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Tao X, Yin T, Shen W. Critical universality and asymmetry of ionic solution {iodobenzene + 1-decyl-3-methyl-imidazolium bis(trifluorosulfonyl)imide}. Phys Chem Chem Phys 2017; 19:22826-22835. [PMID: 28812072 DOI: 10.1039/c7cp03807k] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/13/2023]
Abstract
The liquid-liquid coexistence curve, heat capacity in the critical and noncritical regions, and the turbidity in critical one-phase and two-phase regions of the binary solution {iodobenzene + 1-decyl-3-methylimidazolium bis(trifluorosulfonyl)imide ([C10mim][NTf2])} have been precisely measured. From the data collected in the critical region, the critical exponents α, β, γ and ν, as well as the universal critical amplitude ratios RB and X were obtained and were shown to agree well with their theoretical values for the 3D-Ising universality class, which further confirmed the 3D-Ising criticality of ionic solutions even in a very low relative permittivity solvent. The coulombic character of the studied system was suggested by the small values of the RPM reduced critical temperature and density. Furthermore, it was found that both the asymmetric behaviors of the diameter of the coexistence curve and the osmotic compressibility could be well described using the complete scaling theory.
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Affiliation(s)
- Xiaoyi Tao
- School of Chemistry and Molecular Engineering, East China University of Science and Technology, Shanghai 200237, China.
| | - Tianxiang Yin
- School of Chemistry and Molecular Engineering, East China University of Science and Technology, Shanghai 200237, China.
| | - Weiguo Shen
- School of Chemistry and Molecular Engineering, East China University of Science and Technology, Shanghai 200237, China. and Department of Chemistry, Lanzhou University, Lanzhou, Gansu 730000, China
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Wang X, Wang M, Chen Z, Tao X, Shen W. Critical phenomena of {1-butanol + 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide} binary solution. J Mol Liq 2016. [DOI: 10.1016/j.molliq.2016.09.099] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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3
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Shi S, Xu C, Yin T, Chen Z, Shen W. Critical asymmetry of liquid–liquid coexistence curve of binary mixture nitromethane+3-pentanol. J Mol Liq 2015. [DOI: 10.1016/j.molliq.2015.03.024] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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Yin T, Xu C, Lv H, Liu S, Wang M, Chen Z, Shen W. Asymmetric criticality of binary ionic solutions containing 1-butyl-3-methylimidazolium tetrafluoroborate and alcohol. Phys Chem Chem Phys 2014; 16:17715-23. [DOI: 10.1039/c4cp01344a] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/26/2023]
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Méndez-Castro P, Troncoso J, Peleteiro J, Romaní L. Heat capacity singularity of binary liquid mixtures at the liquid-liquid critical point. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:042107. [PMID: 24229116 DOI: 10.1103/physreve.88.042107] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/05/2013] [Indexed: 06/02/2023]
Abstract
The critical anomaly of the isobaric molar heat capacity for the liquid-liquid phase transition in binary nonionic mixtures is explained through a theory based on the general assumption that their partition function can be exactly mapped into that of the Ising three-dimensional model. Under this approximation, it is found that the heat capacity singularity is directly linked to molar excess enthalpy. In order to check this prediction and complete the available data for such systems, isobaric molar heat capacity and molar excess enthalpy near the liquid-liquid critical point were experimentally determined for a large set of binary liquid mixtures. Agreement between theory and experimental results-both from literature and from present work-is good for most cases. This fact opens a way for explaining and predicting the heat capacity divergence at the liquid-liquid critical point through basically the same microscopic arguments as for molar excess enthalpy, widely used in the frame of solution thermodynamics.
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Affiliation(s)
- Pablo Méndez-Castro
- Departamento de Física Aplicada, Universidad de Vigo, Campus As Lagoas, 32004, Ourense, Spain
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Yin T, Liu S, Xie J, Shen W. Asymmetric criticality of the osmotic compressibility in binary mixtures. J Chem Phys 2013; 138:024504. [PMID: 23320701 DOI: 10.1063/1.4770750] [Citation(s) in RCA: 27] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Heat capacities in the critical and the non-critical regions for {benzonitrile + tridecane} and {benzonitrile + pentadecane}, and light scattering for {benzonitrile + undecane}, {benzonitrile + dodecane}, {benzonitrile + tridecane}, {benzonitrile + tetradecane}, {benzonitrile + pentadecane}, and {benzonitrile + hexadecane} in the critical two-phase region were measured. Light scattering measurements confirmed the existence of the asymmetry for the osmotic compressibility while no such asymmetry was observed for the correlation length. An analysis of the osmotic compressibility asymmetry suggested the dominance of the singular term |ΔT[circumflex]|(β), which supports the complete scaling theory. The consistency of the complete scaling theory in descriptions of different asymmetry behaviors was also discussed. Moreover, it was found that the contribution of the heat capacity-related term is also important in describing the asymmetry of the osmotic compressibility as it was observed in studies of the diameters of the coexistence curves.
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Affiliation(s)
- Tianxiang Yin
- School of Chemistry and Molecular Engineering, East China University of Science and Technology, Shanghai 200237, China
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Méndez-Castro P, Troncoso J, Pérez-Sánchez G, Peleteiro J, Romaní L. Thermal properties of ionic systems near the liquid-liquid critical point. J Chem Phys 2011; 135:214507. [DOI: 10.1063/1.3663857] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2023] Open
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Almasi M, Mousavi L. Excess molar volumes of binary mixtures of aliphatic alcohols (C1–C5) with Nitromethane over the temperature range 293.15 to 308.15K: Application of the ERAS model and cubic EOS. J Mol Liq 2011. [DOI: 10.1016/j.molliq.2011.07.011] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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Losada-Pérez P, Tripathi CSP, Leys J, Glorieux C, Thoen J. Large heat capacity anomaly near the consolute point of the binary mixture nitromethane and 3-pentanol. J Chem Phys 2011; 134:044505. [PMID: 21280746 DOI: 10.1063/1.3535567] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The large critical anomaly in the isobaric heat capacity C(p,x)(T) of the binary mixture nitromethane + 3-pentanol is measured using high-resolution adiabatic scanning calorimetry. The unique features of this technique provided an alternative approach to the study of the critical behavior of C(p,x)(T), providing further C(p,x)(T) related quantities from which valuable information could be extracted. Our data are in full agreement with the predictions of the Modern Theory of Critical Phenomena; specifically, 3D-Ising model values for the critical exponent α and the universal amplitude ratio values of the leading critical amplitudes, as well as for the first correction-to-scaling ones, provide the optimum fits to represent the experimental data. Evidence for the need of higher-order terms, i.e., first correction-to-scaling term, is given. The large value of the coefficient E for the linear temperature dependence of the background obtained is ascribed to a possible contribution of the regular linear background term, of a higher-order asymmetry term, and of the second correction-to-scaling term. Internal consistency of C(p,x)(T) and its related quantities is successfully checked.
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Affiliation(s)
- Patricia Losada-Pérez
- Laboratorium voor Akoestiek en Thermische Fysica, Departement Natuurkunde en Sterrenkunde, Katholieke Universiteit Leuven, Celestijnenlaan 200D, B-3001 Leuven, Belgium
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Pérez-Sánchez G, Losada-Pérez P, Cerdeiriña CA, Thoen J. Critical behavior of static properties for nitrobenzene-alkane mixtures. J Chem Phys 2010; 132:214503. [PMID: 20528027 DOI: 10.1063/1.3431547] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present experimental data of the isobaric heat capacity per unit volume C(p,x)V(-1) for mixtures containing nitrobenzene and an alkane (C(N)H(2N+2), with N ranging from 6 to 15) upon approaching their liquid-liquid critical points along a path of constant composition. Values for the critical amplitude A(+) have been determined. They have been combined with the previously reported ones for the leading term of the coexistence-curve width to obtain, with the aid of well-known universal relations, the critical amplitudes of the correlation length and of the osmotic susceptibility. The trends of all these critical parameters, which exhibit anomalous behavior in the low N region, are discussed in terms of particular microscopic phenomena characterizing NB-C(N)H(2N+2) mixtures. The work is completed with an analysis of the analog of the Yang-Yang anomaly in liquid-liquid criticality: the behavior of the partial molar heat capacities of the two liquid components is found to illustrate previously uncovered asymmetry effects.
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Affiliation(s)
- Germán Pérez-Sánchez
- Departamento de Física Aplicada, Universidad de Vigo, As Lagoas s/n, Ourense 32004, Spain
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Losada-Pérez P, Pérez-Sánchez G, Troncoso J, Cerdeiriña CA. Heat capacity anomalies along the critical isotherm in fluid-fluid phase transitions. J Chem Phys 2010; 132:154509. [DOI: 10.1063/1.3374819] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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12
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Losada-Pérez P, Pérez-Sánchez G, Cerdeiriña CA, Thoen J. Dielectric constant of fluids and fluid mixtures at criticality. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 81:041121. [PMID: 20481691 DOI: 10.1103/physreve.81.041121] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/03/2010] [Indexed: 05/29/2023]
Abstract
The behavior of the dielectric constant epsilon of pure fluids and binary mixtures near liquid-gas and liquid-liquid critical points is studied within the concept of complete scaling of asymmetric fluid-fluid criticality. While mixing of the electric field into the scaling fields plays a role, pressure mixing is crucial as the asymptotic behavior of the coexistence-curve diameter in the epsilon-T plane is concerned. Specifically, it is found that the diameters, characterized by a |T-Tc|1-alpha singularity in the previous scaling formulation [J. V. Sengers, D. Bedeaux, P. Mazur, and S. C. Greer, Physica A 104, 573 (1980)], gain a more dominant |T-Tc|2beta term, whose existence is shown to be supported by literature experimental data. The widely known |T-Tc|1-alpha singularity of epsilon along the critical isopleth in the one-phase region is found to provide information on the effect of electric fields on the liquid-liquid critical temperature: from experimental data it is inferred that Tc usually decreases as the magnitude of the electric field is enhanced. Furthermore, the behavior of mixtures along an isothermal path of approach to criticality is also analyzed: theory explains why the observed anomalies are remarkably higher than those associated to the usual isobaric path.
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Affiliation(s)
- Patricia Losada-Pérez
- Departamento de Física Aplicada, Universidad de Vigo, As Lagoas s/n, Ourense 32004, Spain
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13
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Souto-Caride M, Troncoso J, Losada-Pérez P, Peleteiro J, Carballo E, Romani L. Heat capacity anomalies of associated liquid–alkane mixtures near the liquid–liquid critical point. Chem Phys 2009. [DOI: 10.1016/j.chemphys.2009.04.013] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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14
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Losada-Pérez P, Pérez-Sánchez G, Cerdeiriña CA, Troncoso J, Romaní L. Thermodynamic consistency near the liquid-liquid critical point. J Chem Phys 2009; 130:044506. [PMID: 19191397 DOI: 10.1063/1.3054351] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The thermodynamic consistency of the isobaric heat capacity per unit volume at constant composition C(p,x) and the density rho near the liquid-liquid critical point is studied in detail. To this end, C(p,x)(T), rho(T), and the slope of the critical line (dT/dp)(c) for five binary mixtures composed by 1-nitropropane and an alkane were analyzed. Both C(p,x)(T) and rho(T) data were measured along various quasicritical isopleths with a view to evaluate the effect of the uncertainty in the critical composition value on the corresponding critical amplitudes. By adopting the traditionally employed strategies for data treatment, consistency within 0.01 K MPa(-1) (or 8%) is attained, thereby largely improving the majority of previous results. From temperature range shrinking fits and fits in which higher-order terms in the theoretical expressions for C(p,x)(T) and rho(T) are included, we conclude that discrepancies come mainly from inherent difficulties in determining the critical anomaly of rho accurately: specifically, to get full consistency, higher-order terms in rho(T) are needed; however, the various contributions at play cannot be separated unambiguously. As a consequence, the use of C(p,x)(T) and (dT/dp)(c) for predicting the behavior of rho(T) at near criticality appears to be the best choice at the actual experimental resolution levels. Furthermore, the reasonably good thermodynamic consistency being encountered confirms that previous arguments appealing to the inadequacy of the theoretical expression relating C(p,x) and rho for describing data in the experimentally accessible region must be fairly rejected.
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Affiliation(s)
- Patricia Losada-Pérez
- Departamento de Física Aplicada, Universidad de Vigo, As Lagoas s/n, Ourense 32004, Spain
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Souto-Caride M, Troncoso J, Losada-Pérez P, Peleteiro J, Carballo E, Romani L. Dependence on molecular parameters of the heat capacity critical behaviour for nitroalkane+alcohol binary systems. Chem Phys 2009. [DOI: 10.1016/j.chemphys.2009.02.004] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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16
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González-Salgado D, Valencia JL, Troncoso J, Carballo E, Peleteiro J, Romaní L, Bessières D. Highly precise experimental device for determining the heat capacity of liquids under pressure. THE REVIEW OF SCIENTIFIC INSTRUMENTS 2007; 78:055103. [PMID: 17552856 DOI: 10.1063/1.2736776] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/15/2023]
Abstract
An experimental device for making isobaric heat capacity measurements of liquids under pressure is presented. The device is an adaptation of the Setaram micro-DSC II atmospheric-pressure microcalorimeter, including modifications of vessels and a pressure line allowing the pressure in the measurement system to be set, controlled, and stabilized. The high sensitivity of the apparatus combined with a suitable calibration procedure allows very accurate heat capacity measurements under pressure to be made. The relative uncertainty in the isobaric molar heat capacity measurements provided by the new device is estimated to be 0.08% at atmospheric pressure and 0.2% at higher levels. The device was validated from isobaric molar heat capacity measurements for hexane, nonane, decane, undecane, dodecane, and tridecane, all of which were highly consistent with reported data. It also possesses a high sensitivity as reflected in its response to changes in excess isobaric molar heat capacity with pressure, which were examined in this work for the first time by making heat capacity measurements throughout the composition range of the 1-hexanol+n-hexane system. Finally, preliminary measurements at several pressures near the critical conditions for the nitromethane+2-butanol binary system were made that testify to the usefulness of the proposed device for studying critical phenomena in liquids under pressure.
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Affiliation(s)
- D González-Salgado
- Departamento de Física Aplicada, Facultad de Ciencias de Ourense, As Lagoas s/n, 32004 Ourense, Spain
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Mirzaev S, Iwanowski I, Kaatze U. Dynamic scaling and background relaxation in the ultrasonic spectra of the ethanol–dodecane critical mixture. Chem Phys Lett 2007. [DOI: 10.1016/j.cplett.2006.12.070] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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18
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Souto-Caride M, Troncoso J, Peleteiro J, Carballo E, Romani L. Estimation of critical amplitudes of the correlation length by means of calorimetric and viscosimetric measurements. Chem Phys 2006. [DOI: 10.1016/j.chemphys.2005.11.009] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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Iwanowski I, Sattarow A, Behrends R, Mirzaev SZ, Kaatze U. Dynamic scaling of the critical binary mixture methanol-hexane. J Chem Phys 2006; 124:144505. [PMID: 16626212 DOI: 10.1063/1.2179073] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Acoustical attenuation spectrometry, dynamic light scattering, shear viscosity, density, and heat capacity measurements of the methanol/n-hexane mixture of critical composition have been performed. The critical part in the sonic attenuation coefficients nicely fits to the empirical scaling function of the Bhattacharjee-Ferrell [Phys. Rev. A 24, 1643 (1981)] dynamic scaling model if the theoretically predicted scaled half-attenuation frequency Omega(12) (BF)=2.1 is used. The relaxation rates of order parameter fluctuations, as resulting from the acoustical spectra, within the limits of experimental error agree with those from a combined evaluation of the light scattering and shear viscosity measurements. Both series of data display power law with amplitude Gamma(0)=44x10(9) s(-1). The amplitude of the fluctuation correlation length follows as xi(0)=0.33 nm from the light scattering data and as xi(0)=0.32 nm from the amplitude of the singular part of the heat capacity if the two-scale factor universality relation is used. The adiabatic coupling constant g=0.11 results from the amplitude of the critical contribution to the acoustical spectrum near the critical point, in conformity with g=0.12 as following from the variation of the critical temperature with pressure along the critical line and the thermal expansion coefficient.
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Affiliation(s)
- I Iwanowski
- Drittes Physikalisches Institut, Georg-August-Universität, Friedrich Hund Platz 1, 37077 Göttingen, Germany
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Souto-Caride M, Troncoso J, Peleteiro J, Carballo E, Romaní L. Viscosity anomaly near the critical point in nitrobenzene + alkane binary systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 71:041503. [PMID: 15903673 DOI: 10.1103/physreve.71.041503] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/29/2004] [Indexed: 05/02/2023]
Abstract
The viscosity near the critical point in nitrobenzene+hexane and nitrobenzene+heptane binary systems was studied by examining the viscosity values for critical mixtures at a variable temperature as obtained with a falling-ball viscometer. The regular part of the viscosity of the critical mixtures was calculated by interpolating measurements made at noncritical concentrations. Because viscosity anomaly studies must be conducted at zero shear, a method allowing the estimation of the effective shear for this type of viscometer was developed with a view to introducing the corrections required. This methodology was used to determine the critical exponent for the viscosity anomaly in nitrobenzene+hexane and nitrobenzene+heptane systems, which were found to be 0.0422+/-0.0004 and 0.0432+/-0.0013 , respectively, very consistent with the accepted value: 0.043.
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Affiliation(s)
- M Souto-Caride
- Departamento de Física Aplicada, Universidad de Vigo, Facultad de Ciencias, Campus de Ourense, E 32004 Ourense, Spain
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Troncoso J, González-Salgado D, Cerdeiriña CA, Carballo E, Romaní L. Griffiths-Wheeler geometrical picture of critical phenomena: experimental testing for liquid-liquid critical points. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 71:021503. [PMID: 15783329 DOI: 10.1103/physreve.71.021503] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/13/2004] [Revised: 10/13/2004] [Indexed: 05/24/2023]
Abstract
An experimental approach to the verification of specific relations between thermodynamic properties as predicted from the Griffiths-Wheeler theory of critical phenomena in multicomponent systems is developed for the particular case of ordinary liquid-liquid critical points of binary mixtures. Densities rho(T) , isobaric heat capacities per unit volume C(p)(T) , and previously reported values of the slope of the critical line (dT/dp)c for five critical mixtures are used to check the thermodynamic consistency of C(p) and rho near the critical point. An appropriate treatment of rho (T) data is found to provide the key solution to this issue. In addition, various alternative treatments for C(p)(T) data provide values for both the critical exponent alpha and the ratio between the critical amplitudes of the heat capacity A+/A- that are in agreement with their widely accepted counterparts, whereas two-scale-factor universality is successfully verified in one of the systems studied.
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Affiliation(s)
- Jacobo Troncoso
- Departamento de Física Aplicada, Facultad de Ciencias de Ourense, Universidad de Vigo, Campus As Lagoas 32004 Ourense, Spain
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Behrends R, Iwanowski I, Kosmowska M, Szala A, Kaatze U. Sound attenuation, shear viscosity, and mutual diffusivity behavior in the nitroethane-cyclohexane critical mixture. J Chem Phys 2004; 121:5929-34. [PMID: 15367021 DOI: 10.1063/1.1781614] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
The shear viscosity eta(s), mutual diffusion coefficient D, and ultrasonic attenuation spectra of the nitroethane-cyclohexane mixture of critical composition have been measured at various temperatures near the critical temperature T(c). The relaxation rate of order parameter fluctuations resulting from a combined evaluation of the eta(s) and D data follows power law behavior with the theoretical exponent and with the large amplitude Gamma(o)=(156+/-2)x10(9) s(-1). The ultrasonic spectra have been evaluated in terms of a critical contribution and a noncritical background contribution. The amplitude of the former exhibits a temperature dependence, in conformity with a temperature dependence in the adiabatic coupling constant (|g| = 0.064 near T(c) and 0.1 at T-T(c)=3 K). If the variation of the critical amplitude with T is taken into account the experimental attenuation coefficient data display a scaling function which nicely fits to the theoretical prediction from the Bhattacharjee-Ferrell dynamic scaling model [R. A. Ferrell and J. K. Bhattacharjee, Phys. Rev. A 31, 1788 (1985)].
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Affiliation(s)
- R Behrends
- Drittes Physikalisches Institut, Georg-August-Universität, Bürgerstrasse 42-44, 37073 Göttingen, Germany
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Affiliation(s)
- Sergey Vyazovkin
- Department of Chemistry, University of Alabama at Birmingham, 901S 14th Street, Birmingham, Alabama 35294, USA.
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