Prigogine Flory Patterson Theory Research Articles

Thermophysical properties: Viscosity, density, and excess properties of 2-propanol and n-Decane mixtures from 283.15 K to 343.15 K under atmospheric conditions

To study the effects of temperature as well as molecular interaction of a fluid system on the thermophysical properties of 2-propanol and n-Decane binary mixture, the density (ρ), dynamic viscosity (η), speed of sound (u), and refractive index (nD) of pure 2-propanol and n-Decane, along with their binary mixtures, were experimentally measured across the entire compositional range at temperatures from 283.15 to 343.15 K and atmospheric pressure. These experimental measurements helped in the evaluation of various thermophysical properties, such as excess molar volume (vE), coefficient of thermal expansion (αE), and isentropic compressibility (κsE). The experimental dynamic viscosity (η) and density (ρ) data were used to evaluate kinematic viscosity (v) and Gibbs free energy (ΔG) of flow with an equation based on Eyring's absolute state theory, and their corresponding excess properties. The excess properties of the binary mixtures were correlated using a Redlich-Kister type polynomial equation via the least-squares regression method, with fitting parameters determined for the binary system. Moreover, the Prigogine–Flory–Patterson theory (PFP) was utilized to identify the primary molecular interactions contributing to the excess molar volume at 293.15, 308.15, and 323.15 K for the binary mixtures. Additionally, the capability of the Eyring-NRTL model was tested to predict the viscosity as well as vapor-liquid equilibrium (VLE) of the binary system, and the correlated model results agreed with literature data.

The study of thermodynamic properties of diethylene glycol monoethyl ether with 2-alkanols (C3 − C7) with use of PFP and ERAS modeling

Thermodynamic properties like excess volume VmE, excess partial volume V¯m,iE, in isentropic compressibility deviations Δ Ks, and refractive index deviations ΔnD, have been calculated based on experimental density ρ, speed of sound u, and refractive index nD, by an Anton Paar / DSA 5000/ densimeter and Anton Paar Abbemat / 500/ refractometer. The systems of diethylene glycol monoethyl ether (DEGEE) + 2-propanol, or + 2-butanol, or + 2-pentanol, or + 2-hexanol, or + 2-heptanol, were given at T = (298.15–318.15) in 10 K intervals at ambient pressure (81.5 kPa) have been investigated. Data was fitted by Redlich-Kister relation.TheVmE is negative for + 2-propanol and positive sign for other systems observed. The Δ Ks is negative for all systems, except for + 2-heptanol system is positive. The ΔnD is negative for + 2-hexanol or + 2-heptanol systems and is positive for all the rest. The The intermolecular interactions and structure factors were discussed for the binary mixtures. In addition the Prigogine–Flory–Patterson theory (PFP) and Extended Real Associated Solutions (ERAS) models were used to correlate VmE data of binary mixtures. The fitting data for all systems reasonable consistency with experimental data for all the systems.

Thermophysical properties of binary mixtures of pentyl acetate with butanol at 298.15 K to 318.15 K: PFP theory, FTB model, and Graph theoretical approach

The measured density (ρ) and refractive index (nD) of binary pentyl acetate (1) + isomers of butanol (2) mixtures were reported at T = 298.15 K to 318.15 K and at 0.1 MPa pressure. Using the experimental ρ, u and nD data, excess molar volume (VmE), excess ultrasonic speed (uE), excess isentropic compressibility (κSE), and excess refractive index (nDE) were calculated and correlated with the Redlich–Kister (RK) equation. The findings suggest that the behavior of a mixture is affected by intermolecular interactions (cohesive forces such as dipole–dipole, H–bonding, dispersive force) and structural aspects of the molecules. The Prigogine–Flory–Patterson (PFP) theory, Flory–Treszczanowicz–Benson (FTB) model, and Graph theoretical approach (GTA) accurately analyzed the VmE values. Both the FTB model and PFP theory predicted the VmE curves not only successfully but also accurately represented their shape and magnitude except GTA at a lower mole fraction of pentyl acetate (xA<0.2). The positive values of VmE values were observed for binary mixtures across all temperatures. The intermolecular interactions were also corroborated by uE, κSE and nDE.

FT-IR studies and excess thermodynamic properties of binary mixtures at various temperatures and correlation with the Jouyban–Acree model

ABSTRACT Densities (ρ), speeds of sound (u), and viscosities (η) for three binary mixtures of 4-Hydroxy-4-methyl-pentan-2-one with 3-amino-propan-1-ol, 2-amino-2-methyl-propan-1-ol, and 1-amino propan-2-ol were calculated at temperatures ranging from 303.15 to 313.15 K and atmospheric pressure over the entire composition range. Experimental measurements were used to calculate the excess molar volume, excess isentropic compressibility, deviation in viscosity, and excess Gibbs free energy of the activation of viscous flow. Partial molar properties and infinite dilution molar partial properties are also calculated for each binary system. Heteroassociates molecules forming complexes and chemical forces with specific interactions can be discussed from the results. The Prigogine–Flory–Patterson theory is used to identify the most important interaction. The results of the Jouyban–Acree model are discussed in terms of the mean relative deviation and individual relative between the calculated and experimental densities, speed of sound, and viscosities as an accuracy criterion. FTIR studies confirm the experimental findings of the investigated mixtures.

Density, Speed of Sound, and Refractive Index of Binary Mixtures of Propiophenone + (3-Amino-1-propanol, Propylamine, or Isobutanol) at Temperatures of 298.15 to 308.15 K: Modeling by Prigogine–Flory–Patterson Theory

Density, Speed of Sound, and Refractive Index of Binary Mixtures of Propiophenone + (3-Amino-1-propanol, Propylamine, or Isobutanol) at Temperatures of 298.15 to 308.15 K: Modeling by Prigogine–Flory–Patterson Theory

Volumetric, acoustic, and optical properties of binary mixtures of diethyl ether with alkanol at T = 293.15 K to 303.15 K

Density (ρ), ultrasonic speed (u), and refractive index (nD) of binary liquid mixtures such as diethyl ether (DEE) (1) + alkanol (isomers of propanol and 1-butanol) (2) were experimentally measured at T = 293.15 K to 303.15 K and at 0.1 MPa pressure. By using these measurements excess molar volume (VmE), deviation in ultrasonic speed (Δu), excess isentropic compressibility (κsE), and deviation in refractive index (ΔnD) were computed and associated with the Redlich-Kister polynomial equation. It was found that deviation parameters are influenced by H–bonding, interstitial accommodation, and dipole–dipole molecular interactions between binary mixtures. The VmE values have been interpreted by the Prigogine–Flory–Patterson (PFP) theory and the Flory–Treszczanowicz–Benson (FTB) model. The FTB model and PFP theory anticipated the VmE curves and were able to depict the perfect shape and magnitude of VmE values. The numeric values of u and nD were computed by using several empirical correlations and mixing rules. This study discusses the comparative significance of these relationships with the measured values of u and nD.

Application of ERAS-model and PFP theory on excess and deviation properties for binary systems of ionic liquid + amine derivatives

Thermodynamics of mixtures includes ionic liquid 2-hydroxyethylammonium propionate [2-HEAPr] + 1-propanol, 3-amino-1-propanol [AP], 1-amino-2-propanol [MIPA], and monoethanolamine [MEA] were studied. Density ρ, speed of sound u, and refractive index nD of pure and mixtures were measured at T = (298.15, 308.15, 318.15) K. Excess molar volume VmE, excess partial molar volume Vm,iE, excess thermal expansion coefficient αE, isothermal coefficient of excess molar enthalpy (∂Hm∂P)T,x, deviations in isentropic compressibility Δ ks, and refractive index Δ nD were calculated and data correlated with Redlich-Kister polynomial relation. The Prigogine-Flory-Patterson (PFP) and Extended Real Associated Solution (ERAS) models were applied to analyze intramolecular and intermolecular interactions between like and unlike molecules. The accuracy of theoretical models were found to be in agreement with empirical results. Finally, the study confirmed the structures of the ILs using FT-IR and HNMR analysis.

Study of molecular interactions between 2-methyl 1-propanol and m-substituted aniline at various temperatures (thermodynamic and acoustic properties)

ABSTRACT Excess molar volumes (V E), excess acoustic impedance (Z E), excess isentropic compressibility (κ s E), deviation in viscosity (Δη), excess Gibbs energy of activation of viscous flow (G *E), excess free length (L f E), excess enthalpy (H E) and excess speed of sound (U E) for binary mixtures of 2-methyl-1-propanol with meta-substituted aniline (3-chloroaniline, 3-methoxyaniline and 3-methylaniline) at selected compositions were determined from the measured values of densities (ρ), viscosities (η) and speeds of sound (u) of pure components and their mixtures in range of 303.15–313.15 K. The results are analysed in terms of interactions arising due to the formation of complex hydrogen bond electron in the binary mixtures. Different theoretical models were applied to check the applicability to the present values of speed of sound and viscosity. Finally, the Prigogine–Flory–Patterson theory is applied to identify the most predominant molecular interaction.

The study of intermolecular interactions in [Bmim][PF6] + 1-octyl-2-pyrrolidone binary mixtures from volumetric, acoustic, optical and spectroscopic measurements

Under 101.3 kPa pressure, the densities, speeds of sound, and refractive indices of [Bmim][PF6] + 1-octyl-2-pyrrolidone mixtures were determined experimentally over the whole composition range and at 303.15 to 323.15 K. The excess molar volumes (VmE), excess values of partial molar volumes (V¯mE), partial molar volumes at infinite dilution (V¯mE,∞), excess values of isentropic compressibility (KsE), speeds of sound (uE) and isobaric thermal expansion coefficient (αPE) have been calculated using these experimental data. The Redlich–Kister polynomial equation has been adequately fitted to the computed data. Intermolecular interactions between like and unlike molecules have been interpreted using the experimental and computed data. The Prigogine–Flory–Patterson theory of excess molar volume and IR spectroscopic studies supported the conclusions drawn from volumetric and acoustic properties.

Analysis of thermo-physical properties and qualitative investigation of molecular interactions in terms of Graph Theoretical Approach in binary liquid mixtures containing 1-propanol + Amines (1,3-diaminopropane or 1,2-diaminopropane or 1-amino-2-propanol) at T = 298.15–318.15 K

In the present report, the molecular interactions between 1P (1-propanol) and Amines (1,3-DAP (1,3-diaminopropane) or 1,2-DAP (1,2-diaminopropane) or 1A2P (1-amino-2-propanol)) are examined by insight of thermo-physical properties of binary liquid mixtures. Density (ρ) and speed of sound (u) were measured for 1P, Amines and their binary mixture at T = 298.15–318.15 K at 0.1 MPa. Experimental data of ρ and u were used to evaluate VmE (excess molar volume), ksE (excess molar isentropic compressibility), VfE (excess free volume), uE (excess ultrasonic speed), LfE (excess intermolecular free length) and VaE (excess available volume). Further, these calculated properties were correlated with Redlich-Kister polynomial (R.K.). VmE data is also examined in term of GTA (Graph theoretical approach) and PFP (Prigogine-Flory-Patterson) theory. FT-IR spectroscopic studies supported the results and clearly indicated that a strong intermolecular interactions exist between 1P and Amines components in the binary mixture which is also recognized by GTA. The u data were examined by different correlations like Nomoto, Impedance dependence, Van Dael, JFLT (Jacobson’s free length theory) and CFT (Schaaff’s collision factor theory).

Physicochemical and acoustic characterization of binary mixtures of tetraalkylammonium bromide: PEG based DES and water

In modern green chemistry, Deep eutectic solvents (DESs) have gain appreciable recognition as an analogues of ionic liquids (ILs) due to inexpensive and easy to handle preparation method. DESs exhibit similar physiochemical properties to ILs and considered as a suitable alternative to volatile organic solvents. In present study, DESs were formulated by complexing HBA: Tetraethylammonium bromide and Tetrapropylammonium bromide and HBD: Polyethylene glycol of average molecular weight (200/400/600) in 1:2 M ratio. The densities (ρ), speeds of sound (u) of pure DESs and their binary mixtures with H2O were collected as a function of DES concentration and temperature. The excess molar properties: VmE and Ks,mE were calculated using these data and fitted to the Redlich-Kister equation to estimate standard deviation between the experimental and calculated values of excess molar properties. The trends of variation in calculated values of VmE and Ks,mE were interpreted in light of temperature and DES: H2O interactions occurring within the binary mixtures. The PFPT (Prigogine-Flory-Patterson Theory) and ERAS (Extended Real Associated Solution Model) were applied to evaluate the validity of theories to predict VmE for presently studied binary mixtures.

Volumetric, Optical, and Spectroscopic Study of Molecular Interactions for Binary Liquid Mixtures of Gamma-Valerolactone with 2-Alkoxyethanols

Physical parameters such as densities, ρ, and refractive indices, nD, of pure gamma-valerolactone/2-alkoxyethanols and their binaries have been determined over the whole composition range at different temperatures (298.15, 303.15, 308.15, and 313.15 K) and pressure = 0.1 MPa. From the experimental results, excess properties such as excess molar volumes, VmE, deviations in refractive indices, ΔϕnD, and deviations in molar refractions, ΔϕRM, have been calculated. The predicted data were fitted to the Redlich–Kister-type polynomial equation to derive the binary interaction parameters and recognize standard deviations between experimental and calculated values of the liquid solutions. Furthermore, the partial molar volumes, V¯m,1, V¯m,2, and excess partial molar volumes, V¯m,1E, V¯m,2E, were also computed. The Prigogine–Flory–Patterson theory and Graph theory were employed to correlate experimental VmE values. The departure of real mixtures from ideal behavior was interpreted in terms of strength and nature of molecular interactions. Furthermore, Fourier-transform infrared spectroscopy studies of the investigated solution along with pure components were also reported to obtain a better insight into intermolecular interactions between unlike molecules. In our study, positive values of VmE and negative values of ΔϕnD were observed, which suggests weak dispersion forces between dissimilar molecules.

Insights into experimental and theoretical approach to physicochemical properties of aqueous PEGylated deep eutectic solvents at T=(293.15–323.15) K

This paper demonstrates the excess molar properties: excess molar volumes VmE and excess isentropic compressibilities Ks,mE of aqueous binary mixtures of PEGylated DESs at T = (293.15 - 323.15) K and at atmospheric pressure. The DESs were prepared from combination of Tetrabutylammonium bromide/Benzyltributylammonium chloride as HBA with Polyethylene glycols of different average molar masses 200, 400, and 600 as HBD. The excess molar properties excess molar volumes VmE and excess isentropic compressibilities Ks,mE of DESs binary mixtures were obtained over the entire composition range from experimental values of the density and speed of sound of both pure and aqueous DES mixtures. The Redlich-Kister equation was used to estimate the standard deviation between experimental and calculated excess properties. The stronger interaction between water and components of studied DESs gave negative values for both excess molar properties. This behaviour of the investigated systems was assessed using Extended Real Associated Solution Model (ERAS) and Prigogine-Flory-Patterson theory (PFPT). The obtained results were interpreted in terms of interactions between the mixture components, temperature, structure of HBA and molecular mass of HBD.

Evaluation of molecular interactions in binary mixtures comprising ethylene and di-ethylene glycol with ethyl lactate through thermophysical and spectroscopic studies

In this article, the study of molecular interactions in liquid systems containing industrially and biologically important solvents with minimal environmental damage has been done. Density (ρ) and refractive index (nD) of binary systems comprising ethyl lactate (EL) + ethylene glycol (EG) and di-ethylene glycol (DEG) at various mole fractions and T = (298.15 to 313.15) K along with pure components have been measured. The observed parameters were further used for determination of excess molar volumes (VmE), partial molar volumes (V¯m), excess partial molar volumes (V¯mE), deviations in refractive index (ΔϕnD) and deviations in molar refraction (ΔϕRM). Redlich-Kister coefficients along with standard deviations have been obtained by approximation of data to polynomial equation. The obtained VmE results have been investigated theoretically by means of Prigogine-Flory-Patterson (PFP) and Graph theories to estimate type and nature of interactions among constituent molecules which can be used to explain the changes in physicochemical properties of the mixtures. By analysing experimental data in light of PFP Theory, Interactional and characteristic pressure contributions have been found negative values for both the binary systems whereas free volume contribution possess positive sign. The structural variation of the components in the mixtures due to change in molecular interactions has been discussed by Graph theory. Fourier Transform InfraRed (FT-IR) studies have also been performed for pure and equimolar mixtures to enlighten the experimental outcomes. It confirmed the rupture of pre-existing bonding in lactate and the formation of new hydrogen bonds with glycols.

Thermophysical properties of binary mixtures of 2-chlorotoluene or 4-chlorotoluene or 1,3-dichlorobenzene + 1,4-dioxane at T = (298.15–318.15) K

ABSTRACT Densities (ρ) and ultrasonic speeds () of the binary mixtures 2-chlorotoluene or 4-chlorotoluene or 1,3-dichlorobenzene (1) + 1,4-dioxane (2) were measured at temperature 298.15–318.15 K and atmospheric pressure. Using these measurements, excess volume () and deviation in ultrasonic speed () were calculated. Excess isentropic compressibility () was calculated using ρ and values. The values have been interpreted by Prigogine–Flory–Patterson (PFP) theory also. The obtained using PFP theory agree well with experimental values. The values were also calculated using various empirical relations. The available volume () and intermolecular free length () were calculated using experimental u values by employing Jacobson free length theory.

Investigation of Temperature, Composition, and Alkyl Chain-Dependent Molecular Interactions between Imidazolium-Based Ionic Liquids and Aniline: A Study of Experimental and Theoretical Thermophysical Properties

The versatile features of pure ionic liquids (ILs) can be considerably fine-tuned through mixing with suitable cosolvents, thereby expanding their role as potential green solvents to replace the traditional volatile organic solvents in several industrial processes. In the present work, the excess molar volume (VmE), excess molar isentropic compressibility (Ks,mE), and deviation in refractive index (ΔφnD) have been determined from the measurement of density (ρ), speed of sound (u), and refractive index (nD) by mixing imidazolium-based ILs: 1-methyl-3-alkyl imidazolium tetraflouroborate (alkyl = butyl, hexyl, and octyl) with aniline (AN) over an entire range of compositions and at temperatures ranging from 293.15 to 323.15 K at 5 K intervals and at atmospheric pressure. The magnitude of the negative VmE and Ks,mE increases absolutely as the temperature increases. Ion–dipole interactions and structural factors of the components of the mixture were held responsible for their nonideal behavior and have been interpreted. The influence of the alkyl chain of ILs and temperature on the thermophysical properties of the mixtures had been studied. We have predicted refractive indices for the studied binary mixtures using several mixing rules and compared the experimental values with them through standard deviation. We further compared our excess molar volume calculated through experimental density values with the predicted values using Prigogine–Flory–Patterson theory and Extended Real Association Model.

Thermodynamics of haloarenes with n-hexane at 298.15–318.15 K: Density, ultrasonic speed and viscosity

Densities (ρ), ultrasonic speeds (u) and dynamic viscosity (η) of the binary 2-chlorotoluene or 4-chlorotoluene or 1,3-dichlorobenzene (1) + n-hexane (2) mixtures were measured at (T = 298.15–318.15) K and atmospheric pressure. Using these measurements, excess volume (VmE), excess ultrasonic speed (uE) and deviation in dynamic viscosity (Δη) were calculated. Excess isentropic compressibility (κsE) was calculated using ρ and u values. The VmE values have been interpreted by Prigogine-Flory-Patterson (PFP) theory. The VmEobtained using PFP theory agree well with experimental values. The u values were also calculated using various empirical relations. The available volume (Va) and intermolecular free length (Lf) were calculated using experimental u values employing Jacobson free length theory. The Δη values were coupled with VmE values to understand intermolecular interaction. Further, Bloomfield and Dewan model was applied to calculate η and Δη values of the studied binary mixture and calculated values agree well with experimental values.

Application of Prigogine–Flory–Patterson theory to correlate the thermodynamic properties of aqueous mixtures of some three-component deep eutectic solvents based on choline chloride and carboxylic acids at T = (288.15 to 318.15) K

Thermodynamic properties of some neoteric three-component deep eutectic solvents (DESs) and their mixture with water are of great practical and fundamental importance in various fields of sciences. In this work the measurements of density and speed of sound data for neat four DESs (choline chloride/lactic acid/ethylene glycol, choline chloride/lactic acid/glycerol, choline chloride/oxalic acid/ethylene glycol and choline chloride/oxalic acid/glycerol) and their aqueous mixture were carried out over the entire composition range at T = (288.15 to 318.15) K. Some of the thermodynamic properties including the excess molar volumes (VE), the apparent molar volumes (Vφ,1 and Vφ,2), excess isobaric thermal expansion (αp, mE), the isentropic compressibility deviation (Δκs) and speed of sound deviation (Δu) were computed based on these data. These main properties were evaluated according to numerous solute-solvent interactions among the various components in the mixtures for all of the investigated systems. In addition, the properties were fitted by the Redlich–Kister and Hwang equations. Finally, the capability of Prigogine–Flory–Patterson (PFP) theory for reproducing the main experimentally observed properties of the investigated systems containing DESs. The binary interaction parameter χ12 of PFP theory are negative and these represent the stronger interactions between the components (DESs + water), as compared to the self-interactions among the pure components in the systems.

Thermodynamic Excess Properties for the Ternary Benzene + n-Heptane + n-Octane System at Temperatures of 298.15–318.15 K: Measurement and Correlation

The density (ρ), speed of sound (u), and refractive indices (nD) data at atmospheric pressure for benzene + n-heptane + n-octane mixtures from 298.15 to 318.15 K have been measured. The data were further used to derive excess molar volume (VmE) and deviation in u (Δu) and nD (Δn). The VmE values for the ternary mixtures were positive and predicted from the constituent binary data using various fitting equations, geometrical solution models, and the Prigogine–Flory–Patterson theory. The u data at 298.15 K were analyzed by Schaaff’s collision factor theory and Nomoto correlations. Using the Jacobson free length theory, LfE and VaE were also calculated. The nD data for these mixtures were also predicted from the pure component data.

Excess molar volumes of cyclohexanone with n-, sec-, or tert-butylbenzene: Application of the PFP theory and graph-theoretical approach

Excess molar volumes, VE, for the binary mixtures of cyclohexanone with n-, sec-, or tert-butylbenzene were measured over the entire composition range at (298.15, 303.15, 308.15 and 313.15) K and 0.1 MPa, by means of a vibrating-tube densimeter. VE data are sigmoid shape for the studied mixtures of cyclohexanone + n-butylbenzene (with negative VE values at lower mole fractions of cyclohexanone) and negative for the mixtures of cyclohexanone + sec-butylbenzene, and cyclohexanone + tert-butylbenzene over the whole composition range. The absolute values of excess equimolar volumes vary in the order: tert-butylbenzene > sec-butylbenzene > n-butylbenzene. The VE in the studied systems increase as the rising temperature. The Redlich-Kister equation was applied to fit the experimental data. Using the coefficients of the Redlich–Kister equation, excess partial molar volumes at infinite dilution, V¯iE,∞ were calculated for the three binary systems. Molecular non-bond energy, E for binary mixtures at the mole fraction of 0.5 and temperature of 298.15 K also were calculated by the MD simulations. The Prigogine–Flory–Patterson theory and Graph-theoretical approach were examined for the suitability by correlating experimental VE data with compositions.