Study of surface tension and surface properties of binary alcohol/n-alkyl acetate mixtures

The Butler equation is employed to describe quantitatively the nature, properties, and compositions of surface layers in binary liquid mixtures. Bulk mole fraction, surface molar area, and surface tension of pure components are necessary inputs for this equation. In addition, the UNIFAC group contribution method is applied to account for the nonideality of the bulk liquid as well as that of the surface layer. The average relative error obtained from the comparison of experimental and calculated surface tension values for 12 binary systems is less than 1%. Therefore, the model has good accuracy in comparison with other predictive equations. In addition to finding more information about the surface structure of binary mixtures, surface mole fraction was calculated using relative Gibbs adsorption values and an extended Langmuir model (EL). The obtained results show a good consistency between two models employed, i.e., the Gibbs adsorption model and EL model, based on the UNIFAC method.     

Activity Coefficients in the Surface Phase of Liquid Mixtures

A novel equation for evaluating surface activity coefficients is obtained from a recent thermodynamic formalism describing the surface phase of liquid mixtures. The input quantities are the surface tension, bulk activity coefficients and pure constituent thermophysical properties. It is demonstrated thermodynamically that the order of magnitude of each component surface and bulk activity coefficients must be the same. This order is intrinsically associated with the sign of excess surface tension. Reliable activity coefficients of ethanol and water in the surface phase of their mixtures are computed and reported for the first time, by using literature data for the required input quantities. It is shown that the so‐called transferring method for estimating surface activity coefficients is severely flawed, because it leads to contradictory values of predicted excess surface tensions depending on which component this prediction is based.     

Activity coefficients of associating mixtures by group contribution

A group contribution model is presented for the prediction of activity coefficients in associating mixtures. An association term has been added to the traditional UNIFAC residual and combinatorial contributions to the activity coefficients. The association term is based on Wertheim's theory for fluids with highly directed attractive forces, as applied in the SAFT equation, and it follows the group contribution approach proposed by Gros et al. in the GCA-EOS model. Good predictions of both vapor–liquid and liquid–liquid equilibria are achieved, with a set of group interaction parameters determined from infinite dilution activity coefficients.     

Prediction of phase equilibrium in mixtures containing ionic liquids using UNIFAC

The UNIFAC model is extended to mixtures of ionic liquids consisting of the imidazolium cation and the hexafluorophosphate anion with alkanes, cycloalkanes, alcohols and water. Two new main groups, the imidazolium and the hexafluorophosphate groups, are introduced in UNIFAC. The required group interaction parameters between these groups and the existing UNIFAC main groups, CH₂, OH and H₂O, are determined by fitting binary liquid–liquid equilibrium and infinite dilution activity coefficient experimental data. The predictive capability of the extended UNIFAC model is examined against experimental data for vapour–liquid equilibrium, liquid–liquid equilibrium and activity coefficients at infinite dilution of binary and ternary systems containing 1-alkyl-3-alkyl′-imidazolium hexafluorophosphate ionic liquids, alkanes, cycloalkanes, alcohols and water. The results indicate that UNIFAC is a reliable model for phase equilibrium predictions in mixtures containing this type of ionic liquids.     

Study of the surface properties and surface concentration of ionic liquid–alcohol mixtures

Surface properties for three binary mixtures containing a 1-butyl-3-methylimidazolium thiocyanate ([BMIM][SCN]) and a long-chain alcohol (1-butanol, 1-pentanol and 1-hexanol) were determined by surface tension data at the following temperatures: (298.15, 308.15, 318.15, 328.15 and 338.15) K. The surface tension data over the entire mole fraction range are correlated by the Fu et al.(FLW) and Myers-Scott (MS) models. There is good agreement between the experimental data and the results of correlations for 15 binary systems (the three systems at five temperatures) with an average relative error below 1.5%. In addition, the UNIFAC group contribution method is applied for calculation of activity coefficients of components in solution. Moreover, the relative adsorptions of alcohol at the air/liquid interface are determined using Gibbs adsorption isotherm. The obtained results show that the values of adsorption for mixtures of alcohols/[BMIM][SCN] increase with increasing the alkyl chain length of alcohol and decreasing temperature.     

New Thermodynamics for Evaluating the Surface‐phase Enrichment in the Lower Surface Tension Component

Regarding the surface phase of liquid mixtures as a thermodynamic phase, ideal surface phases are designed so that at fixed bulk‐phase composition, real and ideal surface phases have the same chemical composition and identical limiting slopes for the dependence of surface tension on mole fraction. Standard chemical potentials are introduced for surface phase components, and quasi‐exact expressions are worked out to compute ideal surface tensions and surface‐phase compositions of real liquid mixtures. Guidelines for choosing molecular models to estimate the molar surface area of pure constituents are given. Ideal and excess surface tensions are calculated by using literature data for aqueous ethanol solutions at 298 K. These results show treatment based on Butler’s equations grossly overestimate predicted surface tensions, thus leading to lower ethanol content in the surface phase. These inaccuracies are ascribed to the use of molar surface areas in model equations that are too small.     

Liquid phase equilibria of (water + propionic acid + oleyl alcohol) ternary system at several temperatures

(Liquid–liquid) equilibrium (LLE) data are investigated for mixtures of (water + propionic acid + oleyl alcohol) at 298.15, 308.15 and 318.15 K and atmospheric pressure. The solubility curves and the tie-line end compositions of liquid phases at equilibrium were determined, and the tie-line results were compared with the data predicted by the UNIFAC method. The phase diagrams for the ternary mixtures including both the experimental and correlated tie-lines are presented. The distribution coefficients and the selectivity factors for the immiscibility region are calculated to evaluate the effect of temperature change. The reliability of the experimental tie-lines was confirmed by using Othmer–Tobias correlation. It is concluded that oleyl alcohol may serve as an adequate solvent to extract propionic acid from its dilute aqueous solutions. The UNIFAC model correlates the LLE data for 298.15, 308.15 and 318.15 K with a root mean square deviation of 5.89, 6.46, and 6.69%, respectively, between the observed and calculated mole concentrations.     

Solid-liquid equilibria of binary systems containing <Emphasis Type="Italic">n</Emphasis>-tetracosane with naphthalene or dibenzofuran

A differential scanning calorimeter (DSC) was used to determine binary solid-liquid equilibria (SLE) for dibenzofuran+n-C24 and naphthalene+n-C24 mixtures. Results obtained with this technique were compared with those predicted by two modified UNIFAC (Universal Functional group Acitivity Coefficients) versions. This model is employed with the idea to extensively investigate the validity of UNIFAC (Larsen and Gmehling versions). The corresponding activity coefficients were calculated and applied to the prediction of non-electrolyte mixtures real behavior. Reasons of prediction without success in the case of using original interaction parameters, were analysed and discussed. Interesting representation of solubility diagrams was obtained using partly readjusted UNIFAC interaction parameters. The two systems selected can be used for contributing to develop the data base using group contribution methods. For practical purposes, SLE are of interest in chemical process design, especially when process conditions must be specified to prevent precipitation of a solid.     

PSRK: A Group Contribution Equation of State Based on UNIFAC

A group contribution equation of state called PSRK (Predictive Soave-Redlich-Kwong) which is based on the Soave-Redlich-Kwong equation (Soave, 1972) has been developed. It uses the UNIFAC method to calculate the mixture parameter a and includes all already existing UNIFAC parameters. This concept makes use of recent developments by Michelsen (1990b) and has the main advantage, that vapor-uquid-equilibria (VLB) can be predicted for a large number of systems without introducing new model parameters that must be fitted to experimental VLB-data. The PSRK equation of state can be used for VLB-predictions over a much larger temperature and pressure range than the UNIFAC γ--approach and is easily extended to mixtures containing supercritical compounds. Additional PSRK parameters, which allow the calculation of gas/gas and gas/alkane phase equilibria, are given in this paper. In addition to those mixtures covered by UNIFAC, phase equilibrium calculations may also include gases like CH₄ C₂H₆, C₃H₆, c₄H₁₀, CO₂, N₂, H₂ and CO.     

A modified square well model in obtaining the surface tension of pure and binary mixtures of hydrocarbons

A model based on the perturbation theory of fluids was proposed to correlate the experimental data for surface tension of pure hydrocarbons in a wide range of temperature. The results obtained for the pure hydrocarbons were directly used to predict the surface tension for binary hydrocarbon mixtures at various temperatures. In the proposed model, a modified form of the square well potential energy between the molecules of the reference fluid was taken into account while the Lennard–Jones dispersion energy was considered to be dominant amongst the molecules as the perturbed term to the reference part of the model. In general, the proposed model has three adjustable parameters which are chain length, m, size, σ, and energy, ε/κ, parameters, but in some cases the number of parameters was reduced to two, thereby setting the chain length to be unity for pure hydrocarbons. The regressed values of these parameters were obtained using the experimental data for pure hydrocarbons at different temperatures. The results showed that these parameters can be related to the molar mass of hydrocarbons. The model was also extended to predict the surface tension of binary hydrocarbon mixtures using the parameters obtained for the pure compounds. It is worth noting that no additional parameter has been introduced into the model in the extension of the model to the mixtures studied in this work. The results showed that the proposed model can accurately correlate the surface tension of pure hydrocarbons. Also the results showed that the surface tension for binary mixture of hydrocarbons can be accurately predicted using the proposed model over a wide temperature range.     

Boiling points for five binary systems of sulfolane with aromatic hydrocarbons at 101.33 kPa

Boiling points have been determined at 101.33 kPa for the binary mixtures of sulfolane+o-xylene, sulfolane+m-xylene, sulfolane+p-xylene, sulfolane+ethylbenzene and sulfolane+1,2,4-trimethylbenzene. Calculations of the non-ideality of the vapor phase were made with the second virial coefficients evaluated from the Hayden–O’Connell method. The binary parameters for five activity coefficient models (Margules, van Laar, Wilson, NRTL and UNIQUAC) have been fitted with the experimental boiling points measured in this work. A comparison of model performances has been carried out using the criterion of the average absolute deviations in boiling point. The activity coefficient of the component in the liquid phase is discussed based on the UNIFAC model with the consideration of the dipole–dipole interactions.     

Phase equilibria of binary mixtures containing methyl acetate,water, methanol or ethanol at 101.3 kPa

Isobaric vapor–liquid equilibria data at 101.3?kPa were reported for the binary mixtures (methyl acetate?+?(water or methanol or ethanol), methanol?+?(water or ethanol) and (ethanol?+?water)). The experimental data were tested for thermodynamic consistency by means of the Wisniak method and were demonstrated to be consistent. The experimental data were correlated using Wilson, NRTL and UNIQUAC models for the activity coefficients and predicted using the UNIFAC and PSRK equation of state for testing theirs capability. The results show that the obtained data for the studied binary systems are more reliable than other published data.     

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.     

Simultaneous prediction of interfacial tension and phase equilibria in binary mixtures: An approach based on cubic equations of state with improved mixing rules

Vapor–liquid interfacial tensions of miscible mixtures have been predicted by applying the gradient theory to an improved Peng–Robinson equation of state. The modified Huron–Vidal mixing rule model has been considered for fitting vapor–liquid equilibrium data of miscible polar and non-polar mixtures and, then, for predicting the interfacial tension of these mixtures. According to results, an accurate and globally stable fitting of the vapor–liquid equilibrium data results on a physically coherent prediction of interfacial tensions in the full concentration range. In addition, we present a criteria based on the geometry of the grand potential function along the interface for assessing the predictive value of the GT. Calculations for subcritical binary mixtures are presented and compared to experimental data and the Parachor method for demonstrating the potential of the unified approach suggested in this work.     

Isothermal vapor–liquid equilibria for different binary mixtures involved in the alcoholic distillation

Isothermal vapor–liquid equilibrium (VLE) data for five binary systems ethyl acetate + 3-methyl-1-butanol, ethanol + 3-methyl-1-butanol, ethyl acetate + 2-methyl-1-butanol, ethanol + 2-methyl-1-butanol, ethyl acetate + 2-methyl-1-propanol, involved in the alcoholic distillation have been determined experimentally by headspace gas chromatography. The composition in the liquid phase was corrected with the help of an iterative method by means of a G^E model. However, due to the large density difference between the liquid and the vapor, the correction of the liquid phase composition is nearly negligible. All the binary mixtures show positive deviations from Raoult's law. The experimental VLE data are well predicted by using the modified UNIFAC model (Dortmund).     

Thermodynamics of binary mixtures containing organic carbonates Part XI. SLE measurements for systems of diethyl carbonate with long n-alkanes: comparison with DISQUAC and modified UNIFAC predictions

Using the available interaction parameters for organic carbonate+alkane mixtures the ability of the DISQUAC and modified UNIFAC group contribution model to predict solid–liquid equilibria (SLE) is investigated. Six sets of the SLE temperatures for diethyl carbonate+n-alkane (octadecane, eicosane, docosane, tetracosane, hexacosane, octacosane) systems have been measured by a dynamic method from 278.65 K to the melting point of the long chain n-alkane. The data have been correlated by three equations: Wilson, UNIQUAC and NRTL. The existence of a solid–solid first-order phase transition in n-alkanes has been taken into consideration in the solubility calculations. The relative standard deviations of the solubility temperature correlation for all measured data vary from 0.31 to 0.34 K and depend on the particular equation used.

The SLE curves are usually well predicted by DISQUAC and modified UNIFAC models with average standard deviation of <1.35 K.     

Prediction of thermodynamic properties of polymer solutions by a group-contribution method

The Flory–Huggins lattice-theory expression for solvent activity in a polymer-solution is commonly used to calculate the thermodynamic interaction parameter χ with the aid of experimental data from vapor pressure osmometry. This expression assumes that χ is independent of composition. However, experimental data for a variety of polymer-solvent mixtures indicate that χ exhibits an appreciable concentration dependence. A group contribution method, UNIFAC (UNIQUAC Functional-Group Activity Coefficients) incorporating the free-volume correction of Oishi and Prausnitz is used to predict the dependence of χ on solvent concentration. Agreement with previously reported experimental data is within 15%. Calculated values of χ obtained from the Flory–Huggins expression for solvent activity and from the corresponding Gibbs free energy of mixing (which does not assume that χ is independent of composition) are compared. Calculations based on the Gibbs free energy of mixing predict a somewhat larger value of χ relative to those based on solvent activity. The specific Gibbs free energy of mixing for polystyrene-solvent mixtures is calculated using the UNIFAC model, and is found to represent qualitatively the phase equilibrium behavior. Quantitative discrepancies are observed, however, for the polystyrene-acetone system in light of the actual experimental solubility reported by Suh and Clark (20). Most of the thermodynamic predictions for polymer-solvent systems investigated herein are correlated qualitatively with the relative mismatch between solubility parameters of both components.     

Liquid–liquid equilibrium calculations for methanol–gasoline blends using continuous thermodynamics

This work presents the application of continuous thermodynamics to investigate the limited miscibility of methanol–gasoline blends. To predict the liquid–liquid equilibrium of these systems, the Gaussian distribution function was used to represent the composition of paraffins in the gasoline. The naphthenes and aromatics were represented by model compounds. A model has been developed using three different continuous versions of the UNIFAC model. Methanol is an associating component, and association affects phase equilibria. Therefore, the CONTAS (continuous thermodynamics of associating systems) model based on the Flory–Huggins equation, for multicomponent methanol–gasoline blends has also been investigated. The predicted results including the cloud point curve, shadow curve and phase separation data have been compared with experimental data and good agreement was found for the two UNIFAC and CONTAS models.