Prigogine – Flory – Patterson Research Articles

Excess molar volumes and excess isentropic compressibilities of binary and ternary mixtures of o-chlorotoluene with cyclic ether and amides or cyclohexane at different temperatures

Densities and speeds of sound data for ternary o-chlorotoluene (i)+tetrahydropyran (j)+N-methylformamide or N,N-dimethylformamide or cyclohexane (k) and their sub-binary o-chlorotoluene or (tetrahydropyran+cyclohexane) mixtures have been measured at temperatures (298.15, 303.15, 308.15)K and 0.1MPa. The excess molar volumes, VijkE, VE and excess isentropic compressibilities, (κSE)ijk, κSE for ternary and binary mixtures respectively have been determined from the experimental densities, speeds of sound values and fitted to Redlich–Kister equation to calculate ternary and binary adjustable parameters along with standard deviations. The excess properties, VijkE and (κSE)ijk have been tested in terms of (i) Graph; and (ii) Prigogine–Flory–Patterson (PFP) theories.

Volumetric and transport behaviour of 2-butoxy ethanol with 1-alcohols: application of Prigogine–Flory–Patterson theory

Non-ideal behaviours of binary mixtures of 2-butoxy ethanol with 1-hexanol, 1-octanol and 1-decanol have been analysed at different temperatures and over the whole composition range. For this purpose, experimental densities were used to estimate apparent molar volumes , partial molar volumes , excess partial molar volumes . and their limiting values at infinite dilution , and respectively. Experimental viscosities were used to calculate the deviations in viscosity, ∆η. The calculated properties were interpreted in terms of molecular interactions and structural effects. A volumetric result has been analysed in the light of Prigogine–Flory–Patterson (PFP) statistical mechanical theory. Interaction parameters have been calculated from values for all the studied systems. The solute–solvent interactions have been investigated in terms of each of the three contributions, viz. interactional, free volume and P* obtained from PFP theory at equimolar concentration. The results of calculated from PFP theory are compared with the reported in our earlier communication.

Density and Refractive Index of Binary Mixtures of Two 1-Alkyl-3-methylimidazolium Ionic Liquids with 1,4-Dioxane and Ethylene Glycol

This paper reports experimental data of density and refractive index for the binary systems of 1-butyl-3-methylimidazolium tetrafluoroborate, [Bmim][BF4], with 1,4-dioxane, and 1-ethyl-3-methylimidazolium tetrafluoroborate, [Emim][BF4], with 1,4-dioxane and ethylene glycol (EG). Moreover, for the system [Bmim][BF4] + EG we report here refractive index data. The measurements for the systems with EG were made over the entire composition range at atmospheric pressure (101 ± 2 kPa) and in the temperature range from (293.15 to 353.15) K for densities and from (298.15 to 323.15) K for refractive indices. Because at room temperature the mixtures of both ionic liquids with 1,4-dioxane have indicated partial immiscibility, liquid–liquid phase equilibrium was determined. The excess molar volumes, VE, and deviations in refractive index, Δn, were calculated by using the measured experimental data and correlated by the Redlich–Kister type equations. VE values are positive for the system with EG and negative for both systems with 1,4-dioxane, Δn presenting an opposite sign. To probe the interactions in mixtures and to correlate the excess molar volumes of the mixtures the Prigogine–Flory–Patterson (PFP) theory has been used. Moreover, to correlate VE and predict density and refractive index of the mixtures the Lorentz–Lorenz equation was applied.

Thermodynamic Properties of Ternary Mixtures Containing Ionic Liquid and Organic Liquids: Excess Molar Volume and Excess Isentropic Compressibility

Densities, ρ123, and speeds of sound, u123, of 1-ethyl-3-methylimidazolium tetrafluoroborate (1) + 2-methylaniline (2) + pyridine or α-, β-, or γ-picoline (3) ternary mixtures have been measured over the entire range of composition at 293.15 K, 298.15 K, 303.15 K, and 308.15 K using density and speed of sound analyzer (Anton Paar DSA 5000). The heat capacity, Cp, of pure liquids pyridine and α-, β-, and γ-picoline have also been measured at 293.15 K, 298.15 K, 303.15 K, and 308.15 K using differential scanning calorimeter. The measured data have been employed to determine excess molar volumes, V123E and excess isentropic compressibilities,(κSE)123. The V123E and(κSE)123 data have been fitted to Redlich–Kister equation to calculate ternary adjustable parameters and standard deviations. The thermodynamic properties of the ternary mixtures have been analyzed in terms of Graph (which deals with the topology of the constituent of mixtures) and Prigogine-Flory-Patterson (PFP) theories. It has been observed that...

Excess Molar Properties for Binary Systems of CnMIM-BF4 Ionic Liquids with Alkylamines in the Temperature Range (298.15 to 318.15) K. Experimental Results and Theoretical Model Calculations

The experimental densities ρ and speeds of sound u for pure 1-hexyl-3-methylimidazolium tetrafluoroborate ([C6mim][BF4]), 1-octyl-3-methylimidazolium tetrafluoroborate ([C8mim][BF4]), butylamine (BA), and octylamine (OA) from (293.15 to 323.15) K and binary mixtures of the ionic liquids (ILs) with amines at (298.15, 308.15, and 318.15) K have been reported. The isentropic compressibilities, κS, Rao’s molar sound functions, R, intermolecular free lengths, Lf, excess molar volumes, VmE, and excess isentropic compressibilities, κSE for binary mixtures were derived. The VmE and κSE of the binary mixtures are negative and decrease with increasing temperature, with the exception of VmE being positive for [C6mim][BF4] and [C8mim][BF4] + OA in the high IL mole fraction region. The Prigogine–Flory–Patterson (PFP) theory has been applied to interpret the u and VmE data.

VOLUMETRIC AND THERMODYNAMIC STUDIES OF MOLECULAR INTERACTIONS IN BINARY LIQUID MIXTURES OF N-ALKANES WITH HEPTAN-2-OL AT 298.15 K: COMPARISON WITH PRIGOGINE-FLORY-PATTERSON THEORY

Densities, ρ, viscosities, η, and sound speeds, u, have been measured as a function of composition for binary mixtures of n-octane, n-decane, n-dodecane, and n-tetradecane with heptan-2-ol at 298.15 K and atmospheric pressure. From these measurements the excess molar volume (), deviations in viscosity (Δη), and excess isentropic compressibility (k E s), were calculated. These results were fitted to Redlick-Kister polynomial equations to estimate the binary coefficients and standard errors. The experimental results were used to test the applicability of the Prigogine-Flory-Patterson (PFP) theory. McAllister's multibody interaction model was used to correlate kinematic viscosity data. The Jouyban-Acree model was also used to correlate the experimental values of density, viscosity, and ultrasonic velocity at T = 298.15 K. The effects of size and shape of the components on excess properties are discussed. The results are discussed in terms of molecular interactions prevailing in the mixtures.

Experimental and theoretical excess molar properties of imidazolium based ionic liquids with molecular organic solvents – I. 1-Hexyl-3-methylimidazlouim tetraflouroborate and 1-octyl-3-methylimidazlouim tetraflouroborate with cyclic ethers

Experimental densities, ρ, speeds of sound, u, and refractive indices, nD for pure 1-hexyl-3-methylimidazolium tetrafluoroborate ([C6mim][BF4]), 1-octyl-3-methylimidazolium tetrafluoroborate ([C8mim][BF4]), 1,4 Dioxane (DO) and (THF) between the temperature (293.15 to 323.15K) at 5K interval and their binary mixtures at T=(298.15, 308.15 and 318.15)K at entire range of composition have been measured using an Anton-Paar DSA 5000 and Abemmete refractometer. Experimental measurements were used to estimate Rao’s molar sound functions, R, excess molar volumes, VmE, excess molar isentropic compressibilities, κs,mE, refractive indices deviations ΔϕnD and deviation in molar refraction, ΔRm. Excess properties have been fitted to the Redlich–Kister polynomial equation and binary coefficients were obtained. VmE and κs,mE were observed to be negative and decrease with increasing temperature, whereas ΔϕnD was found to be positive and increases with temperature over the entire composition range. Equations of state and several mixing rules were used to predict refractive indices of the binary mixtures and compared with the experimental values by means of the standard deviation and found to be in excellent agreement. Intermolecular interactions between the unlike molecules of the mixtures have been discussed by well known arguments. Excess molar volumes of the binary mixtures have been analyzed by Prigogine–Flory–Patterson (PFP) theory and results were compared with the experimental results.

Application of the Prigogine–Flory–Patterson model to excess molar enthalpy of binary liquid mixtures of 1-nonanol or 1-decanol with acetonitrile at atmospheric pressure and 298.15, 303.15 and 308.15 K

Excess molar enthalpy data of 1-nonanol+acetonitrile and 1-decanol+acetonitrile mixtures as a function of composition at atmospheric pressure at 298.15, 303.15 and 308.15K have been used to test the applicability of the Prigogine–Flory–Patterson (PFP) model. Both systems exhibit positive excess molar enthalpy values over the whole composition range for the studied temperature range. The model has only one adjustable parameter and correlates the data within a standard deviation up to 309Jmol−1. The interactional contribution of the model is the most important one to describe the experimental values.

Experimental Densities and Speeds of Sound of Substituted Phenols and Their Modeling with the Prigogine–Flory–Patterson Model

This work provides new experimental data of speed of sound and density for seven pure components of pyrolysis bio-oil at atmospheric pressure for several phenols (phenol, o-, m-, and p-cresol), two phenolic ethers (2-methoxyphenol and eugenol) and one phenolic ester (methyl salicylate) at temperatures of (288.15 to 343.15) K. Densities and sound velocities are correlated with the Prigogine–Flory–Patterson (PFP) model. The properties are well described with the PFP model showing a better performance for the denser substances. The relation between density and speed of sound evidence the complex thermophysical behavior of substituted phenols.

Measurement and modeling the excess properties of binary and ternary mixtures containing [Hmim][BF4], 2-methyl-2-propanol, and propylamin compounds at 298.15 K using PFP theory

Density and viscosity of pure components 1-hexyl-3-methylimidazoliumtetrafluoroborate ([Hmim][BF4]), 2-methyl-2-propanol, and propylamin, along with binary mixtures of {x1[Hmim][BF4]+x22-methyl-2-propanol}, {x1[Hmim][BF4]+x2propylamin}, and {x12-methyl-2-propanol+x2propylamin}, and ternary mixture of {x1[Hmim][BF4]+x22-methyl-2-propanol+x3propylamin} were measured over the entire composition range at atmospheric pressure and 298.15K. The results of measuring the density and viscosity were used to calculate the excess molar volumes, partial molar volumes, and viscosity deviations. For all of the binary mixtures, the computed excess molar volumes were correlated by applying Redlich–Kister equation and Prigogine–Flory–Patterson (PFP) theory, while the obtained viscosities were correlated using McAllister, Hind, and Nissan equations. The obtained excess molar volumes, VmE, and viscosity deviations, Δη, of all of the binary mixtures and ternary mixture are negative over the entire composition range. The Cibulka equation was used to correlate the ternary excess molar volumes and viscosity deviations using the Redlich–Kister parameters of the binary mixtures.

Excess molar enthalpies for [emim][BF4] + pyrrolidin-2-one or 1-methyl pyrrolidin-2-one + pyridine or water mixtures

Excess molar enthalpies, HijkE of ternary 1-ethyl-3-methylimidazolium tetrafluoroborate (i)+Pyrrolidin-2-one (j)+Pyridine or Water (k); 1-ethyl-3-methylimidazolium tetrafluoroborate (i) 1-methyl pyrrolidin-2-one (j)+Pyridine or Water (k) and HE of Pyrrolidin-2-one (i)+Pyridine or Water (j); 1-methyl pyrrolidin-2-one (i)+Pyridine (j); 1-ethyl-3-methylimidazolium tetrafluoroborate (i)+Water (j) mixtures have been measured over entire mole fraction range at 298.15K. The HijkE value for 1-ethyl-3-methylimidazolium tetrafluoroborate (i)+Pyrrolidin-2-one (j)+Water (k); 1-ethyl-3-methylimidazolium tetrafluoroborate (i)+1-methyl pyrrolidin-2-one (j)+Pyridine or Water (k) are positive over whole range of composition and for 1-ethyl-3-methylimidazolium tetrafluoroborate (i)+Pyrrolidin-2-one (j)+Pyridine (k) mixture, the sign of HijkE values varies with change in composition of the components. The observed data have been analyzed in terms of (i) Graph; and (ii) Prigogine–Flory–Patterson (PFP) theories. Results indicate that HE and HijkE values obtained by Graph theory are in good agreement with experimental data. The PFP theory correctly predict sign as well as magnitude of HE values for the binary mixtures. However, theory fails to predict the sign of HijkE values for the ternary mixtures.

Isobaric, isothermal theoretical investigation and examination of different prediction equations on some physicochemical properties in PEG liquid polymer system

Densities, viscosities and refractive indices of the {poly(ethylene glycol) 200+ethanol} binary liquid system were determined at three temperatures of (298.15, 303.15, and 308.15)K. From the experimental results, the excess molar volume was obtained and correlated with the Prigogine–Flory–Patterson (PFP) and Extended Real Associated Solution (ERAS) models. Several isobaric and isothermal properties consisting of the isobaric thermal expansion coefficient, excess molar isobaric expansion, excess molar isobaric heat capacity, isothermal coefficient of excess molar enthalpy, activation energy of flow, electron polarizibility, and Gibbs energy of activation were calculated from the experimental measurements. Moreover, the viscosity and refractive index values were correlated and predicted with different semi-empirical equations. To assess the validity of these proposed equations, comparisons were made between the experimental and predicted values.

Excess Molar Volumes and Viscosities for the Binary Mixtures of n-Octane, n-Decane, n-Dodecane, and n-Tetradecane with Octan-2-ol at 298.15 K

Experimental values of densities (ρ) and viscosities (η) in the binary mixtures of n-octane, n-decane, n-dodecane, and n-tetradecane with octan-2-ol are presented over the whole range of mixture composition at T=298.15 K. From these data, excess molar volume (VmE), deviations in viscosity (Δη), and excess Gibbs free energy of activation ΔG∗E have been calculated. These results were fitted to Redlich-Kister polynomial equations to estimate the binary coefficients and standard errors. Jouyban-Acree model is used to correlate the experimental values of density and viscosity at T=298.15 K. The values of VmE have been analyzed using Prigogine-Flory-Patterson (PFP) theory. The results of the viscosity composition are discussed in the light of various viscosity equations suggested by Grunberg-Nissan, Tamara and Kurata, Hind et al., Katti and Chaudhri, Heric, Heric and Brewer, and McAllister multibody model. The values of Δlnη have also been analyzed using Bloomfield and Dewan model. The experiments on the constituted binaries are analyzed to discuss the nature and strength of intermolecular interactions in these mixtures.

Study of thermodynamic and transport properties of binary liquid mixtures of n-decane with hexan-2-ol, heptan-2-ol and octan-2-ol at T = 298.15 K. Experimental results and application of the Prigogine–Flory–Patterson theory

Densities and viscosities of binary mixtures of n-decane with hexan-2-ol, heptan-2-ol and octan-2-ol have been measured over the entire range of composition at T=298.15K and at atmospheric pressure. From the experimental values of density and viscosity, the excess molar volumes (VmE) and excess Gibbs energy of activation of viscous flow (G∗E) have been calculated. These results were fitted to Redlich–Kister polynomial equations to estimate the binary coefficients and standard errors. Jouyban–Acree model is used to correlate the experimental values of density, viscosity and ultrasonic velocity at T=298.15K. The results of the viscosity-composition are discussed in the light of various viscosity semi-empirical equations. The experimental results have been used to test the applicability of the Prigogine–Flory–Patterson (PFP) theory. The values of Δlnη have also been analysed using Bloomfield and Dewan model. The experimental and calculated quantities are used to study the nature of mixing behaviour between the mixtures.

Thermodynamic study on some alkanediol solutions: Measurement and modeling

The densities ρ and viscosities η of 1,2-ethanediol with 1,2-propanediol or 1,3-propanediol, and 1,2-propanediol with 1,3-propanediol binary liquid mixtures over the entire concentration range at temperatures (298.15 to 308.15) K with 5K interval were measured. The experimental data were used to calculate the excess molar volume VmE, partial molar volume V¯m,i, partial molar volume at infinite dilution V¯i∞, apparent molar volume Vφi, coefficient of thermal expansion αp, excess coefficient of thermal expansion αpE, excess viscosity ηE, excess Gibbs energy of activation ΔG*E, and other thermodynamic parameters. A Redlich–Kister equation and Prigogine–Flory–Patterson (PFP) model was applied to correlate the excess molar volume results. Moreover, the viscosity data were correlated with the Grunberg–Nissan, Tamura–Kurata, Hind–Ubbelohde and Katti–Chaudhary equations. Good agreement was found between experimental data and modeling results.

Thermophysical properties of binary mixtures of N,N-dimethylformamide with three cyclic ethers

Densities and viscosities of the binary mixtures consisting of tetrahydrofuran (THF), 1,3-dioxolane (1,3-DO) and 1,4-dioxane (1,4-DO) with N,N-dimethylformamide (DMF) over the entire range of composition were measured at temperatures 298.15, 308.15 and 318.15 K and at atmospheric pressure. Ultrasonic speeds of sound of these binary mixtures were measured at ambient temperature and atmospheric pressure (T = 298.15 K and P = 1.01?105 Pa). The various experimental data were utilized to derive excess molar volumes (VmE), excess viscosities (?E), and excess isentropic compressibilities (?sE). Using the excess molar volumes (VmE), excess partial molar volumes (and ) and excess partial molar volumes at infinite dilution (and ) of each liquid component in the mixtures were derived and discussed. Excess molar volumes (VmE) as a function of composition at ambient temperature and atmospheric pressure were used further to test the applicability of the Prigogine-Flory-Patterson (PFP) theory to the experimental binaries. The excess properties were found to be either negative or positive depending on the nature of molecular interactions and structural effects of liquid mixtures. Em,1V Em,2VE0,m,1VE0,m,2V.

Excess properties of diethyl carbonate + ketone binary mixtures at variable temperatures: Application of PFP theory to excess volumes

Measurements of densities ρ, viscosities η, and refractive indices nD have been carried out for binary mixtures of diethyl carbonate (DEC) with acetophenone, cyclopentanone, cyclohexanone, and 3-pentanone over the entire composition range at the temperatures (303.15, 308.15 and 313.15) K and at atmospheric pressure. From these experimental data, the excess volumes VE, deviation in viscosity Δη and deviation in molar refraction ΔR have been calculated. The Redlich–Kister polynomial equation has been used to estimate the binary fitting parameters and the standard errors. The Prigogine–Flory–Patterson (PFP) theory and its applicability in predicting VE at (303.15, 308.15 and 313.15) K has been tested. The experimental viscosities were analyzed on the basis of Lobe and Auslaender models. Further different mixing rules have been applied to predict the refractive index values of the studied mixtures.

Volumetric Properties of Binary Mixtures of Two 1-Alkyl-3-Methylimidazolium Tetrafluoroborate Ionic Liquids with Molecular Solvents

The densities have been determined for the binary systems of ionic liquids, 1-ethyl-3-methylimidazolium tetrafluoroborate, [Emim][BF4] and 1-hexyl-3-methylimidazolium tetrafluoroborate, [Hmim][BF4], with the molecular solvents dimethyl sulfoxide (DMSO) and acetonitrile (ACN) at atmospheric pressure over the entire range of composition and temperatures from (298.15 to 353.15) K. From experimental densities, the excess molar volumes, VE, were calculated and fitted to a Redlich–Kister equation. Moreover, the VE results have been discussed in terms of the Prigogine–Flory–Patterson (PFP) theory. The VE variation was interpreted in terms of intermolecular interactions and structural effects on mixing.

Excess molar volumes, excess molar enthalpies and refractive index deviations for binary mixtures of propan-1-ol, butan-1-ol and pentan-1-ol with 2,2,4-trimethylpentane at 298.15 K

Density (ρ), refractive index (nD), and molar excess enthalpy (HE) of binary mixtures of propan-1-ol with 2,2,4-trimethylpentane, butan-1-ol with 2,2,4-trimethylpentane and pentan-1-ol with 2,2,4-trimethylpentane at 298.15K and ambient pressure have been experimentally measured in the whole composition range. Excess molar volumes (VE), deviation of refractive indices (ΔnD), deviations of molar refraction (ΔR) and HE data were correlated with Redlich–Kister equation. Refractive indexes estimates were carried out using several mixing rules. An estimation of density of the binary mixture was performed using the equation suggested by Nakata and Sakurai [35] using the Lorentz–Lorenz refractive index mixing rule with densities and refractive indexes of the pure substances. Wilson and Non Random Two Liquids (NRTL) models were applied for HE correlation. The Prigogine–Flory–Patterson (PFP) and Extended Real Association Solution (ERAS) theories have been used to correlate the excess molar volumes of the mixtures. The behavior of the thermophysical properties was analyzed in terms of the length of the alkanol chain and the balance between positive and negative deviations of the ideality.

Thermodynamic modeling and experimental speeds of sound, densities, and refractive indexes of (tetralin + n-dodecane)

This work presents densities, speeds of sound, and refractive indexes for the binary system (tetralin (1,2,3,4-tetrahydronaphthalene)+n-dodecane) along with the properties of the pure components at T=(293.15,303.15,313.15,323.15,333.15, and 343.15)K over whole composition range and atmospheric pressure. From these data, the following derived properties were obtained: isentropic compressibility, molar refractivity, excess volume, excess isentropic compressibility, molar refractivity deviations, and isobaric expansibilities. Several speed of sound mixing rules were tested, and the best result was for Wada mixing rule. Pure component densities and speeds of sound were correlated with Prigogine–Flory–Patterson (PFP) model. The binary interaction parameter for this model was obtained from correlation of excess volumes and isentropic compressibilities. This model correlated experimental densities very well and correlated reasonably well speeds of sound and isobaric expansibilities.