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**Two ways of looking at Prigogine and Defay's equation.** / Rebelo, LPN; Najdanovic-Visak, Vesna; Visak, Zoren P. et al.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Rebelo, LPN, Najdanovic-Visak, V, Visak, ZP, da Ponte, MN, Troncoso, J, Cerdeirina, CA & Romani, L 2002, 'Two ways of looking at Prigogine and Defay's equation', *Physical Chemistry Chemical Physics*, vol. 4, no. 11, pp. 2251-2259. https://doi.org/10.1039/b200292b

Rebelo, LPN., Najdanovic-Visak, V., Visak, Z. P., da Ponte, MN., Troncoso, J., Cerdeirina, CA., & Romani, L. (2002). Two ways of looking at Prigogine and Defay's equation. *Physical Chemistry Chemical Physics*, *4*(11), 2251-2259. https://doi.org/10.1039/b200292b

Rebelo LPN, Najdanovic-Visak V, Visak ZP, da Ponte MN, Troncoso J, Cerdeirina CA et al. Two ways of looking at Prigogine and Defay's equation. Physical Chemistry Chemical Physics. 2002;4(11):2251-2259. doi: 10.1039/b200292b

@article{1de05457ac5847b990422aaacaba0026,

title = "Two ways of looking at Prigogine and Defay's equation",

abstract = "In the search for understanding of several types of abnormal thermodynamic behaviour in the vicinity of critical lines of binary liquid mixtures, we have revisited an apparently forgotten relationship between the pressure dependence of the critical temperature and the second derivatives with respect to the composition of the volumetric and enthalpic properties of the mixture. We refer to an equation originally developed in the fifties by Prigogine and Defay and soon afterwards analysed by others. Under some restrictive assumptions, the T-p slope of the critical locus can simply be inferred from the ratio between v(E) and h(E). The interest and usefulness of this approximate relation is self-evident. Values for any one of the three properties involved, (dT/dp)(c), v(E) or h(E), can be assessed based on the availability of the other two. Moreover, the amplitude of the divergence of thermodynamic response functions to criticality are intimately associated with the slope of the critical locus. A link between critical behaviour and solution excess properties is thus established. For instance, double critical points tend to occur if one of the excess properties changes its sign as the temperature or pressure is varied. In this work, we have started a detailed study of the practical limits of validity of the approximate relation. Five binary liquid mixtures were tested, all of them sharing a UCST/LCSP-type of phase transition. Although, from a theoretical perspective, the original second-derivatives approach should perform better, in practice, the direct ratio of the excess properties constitutes a superior strategy for obtaining (dT/dp)(c) values. The underlying reasons for this are discussed in detail. The T-p critical slope is normally found to play a secondary role in assessing the critical amplitudes of diverging thermodynamic functions.",

keywords = "SYSTEMS, EXCESS VOLUMES, LIGHT-SCATTERING, PHASE-EQUILIBRIA, UPPER CRITICAL-POINT, BINARY-LIQUID MIXTURES, PRESSURE, OLIGOSTYRENE, THERMODYNAMICS, FLUID MIXTURES",

author = "LPN Rebelo and Vesna Najdanovic-Visak and Visak, {Zoren P.} and {da Ponte}, MN and J Troncoso and CA Cerdeirina and L Romani",

year = "2002",

doi = "10.1039/b200292b",

language = "English",

volume = "4",

pages = "2251--2259",

journal = "Physical Chemistry Chemical Physics",

issn = "1463-9076",

publisher = "Royal Society of Chemistry",

number = "11",

}

TY - JOUR

T1 - Two ways of looking at Prigogine and Defay's equation

AU - Rebelo, LPN

AU - Najdanovic-Visak, Vesna

AU - Visak, Zoren P.

AU - da Ponte, MN

AU - Troncoso, J

AU - Cerdeirina, CA

AU - Romani, L

PY - 2002

Y1 - 2002

N2 - In the search for understanding of several types of abnormal thermodynamic behaviour in the vicinity of critical lines of binary liquid mixtures, we have revisited an apparently forgotten relationship between the pressure dependence of the critical temperature and the second derivatives with respect to the composition of the volumetric and enthalpic properties of the mixture. We refer to an equation originally developed in the fifties by Prigogine and Defay and soon afterwards analysed by others. Under some restrictive assumptions, the T-p slope of the critical locus can simply be inferred from the ratio between v(E) and h(E). The interest and usefulness of this approximate relation is self-evident. Values for any one of the three properties involved, (dT/dp)(c), v(E) or h(E), can be assessed based on the availability of the other two. Moreover, the amplitude of the divergence of thermodynamic response functions to criticality are intimately associated with the slope of the critical locus. A link between critical behaviour and solution excess properties is thus established. For instance, double critical points tend to occur if one of the excess properties changes its sign as the temperature or pressure is varied. In this work, we have started a detailed study of the practical limits of validity of the approximate relation. Five binary liquid mixtures were tested, all of them sharing a UCST/LCSP-type of phase transition. Although, from a theoretical perspective, the original second-derivatives approach should perform better, in practice, the direct ratio of the excess properties constitutes a superior strategy for obtaining (dT/dp)(c) values. The underlying reasons for this are discussed in detail. The T-p critical slope is normally found to play a secondary role in assessing the critical amplitudes of diverging thermodynamic functions.

AB - In the search for understanding of several types of abnormal thermodynamic behaviour in the vicinity of critical lines of binary liquid mixtures, we have revisited an apparently forgotten relationship between the pressure dependence of the critical temperature and the second derivatives with respect to the composition of the volumetric and enthalpic properties of the mixture. We refer to an equation originally developed in the fifties by Prigogine and Defay and soon afterwards analysed by others. Under some restrictive assumptions, the T-p slope of the critical locus can simply be inferred from the ratio between v(E) and h(E). The interest and usefulness of this approximate relation is self-evident. Values for any one of the three properties involved, (dT/dp)(c), v(E) or h(E), can be assessed based on the availability of the other two. Moreover, the amplitude of the divergence of thermodynamic response functions to criticality are intimately associated with the slope of the critical locus. A link between critical behaviour and solution excess properties is thus established. For instance, double critical points tend to occur if one of the excess properties changes its sign as the temperature or pressure is varied. In this work, we have started a detailed study of the practical limits of validity of the approximate relation. Five binary liquid mixtures were tested, all of them sharing a UCST/LCSP-type of phase transition. Although, from a theoretical perspective, the original second-derivatives approach should perform better, in practice, the direct ratio of the excess properties constitutes a superior strategy for obtaining (dT/dp)(c) values. The underlying reasons for this are discussed in detail. The T-p critical slope is normally found to play a secondary role in assessing the critical amplitudes of diverging thermodynamic functions.

KW - SYSTEMS

KW - EXCESS VOLUMES

KW - LIGHT-SCATTERING

KW - PHASE-EQUILIBRIA

KW - UPPER CRITICAL-POINT

KW - BINARY-LIQUID MIXTURES

KW - PRESSURE

KW - OLIGOSTYRENE

KW - THERMODYNAMICS

KW - FLUID MIXTURES

U2 - 10.1039/b200292b

DO - 10.1039/b200292b

M3 - Journal article

VL - 4

SP - 2251

EP - 2259

JO - Physical Chemistry Chemical Physics

JF - Physical Chemistry Chemical Physics

SN - 1463-9076

IS - 11

ER -