The liquid–liquid coexistence curves of {benzonitrile + n-pentadecane} and {benzonitrile + n-heptadecane} in the critical region

doi:10.1016/j.jct.2012.05.030

The Journal of Chemical Thermodynamics

Volume 54, November 2012, Pages 438-443

https://doi.org/10.1016/j.jct.2012.05.030 Get rights and content

Abstract

Liquid + liquid coexistence curves for the binary solutions of {benzonitrile + n-pentadecane} and {benzonitrile + n-heptadecane} have been measured in the critical region. The critical exponent β and the critical amplitudes have been deduced and the former is consistent with the theoretic prediction. It was found that the coexistence curves may be well described by the crossover model proposed by Gutkowski et al. The asymmetries of the diameters of the coexistence curves were also discussed in the frame of the complete scaling theory.

Highlights

► Coexistence curves of (benzonitrile + n-pentadecane) and (benzonitrile + n-heptadecane) were measured. ► The values of the critical exponent β are consistent with that predicted by the 3D-Ising model. ► The coexistence curves are well described by the critical crossover model. ► The asymmetry of the diameters of the coexistence curves were discussed by the complete scaling theory.

Introduction

It is well known that fluid mixtures belong to the universality class of 3D-Ising-like systems [1], [2], i.e., systems with short-range interactions and a scalar order parameter. In the near critical region of a binary solution, the difference of the general density variables of two coexisting phases Δρ shows power-law dependence described as follows: $Δ ρ = | ρ^{U} - ρ^{L} | = B τ^{β},$ where τ is the reduced temperature (τ = |T − T_c|/T_c, T_c is the critical temperature); ρ is the general density variable and the superscripts “U” and “L” denote each of the two coexisting phases; β is the critical exponent and B is the critical amplitude corresponding to the difference of the general density variable of two coexisting phases. It has been well confirmed by both of the experimental and theoretical studies that the value of β is 0.326 for 3D-Ising universality class. Moreover, experimental studies often showed the asymmetries of the coexistence curves.

This asymmetric criticality has been paid much attention in recent decade accompanied by the raise of the concept “the complete scaling” proposed by Fisher and co-workers [3], [4], [5], which showed that the scaling fields should be the linear mix of all dependent and independent physical fields. This concept has been applied to explain the singularity of the diameter of the coexistence curves for one-component fluids [6] and for both incompressible and weakly compressible binary fluid systems [7], [8]. Moreover, as we indicated [9], the contribution of the heat capacity plays an important role in describing the asymmetric criticality within the frame of the complete scaling theory.

As a part of the continuous investigations on the critical behavior of the binary mixtures of (benzonitrile + n-alkanes) [10], [11], [12], [13], [14], [15], in this paper, we report the measurements of the liquid + liquid coexistence curves for binary solutions of benzonitrile + n-pentadecane and benzonitrile + n-heptadecane. Detailed analysis of the asymmetry of the coexistence curves and discussion about the validity of the complete scaling theory are presented.

Section snippets

Experimental

The purities and suppliers of the chemicals used in this work are listed in table 1.

Mixtures of {benzonitrile + n-pentadecane} and {benzonitrile + n-heptadecane} were carefully prepared in rectangular fluorimeter cells provided with Ace-thread connections with a reproducible mole fraction of ±0.001. The sample cells were then placed in a water bath with a temperature stability of ±0.002 K measured by a platinum resistance thermometer and Keithley 2700 digital multimeter. The accuracy in measurements

Results and discussion

The critical mole fraction and the critical temperature were determined to be x_c = 0.657 ± 0.001, and T_c = 301.2 ± 0.2 K for {x benzontrile + (1 − x) n-pentadecane} and x_c = 0.695 ± 0.001, and T_c = 306.6 ± 0.2 K for {x benzontrile + (1 − x) n-heptadecane}, where x is the mole fraction of benzonitrile, the subscript “c” denotes the critical value. The measured refractive indexes n for coexisting phases are listed in columns 2 and 3 of TABLE 2, TABLE 3. They are also shown in figures 1a and 2a as the plots of temperature

Acknowledgement

This work was supported by the National Natural Science Foundation of China (Projects 20973061 and 21173080).

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The binary solutions of {n-alkane + benzonitrile} are favorable for precise studies of the critical behaviors of the coexistence curves by refractive index measurements. In the previous studies we reported the critical properties of a series of binary mixtures of {n-alkane + benzonitrile } [10–18]. As a part of our continuous studies, in this work we report the liquid-liquid coexistence curve and the specific isobaric heat capacity for binary solution of {n-decane + benzonitrile}.
The liquid-liquid coexistence curve in a temperature range of about 8 K from the upper consolute point and the specific isobaric heat capacity in a wide temperature range for the critical binary solution of {n-decane + benzonitrile} have been precisely measured. The upper consolute mole fraction x_c of benzonitrile and the upper consolute temperature T_c were determined to be x_c = 0.530, T_c = 286.930 K, respectively. From the data collected near the upper consolute point, the critical exponents corresponding to the heat capacity and the coexistence curve were deduced and found to be consistent with the theoretical predictions of the 3D-Ising universality. The chain-length dependences of the critical properties were investigated, and the asymmetric behavior of the coexistence curve was analyzed based on the complete scaling theory, which confirmed that the heat capacity related term was of importance.
Characterization of 1-alkanol + strongly polar compound mixtures from thermophysical data and the application of the Kirkwood-Buff integrals and Kirkwood-Fröhlich formalisms
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Mixtures formed by 1-alkanol and one strongly polar compound, nitromethane (NM), ethanenitrile (EtN), dimethyl sulfoxide (DMSO, sulfolane (SULF), nitrobenzene (NTBz) or benzonitrile (BzCN), have been investigated on the basis of a set of thermophysical data, which includes: excess molar functions, enthalpies, $H_{m}^{E}$ , Gibbs energies, $G_{m}^{E}$ , entropies, $T S_{m}^{E}$ , isobaric heat capacities, $C_{p m}^{E}$ , volumes, $V_{m}^{E}$ ; liquid-liquid equilibria (LLE), excess permittivies and deviations from the linearity of dynamic viscosities. In addition, calculations have been conducted to determine the Kirkwood-Buff integrals and the Kirkwood correlations factors, $g_{K}$ , of the investigated mixtures. In the former case, DISQUAC has been employed for modeling the needed vapour-liquid equilibria data. Many systems under consideration are characterized by dipolar interactions between like molecules and have positive values of $H_{m}^{E}$ , $C_{p m}^{E}$ and $T S_{m}^{E}$ . On the other hand, alkanol-solvent interactions, for mixtures with a fixed 1-alkanol, become weakened in the sequence: DMSO $\approx$ SULF > EtN > NM > BzCN > NTBz. In systems with a given solvent, such interactions become also weaker when the chain length of the 1-alkanol is increased. Interestingly, the considered mixtures also show strong structural effects. Results on Kirkwood-Buff integrals reveal that nitriles are more preferred than nitroalkanes around a central alcohol molecule. Calculations on $g_{K}$ show that, in terms of the mixture polarization, the systems are rather unstructured, and that this trend becomes more important when the 1-alkanol size increases in solutions with a given solvent.
Measurements of the liquid-liquid coexistence curves of {(1 − x) dimethyl carbonate + x pentadecane} and {(1 − x) dimethyl carbonate + x heptadecane} in the critical region
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As shown in Fig. 1S in Supplementary Material, the refractive indexes of pure pentadecane measured in this work is well agreed with those measured at the same wavelength in the previous work [16], while up to 0.0008 higher than the literature values at the wavelength of 589 nm [17] is indicated, which could not be attributed to that the measurements were carried at different wavelengths because the refractive index should decrease as the wavelength increases. The refractive indexes measured at λ = 632.8 nm for heptadecane are about 0.0006 systematically higher than those determined in our previous work [16]. Most of the differences described above may be attributed to the uncertainties introduced from the linearly extrapolation of temperature dependences of the refractive indexes, using the different techniques for measurement of the refractive index, the chemicals from different batches and as well as the different drying process of the chemicals.
The liquid-liquid coexistence curves in a temperature range of about 10 K from the upper consolute critical temperature for binary solutions of {dimethyl carbonate + pentadecane} and {dimethyl carbonate + heptadecane} have been precisely measured. The upper consolute mole fraction x_c of n-alkane and the upper consolute temperature T_c were determined to be x_c = 0.210, T_c = 312.234 K for {dimethyl carbonate + pentadecane} and x_c = 0.183, T_c = 320.496 K for {dimethyl carbonate + heptadecane}, respectively. From the data collected in the near critical point, the critical exponent β was deduced and shown to be consistent well with its theoretical value for the 3-D Ising universality class. The dependences of critical properties on the chain length of n-alkane for a series of {dimethyl carbonate + n-alkane} binary solutions were investigated. Furthermore, it was found that the asymmetric behaviors of the coexistence curve could be well described by the complete scaling theory. The contribution of the heat capacity related term to the asymmetric behaviors of the coexistence curves was discussed.
Liquid–liquid equilibrium, heat capacity and turbidity of binary solution nitrobenzene + n-pentadecane
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These inconsistencies may be attributed to the different sources of the chemicals and possible introduction of different impurities in experimental procedure. The refractive indexes of pure n-pentadecane measured in this work are agreed well with our previous measurement within the experimental uncertainty [17]. The values of the mole fraction x in the coexisting phases at various temperatures were calculated from the measured refractive index data by simultaneously solving Eqs. (1)–(3) using the iteration method.
The liquid–liquid coexistence curve, the isobaric heat capacity per unit volume and the turbidity for the binary solution of nitrobenzene + n-pentadecane have been measured at various temperatures. The upper consolute mole fraction x_c of nitrobenzene and the upper consolute temperature T_c of the binary solution were determined to be x_c = 0.696 and T_c = 307.298 K, respectively. The values of the critical exponents related to the width of the coexistence curve, the heat capacity, the osmotic compressibility and the correlation length were deduced and found to be in good agreements with that of the 3-D Ising universality. With the heat capacity data the asymmetric behavior of the diameter of the coexistence curve was studied in terms of the complete scaling theory. The critical amplitudes related to the above four quantities were used to calculate the universal scaling ratios and to confirm their theoretical predictions.
Thermodynamics of mixtures containing aromatic nitriles
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The coexistence curves of liquid-liquid equilibrium (LLE) for the mixtures: phenylacetonitrile + heptane, + octane, + nonane, + cyclooctane, or + 2,2,4-trimethylpentane and for 3-phenylpropionitrile + heptane, or + octane are reported. Aromatic nitrile + alkane, + aromatic hydrocarbon or + 1 alkanol systems are investigated using a set of thermophysical properties: phase equilibria (solid-liquid, SLE, vapour-liquid, VLE and LLE), excess molar functions, enthalpies ( $H_{m}^{E}$ ), isochoric internal energies ( $U_{Vm}^{E}$ ), isobaric heat capacities ( $C_{pm}^{E}$ ) and volumes ( $V_{m}^{E}$ ), and the Kirkwood’s correlation factor. Due to proximity effects between the phenyl and the CN groups, dipolar interactions between molecules of aromatic nitriles are stronger than those between molecules of isomeric linear nitriles. Dipolar interactions become weaker in the order: 3-phenylpropionitrile > phenylacetonitrile > benzonitrile. Benzonitrile + aromatic hydrocarbon mixtures are characterized by dispersive interactions and structural effects. The latter are more important in systems with phenylacetonitrile. Structural effects are also present in benzonitrile + n-alkane, or + 1-alkanol + mixtures. The systems mentioned above have been studied using DISQUAC. Interaction parameters for contacts where the CN group in aromatic nitriles participates are given. DISQUAC describes correctly any type of phase equilibria, $C_{pm}^{E}$ of benzonitrile + hydrocarbon mixtures and $H_{m}^{E}$ of benzonitrile + cyclohexane, or 1-alkanol systems. Large differences encountered between theoretical $H_{m}^{E}$ values and experimental data for some solutions are discussed. 1-Alkanol + benzonitrile mixtures are also investigated by means of the ERAS model. ERAS represents well $H_{m}^{E}$ of these systems. The $V_{m}^{E}$ curves of solutions with longer 1-alkanols are more poorly described, which has been explained in terms of the existence of structural effects.
Universal critical amplitude ratios in binary mixtures of {benzonitrile + alkane}
2013, Journal of Chemical Thermodynamics
Citation Excerpt :
Table 1 lists the purities and suppliers of the chemicals used in this work. The critical compositions were carefully measured by the method of “equal volume” [27,28] for {benzonitile + n-dodecane}, {benzonitrile + n-pentadecane}, {benzonitrile + n-hexadecane}, {benzonitrile + n-heptadecane}, and {benzonitrile + n-octadecane} and are compared with that obtained in measurements of coexistence curves [25,27–29] in columns 2 and 3 of table 2. The results coincide with each other within their uncertainties except for the critical mole fraction of {benzonitrile + n-hexadecane} and {benzonitrile + n-octadecane}, which may be attributed to the different sources of the chemicals used in experiments [31].
Turbidity in the one-phase region and the isobaric heat capacity per unit volume in both one-phase and two-phase regions for the critical solutions of {benzonitrile + n-alkane} were measured, from which the values of the system-dependent critical amplitudes for the correlation length, the osmotic compressibility, the heat capacity and the correction-to-scaling term of the heat capacity were deduced. The previously reported data of the coexistence curves for {benzonitrile + n-alkane} were also reanalyzed with the crossover model to obtain the crossover parameters. Subsequently, these results together with the values of the critical amplitude related to the coexistence curve reported previously were used to calculate some universal critical amplitude ratios, which showed reasonable agreement with the theoretical predictions.

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The liquid–liquid coexistence curves of {benzonitrile + n-pentadecane} and {benzonitrile + n-heptadecane} in the critical region

Abstract

Highlights

Introduction

Section snippets

Experimental

Results and discussion

Acknowledgement

J. Chem. Thermodyn.

J. Chem. Thermodyn.

J. Chem. Thermodyn.

J. Chem. Thermodyn.

J. Chem. Thermodyn.

J. Chem. Thermodyn.

Fluid Phase Equilib.

Chem. Phys. Lett.

J. Chem. Thermodyn.

J. Chem. Thermodyn.

Ann. Rev. Phys. Chem.