Collision Factor Theory Research Articles

Volumetric, Ultrasonic and Transport Properties of Binary Liquid Mixtures Containing Dimethyl Formamide at 303.15 K

AbstractExcess volumes (VE), ultrasonic velocities (u), isentropic compressibility (ΔKs) and viscosities (η) for the binary mixtures of dimethyl formamide (DMF) with 1,2‐dichlorobenzene, 1,3‐dichlorobenzene, 1,2,4‐trichlorobenzene, o‐chlorotoluene, m‐chlorotoluene, p‐chlorotoluene, o‐nitrotoluene and m‐nitrotoluene at 303.15 K were studied. Excess volume data exhibit an inversion in sign for the mixtures of dimethyl formamide with 1,2‐ and 1,3‐dichlorobenzenes and the property is completely positive over the entire composition range for the mixtures of dimethyl formamide with 1,2,4‐trichlorobenzene, o‐nitrotoluene and m‐nitrotoluene. On the other hand, the quantity is negative for the mixtures of dimethyl formamide with chlorotoluenes. Isentropic compressibility (Ks) has been computed for the same systems from precise sound velocity and density data. Further, deviation of isentropic compressibility (ΔKs) from ideal behavior was also calculated. ΔKs values are negative over the entire volume fraction range in all the binary mixtures. The experimental sound velocity data were analysed in terms of Free Length Theory (FLT) and Collision Factor Theory (CFT). The viscosity data were analysed on the basis of corresponding state approach. The measured data were discussed on the basis of intermolecular interactions between unlike molecules.

Acoustical and Excess Properties of {Chlorobenzene + 1-Hexanol, or 1-Heptanol, or 1-Octanol, or 1-Nonanol, or 1-Decanol} at (298.15, 303.15, 308.15, and 313.15) K

Isentropic compressibility ks, excess isentropic compressibility , excess molar volume V E, viscosity deviations Δη, and speed of sound deviations uD for {chlorobenzene + 1-hexanol or 1-heptanol, or 1-octanol, or 1-nonanol, or 1-decanol} binary mixtures at temperatures ranging from (298.15 to 313.15) K and at atmospheric pressure were derived from experimental viscosity η, density ρ, and speed of sound u data. The calculated excess and deviation functions were further fitted to the polynomial relation to estimate the coefficients and standard errors. While the experimental viscosity data was compared with the predicted values obtained from empirical expressions, the speeds of sound data was analyzed in term of Schaaffs' collision factor theory and Jacobson's intermolecular free length theory of solutions. The effects of n-alkan-1-ol chain length as well as the temperature on the excess molar volume were studied.

Ultrasonic velocities and isentropic compressibilities of N-methyl-2-pyrrolidone with ketones and branched alcohols at 303.15 K

The ultrasonic sound velocities and densities are measured for the binary mixtures of N-methyl-2-pyrrolidone (NMP) with ketones and branched alcohols at 303.15 K. The ketones include methyl ethyl ketone, methyl propyl ketone, diethyl ketone, methyl isobutyl ketone and cyclohexanone. The branched alcohols include 2-propanol, 2-methyl-1-propanol, 3-methyl-1-butanol, 2-butanol and 2-methyl-2-propanol. The ultrasonic sound velocity data were used to compute isentropic compressibilities (k s). The deviations in the value of k s from ideal value were computed. Except cyclohexanone all the binary mixtures formed by NMP with ketones at 303.15 K exhibit negative deviation from ideal behaviour over the entire range of composition. Cyclohexanone with NMP exhibit positive deviation over the entire range of composition. An inversion in the sign of Δk s from positive to negative was observed for 2-propanol system and negative deviation was observed in four binary mixtures formed by NMP with other branched alcohols at 303.15 K. The ultrasonic sound velocities of these mixtures have been analysed is terms of Free Length Theory (FLT), Collision Factor Theory (CFT) and Nomoto's relation.

Viscosities, Densities, and Speeds of Sound of Binary Mixtures of Benzene, Toluene, o-Xylene, m-Xylene, p-Xylene, and Mesitylene with Anisole at (288.15, 293.15, 298.15, and 303.15) K

The viscosities, densities, and speeds of sound of binary mixtures of anisole with benzene, toluene, o-xylene, m-xylene, p-xylene, and mesitylene over the entire range of mole fraction at temperatures (288.15, 293.15, 298.15, and 303.15) K and atmospheric pressure have been measured. Excess compressibility and deviations in viscosity have been calculated and fitted to the Redlich−Kister polynomial relation to estimate the binary coefficients and standard errors. The deviations in viscosities and excess compressibilities are negative for all binary systems. The speeds of sound have been analyzed in terms of collision factor theory and free length theory. The viscosity data were correlated with equations of Grunberg and Nissan, Tamura and Kurata, Heric and Brewer, and McAllister.

Ultrasonic study on organic liquid and binary organic liquid mixtures by using Schaaffs' collision factor theory

Based on Schaaffs' collision factor theory (CFT) in liquids, the equations for nonlinear ultrasonic parameters in both organic liquid and binary organic liquid mixtures are deduced. The nonlinear ultrasonic parameters, including pressure coefficient, temperature coefficients of ultrasonic velocity, and nonlinear acoustic parameter B/A in both organic liquid and binary organic liquid mixtures, are evaluated for comparison with the measured results and data from other sources. The equations show that the coefficient of ultrasonic velocity and nonlinear acoustic parameter B/A are closely related to molecular interactions. These nonlinear ultrasonic parameters reflect some information of internal structure and outside status of the medium or mixtures. From the exponent of repulsive forces of the molecules, several thermodynamic parameters, pressure and temperature of the medium, the nonlinear ultrasonic parameters and ultrasonic nature of the medium can be evaluated. When evaluating and studying nonlinear acoustic parameter B/A of binary organic liquid mixtures, there is no need to know the nonlinear acoustic parameter B/A of the components. Obviously, the equation reveals the connection between the nonlinear ultrasonic nature and internal structure and outside status of the mixtures more directly and distinctly than traditional mixture law for B/A, e.g. Apfel's and Sehgal's laws for liquid binary mixtures.

Excess volumes, densities, speeds of sound and viscosities for the binary systems of diisopropyl ether with hydrocarbons at 303.15 K

Experimental results of excess volumes, speeds of sound and viscosities at 303.15 K are presented for the binary systems of diisopropyl ether with hexane, heptane, octane, isooctane, benzene, cyclohexane, tetralin and decalin over the entire range of composition. Isentropic compressibilities are calculated from speed of sound and density data. Speeds of sound are evaluated on the basis of Jacobson free length theory and Schaaffs collision factor theory. Further, the viscosity data was analysed on the basis of corresponding states approach and Grunberg and Nissan treatment. The experimental results are discussed in terms of molecular interactions between unlike molecules.

Speeds of Sound and Isentropic Compressibilities in Binary Mixtures of 2-Propanol with Several 1-Alkanols at 298.15 K

Speeds of sound and densities of 2-propanol +1-propanol, 2-propanol + 1-butanol, 2-propanol + 1-octanol, and 2-propanol + 1-hexanol have been measured over the entire composition range at 298.15 K. Speeds of sound of the binary mixtures have also been estimated from free length theory (FLT), collision factor theory (CFT), and Nomoto’s relation (NR) and have been compared with experimental speeds of sound. The isentropic compressibilities, molar isentropic compressibilities, excess molar isentropic compressibilities, and excess speeds of sound have been calculated from experimental densities and speeds of sound. Excess molar isentropic compressibilities and excess speeds of sound of the binary mixtures were fitted to the Redlich–Kister equation

Densities, speeds of sound, excess volumes and viscosities of binary mixtures of mtbe with tetralin and decalin at 303.15 k

Measurements of densities, speeds of sound, excess volumes and viscosities of binary mixture of methyl tert-butyl ether with tetralin and decalin are reported at 303.15 K over the entire range of composition. Excess volumes are measured using batch dilatometer technique. Sound speeds are obtained using ultrasonic interferometer. Densities are computed from excess volume data. Isentropic compressibilities are derived from density and sound speed data. Speeds of sound are evaluated on the basis of Jacobson's free length theory and Schaff's collision factor theory. The predicted values are in good agreement with the experimental results. The viscosity data are analysed on the basis of corresponding states approach. Excess volumes and deviation in isentropic compressibilities are negative and deviation in viscosities are positive over the entire composition range. The experimental results are discussed in terms of possible molecular interactions between unlike molecules.

Speed of sound, isentropic compressibility and refractive index of binary mixtures of alkyl ethanoates with chloroalkanes at 303.15 K

Speeds of sound u, isentropic compressibilities κ S, refractive indices n D, Rao's molar sound function R, excess isentropic compressibilities κ S E of 12 binary mixtures of methyl ethanoate (ME) and pentyl ethanoate (PE) with trichloromethane (triCM), tetrachloromethane (tetCM), 1,2-dichloroethane (diCE), 1,1,1-trichloroethane (triCE) and 1,1,2,2-tetrachloro-ethane (tetCE); and of 3-methyl-1-butyl ethanoate (MBE) with trichloromethane and tetrachloromethane have been reported over the entire range of composition at 303.15 K. The results have been analyzed in terms of molecular interactions between alkyl ethanoate and chloroalkanes. The speeds of sound have been estimated from the collision factor theory (CFT) and free length theory (FLT) of solutions.

Speeds of sound, isentropic compressibilities, viscosities, and excess molar volumes of binary mixtures of alkanoates with tetra- and trichloromethanes at 303.15 K

Speeds of sound u, isentropic compressibilities κ S, viscosities η, excess isentropic compressibilities κ S E, excess molar volumes V E, viscosity deviations Δ η, and excess Gibbs energies of activation Δ G *E of viscous flow have been investigated for six binary mixtures of diethyl malonate, diethyl bromomalonate, and ethyl chloroacetate with tetra- and trichloromethane at 303.15 K. The values of κ S E, V E, Δ η, and Δ G *E are highly dependent on the type of components involved and the composition curves are unsymmetrical. The results obtained for viscosity of binary mixtures were used to test the semi-empirical relations of Grunberg-Nissan, Tamura-Kurata, Hind-McLaughlin-Ubbelohde, Katti-Chaudhri, McAllister, Heric-Brewer and Auslaender. The experimental speeds of sound have been analyzed in terms of collision factor theory and free length theory of solutions.

Study of molecular interaction in ternary mixtures through ultrasonic speed measurements

Density (ρ) and ultrasonic speed (u) of ternary liquid mixtures: acetonitrile (ACN) + 1-propanol + benzene, + toluene, + chlorobenzene and + nitrobenzene, and those of pure components, have been measured as function of composition at 303.15 K. Using experimental data, the values of isentropic compressibility (K s ), intermolecular free length (L f ), molar ultrasonic speed (R m ), acoustic impedance (Z), excess isentropic compressibility ( ), excess free length ( ), excess volume (V E ) and excess acoustic impedance (Z E ) were computed. The increase or decrease of K s , L f , R m and Z with composition indicates the presence of interaction between the component molecules in the mixtures. The excess functions and V E are predominantly negative, while Z E is almost positive. This further supports the presence of significant interactions between the component molecules in these mixtures. Theoretical values of ultrasonic speed have been calculated for all the four ternary mixtures at different compositions using free length theory (FLT), collision factor theory (CFT), Nomoto's (NOM) empirical relation and Van Dael and Vangeel (VDV) ideal mixing relation. A comparison of theoretical values of ultrasonic speed with those obtained experimentally reveals that, in general, CFT predicts the data reasonably well.

Book reviews

Densities, ultrasonic speeds and refractive indices of phenetole (ethoxy benzene or ethyl phenyl ether) with N-methyl-2-pyrrolidone (NMP), N,N-dimethylformamide (DMF) and tetrahydrofuran (THF) binary mixtures over the entire mole fraction range were measured at (298, 303 and 308) K and atmospheric pressure. Excess molar volumes, isentropic compressibilities, refractive indices and ultrasonic speed deviation of these mixtures were calculated. The ultrasonic speeds have been analyzed in term of Schaaffs’ collision factor theory (CFT), Jacobson’s intermolecular free length theory of solutions (FLT), Nomoto relation (NR) and Van Deal ideal mixture relation (IMR). Excess and deviation properties were fitted to the method of least square of the Redlich-Kister (R-K) polynomial to estimate the coefficients and standard deviations. The results were interpreted on possible molecular interactions between components as well as the effect of polarity.

Speeds of sound, isentropic compressibilities, viscosities and excess molar volumes of cyclohexanol+cyclohexane at 303.15 K

Isentropic compressibilities κ S, excess isentropic compressibilities κ S E, excess molar volumes V E, viscosity deviations Δ η and excess Gibbs energy of activation ΔG ∗ E of viscous flow have been determined from measurements of speeds of sound u, densities ρ and viscosities η of cyclohexanol+cyclohexane binary mixture at 303.15 K and over the whole mole fraction range. The values of κ S E and Δ η are negative over the entire range of composition but the V E plot is sigmoid with very small magnitude of V E. The experimental speeds of sound in terms of collision factor theory and free length theory and the excess molar volumes in terms of associated solution theory with a Flory equation of state contribution described by Treszczanowicz and Benson [Fluid Phase Equilib. 23 (1985) 117] and Heintz [Ber. Bunsen-Ges. Phys. Chem. 89 (1985) 172] have been analyzed.

Thermodynamics of binary mixtures of aliphatic linear alkanes (C6–C12) at 298.15 K

This article reports experimental values of speeds of sound, densities and refractive indices on mixing of the binary mixtures n-hexane + (n-heptane, n-octane, n-nonane, n-decane, n-undecane, or n-dodecane) at 298.15 K and atmospheric pressure, over the whole concentration range. The corresponding excess and derived properties were computed from the experimental data. The results were fitted by means of the Redlich–Kister equation, such parameters being gathered. Different estimation methods (equations of state, mixing rules, Collision Factor and Free Length Theory) were applied, qualitative agreement between the experimental and theoretical values both in magnitude and sign being obtained.

Speeds of sound, isentropic compressibilities and excess molar volumes of an alkanol + cycloalkane at 303.15 K: II. Results for alkan-2-ols + cyclohexane and alkan-1-ols + methylcyclohexane and theoretical interpretation

Isentropic compressibilities κ S, excess isentropic compressibilities κ S E and excess molar volumes V E have been determined from measurements of speeds of sound u and densities ρ on binary mixtures of propan-2-ol, butan-2-ol, pentan-2-ol, and octan-2-ol with cyclohexane and of butan-1-ol, pentan-1-ol, hexan-1-ol, and heptan-1-ol with methylcyclohexane at 303.15 K over the whole mole fraction range. The values of V E for all the eight mixtures are positive and the values of V E decrease with the number of carbon atoms in alkanol. The values of κ S E for all four alkan-2-ol + cyclohexane systems are positive while in case of alkan-1-ol + methylcyclohexane systems, positive values of κ S E for butan-1-ol + methylcyclohexane decrease to negative values for heptan-1-ol + methylcyclohexane. The change of sign occurs between pentan-1-ol and hexan-1-ol. The experimental speeds of sound have been analysed in terms of Schaaffs’ collision factor theory and Jacobson’s free length theory while the excess molar volumes of alkan-1-ols + cyclohexane, alkane-2-ols + cyclohexane and alkan-1-ols + methylcyclohexane have been analysed in terms of associated solution theory with a Flory equation of state contribution described by Treszczanowicz and Benson [Fluid Phase Equilib. 23 (1985) 117] and Heintz [Ber. Bunsen. Phys. Chem. 89 (1985) 172].

Speeds of sound and isentropic compressibil- ities of cyclohexane+1,3-dioxolane+2-butanol and n-hexane+1,3-dioxolane+2-butanol

Speeds of sound of the ternary mixtures cyclohexane+1,3-dioxolane+2-butanol and n-hexane+1,3-dioxolane+2-butanol have been measured at the temperatures of 298.15 and 313.15 K. Isentropic compressibilities and excess isentropic compressibilities have been calculated from experimental data. We have also compared the experimental isentropic compressibilities with calculated values from the free length theory and the collision factor theory. Experimental results show positive values of excess isentropic compressibilities in almost the whole composition range for the ternary mixture containing cyclohexane, meanwhile they are negative for the mixture containing n-hexane. Such different behaviour of these systems is related to the large free volume shown by n-hexane.

Thermophysical Properties of Binary Mixtures of Methyl Methacrylate+Di-Ethers (Ethyl, Isopropyl, and Butyl) at 298.15 and 308.15 K

Experimental data for the densities, dynamic viscosities, sound speeds, and relative permittivities and for three binary systems of methyl methacrylate (MMA)+di-ethers (ethyl, isopropyl, and butyl) at 298.15 and 308.15 K and at atmospheric pressure are reported. The mixture viscosities are correlated by Grunberg–Nissan, McAllister, and Auslander equations over the complete composition range. The sound speeds for the mixtures are also calculated by using free length and collision factor theories, and Nomoto and Junjie equations. From the measured primary properties, deviation functions such as deviations in viscosities, sound speeds, relative permittivities, molar polarizations, excess isentropic compressibilities, and molar electrical susceptibilities were calculated, and the compositional dependence of each of the functions was expressed with a Redlich–Kister type equation. The variation of the Kirkwood correlation factor was determined over the complete composition range.

Densities, speed of sound and isentropic compressibilities of the ternary mixture 2-propanol+acetone+cyclohexane and the constituent binary mixtures at 298.15 and 313.15 K

The isentropic compressibilities, speed of sound deviations and changes of isentropic compressibilities of the ternary system 2-propanol+acetone+cyclohexane and the corresponding binary mixtures 2-propanol+acetone, 2-propanol+cyclohexane and acetone+cyclohexane have been evaluated from experimental densities and speed of sound in the complete composition range at 298.15 and 313.15 K. These properties are used to discuss the nature and the extent of intermolecular interaction in the ternary and the constituent binary mixture. Speed of sound deviations, Δ u, changes of isentropic compressibilities, δκ s, have been calculated and fitted by the Redlich–Kister equation for the binary mixtures, while the equation of Cibulka was used to fit the values related to the ternary system. Speed of sound and isentropic compressibilities have been compared with calculated values from free length theory (FLT), collision factor theory (CFT), Nomoto’s relation (NR), Van Deal’s ideal mixing relation (IMR) and Junjie’s relation (JR).

Speeds of sound and isentropic compressibilities of binary mixtures containing trialkylamines with alkanes and mono-alkylamines at 303.15 and 313.15 K

Isentropic compressibilities κ S, and excess isentropic compressibilities κ S E have been determined from measurements of speeds of sound u and densities ρ of 14 binary mixtures of triethylamine (TEA) and tri- n-butylamine (TBA) with n-hexane, n-octane, iso-octane, n-propylamine, n-butylamine, n-hexylamine and n-octylamine. The relative magnitude and sign of κ S E have been interpreted in terms of molecular interactions and interstitial accommodation. The values of κ S E for TEA + alkane are positive while for TBA + alkane are negative. The values of κ S E for TEA + primary amine become progressively less positive and eventually to negative with the increase in chain length of alkylamine. In case of TBA + primary amine, the values of κ S E increase from n-propylamine to n-butylamine, and then decrease with chain length of primary amine. The experimental speeds of sound u have been analyzed in terms of collision factor theory, free length theory and Prigogine–Flory–Patterson statistical theory of solutions.

Densities, Excess Molar Volumes, Viscosities, Speeds of Sound, Excess Isentropic Compressibilities, and Relative Permittivities for Alkyl (Methyl, Ethyl, Butyl, and Isoamyl) Acetates + Glycols at Different Temperatures

New experimental data on densities at (298.15 to 313.15) K, viscosities, speeds of sound, and relative permittivities at (298.15 and 308.15) K for the 10 binary mixtures of alkyl (methyl, ethyl, butyl, and isoamyl) acetates + glycols (ethylene, diethylene, triethylene, and propylene) have been measured as a function of the composition. Deviation functions, such as deviations in speeds of sound and deviations in relative permittivities, and excess functions, such as excess molar volumes and excess isentropic compressibilities, were calculated and fitted to a Redlich−Kister type equation. Grunberg−Nissan, McAllister, and Auslander equations correlated the mixture viscosities adequately. The values of speeds of sound in these mixtures, as predicted by collision factor theory, matched well with experimental data. The variation of the Kirkwood correlation factor with the ester mole fraction was examined. A qualitative analysis of the deviation and excess functions was made to ascertain the nature and type of b...