibria accurately. The calculated results for 19 ternary systems obtained from the present modification are compared with the previous results obtained from other modified Wilson models. The model is further extended to treat quaternary liquid-liquid equilibria for six aqueous systems and one nonaqueous system using binary, ternary, and quaternary parameters. Mutual solubilities for 19 systems over a wide temperature range are represented with the model having temperature-dependent energy parameters.     

Phase equilibria of (water-carboxylic acid-diethyl maleate) ternary liquid systems at 298.15 K

Liquid-liquid equilibrium (LLE) data for the ternary systems of (water-formic acid-diethyl maleate), (water-acetic acid-diethyl maleate), (water-propionic acid-diethyl maleate), (water-butyric acid-diethyl maleate), and (water-valeric acid-diethyl maleate) were investigated at 298.15 K and atmospheric pressure. Complete phase diagrams were obtained by determining solubility and the tie-line data. The tie-line data were compared with the results predicted by the UNIFAC and the modified UNIFAC (Dortmund) methods and correlated by means of UNIQUAC model. The reliability of the experimental tie-line data was confirmed by using the Othmer-Tobias correlation. Distribution coefficients and selectivity were evaluated for the immiscibility region.     

(Liquid + liquid) equilibria of ternary and quaternary systems with two hydrocarbons, an alcohol, and water at 303.15 K. Systems containing cyclohexane, benzene, ethanol, and water

Tie-line data for the water, ethanol, and cyclohexane [{w₁H₂O + w₂C₂H₅OH + (1−w₁−w₂)C₆H₁₂}] ternary system, where w is the mass fraction, was investigated at T=303.15 K. A quaternary system containing these three compounds and benzene {w₁C₂H₅OH + w₂C₆H₆ + w₃C₆H₁₂ + (1−w₁−w₂−w₃)H₂O} was also studied at the same temperature, while data on its other two partially miscible ternary systems were taken from the literature [the fourth {w₁C₂H₅OH + w₂C₆H₆ + (1−w₁−w₂)C₆H₁₂} is not partially miscible]. From our experimental results we conclude that this quaternary system presents a very small water tolerance and that phase separation could produce a considerable loss of C₂H₅OH drawn into the aqueous phase. On the other hand, the results also show that the aqueous phase generally contains a higher concentration of C₆H₆ than of C₆H₁₂. A comparison with other similar quaternary systems investigated in our laboratory was also made. The ternary experimental results were correlated with the UNIQUAC equation, and predicted with the UNIFAC group contribution method. As previously, the equilibrium data of the three ternary systems (including those taken from the literature) were used to determine interaction parameters for the UNIQUAC equation. These parameters were then averaged in order to predict equilibrium data of this quaternary system. The UNIFAC method was also used with the same purpose. The UNIQUAC equation appears to be more accurate than the UNIFAC method for this ternary system. However, this last model is slightly better for the quaternary system, as can be seen from the values of both residuals.     

Molecular simulation of the high-pressure phase equilibria of binary atomic fluid mixtures using the exponential-6 intermolecular potential

Molecular simulation results using the exponential-6 intermolecular potential are reported for the phase behaviour of the atomic binary mixtures of neon+xenon, helium+neon, helium+argon and helium+xenon. These binary mixtures exhibit both vapour–liquid and liquid–liquid phase equilibria up to very high pressures. Comparison with experiment indicates good overall agreement. The results indicate that the exponential-6 intermolecular potential is a useful generic potential for molecular simulation.     

Monte Carlo simulation of a lattice model for ternary polymer mixtures

Monte Carlo studies of symmetrical polymer mixturesAB, modelled by selfavoiding walks withN _A =N _B =N steps on a simple cubic lattice, are presented for arbitrary concentrations of vacancies _v in the range from _v =0.2 to _v =0.8 and chain lengthsN64. We obtained the phase diagrams and the equation of state for three choices of the ratio / _AB ( being the energy between monomers of the same kind, _AB being the energy between different monomers). Flory-Huggins theory provides only a qualitative understanding of these results. If the equation of state is fitted with an effective Flory-Huggins parameter _eff , the latter turns out to be strongly dependent on both concentration and temperature.Contributed paper delivered at the Tagung der Deutschen Physikalischen Gesellschaft, Fachausschuß Polymerphysik, Berlin, March 30–April 3, 1987.     

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.     

Development of a model for the rational design of molecular imprinted polymer: Computational approach for combined molecular dynamics/quantum mechanics calculations

A new rational approach for the preparation of molecularly imprinted polymer (MIP) based on the combination of molecular dynamics (MD) simulations and quantum mechanics (QM) calculations is described in this work. Before performing molecular modeling, a virtual library of functional monomers was created containing forty frequently used monomers. The MD simulations were first conducted to screen the top three monomers from virtual library in each porogen-acetonitrile, chloroform and carbon tetrachloride. QM simulations were then performed with an aim to select the optimum monomer and progen solvent in which the QM simulations were carried out; the monomers giving the highest binding energies were chosen as the candidate to prepare MIP in its corresponding solvent. The acetochlor, a widely used herbicide, was chosen as the target analyte. According to the theoretical calculation results, the MIP with acetochlor as template was prepared by emulsion polymerization method using N,N-methylene bisacrylamide (MBAAM) as functional monomer and divinylbenzene (DVB) as cross-linker in chloroform. The synthesized MIP was then tested by equilibrium-adsorption method, and the MIP demonstrated high removal efficiency to the acetochlor. Mulliken charge distribution and ¹H NMR spectroscopy of the synthesized MIP provided insight on the nature of recognition during the imprinting process probing the governing interactions for selective binding site formation at a molecular level. We think the computer simulation method first proposed in this paper is a novel and reliable method for the design and synthesis of MIP.     

Phase behavior and a modified Kwei equation for ternary polymer blends containing stereoregular PMMA

Previously, poly(methyl methacrylate) (PMMA) was found to be almost immiscible with poly(vinyl acetate) (PVAc) regardless of tacticity of PMMA and casting solvent. Poly(vinyl phenol) (PVPh) was found successful previously in making immiscible atactic PMMA/PVAc miscible. In this investigation, tacticity effect of PMMA on a ternary composed of PMMA, PVAc and PVPh was studied. Isotactic PMMA ternary was shown to be miscible in all the studied compositions on the basis of single T_g observation. However, syndiotactic PMMA ternary demonstrated immiscibility at ca. 25% PVPh and miscibility was observed at higher PVPh concentrations. A modified Kwei equation based on the binary interaction parameters was proposed to describe the experimental T_g of the miscible ternary almost quantitatively.     

Modification of the NRTL model for ternary and quaternary liquid-liquid equilibrium calculations

The original NRTL model is modified for the correlation of ternary liquid-liquid equilibria. The ternary expression of the modified NRTL model includes three additional ternary parameters and the ternary terms vanish when a ternary system degenerates to a binary. The ability of the modified NRTL model has been evaluated in the calculations of ternary vapor-liquid-liquid equilibria and quaternary liquid-liquid equilibria.     

Correlation and prediction of liquid-liquid distribution coefficients in aqueous systems using a modified Wilson model

A modified Wilson model is tested for its ability to correlate and predict distribution coefficients in two representative systems: 1-butanol-water and cyclohexanewater. The model is fitted to ternary equilibrium data for various solutes in these systems using a procedure involving minimization of the least-squares distance between calculated and experimental logarithmic distribution ratios. In addition, benzene-water, hexane-water, and cyclohexane-water distribution coefficients for infinitely diluted liquid solutes are predicted using only binary system information. All computations involve using both van der Waals and molar volumes as structural parameters to account for the geometry of the molecules studied. Satisfactory representations of experimental distribution ratios and fairly accurate distribution coefficients at infinite dilution are obtained for both systems. However, in a number of cyclohexane-water systems, miscibilities of constituent binary mixtures are poorly predicted from ternary system information when van der Waals volumes are used. Replacement of van der Waals volumes by molar volumes has little influence on the fit, but significant improvement is observed for the prediction of both binary miscibility properties and for distribution coefficients at infinite dilution in all the solvent-water systems considered.Presentation to First International Symposium on Solubility Phenomena, University of Western Ontario, London, Ontario, August 21–23, 1984.     

(Liquid + liquid) equilibria of the quaternary system methanol + isooctane + cyclohexane + benzene at T = 303.15 K

Tie line data of the ternary system {methanol + isooctane + cyclohexane} were obtained at T = 303.15 K. A quaternary system containing these three compounds and benzene was also studied at the same temperature, while data for {methanol + benzene + cyclohexane} and {methanol + benzene + isooctane} were taken from literature. In order to obtain the binodal surface of the quaternary system, four quaternary sectional planes with several cyclohexane/isooctane ratios were studied. The distribution of benzene between both phases was also analysed. Ternary experimental results were correlated with the UNIQUAC and NRTL equations and compared with predictions using the UNIFAC group contribution method.     

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.     

On the thermodynamics of partially miscible liquid binary systems

Isobaric coexistence curves of two liquid phases are predicted from the temperature and composition at the consolute point of binary solutions consisting of a hydrocarbon and the corresponding perfluorocarbon. Excess enthalpies obtained from the free volume theory ofFlory as well as from calorimetric measurements are used to account for the temperature dependence of theGibbs energy of mixing. The treatment is based on the extension of theFlory-Huggins model to nonathermal polymer solutions. Formal applicability to mixtures of molecules not largely differing in size is achieved by introducing generalized variables characterizing composition in place of volume fractions. Phase diagrams of following systems are predicted and compared with experimental results: methane+carbontetrafluoride,n-hexane+perfluoro-n-hexane,n-heptane+perfluoro-n-heptane, methylcyclohexane+perfluoromethyl-cyclohexane.

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Zur thermodynamik beschränkt mischbarer flüssiger zweistoffsysteme

Zusammenfassung Isobare Koexistenzkurven zweier flüssiger Phasen werden aus Temperatur und Zusammensetzung am kritischen Entmischungspunkt binärer Lösungen bestehend aus einem Kohlenwasserstoff und dem entsprechenden Perfluor-kohlenstoff vorausgesagt. Die Temperaturabhängigkeit derGibbs-Energie der Mischung wird mit Hilfe von Mischungsenthalpien, die sowohl der Freien Volumentheorie vonFlory als auch kalorimetrischen Messungen entstammen, berücksichtigt. Als Berechnungsgrundlage dient das auf nichtathermische Polymerlösungen erweiterteFlory-Huggins-Modell. Die Einführung verallgemeinerter Variablen zur Charakterisierung der Zusammensetzung an Stelle von Volumenbrüchen ermöglicht die formale Anwendbarkeit auf Mischungen von Molekülen mit wenig verschiedener Größe. Zustandsdiagramme folgender Mischsysteme werden vorausberechnet und mit experimentellen Ergebnissen verglichen: Methan+Tetrafluorkohlenstoff,n-Hexan+Perfluor-n-Hexan,n-Heptan+Perfluor-n-Heptan, Methylcyclohexan+Perfluormethylcyclohexan.