Temperature-dependent Interaction Parameters Research Articles

Thermodynamic property calculations with the universal mixing rule for EoS/ GE models: Results with the Peng–Robinson EoS and a UNIFAC model

The universal mixing rule (UMR), which incorporates an activity coefficient model in a cubic equation of state (EoS), and is applicable to all type of system asymmetries up to solvent/polymer ones, has been recently developed in our laboratory [Voutsas et al., Ind. Eng. Chem. Res. 43 (2004) 6238]. The original UNIFAC model with temperature-independent interaction parameters was used in the original publication, which leads, however, to unsatisfactory VLE predictions at high temperatures and poor heats of mixing predictions. In this study the UMR is applied by coupling the translated and modified Peng–Robinson (t-mPR) EoS with an original UNIFAC-type model that utilizes linearly temperature-dependent interaction parameters, eliminating, thus, the aforementioned weaknesses. The performance of the resulting EoS/ G E model, referred to as UMR-PRU, utilizing the available UNIFAC interaction parameters, as well as some parameters developed here for gas involving pairs, is evaluated in the prediction and, when necessary, correlation/prediction, of various thermodynamic properties, i.e. VLE, LLE, VLLE, SGE and heats of mixing. The results indicate that the new model represents a unique, simple and reliable tool for thermodynamic property calculations for systems of various degrees of non-ideality and asymmetry, including polymer solutions.

Prediction of Liquid−Liquid Equilibrium in the System Furfural + Heavy Neutral Distillate Lubricating Oil

In the lubricating oil manufacturing process, the aromatic content of these products is reduced by solvent extraction. In this work, a thermodynamic model is developed to simulate the properties of these mixtures when liquid−liquid equilibrium (LLE) is established with a suitable solvent. The mixtures involved in the extraction process (feed, raffinates, and extracts) are considered to be a mixture of three types of components: saturates (S), aromatics (A), and polars (P). Pseudo-components were characterized by two properties: the average boiling point obtained from the distillation curve and the specific gravity. LLE was described by means of the nonrandom two-liquid (NRTL) model with temperature-dependent interaction parameters. The use of only three pseudo-components leads to a reduced number of interaction parameters to be determined by correlation of the available experimental equilibrium data. Calculated and experimental compositions and yields of the raffinates and extracts were compared, and good agreement was obtained.

Phase behavior studies of a perfluoropolyether in high-pressure carbon dioxide

This work presents vapor–liquid equilibrium measurements for the binary system carbon dioxide-Krytox 157 FSL, a commercial perfluoropolyether carboxylic acid terminated. The measurements were carried out between 313.15 and 343.15 K and at pressures up to 18 MPa in a static analytical apparatus. Krytox showed high miscibility with CO 2 and it was possible to define the contour of the vapor–liquid equilibrium region as well the determination of the critical line. The Sanchez–Lacombe EOS was able to calculate the liquid equilibrium composition of the CO 2 + Krytox binary system quite adequately, by fitting two temperature dependent interaction parameters, although it did not predict any solubility for the vapor phase. Due to lack of thermodynamic data, the characteristic parameters of Krytox were estimated by a method proposed by Sanchez and Lacombe, using a known heat of vaporization, a vapor pressure and a liquid specific volume at 313 K.

Effect of the Microstructure of Polydiene Block on Order−Disorder Transition in Diblock Copolymers Containing Polystyrene Block or Poly(vinylcyclohexane) Block

The effect of the microstructure of polydiene blocks on order-disorder transition (ODT) in diblock copolymers containing polystyrene (PS) or poly(vinylcyclohexane) (PVCH) blocks was investigated. For the study, a series of polystyrene-block-polybutadiene (SB diblock) copolymers with varying microstructures in the polybutadiene (PB) block and polystyrene-block-polyisoprene (SI diblock) copolymers with varying microstructures in the polyisoprene (PI) block were synthesized. Subsequently, either only the PB block in an SB diblock copolymer was selectively saturated to obtain PS-block-poly(ethylene-co-1-butene) (PEB) copolymer or both blocks were saturated to obtain PVCH-block-PEB copolymer. Also, either only the PI block in an SI diblock copolymer was selectively saturated to obtain PS-block-poly-(ethylene-alt-propylene) (PEP) copolymer or both blocks were saturated to obtain PVCH-block-PEP copolymer. The ODT temperature (T ODT ) of each block copolymer was determined from oscillatory shear rheometry. It has been found that (i) the TOOT of an SB diblock copolymer with predominantly 1,2-addition in the PB block is much higher than that of an SB diblock copolymer with predominantly 1,4-addition in the PB block, (ii) the TOOT of an SI diblock copolymer with high vinyl content (predominantly 3,4- and 1,2-additions) in the PI block is much higher than that of an SI diblock copolymer with predominantly 1,4-addition in the PI block, (iii) the T ODT s of PS-block-PEB and PS-block-PEP copolymers are considerably higher (>100 °C) than those of the unsaturated precursors regardless of the microstructures of polydiene block, and (iv) the T ODT s of PVCH-block-PEB and PVCH-block-PEP copolymers are higher or lower than those of the unsaturated precursors depending upon the microstructure of polydiene block. By curve fitting the experimental phase diagrams, which were obtained from cloud point measurement, to the theoretical phase diagrams based on the Flory-Huggins theory, temperature-dependent segment-segment interaction parameters (χ) were determined for PS/PB, PS/PEB, PVCH/PEB, PS/PI, PS/PEP, and PVCH/ PEB pairs with varying microstructures of polydienes. It is found that while values of χ for the polymer pairs thus determined explain satisfactorily the experimentally determined T ODT s of all the block copolymers investigated, the conformational asymmetry parameter (e) explains the experimentally determined T ODT s of the completely saturated PVCH-block-PEB and PVCH-block-PEP copolymers, but not of the partially saturated PS-block-PEB and PS-block-PEP copolymers. Further, it is found that values of e do not explain the effect of microstructures of PB block on the T ODT of SB diblock copolymer with varying microstructures. Thus, we conclude that a correlation between e and χ seems to exist for completely saturated block copolymers, but not for partially saturated block copolymers.

Vapor−Liquid−Liquid Equilibria, Azeotropic, and Excess Enthalpy Data for the Binary System n-Undecane + Propionamide and Pure-Component Vapor Pressure and Density Data for Propionamide

Vapor−liquid−liquid equilibria (VLLE), azeotropic, and excess enthalpy (HE) data for the binary system n-undecane + propionamide were measured at temperatures from 359.25 to 416.65 K. Additionally, pure-component vapor pressure and density data for propionamide were determined experimentally. The LLE and VLLE measurements were performed in a stirred glass cell and in a static equilibrium cell with a capability to take small samples from the different phases by using pneumatic micro samplers. For the HE measurements, an isothermal flow calorimeter was used, and the azeotropic data were obtained from distillation experiments using a micro spinning band column. The pure-component vapor pressures and densities were measured with the help of the dynamic method (ebulliometer) and a vibrating tube densimeter, respectively. To the experimental mixture data from this work linear temperature-dependent interaction parameters for the NRTL model were fitted. They can be used to represent the phase equilibrium behavior and excess enthalpies of the investigated system.

Extended UNIQUAC model for correlation and prediction of vapor–liquid–liquid–solid equilibria in aqueous salt systems containing non-electrolytes. Part B. Alcohol (ethanol, propanols, butanols)–water–salt systems

The Extended UNIQUAC model for electrolyte solutions is an excess Gibbs energy function consisting of a Debye–Hückel term and a term corresponding to the UNIQUAC equation. For vapor–liquid equilibrium calculations, the fugacities of gas-phase components are calculated with the Soave–Redlich–Kwong equation of state. The model only requires binary, temperature-dependent interaction parameters. It has previously been used to describe the excess Gibbs energy for aqueous electrolyte mixtures and aqueous electrolyte systems containing methanol. It has been found to be an adequate model for representing solid–liquid–vapor equilibrium and thermal property data for strongly non-ideal systems. In this work, the model is extended to aqueous salt systems containing higher alcohols. The calculations are based on an extensive database consisting of salt solubility data, vapor liquid equilibrium data, and liquid–liquid equilibrium data for solvent mixtures and for mixed solvent–electrolyte systems. The application of this model to represent the vapor–liquid–liquid–solid equilibria in aqueous systems containing various non-electrolytes (ethanol, 1-propanol, 2-propanol, 1-butanol, 2- butanol, 2-methyl 1-propanol, 2-methyl 2-propanol) and various ions (Na +, K +, NH 4 +, Cl −, NO 3 −, SO 4 2−, SO 3 2−, HSO 3 −, CO 3 2−, and HCO 3 −) shows the capability of the model to accurately represent the phase behavior of these kinds of systems.

Isothermal Vapor−Liquid Equilibrium and Excess Enthalpy Data for the Binary Systems Propylene Oxide + 2-Methylpentane and Difluoromethane (R32) + Pentafluoroethane (R125)

Isothermal P−x (vapor−liquid equilibria) and excess enthalpy (HE) data for the two binary systems propylene oxide + 2-methylpentane and difluoromethane + pentafluoroethane were measured by means of the static technique and an isothermal flow calorimeter, respectively. The experimental data are presented using temperature-dependent interaction parameters for the nonrandom two-liquid model, which were fitted simultaneously to all measured data. From the experimental P−x data, the azeotropic conditions were determined for both systems. The experimental results from this work were compared with the data of other authors.

Isothermal Vapor−Liquid Equilibrium and Excess Enthalpy Data for the Binary Systems Water + Sulfolane and Methanol + N-Methyl-2-pyrrolidone

Isothermal vapor−liquid equilibrium (VLE) and excess enthalpy (HE) data for the two binary systems water + sulfolane and methanol + N-methyl-2-pyrrolidone (NMP) were measured by means of a static technique and an isothermal flow calorimeter, respectively. The experimental data are presented using temperature-dependent interaction parameters for the nonrandom two-liquid model, which were fitted simultaneously to all experimental data from this work and from the literature, and allow us to compare the measured data with the data of the other authors. Furthermore, the experimental results from this work are compared to predictions using the Mod. UNIFAC (Do) group contribution method.

Isothermal Vapor−Liquid Equilibrium and Excess Enthalpy Data for the Binary Systems Water + 1,2-Ethanediol and Propene + Acetophenone

Isothermal vapor−liquid equilibrium P−x data for the two binary systems water + 1,2-ethanediol and propene + acetophenone were measured by means of a computer-operated static apparatus. Additionally, excess enthalpy (HE) data for the binary system propene + acetophenone were measured with an isothermal flow calorimeter. The experimental data are presented using temperature-dependent interaction parameters for the UNIQUAC model which were fitted simultaneously to all measured data. The experimental results were compared with the data of other authors.

Phase behaviour of the catalyst dicarbonyl(η 5-cyclopentadienyl)-cobalt in carbon dioxide

The phase behaviour of the binary mixture of carbon dioxide and the cobalt complex dicarbonyl(η 5-cyclopentadienyl)-cobalt, CpCo(CO) 2, has been investigated. This organometallic compound is one of the most effective catalysts of cyclotrimerization reactions of arylisocyanates and alkynes. Vapour–liquid equilibrium (VLE) measurements were undertaken in a static analytical apparatus at 313.15, 323.15 and 363.15 K at pressures up to 15 MPa. p, T isopleths were measured by a synthetic method in a Cailletet apparatus. Nine different compositions ranging from 17.56 to 94.23 mol% of CO 2 were measured up to 15 MPa. Modelling with the Peng–Robinson equation of state (PR EOS) gave reasonable results in the correlation of the experimental phase equilibrium compositions using two temperature-dependent interaction parameters.

Propene bulk polymerization kinetics: Role of prepolymerization and hydrogen

AbstractAn experimental setup for the polymerization of liquid propylene was used to carry out main polymerizations with and without a prepolymerization step. Two types of prepolymerization are introduced: at a constant temperature and at rapidly increasing reactor temperatures. With the present catalyst system, at high polymerization temperatures, a prepolymerization step will increase polymerization rate. Hydrogen was used to control the molecular weight of the product. The polymerization reactor was used in combination with a gas chromatograph to determine the vapor‐liquid equilibrium (VLE) of the propylene‐hydrogen system. Measurements are compared to predictions of different equations of state. The Peng‐Robinson equation of state is best able to describe the VLE for this binary system. A temperature‐dependent interaction parameter was derived from the fits to the measured data.

Prediction of Polymer Thermal Diffusion Coefficients from Polymer-Solvent Interaction Parameters: Comparison with Thermal Field Flow Fractionation and Thermal Diffusion Forced Rayleigh Scattering Experiments

In this study a model that allows the qualitative prediction of polymer thermal diffusion coefficients from polymer-solvent interaction parameters is presented. The Flory-Huggins lattice theory served as a starting point for the thermal diffusion model. From this model it follows that D T is determined by the temperature dependence of the polymer-solvent interaction parameter ( h ), the segmental mobility of the polymer chain, and the polymer concentration. In agreement with literature data, the model predicts that D T is independent of the molecular mass of the polymer, D T increases with temperature, and D T is strongly dependent on the interaction between the polymer and the solvent. Furthermore, it follows from the model that D T should decrease with concentration. A good qualitative agreement with experimental data has been found. In order to study the potentials of the model, the D T values of polystyrene (PS) in several solvents were predicted. The required temperature-dependent polymer-solvent interaction parameters were calculated from Hildebrand's solubility parameters of the polymer and of the solvent. The solvent's solubility parameters were estimated using Lee and Kesler's generalized thermodynamic equations of state. The polymer solubility parameters were taken from the literature. Lack of data complicated the comparison. However, a good agreement for PS in THF, MEK, dioxane, and cyclohexane was found. Thermal diffusion values predicted for PS in several aromatic solvents were, however, significantly low. Still, the overall result is satisfactory considering the fact that the Flory-Huggins theory is a highly simplified polymer-solvent theory that was never intended to be used for quantitative purposes. Polymer thermal diffusion model Thermal field-flow fractionation Polymer-solvent interaction parameter Thermal diffusion forced Rayleigh scattering

Segment-segment interactions of poly( N -isopropylacrylamide) in aqueous methanol solutions by using small-angle scattering

Small-angle neutron and X-ray scattering from semidilute solutions of poly(N-isopropylacrylamide) in D2O, methanol and methanol–water mixtures has been measured in the poor solvent regime. The binary and the ternary cluster integrals of polymer segments were determined from the concentration dependence of the correlation length at several temperatures just below the lower critical solution temperature. Then, contributions of segment–segment interactions to the entropy and the enthalpy have been calculated from the temperature dependence of interaction parameters and it has been found that both values are positive in the D2O and the methanol–water systems at a small content of methanol, while both values are negative in the other system.

Consistent analysis of cloud points and spinodal—compatibility of P (αMS-CO-AN) and P (MA-CO-MMA)

The two copolymers poly(α-methylstyrene- co-acrylonitrile) (P(αMS-co-AN)) and poly(methyl acrylate-co-methyl methacrylate) (P(MA-co-MMA)) are traded by the BASF AG, Ludwigshafen, under the names Luran and Lucryl, respectively. We have studied Luran KR2556 with the molar mass of Mw = 92 kg/mole (Mw/Mn = 2.5), which has the copolymer composition of 50% αMS and AN, respectively. Lucryl has a similar molar mass of Mw = 88 kg/mole (Mw/Mn = 2.5) and is available with various MA fractions between 1 and 14%. Luran + Lucryl blends prepared by solution casting from acetone are miscible at temperatures below 130 °C. At higher temperatures they show a lower critical solution temperature (LCST) behavior. Temperatures of demixing depend strongly on the MA fraction. The minima of the cloud point curves are found for Luran concentrations between 20 and 35%. We have used results from transmission electron microscopy (TEM) [1, 2] to reveal the morphologies of demixed Luran + Lucryl blends for different compositions and temperatures. This enables us to distinguish between demixing by nucleation and growth in the meta-stable region of the blend system and the spinodal decomposition. The results from cloud point and TEM measurements yield constraints for the spinodal curve. The spinodal is calculated consistantly utilizing a temperature and concentration dependent interaction parameter defined by Staverman [3]. We also estimate the interaction parameter for blends of Luran with pure PMMA and PMA.

Phase Equilibrium and Excess Enthalpy Data for the System Methanol + 2,2‘-Diethanolamine + Water

Isothermal vapor−liquid equilibrium (VLE) data are reported for the binary systems methanol + 2,2‘-diethanolamine and water + 2,2‘-diethanolamine and for the ternary system methanol + 2,2‘-diethanolamine + water. Moreover, excess enthalpies (HE) were measured for both binary systems with 2,2‘-diethanolamine. The data were measured by means of a computer operated static apparatus and isothermal flow calorimetry, respectively. For the pure component 2,2‘-diethanolamine, also vapor pressure data were measured using the dynamic ebulliometric method. The experimental binary data were correlated using linear or even quadratic temperature-dependent NRTL interaction parameters. The ternary data were used to validate the capability of gE models such as NRTL for the prediction of multicomponent mixtures on the basis of binary information.

Development of a Universal Group Contribution Equation of State. 2. Prediction of Vapor−Liquid Equilibria for Asymmetric Systems

The PSRK method is a well-established group contribution equation of state (GCEOS) for the prediction of vapor−liquid equilibria (VLE) and other properties. A generalized GCEOS has been developed to overcome the still remaining weaknesses of the PSRK model, which is of great interest for industrial chemistry. A generalized volume-translated Peng−Robinson (PR) equation of state (EOS) has been combined with the group contribution method UNIFAC by means of a simple gE mixing rule, derived from the PSRK one. In this new GCEOS, the Flory−Huggins term of the PSRK mixing-rule and the combinatorial part of the UNIFAC model are skipped simultaneously, which leads to a much better description for asymmetric systems. The predictions are further improved by using a quadratic mixing rule for the parameter b with an exponent of 3/4 for the binary parameter bij in the combination rule. Temperature-dependent group interaction parameters are fitted to VLE over a wide range of temperature and pressure. The results of the n...

Liquid–liquid equilibria of a hydrofluoroether + water + ethanol system

The ability to manipulate the liquid–liquid equilibria (LLE) of a commercially available hydrofluoroether (HFE-7100 ®, an approximately equimolar mixture of the isomers methoxy-nonafluoroisobutane and methoxy-nonafluorobutane) + water with the addition of ethanol, which is mutually miscible with both solvents, was examined. LLE data were determined at 298, 308 and 323 K for the system of HFE-7100 ®+water+ethanol. The UNIQUAC and NRTL excess Gibbs energy models were able to adequately represent the type I phase behavior observed over this temperature range. The goodness of the fit of each model was compared for temperature-dependent and temperature-independent binary interaction parameters.

Liquid−Liquid Equilibria for Glycols + Hydrocarbons: Data and Correlation

Liquid−liquid equilibrium data for seven binary glycol−hydrocarbon systems have been measured in the temperature range 32 °C to 80 °C and at the pressure 1 bar. The measured systems are monoethylene glycol (MEG) + heptane, methylcyclohexane (MCH) + hexane, propylene glycol (PG) + heptane, diethylene glycol (DEG) + heptane, triethylene glycol (TEG) + heptane, and tetraethylene glycol (TETRA) + heptane. The data obtained were correlated with the NRTL model and two different versions of the UNIQUAC equation. The NRTL model and one of the UNIQUAC equations (UQ 4) have a linear temperature-dependent interaction parameter term, while the other UNIQUAC equation (UQ 2) has an interaction parameter that is independent of the temperature. There was a fairly good agreement between the experimental data and the models with an average deviation in the composition for both phases of 3% for both NRTL and UQ 4 and 15% for UQ 2. These results indicate the necessity of using the linearly dependent interaction parameters.

Effect of maleic anhydride content on the rheology and phase behavior of poly(styrene-co -maleic anhydride)/ poly(methyl methacrylate) blends

We investigated the thermo- rheological behavior of high glass transition, high molecular weight and small dynamic asymmetry blends of poly(styrene-co-maleic anhydride) (SMA) and poly (methyl methacrylate) (PMMA) with varying amounts of maleic anhydride (MA) content, namely 8 wt%, 14 wt% and 32 wt%, in the SMA component. The phase separation (binodal) temperature of each blend was determined rheologically using a combination of dynamic frequency and temperature sweeps in parallel plate geometry; it was marked by a change in slope of the elastic modulus and the occurrence of a peak in tan δ in temperature sweeps. Failure of the time-temperature superposition principle and observation of two peaks in the Cole-Cole plots corroborated these findings. The blends displayed lower critical solution temperature (LCST) behavior with the critical temperatures exhibiting a non-monotonic dependence on the MA content. From rheological and thermal measurements it was concluded that SMA/PMMA blends containing 14% MA were more miscible than those containing 8% or 32% MA, a finding attributed to the compositional dependence of the interplay between SMA-SMA and SMA-PMMA interactions in the different samples. MA also influenced the dynamic asymmetry and pretransitional concentration fluctuations. The phase diagrams corresponding to each blend were modeled using a two-parameter temperature dependent interaction parameter, based on the concept of generalized Gibbs free energy of mixing. The fitted values of interaction parameter were in good agreement with values calculated explicitly using the Flory-Huggins theory.

Vapor−Liquid Equilibria and Enthalpies of Mixing in a Temperature Range from 298.15 to 413.15 K for the Further Development of Modified UNIFAC (Dortmund)

Isothermal P−x data (VLE) and excess enthalpy (hE) data for the binary systems methyl formate, ethyl formate, and butyl formate + water and toluene + 1,2-ethanediol have been measured with the help of a computer-operated static apparatus and an isothermal flow calorimeter. Additionally, hE data for the binary systems benzene + 1,2-ethanediol and benzene and ethanol + N,N-dimethylacetamide have been determined. The experimental VLE and hE data have been used for the revision and extension of the group contribution method Modified UNIFAC (Dortmund). Besides these new data various types of thermodynamic data (vapor−liquid equilibria (VLE), excess enthalpies (hE), activity coefficients at infinite dilution (γ∞), liquid−liquid equilibria (LLE), solid−liquid equilibria (SLE), and azeotropic data (AZD)) taken from the Dortmund Data Bank have simultaneously been used for fitting temperature-dependent group interaction parameters. The new or revised Modified UNIFAC (Dortmund) parameter pairs for the new main group “dialkylated amides” and the interaction between formates and water are given. The predicted results are in good agreement with the experimental data.