Experimental and theoretical study of surface tension of n-pentane,n-heptane,and some of their mixtures at different temperatures

The surface tension of n-pentane, n-heptane and some of their mixtures were measured at 91.3 kPa and T = (283.15 to 323.15) K by the maximum bubble pressure method. The surface tension results were correlated by a new model obtained from coupling scaled particle theory (SPT) and the MMM equation of state. The parameters of the model (SPTM3) for n-pentane and n-heptane were calculated and reported. The pure component parameters obtained for the model were used for calculating the surface tension of n-pentane and n-heptane binary mixtures at different temperatures. The comparison between the mixture surface tension results and those calculated by the model indicate that the new proposed model can be satisfactorily used for calculating the surface tension of n-pentane, n-heptane and their mixtures.     

Application of the MSA-based models in correlating the surface tension for single and mixed electrolyte solutions

Experimental values for surface tension of single and mixed electrolyte solutions were correlated using the models based on the perturbation theory. The Mean Spherical Approximation (MSA) model, coupled with the Ghotbi–Vera (GV) and the Mansoori et al. (BMCSL) equations of state, were used to correlate the experimental values of the surface tension. The results showed that the models can favourably correlate the experimental values for single electrolyte solutions. However, it was observed that the GV–MSA model can more accurately predict the surface tension for single electrolytes, especially at higher concentrations. Two different expressions for concentration dependency of cation hydrated diameters were used. Therefore, in terms of such dependency different forms of the models, i.e., GV–MSA1, GV–MSA2, BMCSL–MSA1 and BMCSL–MSA2 were introduced. It should be stated that the prediction of the surface tension for the mixed electrolyte solutions were made without introducing any new adjustable parameters. The results showed that GV–MSA2 model can predict more accurately the surface tension of electrolyte mixtures particularly at higher concentrations. Finally, the GV–MSA model was directly used to correlate the experimental results for the surface tension for both single and mixed electrolyte solutions with 2 and 4 adjustable parameters. The results showed that both of the models can accurately predict the experimental data of surface tension. These models can favourably fit and also, predict the surface tension of single electrolyte solutions with less than 1% average absolute relative deviation (AARD). The prediction capability of the proposed models is also acceptable for mixtures of electrolytes.     

The prediction of vapor—liquid equilibrium from heat of mixing data for binary hydrocarbon—ketone mixtures

The method of Hanks et al. for predicting vapor—liquid equilibrium (VLE) from heat of mixing (h^E) data was successfully applied to binary hydrocarbon—ketone mixtures. The LEMF model for the excess free energy was found to be the most adequate to correlate experimental g^E and h^E data simultaneously for these mixtures. The predicted vapor-liquid equilibrium values were compared to experimental values and good agreement was found. The dependence of the accuracy of the VLE data predictions on the experimental uncertainties of heat of mixing data and on the set of parameters obtained by fitting these data to the algebraic equation for h^E is discussed.     

A generalized method for calculation and prediction of vapour-liquid equilibria at high pressures

A generalized method for prediction of vapour-liquid equilibria in hydrocarbon mixtures containing some nonhydrocarbon gases at high pressures has been developed following the approach of Chao and Seader (1961) and Lee et al. (1973). The method proposed is based on three equations: (1) a generalized equation of state for vapour phase calculations, (2) a generalized expression for the pure liquid fugacity coefficient suggested by Lee et al. (1973), and (3) an activity coefficient expression based on a surface modification of the regular solution model. The equations used contain only one partially generalized binary parameter, which has been evaluated from experimental K-value data. The method proposed has been tested by computing K-values and pressures in binary and multicomponent systems consisting of 13 hydrocarbons and three nonhydrocarbon gases. The results have shown that the proposed method can be applied over a wide range of conditions with a good degree of accuracy, which is comparable with that of more complicated methods.     

Interfacial and micellar properties of some anionic/cationic binary surfactant systems. 1. Surface properties and prediction of surface tension

The surface tension equations of binary surfactant mixtures are established by combining the Szyszkowski equation for pure surfactant solutions and extended nonideal theory for mixed adsorption. They are then successfully applied to two relatively long-chain anionic/cationic binary surfactant systems: triethanolammonium dodecylpoly(oxyethylene)sulfate, as an anionic species (containing about 2 ethylene oxide units), mixed with dodecyltrimethylammonium bromide or hexadecyltrimethylammonium bromide. The composition of the mixed monolayer is mixing-ratio dependent and is slightly asymmetric: for overall equimolar mixtures, the larger mole fraction in the mixed monolayer is that of the more surface-active ion. The strong synergetic effects observed in the surface tension reduction efficiency are reflected by large negative β^s parameters, according to regular solution theory. They can be interpreted by the more negative adsorption free energy of each surfactant and the smaller area occupied by surfactant hydrocarbon chains in the mixed monolayer. Received: 20 April 1998 /Accepted in revised form: 27 August 1999     

Solubility of light hydrocarbons and their mixtures in pure water under high pressure

New solubility data of methane, ethane, n-butane and their mixtures in pure water are obtained at 344.25 K, from 2.5 to 100 MPa. The results agree well with those of the literature in the case of pure hydrocarbons in water, but differ significantly for hydrocarbon mixtures. In contrast to the conclusion reached by Amirijafari and Campbell [B. Amirijafari, J. Campbell, Solubility of gaseous hydrocarbon mixtures in water, Soc. Pet. Eng. J. (1972) 21–27.], the experimental solubility data of methane–ethane mixtures shows an ideal solution behavior, while the solubility data of methane–n-butane mixtures shows a weaker non-ideality than that observed by McKetta and Katz [J.J. McKetta, D.L. Katz, Methane–n-butane–water system in two-and three-phase regions, Ind. Eng. Chem. 40 (1948) 853–863]. The pure hydrocarbon solubility data are satisfactorily correlated using the Soreide and Whitson modification [I. Soreide, C.H. Whitson, Peng–Robinson predictions for hydrocarbons, CO2, N2, and H2S with pure water and NaCl brine, Fluid Phase Equilib. 77 (1992) 217–240] of the Peng–Robinson equation of state.     

Density and surface tension of pure ionic liquid 1-butyl-3-methyl-imidazolium l-lactate and its binary mixture with alcohol and water

The density and surface tension of the pure ionic liquid 1-butyl-3-methyl-imidazolium l-lactate were measured from T (293.15 to 343.15) K. The coefficient of thermal expansion, molecular volume, standard entropy, lattice energy, surface entropy, surface enthalpy, and enthalpy of vaporization were calculated from the experimental values. Density and surface tension were also determined for binary mixtures of {1-butyl-3-methyl-imidazolium l-lactate + water/alcohol (methanol, ethanol, and 1-butanol)} systems over the whole composition range from T (298.15 to 318.15) K at atmospheric pressure. The partial molar volume, excess partial molar volume and apparent molar volume of the component IL and alcohol/water in the binary mixtures were discussed as well as limiting properties at infinite dilution and the thermal expansion coefficients of the four binary mixtures. The surface properties of the four binary mixtures were also discussed.     

Investigation of the surface tension of methane and n-alkane mixtures by perturbed-chain statistical associating fluid theory combined with density-gradient theory

The perturbed-chain statistical associating fluid theory (PC-SAFT) and density-gradient theory are used to construct an equation of state to describe the phase behavior of binary methane–n-alkane mixtures. With the molecular parameters and influence parameters regressed from bulk properties and surface tensions of pure fluids, respectively as input, both the bulk and interfacial properties are investigated. The surface tension of the binary systems methane–propane, methane–pentane, methane–heptane and methane–decane are predicted, and the results are satisfactory compared with the experimental data. Our results show that PC-SAFT combined with density-gradient theory is able to describe the interfacial properties of binary methane–n-alkane mixtures in wide temperature and pressure ranges, and illustrate the influence of the equilibrium bulk properties and chain length of n-alkane molecule on the interfacial properties.     

A new equation for the correlation of surface tension–composition data of solvent–solvent and solvent–fused salt mixtures

An attempt has been made to propose accurate equations for correlating the surface tension of binary liquid mixtures. The method is applicable to the systems comprising of components with widely different molecular sizes. Two adjustable parameters, δ_p and δ_m obtained from the least squares analyses of the surface tension–composition data are reported for a number of systems. Temperature dependence of δ_p and δ_m is demonstrated for a few systems. The framework of operational equations has later been applied to cover multi-component systems comprising of fused salts with a single liquid component in full mole fraction range. Excellent fits of the surface tension for binary, ternary and multi-component ionic systems in aqueous or non-aqueous media have been obtained from the proposed method. The surface tension–composition data of 59 different types of systems with about 400 data points can be correlated by the equation with an average percent deviation of about 0.61. In contrast to previous equations from literature to calculate surface tension data, the proposed correlation is noted to be more accurate in different situations.     

Vapor–liquid equilibria predictions of hydrogen–hydrocarbon mixtures with the Huron–Vidal mixing rule

An excess Gibbs-equation of state (G^E-EoS) framework based on the Huron–Vidal mixing rule, has been applied to study vapor–liquid equilibria (VLE) of hydrogen–hydrocarbon mixtures. The mixing rule couples the Peng–Robinson–Stryjek–Vera (PRSV) EoS with a local composition solution model. The solution model is based on one-fluid theory treatment and assigns a single energy parameter to each binary pair. This energy parameter relates to the preference of the molecules for like to unlike interactions. The allocation of a system's number of interactions to the individual species in a binary mixture, incorporates the use of size parameters which gain significance only in the liquid phase. In a two parameter form, the framework has been used for the simultaneous data reduction of a large number of binary and several ternary hydrogen–hydrocarbon mixtures. These systems were taken over an extended range of pressures and temperatures. Results from the data reduction are reported in both tabular and graphical forms. Correlations for the model parameters have been identified with the acentric factor of the hydrocarbon in hydrogen–hydrocarbon binary mixtures. In a fully predictive mode, the model has shown to describe well VLE of binary hydrogen–linear alkane systems. Comparisons of these results with calculations from the Peng–Robinson (PR) EoS and the classical mixing rule (vdW) are included.     

Correlation and prediction the activity coefficients and solubility of amino acids and simple peptide in aqueous solution using the modified local composition model

In this work, the modified Wilson model was used to obtain the activity coefficients of amino acids and simple peptides in non-electrolyte aqueous solutions. The Wilson model was modified using the new local mole fraction proposed by Zhao et al. and non-random case for the reference state. The binary interaction parameters (BIP) of the modified Wilson model for amino acid–water pairs were obtained using the experimental data of the activity coefficients for amino acids available in the literature. The modified Wilson model was also used to correlate the solubility of amino acids in water and the values of Δh/R, Δs/R, and Δg/R of the solutions studied were reported. The results obtained showed that the modified Wilson model can accurately correlate the activity coefficients as well as the solubility of amino acids and simple peptides in aqueous solutions. Also the modified Wilson model was coupled with the Pazuki–Rohani model to correlate the mean ionic activity coefficients of electrolytes in aqueous amino acid solutions. The results showed that the proposed model can accurately correlate the activity coefficients of the electrolytes in aqueous amino acid solution.     

Modeling high-pressure densities at wide temperature range with volume scaling: Cyclohexane + n-hexadecane mixtures

High-pressure density data for cyclohexane + n-hexadecane mixtures at a wide temperature range was modeled with several classical equations of state (EOS) and correlative models. A modification for softening the co-volume and another for a volume scaling of the Peng–Robinson EOS (VS-PR) were proposed. The VS-PR model is able to correlate the pure component experimental data employing only five adjustable parameters, with root-mean-square deviation (RMSD) between calculated and experimental densities essentially within the experimental error. This result is superior to widely used approaches, i.e., a six parameter Tait model and six parameter volume translations (temperature and pressure dependent) for Peng–Robinson and Patel–Teja EOS. The VS-PR model also represents well the isobaric thermal expansion and the isothermal compressibility coefficients of the pure cyclohexane, a small naphthenic substance as well as a long chain n-alkane hydrocarbon, n-hexadecane. When modeling the mixture data, the use of VS-PR model of pure components along with the Redlich–Kister expansion, truncated at the first term, the density was correlated within a RMSD only 60% greater than the experimental error. The proposed model is able to accurately represent all the tested mixture data with a relatively small number of parameters.     

Surface tension correlation for pure polar fluids by a new molecular model and SRK equation of state

In this work, a new model based on molecular thermodynamic was presented to correlate the surface tension of pure polar liquids. This model was developed based on the Davis theory. According to this theory, the surface tension is defined as a function of radial distribution function (RDF) and potential function (PF) as well. The proposed model includes three additive terms; hard sphere, dispersion and polar interactions. The RDF of Kolafa equation of state and Dirac delta function as a PF were used for hard sphere interaction. The RDF expression of Xu and Hu was considered for both dispersion and polar interactions. The presented model has two adjustable parameters, size and energy, which were obtained by optimization of an objective function for each pure fluid. This proposed approach was used for 19 pure polar fluids divided into 6 groups; organic acids, alcohols, ketones, ethers, aldehydes, and water. The average absolute deviation percent (AAD%) obtained for 19 fluids are 0.74. Also the surface tension of these 19 fluids was calculated by the use of SRK EOS and Sugden empirical formula in two cases. In case 1, Sugden's Parachor was calculated from Hugill and van Welsenes correlation and in case 2, it was obtained by optimization of an objective function for each component. The values of AAD% are 43.544 and 2.281 for cases 1 and 2, respectively. These results show the new model, which includes two adjustable parameters, can correlate the surface tension of the pure polar liquids with a high accuracy.     

Peng-Robinson equation of state for vapor-liquid equilibrium calculations for carbon dioxide + hydrocarbon mixtures

Lin, H.-M., 1984. Peng-Robinson equation of state for vapor-liquid equilibrium calculations for carbon dioxide + hydrocarbon mixtures. Fluid Phase Equilibria, 16: 151–169.Binary interaction parameters δ_ij in the Peng-Robinson equation of state have been determined from vapor-liquid equilibrium data for binary mixtures of carbon dioxide with a variety of hydrocarbons. A constant value of δ_ij ? 0.125 appears to represent the experimental data well in most cases. Comments are made on the recent work of Kato, Nagahama and Hirata, who correlated δ_ij as a function of temperature for CO₂ + n-paraffin binary mixtures.     

Volumetric and surface properties of pure ionic liquid n-octyl-pyridinium nitrate and its binary mixture with alcohol

The density and surface tension for pure ionic liquid N-octyl-pyridinium nitrate were measured from (293.15 to 328.15) K. The coefficient of thermal expansion, molecular volume, standard entropies, and lattice energy were calculated from the experimental density values. The critical temperature, surface entropy, surface enthalpy, and enthalpy of vaporization were also studied from the experimental surface tension results. Density and surface tension were also determined for binary mixtures of (N-octyl-pyridinium nitrate + alcohol) (methanol, ethanol, and 1-butanol) systems over the whole composition range at 298.15 K and atmospheric pressure. Excess molar volumes and surface tension deviations for the binary systems have been calculated and were fitted to a Redlich–Kister equation to determine the fitting parameters and the root mean square deviations. The partial molar volume, excess partial molar volume, and apparent molar volume of the component IL and alcohol in the binary mixtures were also discussed.     

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.     

Surface Tension Measurements for Binary Mixtures of Chlorobenzene or Chlorocyclohexane + Tetrahydrofuran at 298.15 K

Surface tensions (σ) for the binary mixtures chlorocyclohexane + tetrahydrofuran and chlorobenzene + tetrahydrofuran at 298.15 K and 1.013 bar have been determined as a function of the mole fraction. In order to analyze the surface tension behavior, the extended Langmuir (EL) and Shereshefsky models were used and parameters of the models were obtained for these mixtures. The standard Gibbs energy of adsorption (\( - \Delta G^{\circ} \)) was calculated using both models. The Gibbs energy change for replacing 1 mol of solute with 1 mol of solvent in the surface region (?G _S), and the excess number of molecular layers of solute in the surface region, were calculated using Shereshefsky’s model. The magnitudes of ?G _S and \( - \Delta G^{\circ} \) are discussed in terms of the nature and type of intermolecular interactions in the binary mixtures.     

A Corresponding-state Model for Predicting Surface Tension

A generalized corresponding-state model based on two reference fluids was developed for the prediction of surface tensions for non-polar and weakly polar pure fluids and their binary mixtures. Four parameters,po, Tc, Vc and ω, were used in this model, and the acentric factor ω was used as a scaling parameter. This model has been tested for 69 pure substances and 20 binary mixtures; the average absolute deviations are 0. 28 and 0. 20 mN/m, respectively. The results indicate that the predictions by means of this model were in good agreement with experimental data. In addition, the calculated deviation would increase with the excess surface tension rising, and if the excess surface tension is less than 3 mN/m, the prediction will be good and credible.