Prigogine Flory Patterson Theory Research Articles

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.

Thermodynamic Properties of Binary Liquid Mixtures of n-Dodecane with an Alkan-1-ol or an Alkan-2-ol at 298.15 K: A Comparative Study

Experimental densities (ρ), viscosities (η), and speeds of sound (u) of the binary mixtures of n-dodecane with an alkan-1-ol (hexan-1-ol, heptan-1-ol, octan-1-ol) or an alkan-2-ol (hexan-2-ol, heptan-2-ol and octan-2-ol) were measured over the whole mixture composition range at T = 298.15 K. From these data, the excess molar volume (\( V_{\text{m}}^{\text{E}} \)), deviations in viscosity (Δη), and excess isentropic compressibility (\( \kappa_{S}^{\text{E}} \)) have been calculated. The results were fitted by means of the Redlich–Kister equation, in order to estimate the binary coefficients and standard errors. Differences among these binary systems are ascribed to the different association abilities of the alkan-1-ols and alkan-2-ols. Experimental data on the constituted binaries were analyzed using McAllister’s multi-body interaction model, the Jouyban–Acree model, the Prigogine–Flory–Patterson theory, and the Bloomfield and Dewan model. The experimental and calculated quantities are used to study the nature of mixing behavior among the 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.

Molecular Interactions in 1-Ethyl-3-Methylimidazolim Tetrafluoroborate + Amide Mixtures: Excess Molar Volumes, Excess Isentropic Compressibilities and Excess Molar Enthalpies

The densities, ρ12, and speeds of sound, u12, of 1-ethyl-3-methylimidazolium tetrafluoroborate (1) + N-methylformamide or N,N-dimethylformamide (2) binary mixtures at (293.15. 298.15. 303.15, 308.15 K), and excess molar enthalpies, \( H_{12}^{\text{E}} \), of the same mixtures at 298.15 K have been measured over the entire mole fraction range using a density and sound analyzer (Anton Paar DSA-5000) and a 2-drop microcalorimeter, respectively. Excess molar volume, \( V_{12}^{\text{E}} \), and excess isentropic compressibility, \( \left( {\kappa_{S}^{\text{E}} } \right)_{12} \), values have been calculated by utilizing the measured density and speed of sound data. The observed data have been analyzed in terms of: (i) Graph theory and (ii) the Prigogine–Flory–Patterson theory. Analysis of the \( V_{12}^{\text{E}} \) data in terms of Graph theory suggest that: (i) in pure 1-ethyl-3-methylimidazolium tetrafluoroborate, the tetrafluoroborate anion is positioned over the imidazoliun ring and there are interactions between the hydrogen atom of (C–H{edge}) and proton of the –CH3 group (imidazolium ring) with fluorine atoms of tetrafluoroborate anion, and (ii) (1 + 2) mixtures are characterized by ion–dipole interactions to form a 1:1 molecular complex. Further, the \( V_{12}^{\text{E}} \), \( H_{12}^{\text{E}} \) and \( \left( {\kappa_{S}^{\text{E}} } \right)_{12} \) values determined from Graph theory compare well with their measured experimental data.

Excess molar enthalpies of binary mixtures of formamide with butanol at 298.15 K: Application of Prigogine–Flory–Patterson theory and Treszczanowicz–Benson association model

Excess molar enthalpies (HmE) of formamide (1)+1-butanol or 2-methyl-1-propanol or 2-methyl-2-propanol (2) mixtures have been measured at 298.15K over the entire composition range using flow micro calorimeter. The excess enthalpy data along with previously published excess volumes data (VmE) (M. Rani, S. Maken, J. Ind. Eng. Chem. 18 (2012) 1694) have been utilised to study the thermodynamics of molecular interactions in terms of Prigogine–Flory–Patterson theory and Treszczanowicz–Benson association model with a Flory contribution term. The Treszczanowicz–Benson model was developed for alkane+alkanol systems considering Mecke–Kempter type of association in alkanol. In this paper the Treszczanowicz–Benson association model was applied, for the first time, to binary mixtures containing both components associated (butanol and formamide) through hydrogen bonding. In both the cases, when either of formamide or butanol was assumed to be associated, the calculated HmE and VmE values compared reasonably well with the corresponding experimental data, but the agreement is not very impressive for excess enthalpy in formamide+2-methyl-2-propanol mixtures. Extent of inter-molecular H-bonding in formamide and butanols in their binary mixtures was also reflected in their molar enthalpy of association of H-bonding ΔhH0.

Excess molar enthalpies and excess molar volumes of formamide + 1-propanol or 2-propanol and thermodynamic modeling by Prigogine–Flory–Patterson theory and Treszczanowicz–Benson association model

Excess molar enthalpies (HmE) at 298.15K and 308.15K and excess molar volumes (VmE) at 308.15K for formamide (1)+1-propanol or 2-propanol (2) mixtures have been measured over the entire composition range. The excess enthalpies and excess volumes data have been utilized to study the thermodynamics of molecular interactions in terms of Prigogine–Flory–Patterson theory and Treszczanowicz–Benson association model with a Flory contribution term. In this paper, this Treszczanowicz–Benson association model was applied, for the first time, to binary mixtures containing both components associated (propanol and formamide) through hydrogen bonding. In both the cases, when either of formamide or propanol was assumed to be associated, the calculated HmE and VmE values compared well with corresponding experimental data. Extent of inter-molecular H-bonding in formamide and propanol in their binary mixtures was also reflected in their molar enthalpy of association of H-bonding ΔhH0 and association constant KH.

Excess Molar Volumes, Excess Molar Enthalpies and Excess Isentropic Compressibilities of 1-Methyl Pyrrolidin-2-one with Water and Propanols

Excess molar volumes V E, excess molar enthalpies H E, and speeds of sound u for 1-methyl pyrrolidin-2-one (1) + water or propan-1-ol or propan-2-ol (2) binary mixtures have been measured over the entire composition range (at 308.15 K) using a dilatometer, calorimeter and interferometer. Speeds of sound data, u, of (1 + 2) binary mixtures have been utilized to determine excess isentropic compressibilities, $$ \kappa_{S}^{\text{E}} $$ . The observed V E, H E and $$ \kappa_{S}^{\text{E}} $$ data have been analyzed in terms of (1) Graph theory (which involves the topology of the constituents of mixture), and (2) the Prigogine–Flory–Patterson theory. Analysis of V E data in terms of Graph theory suggests that 1-methyl pyrrolidin-2-one, water, propan-1-ol, and propan-2-ol exist as associated molecular entities. IR studies lend additional support to the proposed molecular entities in (1 + 2) mixtures. It has been observed that V E, H E and $$ \kappa_{S}^{\text{E}} $$ values predicted by Graph theory compare well with their corresponding experimental values.

Investigation on some thermophysical properties of poly(ethylene glycol) binary mixtures at different temperatures

Densities ρ and viscosities η for the binary mixtures of poly(ethylene glycol)+water,+1,2-ethanediol,+1,3-propanediol,+1,4-butanediol over the entire concentration range were determined at temperatures (298.15 to 308.15)K with 5K interval. The experimental data were used to calculate the excess molar volume VmE, coefficient of thermal expansion α, excess coefficient of thermal expansion αE, excess Gibbs free energy of activation ΔG∗E, and other activation parameters (i.e., ΔG∗,ΔH∗,ΔS∗). The values of excess properties were fitted to Redlich–Kister polynomial equation to estimate the binary coefficients. The excess refractive index nE and electronic polarizability αe of PEG+water binary mixtures were also determined from the experimental values of refractive indices. The viscosity data were correlated with Grunberg–Nissan and Tamura–Kurata equations. Moreover, the Prigogine–Flory–Patterson theory has been used to correlate the excess molar volumes of the studied mixtures.

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.

Temperature dependence of densities, speeds of sound, and derived properties of cyclohexylamine + cyclohexane or benzene in the temperature range 293.15–323.15 K

Densities ρ and speeds of sound u for binary mixtures cyclohexylamine+cyclohexane and +benzene have been measured over the entire range of composition at temperatures from 293.15 to 323.15K using an Anton-Paar DSA 5000. The molar isentropic compressibilities KS,m, Rao's molar sound functions R, thermal expansion coefficients αP, excess molar volumes VmE, and excess molar isentropic compressibilities KS,mE have been calculated from these data. VmE and KS,mE for both the mixtures are positive at all temperatures and over entire range of compositions. The values of VmE for cyclohexylamine+cyclohexane increase with rise in temperature while decrease for cyclohexylamine+benzene. The values of αPE are positive for cyclohexylamine+cyclohexane and negative for cyclohexylamine+benzene. The results of u, VmE, (∂VmE/∂T)P, and (∂HmE/∂P)T are compared with the theoretical predictions of the Prigogine–Flory–Patterson theory.

Experimental excess molar properties of binary mixtures of (3-amino-1-propanol + isobutanol, 2-propanol) at T = (293.15 to 333.15) K and modelling the excess molar volume by Prigogine–Flory–Patterson theory

Density and viscosity of binary mixtures of (x13-amino-1-propanol+x2isobutanol) and (x13-amino-1-propanol+x22-propanol) were measured over the entire composition range and from temperatures (293.15 to 333.15)K at ambient pressure. The excess molar volumes and viscosity deviations were calculated and correlated by the Redlich–Kister (RK) equation. The thermal expansion coefficient and its excess value, isothermal coefficient of excess molar enthalpy, and excess partial molar volumes were determined by using the experimental values of density and are described as a function of composition and temperature. The excess molar volumes are negative over the entire mole fraction range for both mixtures and increase with increasing temperature. The excess molar volumes obtained were correlated by the Prigogine–Flory–Patterson (PFP) model. The viscosity deviations of the binary mixtures are negative over the entire composition range and decrease with increasing temperature.

Excess molar enthalpies of ternary mixtures containing o-toluidine + tetrahydropyran with pyridine or isomeric picolines or benzene or toluene at 308.15 K

Excess molar enthalpies, HijkE of o-toluidine (i)+tetrahydropyran (j)+pyridine or α- or β- or γ-picoline or benzene or toluene (k) ternary mixtures have been measured over entire mole fraction at 308.15K using 2-drop calorimeter. The experimental data have been fitted to Redlich–Kister equation to evaluate ternary parameters along with their standard deviations. The HijkE values for the studied mixtures except those of o-toluidine (i)+tetrahydropyran (j)+toluene (k) are negative over entire composition range. The topology of the constituents of the mixtures has been utilized to (Graph theory) predict HijkE values of the investigated mixtures. The observed data have also been analyzed in terms of Prigogine–Flory–Patterson theory, It has been observed that HijkE values predicted by Graph theory compare well with their corresponding experimental values.

Measurement and modeling the excess molar properties of binary mixtures of {[C6mim][BF4] + 3-amino-1-propanol} and {[C6mim][BF4] + isobutanol}: Application of Prigogine–Flory–Patterson theory

In this work, densities, ρ, and viscosities, η, of pure 1-hexyl-3-methylimidazoliumtetrafluoro borate {[C6mim][BF4]}, 3-amino-1-propanol (AP), and isobutanol, along with their binary mixtures of {x1[C6mim][BF4]+x2AP} and {x1[C6mim][BF4]+x2isobutanol} were measured over entire composition range at ambient pressure (81.5kPa) and in the temperature range of (303.15 to 338.15)K. The excess molar volume, VmE, thermal expansion coefficient, α, and its excess value, αE, isothermal coefficient of excess molar enthalpy, (∂HmE/∂p)T,x, and viscosity deviation, Δη, for both of the mixtures were calculated from the experimental values of densities and viscosities. The values of VmE for binary mixture of {x1[C6mim][BF4]+x2AP} shows a S-shaped dependence on composition with positive values in the [C6mim][BF4] rich-region and negative values at the opposite extreme, and increase with increasing temperature. This quantity is negative for binary mixture of {x1[C6mim][BF4]+x2isobutanol} in the entire composition range and increases with increasing temperature. Viscosity deviations, Δη, are negative over the entire composition range and decrease with increasing temperature for both of the mixtures. These data were correlated by Treszczanowiczb–Benson and Redlich–Kister equations, and the fitting parameters and standard deviations were determined. The Prigogine–Flory–Patterson theory has been used to correlate the excess molar volumes of the mixtures.

Excess molar enthalpies for binary and ternary mixtures containing cyclic ether, 2-methylaniline and aromatic hydrocarbons

Excess molar enthalpies, H ijk E , of 1,4-dioxane (i) + 2-methylaniline (j) + benzene or methylbenzene or 1,3-dimethylbenzene or 1,4-dimethylbenzene (k) ternary and H ik E of 1,4-dioxane (i) + 1,3-dimethylbenzene or 1,4-dimethylbenzene (k) binary mixtures have been measured as a function of composition at T = 308.15 K using 2-drop calorimeter. The resulting data have been fitted to Redlich–Kister equation to evaluate binary and ternary parameters along with their standard deviations. The observed data have been analyzed in terms of (a) Graph theory (which involve the topology of the mixtures constituents), and (b) Prigogine–Flory–Patterson theory. It has been observed that H ik E and H ijk E values predicted by Graph theory compare well with their corresponding experimental values. However, although H ijk E values calculated by Prigogine–Flory–Patterson theory are of same sign, the qualitative agreement is not impressive.

Thermodynamic study of binary mixture of x1[C 6mim][BF 4] + x21-propanol: Measurements and molecular modeling

Densities, ρ, and viscosities, η, of pure 1-hexyl-3-methylimidazoliumtetrafluoro borate ([C 6mim][BF 4]) and 1-propanol, and their binary mixture { x 1[C 6mim][BF 4] + x 21-propanol} were measured at atmospheric pressure and in the temperature range of 293.15–333.15 K. The excess molar volumes, V m E , thermal expansion coefficients, α, and their excess values, α E , isothermal coefficient of excess molar enthalpy, ( ∂ H m E / ∂ p ) T , x and excess viscosities, η E , were calculated from the experimental values of densities and viscosities. The excess molar volumes of the binary mixture are negative over the entire mole fraction range and increase with increasing temperature. Excess viscosities are negative over the entire mole fraction range of the mixture and decrease with increasing temperature. The obtained excess molar volumes and excess viscosities were correlated with the Redlich–Kister equation. The experimental results have also been used to examine the applicability of Prigogine–Flory–Patterson (PFP) theory in predicting the excess molar volume of the binary mixture. It is indicated that agreement between excess molar volumes calculated via PFP theory and the experimental results is good in all temperatures.

Thermodynamic and topological investigations of ternary mixtures with o-toluidine, tetrahydropyran, and picolines: Excess molar volume and excess isentropic compressibility

The density, ρ ijk and speed of sound, u ijk , ternary { o-toluidine (i) + tetrahydropyran (j) + α-, β-, or γ-picoline (k)} mixtures have been measured over the entire composition range at T = (298.15, 303.15, and 308.15) K. The excess molar volume, V ijk E and excess isentropic compressibility, ( κ S E ) ijk values of the mixtures have been predicted by using the experimental results. The observed thermodynamic properties have been fitted to Redlich–Kister equation to determine ternary adjustable parameters and standard deviations. The V ijk E and ( κ S E ) ijk values have also been analyzed in terms of (1) Graph theory and (2) Prigogine–Flory–Patterson theory (PFP). It has been observed that V ijk E and ( κ S E ) ijk data determined by Graph theory compare well with experimental values.

Ultrasonic and Volumetric Properties of 1-Ethyl-3-methylimidazolium Trifluoromethanesulfonate Ionic Liquid with 2-Propanol or Tetrahydrofuran at Several Temperatures

Densities and speeds of sound of 1-ethyl-3-methylimidazolium trifluoromethanesulfonate mixtures with 2-propanol and tetrahydrofuran (THF), as well as of the pure components, have been measured over the whole range of compositions at T = (278.15 to 328.15) K and P = (101 ± 2) kPa. From these experimental data, the excess molar volume, excess speed of sound, and excess isentropic compressibility have been calculated and fitted to an extended version of the Redlich–Kister equation, which takes into account the dependence on composition and temperature simultaneously. The Prigogine–Flory–Patterson theory has also been used to explain the behavior of these systems.

Application of ERAS-model and Prigogine–Flory–Patterson theory to excess molar volumes for ternary mixtures of (2-chlorobutane + butylacetate + isobutanol) at T = 298.15 K

Densities of the ternary mixture consisting of {2-chlorobutane (1)+butylacetate (2)+isobutanol (3)} and related binary mixtures were measured over the whole range of composition at T=298.15K and ambient pressure. Excess molar volumes VmE for the mixtures were derived and correlated as a function of mole fraction by using the Redlich–Kister and the Cibulka equations for binary and ternary mixtures, respectively. From the experimental data, partial molar volumes, V¯m,i excess partial molar volumes, V¯iE partial molar volumes at infinite dilution V¯m,i0 and apparent molar volumes V¯φ,i were also calculated. For all binary mixtures over the entire range of mole fractions VmE data are positive. The experimental results of the constituted binary mixtures have been used to test the applicability of the extended real associated solution (ERAS-model) and Prigogine–Flory–Paterson (PFP) theory.

Application of Prigogine–Flory–Patterson theory to volumetric, ultrasonic, and compressibility parameters of (glycylglycine + CuCl 2) in aqueous ethanol mixtures

The molar volume and compressibility of (glycylglycine + CuCl 2) in aqueous ethanol mixtures have been obtained at four different temperatures T = (288.15 to 318.15) K from ultrasonic velocity and density measurements. Excess molar volumes were found to be negative throughout the composition range indicating notable changes in hydrogen bonding and electrostatic interactions. Using the Prigogine–Flory–Patterson theory, quantitative estimation of different contributions, i.e. interactional, free volume, and P ∗ effect to V E have been obtained. The molar isentropic compressibility has been computed using the ultrasonic velocity and excess volume data. The trends in κ S E are affected by the size of the molecule leading to negative contributions. In order to compare the theoretical values of ultrasonic velocity, the equations of Nomoto and Junjie were used and found to predict the experimental data very well.

Thermodynamic properties of binary mixtures of tetrahydropyran with pyridine and isomeric picolines: Excess molar volumes, excess molar enthalpies and excess isentropic compressibilities

Densities, ρ and speeds of sound, u of tetrahydropyran (i) + pyridine or α-, β- or γ- picoline (j) binary mixtures at 298.15, 303.15 and 308.15 K and excess molar enthalpies, H E of the same set of mixtures at 308.15 K have been measured as a function of composition using an anton Parr vibrating-tube digital density and sound analyzer (model DSA 5000) and 2-drop micro-calorimeter, respectively. The resulting density and speed of sound data of the investigated mixtures have been utilized to predict excess molar volumes, V E and excess isentropic compressibilities, κ S E . The observed data have been analyzed in terms of (i) Graph theory; (ii) Prigogine–Flory–Patterson theory. It has been observed that V E , H E and κ S E data predicted by Graph theory compare well with their experimental values.