Isobaric Thermal Expansion Research Articles

Determination of Compressed Liquid Densities for CO2 + n-Decane Using a Vibrating Tube Densimeter

Understanding the density of CO2 + n-decane is crucial for designing and operating CO2 capture, transport, and storage. The safety and effectiveness of CO2 burial is directly affected by the density of CO2 + n-decane mixtures. The liquid densities of CO2(1) + n-decane(2) mixtures with mole fractions of CO2 x1 = 0, 0.2032, 0.4434, 0.7589, and 0.8947 were measured using a vibrating tube densimeter. The combined expanded uncertainties of density with a level of confidence of 0.95 are estimated to be 0.6 kg·m−3. A total of 221 compressed liquid densities of CO2(1) + n-decane(2) mixtures along the five isotherms between T = (283 and 363) K with pressures up to 100 MPa were presented. The densities of mixtures were correlated by the modified Tait equation, resulting in absolute average deviations between the experimental and calculated values of 0.028%, 0.013%, 0.017%, 0.044%, and 0.042%. In addition, the isothermal compressibility, isobaric thermal expansivity, and excess molar volume were derived from the modified Tait equation.

Thermodynamic and transport properties of binary mixtures containing 1,2-propanediol with 2-methoxyethanol and 2-ethoxyethanol at different temperatures

In the present investigation density, speed of sound, and viscosity have been reported for binary liquid mixtures of 1,2-propanediol (1,2-PD) with 2-methoxyethanol (2-ME) and 2-ethoxyethanol (2-EE) over the entire composition range at T= (298.15–323.15) K. From the experimental data, excess molar volume, (VmE), excess isentropic compressibility, (κsE), excess molar isentropic compressibility, (κs,mE), excess speed of sound, (uE), excess isobaric thermal expansion,αpE, and deviation in viscosity (Δη) of liquid mixtures have been calculated. The excess partial molar volume,V¯m,1E, V¯m,2E , excess partial molar isentropic compressibility, K¯s,m,1EK¯s,m,2E over the whole composition range together with partial molar volume,V¯m,10, V¯m,20, partial molar isentropic compressibility K¯s,m,10,K¯s,m,20, excess partial molar volume,V¯m,10E, V¯m,20E and excess partial molar isentropic compressibility, K¯s,m,10E,K¯s,m,20E at infinite dilution have also been calculated. All excess properties have been correlated using the Redlich-Kister smoothing polynomial equation. The VmE results are analysed in the light of Prigogine-Flory-Patterson theory. Analysis of each of the three contributions viz. interactional, free volume, and P* to VmE has shown that interactional contribution and free volume effect are negative for all the mixtures, and P* contribution is positive for the mixtures of 2-ME. The variations of these parameters with changes in composition and temperature have been discussed in terms of intermolecular interactions prevailing in these mixtures. Further, the viscosities of these binary mixtures were correlated theoretically by using various empirical and semi-empirical models and the results were compared with the experimental findings.

Thermal Transport and Thermal Polarization of Water in the Supercooled Regime.

The behavior of water in the deep supercooled regime has attracted significant interest, motivated by the hypothesis of the second critical point of water. Previous studies indicated the existence of a water anomaly, characterized by a minimum in the thermal conductivity of water. Here, we employ nonequilibrium molecular dynamics computer simulation and the TIP4P/2005 water force field to investigate the thermal conductivity of supercooled water targeting four different isobars, 1, 200, 700, and 1200 bar. We demonstrate using NEMD simulations the existence of minima in thermal conductivity associated with the maximum isothermal compressibility and the minimum speed of sound in water, hence establishing a firm connection with the second critical point of liquid water. Moreover, we demonstrate that thermal gradients polarize supercooled water with a thermal polarization coefficient of several mV/K. We explain the thermal polarization effect using a theoretical formulation introduced recently that connects the thermal polarization effect to the isobaric thermal expansion coefficient.

On the Solute-Induced Structure-Making/Breaking Phenomena: Myths, Verities, and Misuses in Solvation Thermodynamics

We review the statistical mechanic foundations of the fundamental structure-making/breaking functions, leading to the rigorous description of the solute-induced perturbation of the solvent environment for the understanding of the solvation process of any species regardless of the type and nature of the solute–solvent interactions. Then, we highlight how these functions are linked to unambiguous thermodynamic responses resulting from changes in state conditions, composition, and solute–solvent intermolecular interaction asymmetries. Finally, we identify and illustrate the pitfalls behind the use of surrogate approaches to structure-making/breaking markers, including those based on Jones–Dole’s B-coefficient and Hepler’s isobaric-thermal expansivity, while highlighting their ambiguities and lack of consistency and the sources of misinterpretations.

BF3 Complexing Phosphate/Phosphonate Ionic Liquids: Synthesis, Characterization and Thermophysical Properties.

A new group of BF3 complexing phosphate/phosphonate ionic liquids (ILs) [Emim][X(BF3)2] (X=dimethyl phosphate, diethyl phosphate, methyl phosphonate, and ethyl phosphonate) were synthesized and characterized. Key thermophysical properties of the new complex ionic liquids, including density, viscosity, conductivity, surface tension, solid-liquid phase transition, and thermal stability were determined and compared with those of [Emim][X]. Some other important thermophysical properties such as isobaric thermal expansion coefficient, molecular volume, standard molar entropy, and lattice potential energy were obtained from measured density data, and the free volume was estimated by a linear equation presented in this article, while critical temperature, normal boiling temperature, and enthalpy of vaporization were estimated from measured surface tension and density data. Furthermore, Fragility study shows that [Emim][X(BF3)2] should be considered as fragile liquids, while [Emim][X] could be considered as extremely fragile liquids. The ionicity of [Emim][X(BF3)2] was predicted by Walden rule, and the result shows that these ILs fit well with Walden law. The key features of these complex ILs are their extremely low glass transition (-95.33~-98.46 °C) without melting, considerably low viscosities (33.876~58.117 mPa ⋅ s), and high values of free volume fraction (comparable to [Omim][BF4], [Emim][NTf2], and [Emim][TCB]).

A study on thermophysical properties of binary mixtures of n-hexane with benzene and some alkyl-substituted benzenes within temperature range (293.15–323.15) K: Experimental and modeling approach

The current work reports densities and sound speeds, and related thermodynamic excess properties, namely excess molar volumes and excess isentropic compressibilities, measured at temperatures from (293.15 to 323.15) K and under atmospheric pressure conditions for binary mixtures of n-hexane with benzene, toluene, ethylbenzene, o-xylene, m-xylene, and p-xylene. Redlich-Kister polynomial correlated the thermodynamic excess properties to test the quality of experimental data. Excess properties contributed to understanding molecular interactions between involved molecules and the peculiarities of their packing in the mixture. The Jouyban-Acree model was used to correlate the mixtures' experimental densities, sound speeds, and their related derived properties, namely isobaric thermal expansivities and isentropic compressibilities. The average absolute percentage deviation of the correlated values from the experimental ones was better than 0.036 %, 0.058 %, 0.040 %, and 0.146 % for density, sound speed, isobaric thermal expansivity, and isentropic compressibility, respectively, attesting to the robustness of the Jouyban-Acree correlations. Additionally, the Perturbed Chain Statistical Associating Fluid Theory Equation of State modeled the densities of the current mixtures. Schaaff's Collision Factor Theory and Nomoto's relation were compared for their ability to model the sound speeds of the mixtures. The efficacy of these models was tested by computing the average absolute percentage deviations between experimental and computed values. The modeled densities are reasonably concordant with experimental data, with an overall deviation of 0.02 %. Notably, Nomoto's relation exhibited superior performance over Schaaff's theory in modeling sound speeds of current mixtures, with an overall deviation of 0.33 %. The current findings underline the efficacy and versatility of the used models for thermodynamic modeling in systems of varying complexity.

Density, Speed of Sound and Derived Properties of Binary Mixtures Propiophenone + Butoxyethanol at T = (303.15, 308.15, 313.15 and 318.15) K

The current study reports the experimental density (ρ) and sound speed (u) values for binary mixes of liquids propiophenone + 2-butoxyethanol at atmospheric pressure (0.1 MPa) and T = (303.15, 308.15, 313.15 and 318.15) K for the full spectrum of composition. densities and sound speed measurements from experiments have been used to estimate excess isentropic compressibility (κsE), excess molar volume (VEm), excess molar isentropic compressibility (KEs,m), excess isobaric thermal expansivity (αEp) and excess sound speed (uE). The Redlich-Kister polynomials were used to correlate excess parameters. Excess partial molar volume quantities (VEm,1 and VEm,2) at infinite dilution and their limiting values (V0Em,1 and V0Em,2) have been analytically determined using Redlich-Kister polynomials from the experimental density data. The results have been analyzed in light of strength and interactions among molecular entities scope and extent prevalent in these mixtures.

Thermodynamic investigation on the aqueous mixtures of choline chloride/propylene glycol deep eutectic solvent at T = (293.15 to 313.15) K

This work focuses on physicochemical features of the choline chloride/propylene glycol deep eutectic solvent (DES) + water mixtures by determining their density values in mono- and mixed- states over various temperatures in the range of 293.15–318.15 K. The density data obtained from measurements were utilized for the computation of various quantities such as excess molar volumes, molar volume, apparent molar volume, limiting apparent molar expansibility, and isobaric thermal expansion coefficient. Furthermore, the experimental densities were fitted to some mathematical equations such as Jouyban-Acree, Jouyban-Acreevan’t Hoff, modified Jouyban-Acree-van’t Hoff, Redlich–Kister and Emmerling. Studies of this nature can provide useful insights into solute–solvent interactions in aqueous solutions of DES, especially about to their novel application in drug solubilization.

Liquid density of binary mixtures of n-pentane and n-dodecane at temperatures from 283K to 363K and pressures up to 100MPa

The compressed liquid densities of n-pentane(1) + n-dodecane(2) binary mixtures were measured using a high pressure vibrating-tube densimeter at temperatures from 283 K to 363 K, pressures up to 100 MPa, and five different compositions (x1 = 0.3778, 0.6230, 0.7968, 0.9051, and 1). The densities of binary mixtures were correlated using the modified Tait equation, and the absolute average deviations of the experimental and calculated values were 0.010 %, 0.019 %, 0.016 %, 0.025 %, and 0.017 %, respectively. In addition, the isothermal compressibility and the isobaric thermal expansivity were calculated from the obtained densities.

Liquid to solid phase transition detection by using a vibrating tube densimeter along with densities up to 137 MPa of beef tallow fatty acid alkyl esters

Phase behavior and thermophysical properties of biodiesel at high pressure and high temperature are limited in the literature. These are useful to develop models and to understand their behavior having in mind the use of biodiesel in engines. Liquid to solid phase transitions, by using a vibrating tube densimeter, along with densities of three beef tallow fatty acid alkyl esters were studied in this work. Measurements of the oscillating period for each biofuel were carried out in a modular array constituted by two vibrating tube densimeters coupled in series and connected to a single loading cell. The oscillating period was converted to density by the forced path mechanical calibration (FPMC) method. Experimental liquid density sets for three beef tallow biodiesel samples based on fatty acid alkyl esters (FAAEs) are reported for the first time for pressures up to 137 MPa. These biofuels, named fatty acid methyl esters (FAMEs), fatty acid ethyl esters (FAEEs) and fatty acid butyl esters (FABEs), were measured in the temperature range of 286–393 K. The detection procedure for the beginning of the high-pressure solidification was focused on the beef tallow FABEs sample based upon its lower cloud point (CPFABEs = 281.15 K) in comparison with the reported property for the other esters (CPFAEEs = 289.15 K, CPFAMEs = 291 K) with the same feedstock; therefore, the conditions for the metastable liquid to solid phase transition associated to the effect of high pressure was detailed for waste beef tallow butyl ester biodiesel by performing step-by-step compressions in the interval of 286.20–298.13 K and with the help of the vibrating tube densimeters. FABEs had the lower density in contrast with FAEEs and FAMEs, this one being the denser biofuel. Modeling of liquid density data was performed by the perturbed-chain statistical associating fluid theory (PC-SAFT) Equation of State and the Tammann-Tait equation with maximum absolute average deviations of 0.15 % and 0.05 %, respectively. Both models were applied for correlating the thermodynamic derived properties of the fluid phase: isobaric thermal expansivity and isothermal compressibility.

Densities and excess molar volumes of thiophene + heptane and thiophene + octane at temperatures between (313 K and 363) K and pressures up to 25 MPa using three calibration methods

New compressed liquid densities (ρ) of thiophene + heptane and thiophene + octane are reported in the temperature range from (313 to 363) K, with pressure up to 25 MPa. The compositions are x(1) = 0.1049, 0.2471, 0.5097, 0.7494, and 0.8994 for thiophene (1) + heptane (2), and x(1) = 0.1042, 0.2530, 0.5037, 0.7516, and 0.8988 for thiophene (1) + octane (2). The experimental system uses a vibrating tube densimeter (VTD) and three calibration methods (the first uses hexane and water, the second uses nitrogen and water, and the third uses water and applying vacuum to the VTD as calibration reference fluids). The reported density data are determined using the third method, which notifies the lowest uncertainty and estimates a maximum relative expanded uncertainty (k=2) of 0.21 % in the temperature range from (313 to 363) K and pressures up to 25 MPa. The pure compound densities were calculated from previous density measurements represented by the Pimentel-Galicia model. This empirical correlation of the pure compounds was used before for the excess molar volume calculation. The experimental data of the mixtures reported in this work were modeled by the Pimentel-Galicia model at each composition with deviations not higher than 0.07 %. The combined standard uncertainty for composition (considering the purities of the samples) is ucx= 0.0026. Finally, the isothermal compressibility and isobaric thermal expansivity were evaluated from density data.

Dependence of Linear Isobaric Thermal Expansivity of Polymers on Their Flexibility

We have obtained an equation for polymers relating their flexibility Y defined in 2019 to the linear isobaric thermal expansivity L. This way we have connected quantitatively a thermodynamic property to a mechanical one. The expansivity is important since different materials expand at different rates on the increase of temperature; the same applies to contraction resulting from cooling. Thus, a temperature change can cause disintegration of a composite with no mechanical force involved.

Density and speed of sound of (iodobenzene + n-alkane) liquid mixtures at T = (288.15 to 308.15) K. Application of the Prigogine-Flory-Patterson model

(Iodobenzene + n-alkane) liquid mixtures have been studied experimentally, in terms of densities (ρ) and speeds of sound (c), and theoretically, by the application of the Prigogine-Flory-Patterson (PFP) model. The n-alkanes considered are n-heptane, n-decane, n-dodecane, and n-tetradecane. ρ and c measurements have been performed at a pressure p = 0.1 MPa and in the temperature range T = (288.15 to 308.15) K. Excess molar volumes (VmE) and excess isentropic compressibilities (κSE) have been calculated and correlated by Redlich-Kister polynomials. (∂VmE/∂T)p curves at the same (p,T) conditions have been obtained from correlated VmE values. The mixtures are characterized by the following features: (i) VmE increases with the number of carbon atoms of the n-alkane (n), being negative for n = 7, small and S-shaped with positive and negative values for n = 10, and positive for n = 12 and n = 14; (ii) κSE and (∂VmE/∂T)p are negative, increase with n and are very close to zero for n = 14. From these experimental results and the knowledge of the excess molar enthalpies of mixtures containing fluorobenzene, chlorobenzene or bromobenzene with n-alkanes, we have inferred the presence of structural effects, especially important for n = 7 and less relevant for volumetric properties as n increases. The VmE obtained are compared with those of other (halogenated benzene + n-alkane) liquid mixtures existing in the literature, namely systems with fluorobenzene, chlorobenzene, and bromobenzene. From this comparison and the analysis of the isobaric thermal expansion coefficients of the pure compounds, it is inferred that the interactional effects on VmE do not vary appreciably with the length of the n-alkane, so the observed VmE variation is fundamentally determined by the corresponding variation of the contribution from structural effects. Moreover, the application of the PFP model supports this interpretation, providing free volume contributions to VmE that vary parallelly to VmE with the length of the n-alkane, and interactional contributions that rest approximately constant independently of the n-alkane size.

Volumetric and acoustic studies of binary mixtures of DEC with isomeric chlorobenzene at various temperatures

ABSTRACT Densities, ρ, and speeds of sound, u, of binary liquid mixtures of diethyl carbonate with 1,2-dichlorobenzene, 1,3-dichlorobenzene and 1,2,4-trichlorobenzene have been measured over the entire range of composition at 303.15 K, 308.15 K, 313.15 K and 318.15 K and at atmospheric pressure. From the experimental data of the density and speed of sound, the excess properties such as excess molar volume, V m E , excess isentropic compressibility, κ s E , excess molar isentropic compressibility, K s , m E , excess speed of sound, u E , and excess isobaric thermal expansion, α p E , have been calculated. For better knowledge of the solute and solvent interaction, excess partial molar volumes, V ˉ m , 1 E and V ˉ m , 2 E , and excess partial molar volumes, V ˉ m , 1 ∘ E and V ˉ m , 2 ∘ E of the components at infinite dilution have been measured. All the excess parameter values have been fitted using the Redlich–Kister polynomial smoothing equation. The calculated excess values have been analysed in terms of molecular interactions and structural effects.

Acoustic and volumetric study of binary mixtures containing Ethyl propionate with amides at various temperatures

The development of biofuels to replace fossil fuels has recently increased at an exponential rate. Many chemical molecules with a wide range of functional groups make up biofuels. There is a strong correlation between the interactions between these molecules and the performance of biofuels. In this paper, the authors presented the new findings related to interactions existing in ethyl propionate and Formamide(F), N-Methylformamide (NMF), and N, N-Dimethylformamide (DMF) in a pure state as well as in their mixtures. Densities and speeds of sound at various temperatures (298.15–323.15 K) and at ambient pressure 0.1 MPa have been measured for these mixtures. From experimental data, the excess properties such as excess molar volume, VmE, excess isentropic compressibility, κsE, excess molar isentropic compressibility, Ks,mE, excess speed of sound, uE, and excess isobaric thermal expansivity, αpE, of the investigated mixtures were calculated. All the excess parameter values were fitted using the Redlich-Kister polynomial smoothing equation. The results were analysed in terms of molecular interactions. The excess partial molar volume, V¯m,1E, V¯m,2E , excess partial molar isentropic compressibility, K¯s,m,1EK¯s,m,2E over the whole composition range together with partial molar volume, V¯m,10, V¯m,20, partial molar isentropic compressibility K¯s,m,10, K¯s,m,20, excess partial molar volume, V¯m,10E, V¯m,20E and excess partial molar isentropic compressibility, K¯s,m,10E,K¯s,m,20E at infinite dilution have also been calculated from the experimental density measurements and analytically obtained using Redlich-Kister polynomials. The variations of these parameters with changes in composition and temperature have been discussed in terms of intermolecular interactions prevailing in these mixtures.

Partial Differentiation and the Coefficient of Thermal Expansion: A Multivariable Calculus Activity Connecting with Chemistry

We describe the components and implementation of an activity for multivariable calculus featuring applications to the field of chemistry. This activity focuses on the isobaric thermal expansion coefficient found using partial differentiation of the volume of an ideal gas with respect to temperature as pressure is held constant. Broader goals of this activity include enhancing calculus conceptual understanding, encouraging further interdisciplinary study and exploration, and cultivating mathematicians and scientists with broader and deeper backgrounds.

P[formula omitted]T measurements of Glycols (Mono-, Di- and Triethylene glycol) up to 423.15 K and 140.0 MPa and their aqueous solutions at atmospheric pressure

The density of three glycols, namely Monoethylene glycol (MEG), Diethylene glycol (DEG), and Triethylene glycol (TEG) was measured in the temperature range from 298.15 K to 423.15 K and pressures up to 140.0 MPa using a vibrating tube density meter Anton Paar DMA-HPM, coupled with a high-pressure mPDS 5 unit. The modified Tait-Tammann equation was used to correlate the experimental density, which gave an absolute average relative deviation (AARD) of less than 0.2 %. Derived properties such as isobaric thermal expansion and isothermal compressibility coefficients were estimated and discussed. Furthermore, the density of the binary systems composed by the aforementioned glycols (1) + water (2) was also measured in the (273.15, 373.15) K temperature range at atmospheric pressure. The Cubic-Plus-Association (CPA) and the simplified version of the Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) equations of state were used to correlate the newly measured data, with deviations less than 3.7 % for pure component and 12.0 % for the binary systems.

PvT properties of heptane, octane, nonane, decane, thiophene, and eugenol at temperatures between (313 and 363) K and pressures up to 25 MPa comparing three calibration methods

Compressed liquid densities (ρ) of heptane, octane, nonane, decane, thiophene, and eugenol are reported in the temperature range from (313 to 363) K and pressures up to 25 MPa. The experimental measurements were performed by a vibrating tube densimeter (VTD) using three different calibration methods (classical using nitrogen and water as references, classical with hexane and water as references, and with water and applying vacuum to the VTD). The reliability and validation of this equipment were verified by determining and comparing the experimental density data of heptane, octane, nonane, and decane with models available in the international literature obtaining a maximum deviation of 0.21 %, 0.15 % and 0.09 % for the classical method (with nitrogen and water as references), classical method (with hexane and water as references) and with water and applying vacuum, respectively. The reported density data are obtained using the vacuum applied method, estimating a maximum relative expanded uncertainty (k=2) of 0.21 % in the temperature range from (313 to 363) K and pressures up to 25 MPa. The pure compound densities were successfully modeled with an empirical equation reporting a maximum deviation of 0.09 %. Finally, the isothermal compressibility and isobaric thermal expansivity were evaluated from density data.

Thermodynamic anomalies of water near its singular temperature of 42 °C

The anomalous behavior of such thermodynamic responses of water as isothermal compressibility, isobaric thermal expansion coefficient and isobaric heat capacity have been analyzed using reliable physical–chemical databases. The “thermodynamic tree of derivatives” has been introduced for the thermodynamic potential, being the Gibbs free energy, with a chemical potential at the vertex. The expressions for thermodynamic responses were obtained containing three contributions that are related to the derivatives of entropy, volume and internal energy with respect to thermodynamic variables. It was proved that the volume contribution could be neglected in the temperature range θ≈(0÷200) °C for water in the liquid state. The calculations also showed that the temperature dependence of the derivative -(∂V/∂P)T, which determined the isothermal water compressibility, reached its minimum value in the vicinity of a singular temperature of θ=(42.2±0.2) °C. On the basis of experimental data, a comparison of the proposed expressions for water and argon was carried out, confirming that the anomalous behavior of isothermal compressibility, isobaric expansion coefficient, and isobaric heat capacity turned out to be associated precisely with the entropy contribution in the vicinity of a singular water temperature of θ=(42.2±0.2) °C.

Thermodynamic properties of {glycerol (1) + tert-butanol (2)} mixtures at temperatures from 278 K to 323 K and pressures up to 100 MPa

In the present study the densities at atmospheric pressure and the compression coefficients of a binary liquid mixture {glycerol (1) + tert-butanol (2)} were measured within the temperature range from 278.15 K to 323.15 K (278.15, 288.15, 288.15, 308.15 and 323.15) and pressures up to 100 MPa (10, 25, 50, 75 and 100). Due to the limited solubility of tert-butanol in glycerol and the transition of the mixture to the solid phase the measurements at 278.15 K and 100 MPa were carried out up tox2 = 0.45 (x2 is the mole fraction of tert–butanol). The excess molar volumes, molar isothermal compression, molar isobaric thermal expansion, isochoric coefficient of thermal pressure mixtures, as well as the partial molar volumes of the mixture components, including their limit values, were calculated. The excess molar volume values at 323.15 K (the only temperature at which the compression was measured over the entire composition range) were found to be negative. The partial molar volume of glycerol (GL) at 323.15 K was characterized by the presence of a baric inversion region. The limiting partial molar volume of GL was shown to decrease in its own environment as the pressure rose and to increase in the TBA environment. The molar isothermal compression of the mixture varied depending on the composition without extremes, and the partial molar isothermal compression of GL had negative values. The molar isobaric thermal expansion of the mixture in the area of small tert-butanol (TBA) additives changed slightly at low temperatures and pressures and the increase in both the pressure and the temperature led to dispersion of their concentration dependences. The isochoric coefficient of thermal pressure decreased with an increase in x2, forming a small plateau at small TBA additions. The results obtained were discussed from the perspective of solute–solvent and solute–solute interactions.