(CO2 + 2‐propanol) mixture as a foaming agent for polystyrene: A simple thermodynamic model for the high pressure VLE‐phase diagrams taking into account the foam vitrification

The equation of state model developed by Lacombe and Sanchez (J Phys Chem 1976, 80, 2352) is used in the form proposed later by Sanchez and Stone (Polymer Blends, Vol. 1: Formulation, 2000; Chapter 2) to correlate experimental vapor‐liquid equilibrium (VLE) data for the three binaries and the ternary systems. Experimental data from the binary systems carbon dioxide‐isopropyl alcohol (CO₂‐IPrOH), isopropyl alcohol‐polystyrene (IPrOH‐PS), and carbon dioxide‐polystyrene (CO₂‐PS) are used to calculate VLE properties for the ternary system CO₂‐IPrOH‐PS. Two‐dimensional VLE‐phase diagrams were calculated and used to describe from a thermodynamic point of view the pressure, volume, and temperature values that characterize a thermoplastic foam evolution process, from the extruder to the foaming die. For different initial mixture CO₂ + IPrOH concentrations, pressure reduction produces liquid foaming until the vitrification curve arrests the final foam volume expansion. The dependence of the vitreous transition with the system CO₂ + IPrOH concentration while foaming is represented by the Chow (Macromolecules 1980, 13, 362) equation. The calculation procedure is proposed as a design tool to reduce the amount of experimental data usually needed as a requirement previous to the design stage. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci 104: 2663–2671, 2007     

多元渗透维里方程通式的表达：双水相系统的液液平衡计算

提出了基于三元系修正Ｐｉｔｚｅｒ模型的多元渗透维里方程通式，并应用于双水相系统液液平衡性质的关联和预测，用汽液平衡数据关联模型参数，预测了聚乙二醇／硫酸镁双水相系统的液液平衡；用汽液平衡数据和尽可能少的液液平衡数据关联模型参数。同时预测了焦点或不含电解质的ＰＥＧ／葡萄糖双水相系统的液液平衡和ＫＣｌ电解质在ＰＥＧ／ＤＥＸ系统中的分配系数。计算结果表明，模型有较好的预测功能。     

Thermodynamic assessment within the Zr–B–C–O quaternary system

Thermodynamic modeling of Zr–B–C–O quaternary system is conducted within the CALPHAD framework by employing data obtained from first-principle calculations and literature. The lower order binary B–O is assessed in this work by estimating the thermodynamic properties of stable solid phases of B₂O₃ and B₆O and by estimating the gas and liquid phases. First-principle calculations, in conjunction with special quasirandom structure were used to predict enthalpies of mixing for the ternary solid-solution phase of FCC-Zr(C, O). The calculated results were used to optimize the model parameters pertaining to the cubic phase, which is described by a two-sublattice model. The modeled Zr–C–O ternary phase diagrams calculated at 1923 and 2273 K under ambient pressure and 4 Pa, respectively, are in agreement with experimental phase diagrams.     

甲胺与水多元系常压汽液平衡研究

用新型泵式沸点仪测定了常压下一甲胺-二甲胺-三甲胺-水四元系在不同液相组成时的沸点;由所测的甲胺-水二元系数据,用过量自由焓Q函数间接法推算了与之平衡的汽相组成,再用最小二乘法求出甲胺与水间二元体系的液相活度系数模型参数：甲胺与甲胺间二元体系的液相活度系数模型参数则通过拟合它们与水构成的三元系获取;由所得的最佳二元系参数用于该体系四元系汽液相平衡数据的预测,将计算的泡点与实验测得的沸点作了比较,结果表明两者吻合良好。     

甲基二氯硅烷+甲基三氯硅烷+二甲基二氯硅烷+苯多元系常压汽液平衡研究

卤代硅烷的相平衡数据为硅烷生产所需,而这方面的研究又较缺乏,尤其是甲基乙烯基二氯硅烷生产中所需的汽液相平衡数据尚未见报道.今用新型泵式沸点仪测定了常压(101.325 kPa)下甲基二氯硅烷 甲基三氯硅烷 二甲基二氯硅烷 苯四元系及其四个三元体系和六个二元体系在不同液相组成时的泡点.由所测的二元系数据,用过量自由焓Q函数间接法推算了与之平衡的汽相组成.再用最小二乘法求出二元体系的最佳配偶液相活度系数模型参数.所得的六组最佳二元系Wilson模型参数符合热力学一致性,并用于该体系三元和四元系汽液相平衡数据的预测,将计算的泡点与实验测得的泡点作了比较,其拟合精度良好,关联结果令人满意,硅烷二元系、多元系的热力学模型及VLE数据可为该体系的分离设计提供必要的理论依据.     

DME-CO2-CH3OH和DME-CO2-C2H5OH体系的高压汽液相平衡研究

In this study, the Gibbs-Duhem equation was applied to make the thermodynamic consistency test and thermodynamic model estimation for systems of CO2-DME （dimethyl ether）, DME-CH3OH, CO2-CH3OH and DME-C2H5OH systems on the basis of the vapor-liquid equilibrium （VLE） experimental data in published reports. And the NRTL binary interaction parameters of the systems mentioned above were regressed by the VLE data and were subjected to a thermodynamic consistency test because the study showed that PR-NRTL model combination was appropriate for the four systems mentioned above. The regressed binary interaction parameters were used to estimate the VLE for DME-CO2-CH3OH at temperatures of 313.15K and 333.15K, and the estimated result was coincident with the experimental data. On the basis of the predicted VLE data for systems of DME-CO2-CH3OH and DME-CO2-C2H5OH, the VLE behaviors of the two systems were studied by the phase diagrams of these two ternary systems, with the forms of both the two dimensional and three dimensional phase diagrams, respectively.     

Solubility measurement and prediction of phase equilibria in the quaternary system LiCl + NaCl + KCl + H_2O and ternary subsystem LiCl+ NaCl + H_2O at 288.15 K

Using isothermal dissolution method, the phase equilibrium relationship in quaternary system LiCl + NaCl + KCl+ H_2O and the ternary subsystem LiCl + NaCl + H_2O at 288.15 K were investigated. Each phase diagram of two systems was drawn. The phase diagram of LiCl + NaCl + H_2O system contains two solid phase regions of crystallization LiCl·2H_2O and NaCl. In the phase diagram of LiCl + NaCl + KCl + H_2O system, there are three crystallization regions: LiCl·2H_2O, NaCl and KCl respectively. In this paper, the solubilities of phase equilibria in two systems were calculated by Pitzer's model at 288.15 K. The predicted phase diagrams generally agree with the experimental phase diagrams.     

Enhanced solubility of hydrogen and carbon monoxide in propane‐ and propylene‐expanded liquids

Conventional propylene hydroformylation occurs in a gas‐expanded liquid phase. Reliable knowledge of the phase equilibria of such systems, including the solubilities of CO and H₂ in propylene‐expanded solvents, is essential for rational process design and development. Herein, we report the vapor–liquid equilibrium (VLE) data of the following ternary systems involving CO, H₂, propane, propylene, toluene and NX‐795 at temperatures from 70 to 90°C and pressures up to 1.5 MPa: propane/H₂/toluene, propane/CO/toluene, propylene/H₂/toluene, propylene/CO/toluene, propane/H₂/NX‐795, propane/CO/NX‐795, propylene/H₂/NX‐795 and propylene/CO/NX‐795. The solubilities of H₂ and CO in either propane‐expanded or propylene‐expanded phases are observed to be greater than those in the neat organic solvents, by as high as 78% at 70°C and 1.5 MPa. By modeling the vapor and the liquid phases as pseudo‐binary systems, the Peng‐Robinson equation of state (PR‐EoS) with van der Waals’ mixing rules and binary interaction parameters is shown to satisfactorily predict the experimental VLE data. © 2017 American Institute of Chemical Engineers AIChE J, 64: 970–980, 2018     

三元体系Me2+-NH4+-SO42--H2O相平衡和溶液物化性质

用等温溶解平衡法,测定了Me2 -NH4 -SO42--H2O三元体系298K的相平衡及饱和溶液的物化性质,绘制了溶解度平衡相图.结果表明:在Me2 -NH4 -SO42--H2O体系中,均存在三个纯盐结晶区、三条溶解度饱和曲线及两个共饱和点.测定了Me2 -NH4 -SO42--H2O体系中饱和溶液的密度和pH,并根据经验公式进行了该体系的密度计算.物化性质研究结果表明,Mn2 -NH4 -SO42--H2O体系中密度的计算值与测定值误差较大,Zn2 -NH4 -SO42--H2O体系中密度的测定值与计算值的相对误差小于1.0%.本研究结果为含Fe2 ,Mn2 和Zn2 溶液的复盐沉淀深度净化的研究提供了理论指导,同时给四元体系的研究奠定了基础.     

PMMA‐modified divinylester/styrene resins: Phase diagrams and morphologies

Binary and ternary experimental cloud‐point curves (CPCs) for systems formulated with a low molar mass synthesized divinylester (DVE) resin, styrene (St), and poly(methyl methacrylate) (PMMA) were determined. The CPCs results were analyzed with the Flory–Huggins (F‐H) thermodynamic model taking into account the polydispersity of the DVE and PMMA components, to calculate the different binary interaction parameters and their temperature dependences. The St‐DVE system is miscible in all the composition range and down to the crystallization temperature of the St; therefore, the interaction parameter expression reported for a higher molar mass DVE was adapted. The interaction parameters obtained were used to calculate the phase diagrams of the St‐PMMA and the DVE‐PMMA binary systems and that of the St‐DVE‐PMMA ternary system at three different temperatures. Quasiternary phase diagrams show liquid–liquid partial miscibility of the St‐PMMA and DVE‐PMMA pairs. At room temperature, the St‐DVE‐PMMA system is miscible at all compositions. Final morphologies of PMMA‐modified cured St‐DVE materials were generated by polymerization‐induced phase separation (PIPS) mechanism from initial homogeneous mixtures. SEM and TEM micrographs were obtained to analyze the generated final morphologies, which showed a direct correlation with the initial miscibility of the system. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 100: 4539–4549, 2006     

Application of UNIFAC models for prediction of vapor-liquid and liquid-liquid equilibria relevant to separation and purification processes of crude biodiesel fuel

Vapor-liquid equilibrium (VLE) of the methanol-biodiesel (BDF)/glycerin binary system and liquid-liquid equilibrium (LLE) of the water-BDF binary system and the methanol-BDF-glycerin and methanol-water-BDF ternary systems were predicted using several UNIFAC models: the latest original UNIFAC model, Kikic’s model, Fornari’s model, Dortmund-UNIFAC model, and LLE-UNIFAC model. The former VLE and latter LLE are used to design methanol recovery processes and separation and purification processes of crude BDF, respectively. Unfortunately, LLE data on the water-BDF binary system was not available. Instead, solubility of water in fatty acid methyl ester (one of the BDF constituents) was measured. By examining the deviation between predicted and experimental results, we determined which of the UNIFAC models was more useful for the design of those processes as follows: either the original UNIFAC model or Dortmund-UNIFAC model should be used for the methanol recovery process. The LLE-UNIFAC model and Dortmund-UNIFAC model were more useful for the recovery and water-washing processes of crude BDF and purification process of water-washed BDF, respectively.     

Isobaric vapor–liquid equilibria for mixtures of tetrahydrofuran, 2-propanol, and 2,2,4-trimethylpentane at 101.3 kPa

Vapor–liquid equilibrium (VLE) at 101.3 kPa have been determined for a ternary system (tetrahydofuran + 2-propanol + 2,2,4-trimethylpentane) and its constituent binary systems (tetrahydrofuran + 2-propanol, tetrahydrofuran + 2,2,4-trimethylpentane, and 2-propanol + 2,2,4-trimethylpentane). The activity coefficients of liquid mixtures were calculated from the modified Raoult's law. Thermodynamic consistency tests were performed for all VLE data. The VLE data of the binary mixtures and ternary mixtures were correlated using the Margules, Wilson, NRTL, and UNIQUAC activity-coefficient models. The models with their best-fitted interaction parameters of the binary systems were used to predict the ternary vapor–liquid equilibrium. All VLE data are also used to calculate the reduced excess molar Gibbs free energy g^E/RT and the deviations in the boiling point ΔT. The calculated quantities of g^E/RT and ΔT were fitted to variable-degree polynomials in terms of liquid composition.     

Liquid–liquid phase separation in polysulfone/polyethersulfone/N‐methyl‐2‐ pyrrolidone/water quaternary system

To construct a phase diagram of the polysulfone (PSF)/polyethersulfone (PES)/N‐methyl‐2‐pyrrolidone (NMP)/water quaternary system, cloud point measurements were carried out by a titration method. The miscible region in the PSF/PES/NMP/water quaternary system was narrow compared to the PSF/NMP/water and PES/NMP/water ternary systems. The binary interaction parameters between PSF and PES were estimated by water sorption experiments. The calculated phase diagram based on the Flory–Huggins theory fit the experimental cloud points well. In addition to the usual polymer–liquid phase separation, polymer–polymer phase separation, which resulted in a PSF‐rich phase and a PES‐rich phase, was observed with the addition of a small amount of nonsolvent. The boundary separating these two modes of phase separation could be well described and predicted from the calculated phase diagrams with the estimated binary interaction parameters of the components. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 74: 2113–2123, 1999     

甲基二氯硅烷-甲基三氯硅烷-苯三元体系等压汽液平衡

利用新型泵式沸点仪,在101.3 kPa下测定了甲基二氯硅烷-甲基三氯硅烷-苯体系以及3个二元体系在不同液相组成时的沸点;对所测的二元系数据,采用间接法由TPx推算了与之平衡的汽相组成,再用最小二乘法分别求出了二元体系的Wilson、NRTL、Margules和van Laar 4种模型的最佳配偶液相活度系数模型参数,并由二元最佳配偶参数推算了甲基二氯硅烷-甲基三氯硅烷-苯三元体系的气相组成和泡点温度,与实验测得的温度值进行了比较,其拟合精度良好,关联结果令人满意.     

盐效分离作用理论预测

研究了盐效分离基本原理,采用选择性溶剂化模型,利用定标粒子理论计算盐在含水体系中的标准摩尔迁移自由能。提出了将迁移自由能与相平衡中盐效应的大小结合起来,用迁移自由能理论解释相平衡中的盐效应。文中计算了盐在6种含水体系的标准摩尔迁移自由能,并与其盐效应进行了对比,研究发现在含水体系中盐效应随盐的标准摩尔迁移自由能增大而增大,因此在盐效分离过程中可以采用标准摩尔迁移自由能模型选择有效的盐作分离剂。     

Experimental investigation of the LiAlSi2O6‐MgSiO3 and LiAlSi2O6‐CaMgSi2O6 isopleths at 1 atm

The phase diagrams of the LiAlSi₂O₆‐MgSiO₃ and LiAlSi₂O₆‐CaMgSi₂O₆ isopleths were experimentally investigated at 1 atm using the quenching method and differential scanning calorimetry and the phases produced were characterized with the help of X‐ray diffraction and electron probe microanalysis. With the help of thermodynamic optimization, the phase diagrams of both systems were more accurately reported. No detectable solubility of Li₂O in diopside and enstatite was found. However, both systems are not simple binary eutectic systems because their phase equilibria are somewhat complex due to the presence of some β‐spodumene solid solution. In the β‐spodumene solid solution, no notable solubility of MgO and CaO was detected; evidence of significant solubility of SiO₂ was confirmed.     

Calculations of complex phase equilibrium by equal‐area method

The equal‐area (EA) method is studied with respect to its applicability to a wide range of phase equilibrium scenarios for pure fluids and binary mixtures. The study covers vapor‐liquid equilibrium (VLE), liquid–liquid equilibrium (LLE), solid‐liquid equilibrium (SLE) and their crossover transitions. The thermodynamic models studied include equation of state, activity coefficient and solid solubility models and their combinations. The performance of the EA method for chain molecules, at very low temperature and nearby the critical point is also investigated. We conclude that the EA method is very reliable and efficient and has a number of advantages over the conventional method. Finally, we apply the EA method to the regression of the model parameters to demonstrate its attractive application. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

甲基二氯硅烷-甲基乙烯基二氯硅烷-甲苯三元体系等压汽液平衡

Vapor-liquid euilibrium (VLE) for a ternary system of Methyldichlorosilane methylvinyldichlorosilane toluene and constituent binary systems were measured at 101.3kPa using a new type of magnetical pump-ebulliometer,The equilibrium conpositions of the vapor phase of binary systems were calculated indirectly from the total pressure-temperature-liquid composition(pTx).The experimental data were correlated with the Wilson and NRTL(non-random two liquid )equations.The parameters of the Wilson moldel were employed to predict the ternary VLE data .The calculated boiling points were in good agreement with the experimental ones.     

甲醇-乙酸-丙酸多元体系汽液平衡

用新型泵式沸点仪测定了在100kPa下甲醇-乙酸、甲醇-丙酸、乙酸-丙酸3个二元体系以及甲醇-乙酸-丙酸三元系在不同液相组成时的沸点,并用间接法T-p-x(温度、压力和液相摩尔分数)推算了3个二元体系的汽相平衡组成。3个二元体系活度系数分别用Wilson模型、NRTL模型、Margules模型和van Laar模型进行关联,用最小二乘法求出了它们的液相活度系数模型参数,同时,用这些模型参数来计算它们的汽相摩尔分数。所得的液相活度系数来计算3个二元体系的过量吉布斯自由能函数,且所研究的所有体系中各组分之间不存在共沸点。用3个二元体系Wilson模型参数对所测的三元体系数据进行关联,建立该系统汽液平衡的热力学模型并计算平衡时的汽相摩尔分数和泡点温度。由面积积分法检验这些模型参数计算的3个二元体系相平衡数据,得到很好的热力学一致性。     

On the predictive capabilities of CPA for applications in the chemical industry: Multicomponent mixtures containing methyl-methacrylate,dimethyl-ether or acetic acid

The predictive performance of the CPA (Cubic-Plus-Association) equation of state for applications relevant to the chemical industry is illustrated in this work. Three such applications inspired by industrial requests/interest are illustrated here, all of which involve aqueous multicomponent mixtures exhibiting vapor–liquid (VLE) and/or liquid–liquid (LLE) equilibrium. The first two cases include mixtures of methyl-methacrylate with acetone or methanol and dimethyl-ether with ethanol, respectively. In these two cases, the classical form of CPA is used. The third case involves aqueous mixtures with acetic acid, esters, ethers and alcohols, and in this case for water–acetic acid the CPA-Huron Vidal (CPA-HV) version of the model is used. For the latter binary mixture, new CPA-HV binary parameter sets are estimated using, among others, data for activity coefficients at infinite dilutions. The modeling approach is similar in all three cases, i.e. the binary parameters are solely fitted to binary data and thus all multicomponent calculations are considered predictions.It is shown that CPA correlations for binary systems are excellent in all cases using temperature independent parameters except for the acetic acid–water system for which different parameter sets at different temperatures can be recommended. Even with the use of CPA-HV mixing rules, modeling of the acetic acid–water system with few interaction parameters remains a challenging task. Excellent simultaneous VLE and LLE correlation is obtained for complex systems such as aqueous mixtures with ethers and esters. The multicomponent results are, with a few exceptions, very satisfactory, especially for the vapor–liquid equilibrium cases. For the demanding aqueous acetic acid–water containing systems, one parameter set is recommended at the end for modeling ternary or multicomponent mixtures containing acetic acid and water.