Deviation In Molar Refraction Research Articles

Experimental and theoretical studies to investigate molecular interactions between ethylene glycol oligomers and 1-butyl-3-methylimidazolium bromide

The thermophysical characteristics of pure liquids and their mixes are substantial in applied as well as theoretical research. This paper presents the measured data on: density (ρ), viscosity (η), refractive index (nD) and consequent calculated parameters: {excess molar volume (VmE), partial molar volume (V¯m), excess partial molar volume (V¯mE), deviation in viscosity (Δη), excess Gibbs energy of activation of viscous flow (ΔG∗E), deviation in refractive index (ΔϕnD) and deviation in molar refraction (ΔxRM)} of binaries containing 1-butyl-3-methylimidazolium bromide ([BMIM]Br) with glycol oligomers (mono/di/tri/tetra-ethylene glycol) at T/K = 298.15–313.15 and pressure p/MPa = 0.1. The Redlich-Kister equation efficiently estimates the standard deviation between the experimental and calculated excess properties. The interactions between constituents were considered while interpreting the obtained results. The values of VmE, V¯mE, Δη, ΔϕnD and ΔxRM exhibited negative trends throughout the range, whereas ΔG∗E values displayed a sigmoidal shift (negative to positive) with increasing [BMIM]Br concentration. The VmE data has been explored in terms of Prigogine-Flory-Patterson (PFP) and Graph theories to elucidate the deviations in thermophysical properties of the mixtures caused by variations in strength and magnitude of interactions. Additionally, the η values were correlated using ten models and their correlation ability has been perceived via the average standard deviation percentage. The pure and binary mixtures were also spectroscopically examined using Fourier Transform InfraRed (FT-IR) and Raman spectroscopy to elucidate the structural variations.

A Theoretical and Experimental Approach to Ultrasonic Velocities, Densities, and Refractive Indices in Benzene and Aniline Mixture

The study investigates the theoretical velocities of binary liquid mixtures comprising Aniline and Benzene under 2MHz ultrasonic waves at temperatures of 303.15K, 308.15K, and 313.15K, examined in relation to mole fraction. Experimental data is compared with various theoretical models, including Nomoto theory (NOM), Ideal mixing relation (IMR), Impedance Relation (IR), Rao’s Specific Velocity Method (R), and Junjie’s relations (JR). The work reflects the changes in refractive index with varying liquid density across different mole fractions, explaining observed impacts on ultrasonic velocities. To assess the goodness of fit, Chi-square tests and average percentage errors are employed, allowing for an evaluation of the relative applicability of these theories within the studied systems. The study also explores how the thermos-acoustical characteristics of the systems evolve concerning the mole fraction of a common molecule, shedding light on molecular interactions. Furthermore, various parameters for the binary mixture, such as discrepancies in ultrasonic velocity, excess isentropic compressibility, surplus acoustic impedance, excess intermolecular free length, and molar refraction deviation, are computed using experimental data of density, refractive index, and ultrasonic velocities at different mole fractions of benzene in the aniline-benzene mixture. These calculations serve to reflect the intermolecular interactions present in the binary liquid mixture.

Viscometric and refractive index study of intermolecular interaction between binary mixtures of terpinolene with o-, m- and p-cresol at 303.15, 308.15 and 313.15 K

Viscosities and refractive indexes  were experimentally measured for binary mixtures of terpinolene with o-, m- and p-cresol for entire composition range at 303.15, 308.15 and 313.15 K and at atmospheric pressure. Deviation in viscosity , excess Gibbs energy of activation for viscous flow , enthalpy  and entropy  of viscous flow, deviation in refractive index , molar refraction  and deviation in molar refraction  were also calculated. Various theoretical viscosity relations such as Dolezalek-Schulze ( , Grunberg-Nissan , Tamura-Kurata  Katti-Chaudhri ( , McAllister relation (  and ), Kendall-Munroe relation, Bingham relation and Arrhenius-Eyring relation were calculated. Similarly, nine theoretical refractive index relations such as Arago-Biot (A-B), Dale-Glastone (D-G), Lorentz-Lorentz (L-L), Eykman (Eyk), Weiner (WR), Heller (Hr), Newton (Nw), Oster (Os) and Eyring-John (E-J) were also calculated with their standard deviation  values. Results were discussed in terms of the presence of intermolecular interactions between the components of binary mixtures.

Volumetric, Acoustic, and Refractive Behavior of Acid Gas Absorbers: N-Vinyl-2-pyrrolidinone and Glycol Ethers (2-(2-Ethoxyethoxy)ethanol, 2-(2-Butoxyethoxy)ethanol, and 2-(2-(2-Methoxyethoxy)ethoxy)ethanol)

Thermophysical properties such as density (ρ), speed of sound (u), and refractive index (nD) for pure N-vinyl-2-pyrrolidinone (NVP) and binary mixtures of NVP with 2-(2-ethoxyethoxy)ethanol (DEGMEE), 2-(2-butoxyethoxy)ethanol (DEGMBE), and 2-(2-(2-ethoxyethoxy)ethoxy)ethanol (TEGMME) have been measured over the whole range of mole fraction from temperature T = (298.15 to 323.15) K and at 0.1 MPa pressure employing an Anton Paar vibrating U-tube density and sound velocity meter (DSA 5000 M) and an Abbemat refractometer, respectively. To quantify the nonideality in these systems, the experimental data has been used to evaluate various acoustical and thermodynamic parameters, such as excess molar volume (VmE), deviation in the speed of sound (Δu), isentropic compressibility (κs), excess isentropic compressibility (κsE), deviation in refractive index (ΔnD), molar refraction (Rm), and polarizability (α). Molecular interactions prevailing in these systems have been explained in terms of variation in the measured and calculated values of physicochemical parameters. The collected thermophysical data can be employed in the optimization and design of a desulfurization/CO2-capture process utilizing the studied solutions. Furthermore, this data can also be utilized for the theoretical model extension as well as in solving many difficult engineering problems such as fluid flow, heat and mass transfer, and energy transformations.

Density, viscosity, refractive index and molecular interaction of polyethylene glycol 400 + 1,3-propanediamine deep eutectic solvent for CO2 capture

A new deep eutectic solvent (DES) was obtained using polyethylene glycol 400 (PEG400) as the H bond donor (HBD) and 1,3-propanediamine (PDA) as the H bond acceptor (HBA). Meanwhile, density(ρ), viscosity (η) and refractive index (nD) of (PEG400 + PDA) DES at T = (293.15 to 318.15) K with the step size of 5 K were measured under atmospheric pressure. Through the measured base data, excess molar volume (VmE), excess refractive index (nDE), viscosity deviation (Δη), deviation in molar refraction (ΔRM), refractive index deviation(ΔnD), excess Gibbs energy of activation of viscous flow (ΔG∗E), partial molar volume (V1¯ and V2¯), apparent molar volume (Vφ,1 and Vφ,2), molar isobaric thermal expansion (Ep,m) and thermal expansion coefficient (αρ), were systematically calculated and analyzed, and the Redlich-Kister (R-K) equation was used for fitting VmE, nDE, ΔRM, Δη, ΔnD, and ΔG∗E. In addition, several theoretical mixing rules related to refractive index were evaluated and compared with the experimental data. The results showed that there was a specific intermolecular hydrogen bonding interaction in (PEG400 + PDA) DES, which was systemically discussed on the basis of UV–vis, FLS, FTIR and Raman spectral technologies. At the molar fraction with the strongest intermolecular force, the maximum solubility of CO2 per 1 mol PDA was 0.99 mol CO2 at 150 mL/min CO2 flow rate.

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.

Insight into molecular interactions and structural changes of ethyl lactate and (tri/tetra)-ethylene glycol binary mixture: A thermophysical and spectral depiction

The current work deals with the analysis of the molecular interactions amongst the binary systems formed by significant solvents with environment friendly characteristics. The density (ρ) and refractive index (nD) of pure liquids and mixtures containing L-Ethyl Lactate (EL) + Tri-Ethylene Glycol (TrEG) or Tetra-Ethylene Glycol (TeEG) over the entire composition have been measured at four equidistant temperatures from T/(K) = 298.15 to 313.15 and pressure p/(MPa) = 0.1. Based on the experimental data, calculation of derived properties (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)) was done. The consequent properties were fitted to the Redlich-Kister polynomial equation to recognize the interaction coefficients and standard deviations. The obtained outcomes were examined theoretically through Prigogine-Flory-Patterson (PFP) theory and Graph theory to elucidate the non-ideal behaviour of investigated mixtures. The theoretical interpretations were found to be in harmony with experimental observations. Spectroscopic data from UltraViolet (UV) and Fourier Transform InfraRed (FT-IR) analysis ascertains the dominance of solute-solvent interactions in mixed state hereby supporting the experimental and theoretical analysis.

Ultrasonic velocities and refractive indies of binary liquid mixtures of 1, 4-dioxane with 1 – alkanols (C3, C4, C6 , C8 ) at 303.15 K

Density (ρ), ultrasonic velocities (u) and refractive indices (n) of the binary mixture between cyclic ether with 1-propanol, 1-butanol, 1-hexanol, 1-octanol for the entire concentration range have been measured at 303.15K, furthermore, deviation in refractive indies from ideal mixture, molar refraction, deviation in molar refraction from ideal values for these mixture has also been evaluated. The deviations from ideality of the acoustical parameters are explained on the basis of molecular interaction between the component molecules in these binary liquid mixtures. The molecular refraction (Rm), excess molecular refraction ( ) and excess molar volume (VE) were calculated from the experimental data. The results are discussed in term of molecular interactions between the components of the binary mixtures.  Â

Analysis of H-bonded molecular association in formamide with alcohols

Ultrasonic velocity, density, viscosity, and refractive index have been measured in binary liquid mixtures of formamide with 1-propanol and 2-propanol at atmospheric pressure and 293 K, 303 K, and 313 K temperatures over the entire range of composition. Experimentally determined values have been used to calculate excess Gibb’s free energy of activation for viscous flow ‘ΔG*E’, excess internal pressure ‘πiE’, and deviation in molar refraction ‘ΔRm’. All the excess and deviated functions have been plotted against the mole fraction of formamide and calculated values have been fitted to the Redlich-Kister polynomial equation. The calculated excess values or deviation parameters have been discussed on the basis of molecular association in these binary mixtures.Further, refractive index of these liquid mixtures has been predicted using various theoretical mixing rules.

Densities, speeds of sound, refractive indices, excess and partial molar properties of polyethylene glycol 200 + benzyl methacrylate binary mixtures at temperatures from 293.15 to 318.15 K

Green and biodegradable solvents are requisite replacements to volatile organic solvents. Polyethylene glycols have been recognized as alternatives to volatile organic solvents in numerous industrial and pharmaceutical applications because of their unique properties. In this work the measurements of physicochemical properties, viz., densities, ρ, speeds of sound, u and refractive indices, nD of the binary mixtures of PEG 200 with benzyl methacrylate, including pure liquids, over the entire mole fraction range at the temperatures, T/K = 293.15 to 318.15 and at atmospheric pressure, p = 101 kPa. The experimental data were used to calculate the excess molar volume, VmE, excess isentropic compressibility, κsE, excess speed of sound, uE, excess acoustic impedance, ZE, excess molar isentropic compressibility, Ks,mE, excess refractive index, nDE and deviation in molar refraction, ΔRM . These excess properties were fitted with the Redlich-Kister polynomial equation. In addition, the partial molar volumes and partial molar compressibilities and excess partial molar volumes and excess partial molar compressibilities over the entire mole fraction range; and at infinite dilution were also calculated. The trends of these parameters with composition and temperature were discoursed from the point of view of intermolecular interactions existed in these mixtures.

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.

Optical and viscometric properties for 1-chlorohexane + toluene/tetradecane binary mixtures at temperatures from 298.15 K to 318.15 K and atmospheric pressure

The optical and viscometric properties for two binary mixtures of 1-chorohexane with toluene and tetradecane, were measured at several temperatures in the range of (298.15–318.15) K and atmospheric pressure.The experimental values for refractive indices and viscosities, for both systems were correlated by the Jouyban-Acree model with good accuracy.By using the obtained experimental results, the related excess and deviation quantities, as the deviation in refractive indices, the molar refractions, the deviation in molar refraction and the deviation in viscosities, were calculated and reported in this work. All these excess properties were correlated with the Redlich-Kister polynomial equation.The Lorentz–Lorenz, Gladstone–Dale, Arago–Biot, Edwards, and Eykman predictive equations have been used to calculate the refractive index on basis of measured density, and their accuracy was analyzed.Some different equations: Grunberg–Nissan, Katti Chaudry, Hind, Dolezalek, and three-body McAllister interaction model, were used to calculate the viscosities values and a comparison with those values with the experimental data was made. From the viscosity experimental data, the molar enthalpy of activation and the molar entropy of activation for viscous flow, as well as the excess Gibbs energy of activation for viscous flow, were calculated for both studied binary mixtures.Discussions concerning the experimental and calculated results in relation to the molecular interactions and structural effects between components of mixtures are presented.

Insight into structural properties and molecular interactions of maline (choline chloride + malonic acid) and 1, 4- butanediol based pseudo-binary mixture: A thermophysical, spectral, and simulation portrayal

The current study elucidate the thermophysical, spectral, and simulation depiction of the prepared deep eutectic solvent (DES) named as maline comprising of an equimolar mixture of choline chloride (ChCl) as hydrogen bond acceptor (HBA) and malonic acid (MA) as hydrogen bond donor (HBD) in the presence of 1, 4-butanediol (BTD) as other HBD (cosolvent). Various thermophysical properties viz., (densities, ρ, speeds of sound, u, viscosity, η and refractive index, nD) were comprehended for the examined pseudo-binary (maline and BTD) mixtures as a function of composition and temperature. The derived thermophysical properties viz., excess molar volume, VmE, excess isentropic compressibility, κsE, excess intermolecular free length, LfE, deviation in viscosity, Δη, and deviation in molar refraction, ΔRM were found to be negative while the excess speed of sound, uE, excess acoustic impedance, ZE, and deviation in refractive index, ΔnDwere found to be positive which signified the favourable hydrogen bonding interactions between maline and BTD. The partial molar volumes, V¯m,1, V¯m,2 and excess partial molar volumes, V¯m,1o and V¯m,2o of the components at infinite dilution exhibited the negative value due to the contraction in volume over the entire concentration thereby strengthening the presence of specific interaction. The molecular interaction in the examined pseudo-binary system conferred in terms of excess parameters with composition and temperature have also been correlated using the Redlich-Kister (R-K) equation. The significant shifting in the spectral profile as observed from FT-IR (Fourier-transform infrared) spectroscopy evidently inferred the favorable inter-molecular interaction within the maline and BTD based pseudo-binary mixture. A noteworthy change in the chemical shifts as deduced from1H- and 13C- NMR (Nuclear Magnetic Resonance) spectral peaks confirmed the hydrogen bonding networks between maline and BTD. Additionally, the 2D 1H–1H COSY (correlation spectroscopy) outcomes exposed the degree of variation in the inter-molecular interactions and structural arrangement between maline and BTD system. The spectral results were further validated employing theoretical (computational simulation) analysis which accounted the extensive hydrogen bonding from the evaluated computed descriptors Also, the 3D-molecular electrostatic potential (3D-MEP) explicated the effect of charge delocalization in the proximity of hydrogen bonding networks.

Experimental and theoretical studies of transport and optical properties of binary mixtures of acetonitrile with some alkyl methacrylates at temperatures from 298.15 to 318.15 K

The viscosities, η and refractive indices, nD of pure acetonitrile, methyl methacrylate, ethyl methacrylate, butyl methacrylate and of their binary mixtures with acetonitrile as the common component, covering the entire composition range were measured at temperatures (298.15, 303.15, 308.15, 313.15 and 318.15) K and atmospheric pressure. Using these experimental data, the deviations in viscosity ∆η, deviations in refractive index, ∆nD , deviations in molar refraction, ∆Rm have been calculated. These excess properties were correlated by the Redlich-Kister polynomial equation. The variations of ∆η, ∆nD and ∆Rm with composition and temperature has been discussed terms of intermolecular interactions existing in these mixtures. Further, the viscosities and refractive indices of these binary mixtures were calculated theoretically by using various empirical and semi-empirical relations and the results were compared with the experimental findings.

Excess Thermodynamic Properties and Molecular Interactions in Binary Liquid Mixture of o-xylene and N-nonane

Experimentally measured data for viscosity and refractive index of (o-Xylene + n-Nonane) binary mixture are reported in this research paper for various compositions for three different temperatures at atmospheric pressure. Modified Ubbelholde viscometer and Abbe-3L Refractometer were used for experimental measurements. Deviation in molar refraction (ΔR) and deviation in viscosity (Δη) w.r.t composition have been calculated from the experimental data. ‘Grunberg and Nissan’ equation and Herric’s Correlation were used to correlate the viscosity data. Excess thermodynamic properties were fitted to Redlich-Kister equation. Coefficients and standard deviations, hence obtained are reported. Variation in Excess Thermodynamic properties for the mixture have been discussed in terms of intermolecular interactions.

Densities, speeds of sound, viscosities, refractive indices, excess and partial molar properties of binary mixtures of 1-butyl-3-methylimidazolium tetrafluoroborate with formamide at temperatures from 293.15 to 318.15 K

Abstract The densities, ρ, speeds of sound, u, viscosities, η and refractive indices, nD of the binary solutions of 1-butyl-3-methylimidazolium tetrafluoroborate [Bmim][BF4] with Formamide (FA), including those of pure liquids, have been measured over the whole range of composition at different temperatures (T/K = 293.15 to 318.15) and at atmospheric pressure, p = 101 kPa. The experimental data were used to calculate the excess properties such as excess molar volume, V m E , excess isentropic compressibility, K S E , excess speed of sound, uE, excess molar isentropic compressibility, K s , m E , deviations in viscosity, Δη, deviations in refractive index, ΔϕnD and deviations in molar refraction, ΔRM. These excess parameters were fitted to a Redlich-Kister type polynomial equation. The partial molar volumes and partial molar compressibilities and excess partial molar volumes and excess partial molar compressibilities over the whole composition range; and at infinite dilution were also calculated. The obtained results were interpreted in terms of intermolecular interactions occurring in these mixtures.

Physicochemical studies of intermolecular interactions in 1-butyl-3-methylimidazolium tetrafluoroborate + benzonitrile binary mixtures at temperatures from 293.15 to 318.15 K

ABSTRACT The densities, ρ, speeds of sound, u, viscosity, η and refractive indices, n D of 1-butyl-3-methylimidazolium tetrafluoroborate [Bmim][BF4] and Benzonitrile (BN) binary mixture, including those of pure liquids have been measured over the entire composition range at temperatures (293.15, 298.15, 303.15, 308.15, 313.15 and 318.15 K) and at atmospheric pressure. From the experimental values, excess molar volumes, , excess isentropic compressibilities, , excess speeds of sound, , excess molar isentropic compressibilities, and deviations in viscosity, Δη, deviations in refractive index, and deviations in molar refraction, were calculated. The partial molar volumes and partial molar isentropic compressibilities along with their excess values over whole composition range and those of the components at infinite dilution were also calculated. The resultant positive or negative deviations of these parameters have been analysed in terms of molecular interactions prevailing in these mixtures. The applicability of Prigogine–Flory–Patterson (PFP) theory in predicting the values is checked.

Investigation of Molecular Interaction in Benzene + Cyanex 923 Binary Mixtures at 298.15 K with Reduced Redlich–Kister Functions

Excess dielectric constant, excess molar volume, deviation in molar refraction, deviation in refractive index and molar polarization in benzene + cyanex 923 binary mixtures at the temperature of 298.15 K were calculated from the experimentally determined values of dielectric constant, density, molar polarization, molar volume, molar refraction and refractive index which were already published. The experimental values and their corresponding derived properties were utilized to examine the applicability of the reduced Redlich–Kister function. These relative reduced properties are interesting to minimize the temperature effect and, thus, to uncover the effects of different types of molecular interactions in the studied binary mixture.

Volumetric, acoustic and viscometric studies of intermolecular interactions in polyethylene glycol 400 + alkyl acrylate binary mixtures at temperatures from 293.15 to 318.15 K

ABSTRACT Densities, ρ, speeds of sound, u and refractive index, n D of binary solutions of polyethylene glycol 400 with methyl acrylate (MA), ethyl acrylate (EA), n-butyl acrylate (n-BA), including those of pure components, have been measured over the whole composition range at temperatures (293.15–318.15) K and atmospheric pressure. From experimental data, excess molar volume, , excess isentropic compressibility, , excess speed of sound, , excess molar isentropic compressibility, , deviations in refractive indices, and deviations in molar refraction, . The partial and excess molar volumes and compressibilities covering the entire mole fraction range, and at infinite dilution were also calculated. These parameters variation with composition and temperature of mixtures suggest the difference in shape and size of molecules of components and formation of hydrogen bonding between unlike molecules. Moreover, the refractive indices of binary solutions are predicted by various empirical mixing rules and compared with experimental findings.

Volumetric and Optical Properties of Dimethylvinylethoxysilane with n-Alkanes (C7 to C10) at Temperatures in the Range (298.15 to 318.15) K

Densities and refractive indices are investigated for four binary mixture systems of dimethylvinylethoxysilane with n-heptane, n-octane, n-nonane and n-decane at different temperatures (298.15, 303.15, 308.15, 313.15 and 318.15 K) and atmospheric pressure. From these experimental data, the excess molar volume, isobaric coefficient of thermal expansion, deviation in refractive index, molar refraction, and deviation in the molar refraction have been calculated. The computed quantities have been fitted with the Redlich–Kister equation to derive the coefficients and estimate the standard deviations. The values of the partial excess volume at infinite dilution were calculated using the coefficients of the Redlich–Kister smoothing equation. The effects of composition and temperature on these properties are discussed.