Skip to main content
SpringerLink
Log in

Mitigating Complexity: Cohesion Parameters and Related Topics. I: The Hildebrand Solubility Parameter

  • Published:
Journal of Solution Chemistry Aims and scope Submit manuscript

Abstract

The objective of this review in two parts is to present a compact overview of the development of the solubility parameter \(\left( {\delta_{i} } \right)\) concept: from the seminal work of van Laar in 1910, to the contributions of Scatchard, Hildebrand, Scott and Prausnitz, leading finally to the generalized multi-component (multi-dimensional) cohesion parameters, with the Hansen solubility parameter being the most prominent representative. In this first part, physico-chemical aspects concerning \(\delta_{i}\)-related models in solution chemistry and chemical engineering will be presented, and recent theoretical efforts in this field, that is, equation-of-state approaches and computer simulation methods for the estimation of solubility parameters, will be indicated. Indeed, prediction of thermodynamic properties of liquid nonelectrolyte solutions from properties of the corresponding pure constituents has come a long way since the classic studies by Hildebrand and by Scatchard leading to regular solution theory (RST), in which the solubility parameter is the property of central importance. Selected aspects of RST will be discussed, including the influence of T and of P on \(\delta_{i}\) and their reliable estimation, thereby clearing up misconceptions and pointing out pitfalls not generally recognized. Extending the dicussion to supercritical conditions, the use of solubility parameters in supercritical fluid (SCF) technologies will be indicated, focusing on practical implications of some of the unique phenomena happening in the near supercritical region, which provide the basis of SCF extraction in industries devoted to food-processing, nutraceuticals, pharmaceuticals and biotechnology.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Notes

  1. Max Margules was an Austrian physicist. Born in Brody, Galicia, a former crown-land of the Austro-Hungarian Empire, on April 23, 1856, he started his studies in mathematics, physics and chemistry at the University of Wien (Vienna), Austria, in 1872. Among his teachers were Ludwig Boltzmann and Josef Loschmidt. After a few years as Assistant at the Central Institute of Meteorology in Wien, he went to Berlin for additional studies in mathematical physics (1879/1880), and was habilitated at the University of Wien after his return. However, in 1882 Margules resigned from this academic position and rejoined the Central Institute of Meteorology. During the first years at this institution, he continued to pursue physical and physical–chemical research parallel to his work on theoretical meteorology. In 1906 he voluntarily retired at the age of fifty on a very modest pension. This was also the year of his last meteorological publication, dedicated to the theory of storms: Margules, M.: Zur Sturmtheorie. Meteorolog. Z. 23, 481–497 (1906). His small pension and the inflation after the end of World War I led to a life in poverty, which was compounded by the general state of malnutrition of the Austrian population and his refusal to accept help from colleagues and/or the Austrian Meteorological Society (he was awarded the Hann Medal in 1919 but declined the associated honorarium). Max Margules died of starvation in Perchtoldsdorf near Wien (Vienna), Austria, on October 4, 1920. He contributed significantly and lastingly to meteorology and thermodynamics [55]. Obituaries were prepared by F. M. Exner (Meteorolog. Z. 37, 322–324 (1920)) and E. Gold (Nature 106, 286–287 (1920)).

  2. At low temperatures, the second virial coefficient \(B_{i}\) is negative. As a rough estimate, \(B_{i}\) for vapors of common organic liquids at \(T_{{{\text{bp,}}i}}\) is in the range of about − 1000 cm3·mol−1 to − 2000 cm3·mol−1. With increasing temperature \(B_{i}\) becomes less negative, i.e., \({{{\text{d}}B_{i} } \mathord{\left/ {\vphantom {{{\text{d}}B_{i} } {{\text{d}}T}}} \right. \kern-0pt} {{\text{d}}T}}\) is positive, and at the Boyle temperature \(B_{i} = 0\). For simple fluids, \(T_{{{\text{Boyle,}}i}}\) corresponds to a reduced temperature of ca. \(T_{{{\text{r}},i}} = 2.7\). At higher temperatures, repulsive intermolecular interactions dominate and \(B_{i}\) becomes positive, increasing slowly with increasing T. Eventually, \(B_{i}\) will pass through a very flat maximum, though such a maximum has only been observed for fluids with very low critical temperatures, such as helium and hydrogen.

  3. This terminology is not related to the concept of residual properties presented below and in some detail in Appendix 2.

  4. \(\left( {\frac{\text{cal}}{{{\text{cm}}^{3} {\cdot} {\text{atm}}}}} \right)^{{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-0pt} 2}}} = \left( {\frac{4.184}{{10^{ - 6} \times 1.01325 \times 10^{5} }}} \right)^{{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-0pt} 2}}} \left( {\frac{\text{J}}{{{\text{m}}^{3} {\cdot} {\text{Pa}}}}} \right)^{{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-0pt} 2}}} = 6.42595\left( {\frac{\text{J}}{{{\text{m}}^{3} {\cdot} {\text{Pa}}}}} \right)^{{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-0pt} 2}}} .\)

  5. The frequently given reference quotation “Berthelot, D.: Sur une méthode purement physique pour la détermination des poids moléculaires des gaz et des poids atomiques des leurs éléments. J. Phys. 8, 263–274 (1899)”, is incorrect: in this article Berthelot uses the van der Waals EOS (cf. p. 265, Eq. 2).

  6. At the critical point \(\left( {T_{\text{c}} ,P_{\text{c}} } \right)\), \(\gamma_{V}\) and the slope of the vapor-pressure curve \({{{\text{d}}P_{\sigma } } \mathord{\left/ {\vphantom {{{\text{d}}P_{\sigma } } {{\text{d}}T}}} \right. \kern-0pt} {{\text{d}}T}} = \left( {{{\partial P} \mathord{\left/ {\vphantom {{\partial P} {\partial T}}} \right. \kern-0pt} {\partial T}}} \right)_{\sigma } \equiv \gamma_{\sigma }\) become equal. Even here is \(T\gamma_{V}\) significantly larger than \(P = P_{\text{c}}\): \({\text{Ar}}:T_{\text{c}} \gamma_{{V,{\text{c}}}} = 27.15{\text{ MPa}}\), \(P_{\text{c}} = 4.90{\text{ MPa}}\); \({\text{CCl}}_{ 4} :T_{\text{c}} \gamma_{{V,{\text{c}}}} = 32.27{\text{ MPa}}\), \(P_{\text{c}} = 4.56{\text{ MPa}}\); \(n{\text{ - C}}_{ 7} {\text{H}}_{ 1 6} :T_{\text{c}} \gamma_{{V,{\text{c}}}} = 18.91{\text{ MPa}}\), \(P_{\text{c}} = 2.74{\text{ MPa}}\); \({\text{C}}_{ 6} {\text{H}}_{ 6} :T_{\text{c}} \gamma_{{V,{\text{c}}}} = 34.85{\text{ MPa}}\), \(P_{\text{c}} = 4.90{\text{ MPa}}\); \({\text{H}}_{ 2} {\text{O}}:T_{\text{c}} \gamma_{{V,{\text{c}}}} = 170.83{\text{ MPa}}\), \(P_{\text{c}} = 22.06{\text{ MPa}}\).

  7. The SI unit for \(\alpha_{\text{pol}}\) is \({\text{C}}^{2} {\cdot} {\text{J}}^{ - 1} {\cdot} {\text{m}}^{2} = {\text{F}} {\cdot} {\text{m}}^{2}\) [406], but values of this scalar property known as average molecular polarizability are commonly quoted as the value \({{\alpha_{\text{pol}} } \mathord{\left/ {\vphantom {{\alpha_{\text{pol}} } {4\pi }}} \right. \kern-0pt} {4\pi }}\varepsilon_{0}\), which has the dimension of a volume \(\left( {{\text{m}}^{3} } \right)\) since the permittivity of vacuum (or the electric constant) is \(\varepsilon_{0} = 8.854{ 187 } \ldots \times 1 0^{ - 12} {\text{ C}}^{2}{ \cdot} {\text{J}}^{ - 1} {\cdot} {\text{m}}^{ - 1}\), with \({\text{C}}^{2} {\cdot} {\text{J}}^{ - 1} {\cdot} {\text{m}}^{ - 1} = {\text{F}}{\cdot} {\text{m}}^{ - 1}\). The quantity \({{\alpha _{{{\text{pol}}}} } \mathord{\left/ {\vphantom {{\alpha _{{{\text{pol}}}} } {4\pi \varepsilon _{0} }}} \right. \kern-\nulldelimiterspace} {4\pi \varepsilon _{0} }}\) is thus frequently called the polarizability volume; most conveniently, the tabulated numerical values [396] are directly comparable with values given in older tables that report molecular polarizabilities in units \(10^{ - 24} {\text{ cm}}^{3}\) or Å3 (Å = 10−8 cm).

References

  1. Prausnitz, J.M., Lichtenthaler, R.N., de Azevedo, E.G.: Molecular Thermodynamics of Fluid Phase Equilibria, 3rd edn. Prentice Hall PTR, Upper Saddle River (1999)

    Google Scholar 

  2. Kister, H.Z.: Distillation Operation. McGraw-Hill, New York (1990)

    Google Scholar 

  3. Kister, H.Z.: Distillation Design. McGraw-Hill, New York (1992)

    Google Scholar 

  4. Kister, H.Z.: Distillation Troubleshooting. McGraw-Hill, New York (2006)

    Google Scholar 

  5. McCabe, W.L., Smith, J.C., Harriott, P.: Unit Operations of Chemical Engineering, 7th edn. McGraw-Hill, New York (2006)

    Google Scholar 

  6. Letcher, T.M. (ed.): Developments and Applications in Solubility. The Royal Society of Chemistry, Cambridge (2007)

    Google Scholar 

  7. Seader, J.D., Henley, E.J., Roper, D.K.: Separation Process Principles with Applications Using Process Simulators, 4th edn. Wiley, New Jersey (2016)

    Google Scholar 

  8. Sandler, S.I.: Chemical, Biochemical, and Engineering Thermodynamics, 5th edn. Wiley, New York (2017)

    Google Scholar 

  9. Van Ness, H.C., Abbott, M.M.: Classical Thermodynamics of Nonelectrolyte Solutions; with Applications to Phase Equilibria. McGraw–Hill Book Company, New York (1982)

    Google Scholar 

  10. Smith, J.M., Van Ness, H.C., Abbott, M.M., Swihart, M.T.: Introduction to Chemical Engineering Thermodynamics, 8th edn. McGraw-Hill Education, New York (2018)

    Google Scholar 

  11. Popper, K.R.: The Logic of Scientific Discovery. Routledge, London (2002)

    Google Scholar 

  12. van Kloster, H.S.: J. J. van Laar: pioneer in chemical thermodynamics. J. Chem. Educ. 39, 74–76 (1962)

    Google Scholar 

  13. Wisniak, J.: Johannes Jacobus van Laar: unappreciated scientist. Chem. Educ. 5, 335–339 (2000)

    CAS  Google Scholar 

  14. van der Waals, J.D.: Over de continuiteit van den gas- en vloeistoftoestand. Doctoral thesis in wis- en natuurkunde. University of Leiden, The Netherlands (1873) For an English translation, On the Continuity of the Gaseous and Liquid States, see Rowlinson, J.S. (ed.), North-Holland, Amsterdam (1988)

  15. Kipnis, A.Y., Yavelov, B.E., Rowlinson, J.S.: Van der Waals and Molecular Science. Clarendon Press, Oxford (1996)

    Google Scholar 

  16. Rowlinson, J.S.: Cohesion. A Scientific History of Intermolecular Forces. Cambridge University Press, Cambridge (2002)

    Google Scholar 

  17. van der Waals, J.D.: Molekulartheorie eines Körpers, der aus zwei verschiedenen Stoffen besteht. Z. physik. Chem. 5, 133–173 (1890)

    Google Scholar 

  18. Kohler, F., Wilhelm, E., Posch, H.: Recent advances in the physical chemistry of the liquid state. Adv. Molec. Relax. Processes 8, 193–239 (1976)

    Google Scholar 

  19. Rowlinson, J.S.: Legacy of van der Waals. Nature 244, 414–417 (1973)

    CAS  Google Scholar 

  20. Pitzer, K.S.: Correponding states for perfect liquids. J. Chem. Phys. 7, 583–590 (1939)

    CAS  Google Scholar 

  21. Dieterici, C.: Über den kritischen Zustand. Ann. Physik u. Chem. Neue Folge 69, 685–705 (1899)

    Google Scholar 

  22. MacDougall, F.H.: The equation of state for gases and liquids. J. Am. Chem. Soc. 38, 528–555 (1916)

    CAS  Google Scholar 

  23. MacDougall, F.H.: On the Dieterici equation of state. J. Am. Chem. Soc. 39, 1229–1235 (1917)

    CAS  Google Scholar 

  24. Sadus, R.J.: Equations of state for fluids: the Dieterici approach revisited. J. Chem. Phys. 115, 1460–1462 (2001)

    CAS  Google Scholar 

  25. Sadus, R.J.: The Dieterici alternative to the van der Waals approach for equations of state: second virial coefficienrs. Phys. Chem. Chem. Phys. 4, 919–921 (2002)

    CAS  Google Scholar 

  26. Sadus, R.J.: New Dieterici-type equations of state for fluid phase equilibria. Fluid Phase Equil. 212, 31–39 (2003)

    CAS  Google Scholar 

  27. Román, F.L., Mulero, A., Cuadros, F.: Simple modifications of the van der Waals and Dieterici equations of state: vapour–liquid equilibrium properties. Phys. Chem. Chem. Phys. 6, 5402–5409 (2004)

    Google Scholar 

  28. Balasubramanian, R., Gunavathi, K., Jegan, R., Roobanguru, D.: Open. J. Mod. Phys. 1, 34–40 (2014)

    Google Scholar 

  29. Barton, A.F.M.: CRC Handbook of Solubility Parameters and other Cohesion Parameters, 2nd edn. CRC Press, Boca Raton (1991)

    Google Scholar 

  30. Marcus, Y.: Solvent Properties and Selective Solvation. Marcel Dekker, New York (2002)

    Google Scholar 

  31. Hansen, C.M.: Hansen Solubility Parameters. A User’s Handbook, 2nd edn. CRC Press, Boca Raton (2007)

    Google Scholar 

  32. Goodwin, A.R.H., Sandler, S.I.: Mixing and combining rules. In: Goodwin, A.R.H., Sengers, J.V., Peters, C.J. (eds.) Applied Thermodynamics of Fluids, pp. 84–134. The Royal Society of Chemistry/IUPAC & IACT, Cambridge (2010)

    Google Scholar 

  33. Kontogeorgis, G.M., Folas, G.K.: Thermodynamic Models for Industrial Applications: From Classical and Advanced Mixing Rules to Association Theories. Wiley, Chichester (2010)

    Google Scholar 

  34. Wilhelm, E.: Internal energy and enthalpy: introduction, concepts and selected applications. In: Wilhelm, E., Letcher, T.M. (eds.) Enthalpy and Internal Energy: Liquids, Solutions and Vapours, pp. 1–61. The Royal Society of Chemistry/IACT, Cambridge (2018)

    Google Scholar 

  35. Abdulagatov, I.M., Magee, J.W., Polikhronidi, N.G., Batyrova, R.G.: Internal pressure and internal energy of saturated and compressed phases. In: Wilhelm, E., Letcher, T.M. (eds.) Enthalpy and Internal Energy: Liquids, Solutions and Vapours, pp. 411–446. The Royal Society of Chemistry/IACT, Cambridge (2018)

    Google Scholar 

  36. Wilhelm, E.: Solubility parameters: a brief review. In: Wilhelm, E., Letcher, T.M. (eds.) Enthalpy and Internal Energy: Liquids, Solutions and Vapours, pp. 447–476. The Royal Society of Chemistry/IACT, Cambridge (2018)

    Google Scholar 

  37. Marcus, Y.: Internal pressure of liquids: a review. In: Wilhelm, E., Letcher, T.M. (eds.) Enthalpy and Internal Energy: Liquids, Solutions and Vapours, pp. 477–504. The Royal Society of Chemistry/IACT, Cambridge (2018)

    Google Scholar 

  38. Galitzine, B.: Über das Dalton‘sche Gesetz. III. Theil: Theoretische Untersuchungen. Ann. Physik u. Chem. Neue Folge 41, 770–800 (1890)

    Google Scholar 

  39. Berthelot, D.: Sur le mélange des gaz. C. R. Seances Acad. Sci. 126, 1703–1706 (1898)

    Google Scholar 

  40. Berthelot, D.: Sur le mélange des gaz. C. R. Seances Acad. Sci. 126, 1857–1858 (1898)

    Google Scholar 

  41. London, F.: The general theory of molecular forces. Trans. Faraday Soc. 33, 8–26 (1937)

    CAS  Google Scholar 

  42. Kohler, F., Fischer, J., Wilhelm, E.: Intermolecular force parameters for unlike pairs. J. Mol. Struct. 84, 245–250 (1982)

    CAS  Google Scholar 

  43. Maitland, G.C., Rigby, M., Smith, E.B., Wakeham, W.A.: Intermolecular Forces: Their Origin and Determination. Clarendon Press, Oxford (1981)

    Google Scholar 

  44. Stone, A.: The Theory of Intermolecular Forces, 2nd edn. Oxford University Press, Oxford (2013)

    Google Scholar 

  45. Lorentz, H.A.: Über die Anwendung des Satzes vom Virial in der kinetischen Theorie der Gase. Ann. Physik u. Chem. Neue Folge 12, 127–136 (1881). Addendum: ibid., pp. 660–661

    Google Scholar 

  46. van Laar, J.J.: Die Thermodynamik in der Chemie. S.L. van Looy & H. Gerlings, Amsterdam and Wilhelm Engelmann, Leipzig (1893)

  47. van Laar, J.J.: Sechs Vorträge über das thermodynamische Potential und seine Anwendungen auf chemische und physikalische Gleichgewichtsprobleme, eingeleitet durch zwei Vorträge über nichtverdünnte Lösungen und über den osmotischen Druck. F. Vieweg und Sohn, Braunschweig (1906)

    Google Scholar 

  48. van Laar, J.J.: Über Dampfspannungen von binären Gemischen. Z. Phys. Chem. 72, 723–751 (1910)

    Google Scholar 

  49. van Laar, J.J.: Über den Zusammenhang zwischen der Abweichung der Dampfdruckkurve von binären Gemischen normaler Stoffe von der geraden Linie, und der Mischungswärme in der flüssigen Phase. Z. Phys. Chem. 137A, 421–446 (1928)

    Google Scholar 

  50. Dolezalek, F.: Zur Theorie der binären Gemische und konzentrierten Lösungen. III. Erwiderung an die Herren T. S. Patterson und J. J. van Laar. Z. Phys. Chem. 83, 40–44 (1913)

    CAS  Google Scholar 

  51. van Laar, J.J.: Zur Theorie der Dampfspannungen von binären Gemischen. Erwiderung an Herrn F. Dolezalek. Z. Phys. Chem. 83, 599–608 (1913)

    Google Scholar 

  52. Wilhelm, E.: Solubilities, fugacities and all that in solution chemistry. J. Solution Chem. 44, 1004–1061 (2015)

    CAS  Google Scholar 

  53. Margules, M.: Über die Zusammensetzung der gesättigten Dämpfe von Mischungen. Sitzungsber. Kaiserl. Akad. Wiss. Wien, mathem.-naturwiss. Cl. Abt. IIa 104, 1243–1278 (1895)

    Google Scholar 

  54. Tomiska, J., Neckel, A.: The Margules concept: the basis of modern algebraic representations of thermodynamic excess properties. J. Phase Equilib. 17, 11–20 (1996)

    CAS  Google Scholar 

  55. Wisniak, J.: Max Margules—a cocktail of meteorology and thermodynamics. J. Phase Equilib. 24, 103–109 (2003)

    CAS  Google Scholar 

  56. Wohl, K.: Thermodynamic evaluation of binary and ternary liquid systems. Trans. AIChE 42, 215–249 (1946)

    CAS  Google Scholar 

  57. Wohl, K.: Thermodynamic evaluation of binary and ternary liquid systems. Chem. Eng. Progress 49, 218–219 (1953)

    Google Scholar 

  58. van Laar, J.J., Lorenz, R.: Berechnung von Mischungswärmen kondensierter Systeme. Z. Anorg. Allg. Chem. 146, 42–45 (1925)

    Google Scholar 

  59. Hildebrand, J.H., Scott, R.L.: The Solubility of Nonelectrolytes, 3rd edn. Reinhold Publishing Corporation, New York (1950)

    Google Scholar 

  60. van Laar, J.J: Die Thermodynamik einheitlicher Stoffe und binärer Gemische, mit Anwendungen auf verschiedene physikalisch-chemische Probleme. P. Noordhoff, Groningen und Batavia (1935)

  61. Drossbach, P.: Über die Theorie binärer Gemische von van Laar. Z. Anorg. Allg. Chem. 234, 298–306 (1937)

    CAS  Google Scholar 

  62. Pitzer, K.S.: Joel Henry Hildebrand, 1881–1983. Biogr. Mem. Natl. Acad. Sci. 62, 224–257 (1993)

    Google Scholar 

  63. Hildebrand, J.H.: A quantitative treatment of deviations from Raoult’s law. Proc. Natl. Acad. Sci. USA 13, 267–272 (1927)

    CAS  PubMed  Google Scholar 

  64. Hildebrand, J.H.: Solubility. XII. Regular solutions. J. Am. Chem. Soc. 51, 66–80 (1929)

    CAS  Google Scholar 

  65. Scatchard, G.: Equilibria in non-electrolyte solutions in relation to the vapor pressures and densities of the components. Chem. Rev. 8, 321–333 (1931)

    CAS  Google Scholar 

  66. Edsall, J.T., Stockmayer, W.: George Scatchard, 1892–1973. Biogr. Mem. Natl. Acad. Sci. 52, 334–377 (1980)

    Google Scholar 

  67. Scatchard, G.: The attraction of proteins for small molecules and ions. Ann. N. Y. Acad. Sci. 51, 660–672 (1949)

    CAS  Google Scholar 

  68. Scatchard, G.: Change of volume on mixing and the equations for non-electrolyte mixtures. Trans. Faraday Soc. 33, 160–166 (1937)

    CAS  Google Scholar 

  69. Scatchard, G.: Equilibrium in non-electrolyte mixtures. Chem. Rev. 44, 7–35 (1949)

    CAS  PubMed  Google Scholar 

  70. Hildebrand, J.H., Wood, S.E.: The derivation of equations for regular solutions. J. Chem. Phys. 1, 817–822 (1933)

    CAS  Google Scholar 

  71. Hildebrand, J.H., Scott, R.L.: Regular Solutions. Prentice Hall, Englewood Cliffs (1962)

    Google Scholar 

  72. Hildebrand, J.H., Prausnitz, J.M., Scott, R.L.: Regular and Related Solutions: The Solubility of Gases, Liquids, and Solids. Van Nostrand Reinhold Company, New York (1970)

    Google Scholar 

  73. Hildebrand, J.H.: A history of solution theory. Annu. Rev. Phys. Chem. 32, 1–23 (1981)

    CAS  PubMed  Google Scholar 

  74. Ely, J.F.: The corresponding-states principle. In: Goodwin, A.R.H., Sengers, J.V., Peters, C.J. (eds.) Applied Thermodynamics of Fluids, pp. 135–171. The Royal Society of Chemistry/IUPAC & IACT, Cambridge (2010)

    Google Scholar 

  75. Wilhelm, E.: Volumetric properties: introduction, concepts and selected applications. In: Wilhelm, E., Letcher, T.M. (eds.) Volume Properties: Liquids, Solutions and Vapours, pp. 1–72. The Royal Society of Chemistry/IUPAC & IACT, Cambridge (2015)

    Google Scholar 

  76. Economou, I.G.: Cubic and generalized van der Waals equations of state. In: Goodwin, A.R.H., Sengers, J.V., Peters, C.J. (eds.) Applied Thermodynamics of Fluids, pp. 53–83. The Royal Society of Chemistry/IUPAC & IACT, Cambridge (2010)

    Google Scholar 

  77. Span, R., Lemmon, E.W.: Volumetric properties from multiparameter equations of state. In: Wilhelm, E., Letcher, T.M. (eds.) Volume Properties: Liquids, Solutions and Vapours, pp. 125–151. The Royal Society of Chemistry/IUPAC & IACT, Cambridge (2015)

    Google Scholar 

  78. Trusler, J.P.M.: Virial coefficients. In: Wilhelm, E., Letcher, T.M. (eds.) Volume Properties: Liquids, Solutions and Vapours, pp. 152–162. The Royal Society of Chemistry/IUPAC & IACT, Cambridge (2015)

    Google Scholar 

  79. Dymond, J.H., Marsh, K.N., Wilhoit, R.C., Wong, K.C.: Virial coefficients of pure gases. In: Frenkel, M., Marsh, K.N. (eds.) Landolt-Börnstein, New Series; Group IV: Physical Chemistry, Virial Coefficients of Pure Gases and Mixtures, vol. 21A. Springer, Heidelberg (2002)

    Google Scholar 

  80. Dymond, J.H., Marsh, K.N., Wilhoit, R.C.: Virial coefficients of mixtures. In: Frenkel, M., Marsh, K.N. (eds.) Landolt-Börnstein, New Series; Group IV: Physical Chemistry, Virial Coefficients of Pure Gases and Mixtures, vol. 21B. Springer, Heidelberg (2003)

    Google Scholar 

  81. Haar, L., Gallagher, J.S., Kell, G.S.: NBS/NRC Steam Tables (NSRDS). Thermodynamic and Transport Properties and Computer Programs for Vapor and Liquid States of Water in SI Units. Hemisphere Publishing Corporation, New York (1984)

    Google Scholar 

  82. Hill, P.G., MacMillan, R.D.C.: Virial equation for light and heavy water. Ind. Eng. Chem. Res. 27, 874–882 (1988)

    CAS  Google Scholar 

  83. Wagner, W., Pruß, A.: The IAPWS formulation 1995 for the thermodynamic properties of ordinary water substance for general and scientific use. J. Phys. Chem. Ref. Data 31, 387–535 (2002)

    CAS  Google Scholar 

  84. Wypych, G. (ed.): Handbook of Solvents, Vol. 1: Properties, 2nd edn. ChemTec Publishing/Elsevier Science Limited, Toronto (2014)

    Google Scholar 

  85. Abbott, S., Hansen, C.M., Yamamoto, H., Valpey III, R.S.: Hansen Solubility Parameters in Practice Complete with eBook Software and Data, 5th edn. Hansen-Solubility.com (2015)

  86. Majer, V., Svoboda, V.: Enthalpies of Vaporization of Organic Compounds. A Critical Review and Data Compilation. Blackwell Scientific Publications/IUPAC, Oxford (1985)

    Google Scholar 

  87. Tamir, A., Tamir, E., Stephan, K.: Heats of Phase Change of Pure Components and Mixtures. Elsevier, Amsterdam (1983)

    Google Scholar 

  88. Poling, B.E., Prausnitz, J.M., O’Connell, J.P.: The Properties of Gases and Liquids, 5th edn. McGraw-Hill, New York (2001)

    Google Scholar 

  89. Dortmund Data Bank Software and Separation Technology: http://www.ddbst.de

  90. Wilhoit, R.C., Marsh, K.N., Hong, X., Gadalla, N., Frenkel, M.: Densities of aliphatic hydrocarbons–alkanes. In: Marsh, K.N. (ed.) Landolt–Börnstein, New Series; Group IV: Physical Chemistry, vol. 8B. Springer, Berlin (1996)

  91. Wilhoit, R.C., Marsh, K.N., Hong, X., Gadalla, N., Frenkel, M.: Densities of aliphatic hydrocarbons—alkenes, alkadienes, alkynes, and miscellaneous compounds. In: Marsh, K.N. (ed.) Landolt–Börnstein, New Series; Group IV: Physical Chemistry, vol. 8C. Springer, Berlin (1996)

  92. Wilhoit, R.C., Hong, X., Frenkel, M., Hall, K.R.: Densities of monocyclic hydrocarbons. In: Hall, K.R., Marsh, K.N. (eds.) Landolt-Börnstein, New Series; Group IV: Physical Chemistry, vol. 8D. Springer, Berlin (1997)

  93. Wilhoit, R.C., Hong, X., Frenkel, M., Hall, K.R.: Densities of aromatic hydrocarbons. In: Hall, K.R., Marsh, K.N. (eds.) Landolt-Börnstein, New Series; Group IV: Physical Chemistry, vol. 8E. Springer, Berlin (1998)

  94. Wilhoit, R.C., Hong, X., Frenkel, M., Hall, K.R.: Densities of polycyclic hydrocarbons. In: Hall, K.R., Marsh, K.N. (eds.) Landolt-Börnstein, New Series; Group IV: Physical Chemistry, vol. 8F. Springer, Berlin (1998)

  95. Frenkel, M., Hong, X., Wilhoit, R.C., Hall, K.R.: Densities of alcohols. In: Hall, K.R., Marsh, K.N. (eds.) Landolt-Börnstein, New Series; Group IV: Physical Chemistry, vol. 8G. Springer, Berlin (1998)

  96. Frenkel, M., Hong, X., Wilhoit, R.C., Hall, K.R.: Densities of esters and ethers. In: Hall, K.R., Marsh, K.N. (eds.) Landolt-Börnstein, New Series; Group IV: Physical Chemistry, vol. 8H. Springer, Berlin (2001)

  97. Frenkel, M., Hong, X.: Dong, Q, Yan, X, Chirico, R.D.: Densities of phenols, aldehydes, ketones, carboxylic acids, amines, nitriles, and nitrohydrocarbons. In: Hall, K.R., Marsh, K.N. (eds.) Landolt-Börnstein, New Series; Group IV: Physical Chemistry, vol. 8I. Springer, Berlin (2002)

  98. Frenkel, M., Hong, X.: Dong, Q, Yan, X, Chirico, R.D.: Densities of halohydrocarbons. In: Frenkel, M., Marsh, K.N. (eds.) Landolt-Börnstein, New Series; Group IV: Physical Chemistry, vol. 8J. Springer, Berlin (2003)

  99. Funk, E.W., Prausnitz, J.M.: Thermodynamic properties of liquid mixtures: aromatic-saturated hydrocarbon systems. Ind. Eng. Chem. 62(9), 8–15 (1970)

    CAS  Google Scholar 

  100. Robinson, R.L., Chao, K.-C.: A correlation of vaporization equilibrium ratios for gas processing systems. Ind. Eng. Chem. Process Des. Dev. 10, 221–229 (1971)

    CAS  Google Scholar 

  101. Martin, A., Newburger, J., Adjei, A.: Extended Hildebrand solubility approach: solubility of theophylline in polar binary solvents. J. Pharm. Sci. 69, 487–491 (1980)

    CAS  PubMed  Google Scholar 

  102. Adjei, A., Newburger, J., Martin, A.: Extended Hildebrand approach: solubility of caffeine in dioxane–water mixtures. J. Pharm. Sci. 69, 659–661 (1980)

    CAS  PubMed  Google Scholar 

  103. Martin, A., Paruta, A.N., Adjei, A.: Extended Hildebrand solubility approach: methylxanthines in mixed solvents. J. Pharm. Sci. 70, 1115–1120 (1981)

    CAS  PubMed  Google Scholar 

  104. Martin, A., Wu, P.L., Adjei, A., Mehdizadeh, M., James, K.C., Metzler, C.: Extended Hildebrand solubility approach: testosterone and testosterone propionate in binary solvents. J. Pharm. Sci. 71, 1334–1340 (1982)

    CAS  PubMed  Google Scholar 

  105. Martin, A., Wu, P.L., Velásquez, T.: Extended Hildebrand solubility approach: sulfonamides in binary and ternary solvents. J. Pharm. Sci. 74, 277–282 (1985)

    CAS  PubMed  Google Scholar 

  106. Martin, A., Bustamante, P.: Physical Pharmacy: Chemical Principles in the Pharmaceutical Sciences, 4th edn. Lippincott Williams & Wilkins, Philadelphia, PA (1993)

    Google Scholar 

  107. Bustamante, P., Escalera, B., Martin, A., Selles, E.: A modification of the extended Hildebrand approach to predict the solubility of structurally related drugs in solvent mixtures. J. Pharm. Pharmacol. 45, 253–257 (1993)

    CAS  PubMed  Google Scholar 

  108. Peña, M.Á., Reíllo, A., Escalera, B., Bustamante, P.: Solubility parameter of drugs for predicting the solubility profile type within a wide polarity range in solvent mixtures. Int. J. Pharm. 321, 155–161 (2006)

    PubMed  Google Scholar 

  109. Sotomayor, R.G., Holguín, A.R., Cristancho, D.M., Delgado, D.R., Martinez, F.: Extended Hildebrand solubility approach applied to piroxicam in ethanol + water mixtures. J. Mol. Liq. 180, 34–38 (2013)

    CAS  Google Scholar 

  110. Cárdenas, Z.J., Jiménez, D.M., Delgado, D.R., Peña, M.Á., Martinez, F.: Extended Hildebrand solubility approach applied to some sulphonamides in propylene glycol + water mixtures. Phys. Chem. Liq. 53, 763–775 (2015)

    Google Scholar 

  111. Delgado, D.R., Peña, M.Á., Martinez, F.: Extended Hildebrand solubility approach applied to some sulphapyrimidines in some methanol (1) + water (2) mixtures. Phys. Chem. Liq. 56, 176–188 (2018)

    CAS  Google Scholar 

  112. Huggins, M.L.: Solutions of long chain compounds. J. Chem. Phys. 9, 440 (1941)

    CAS  Google Scholar 

  113. Huggins, M.L.: Some properties of solutions of long-chain compounds. J. Phys. Chem. 46, 151–158 (1942)

    CAS  Google Scholar 

  114. Huggins, M.L.: Thermodynamic properties of solutions of long-chain compounds. Ann. N. Y. Acad. Sci. 43, 1–32 (1942)

    CAS  Google Scholar 

  115. Huggins, M.L.: Theory of solutions of high polymers. J. Am. Chem. Soc. 64, 1712–1719 (1942)

    CAS  Google Scholar 

  116. Huggins, M.L.: Physical Chemistry of High Polymers. Wiley, New York (1958)

    Google Scholar 

  117. Flory, P.J.: Thermodynamics of high polymer solutions. J. Chem. Phys. 9, 660–661 (1941)

    CAS  Google Scholar 

  118. Flory, P.J.: Thermodynamics of high polymer solutions. J. Chem. Phys. 10, 51–61 (1942)

    CAS  Google Scholar 

  119. Flory, P.J.: Thermodynamics of heterogeneous polymers and their solutions. J. Chem. Phys. 12, 425–438 (1944)

    CAS  Google Scholar 

  120. Flory, P.J.: Principles of Polymer Chemistry. Cornell University Press, Ithaca (1953)

    Google Scholar 

  121. Wolf, B.A.: Making Flory-Huggins practical: thermodynamics of polymer-containing mixtures. Adv. Polym. Sci. 238, 1–66 (2011)

    CAS  Google Scholar 

  122. Abrams, D.S., Prausnitz, J.M.: Statistical thermodynamics of liquid mixtures: a new expression for the excess Gibbs energy of partly or completely miscible systems. AIChE J. 21, 116–128 (1975)

    CAS  Google Scholar 

  123. Guggenheim, E.A.: The Theory of the Equilibrium Properties of Some Simple Classes of Mixtures, Solutions and Alloys. Clarendon Press, London (1952)

    Google Scholar 

  124. Stavermann, A.J.: The entropy of high polymer solutions: generalization of formulae. Rec. Trav. Chim. Pays-Bas 69, 163–174 (1950)

    Google Scholar 

  125. Bondi, A.: Physical Properties of Molecular Crystals, Liquids, and Glasses. Wiley, New York (1968)

    Google Scholar 

  126. Gmehling, J., Kolbe, B., Kleiber, M., Rarey, J.: Chemical Thermodynamics for Process Simulation. Wiley-VCH Verlag, Weinheim (2012)

    Google Scholar 

  127. Wilson, G.M.: Vapor–liquid equilibrium. XI. A new expression for the excess free energy of mixing. J. Am. Chem. Soc. 86, 127–130 (1964)

    CAS  Google Scholar 

  128. Scatchard, G., Wilson, G.M.: Vapor–liquid equilibrium. XIII. The system water–butyl glycol from 5 to 85°. J. Am. Chem. Soc. 86, 133–137 (1964)

    CAS  Google Scholar 

  129. Renon, H., Prausnitz, J.M.: Local compositions in thermodynamic excess functions for liquid mixtures. AIChE J. 14, 135–144 (1968)

    CAS  Google Scholar 

  130. Renon, H., Prausnitz, J.M.: Derivation of the three-parameter Wilson equation for the excess Gibbs energy of liquid mixtures. AIChE J. 15, 785 (1969)

    CAS  Google Scholar 

  131. Maurer, G., Prausnitz, J.M.: On the derivation and extension of the UNIQUAC equation. Fluid Phase Equilib. 2, 91–99 (1978)

    CAS  Google Scholar 

  132. Anderson, T.F., Prausnitz, J.M.: Application of the UNIQUAC equation to calculation of multicomponent phase equilibria. 1. Vapor–liquid equilibria. Ind. Eng. Chem. Process Des. Dev. 17, 552–560 (1978)

    CAS  Google Scholar 

  133. Anderson, T.F., Prausnitz, J.M.: Application of the UNIQUAC equation to calculation of multicomponent phase equilibria. 2. Liquid–iquid equilibria. Ind. Eng. Chem. Process Des. Dev. 17, 561–567 (1978)

    CAS  Google Scholar 

  134. Fredenslund, A., Jones, R.L., Prausnitz, J.M.: Group-contribution estimation of activity coefficients in nonideal liquid mixtures. AIChE J. 21, 1086–1099 (1975)

    CAS  Google Scholar 

  135. Fredenslund, A., Gmehling, J., Michelsen, M.L., Rasmussen, P., Prausnitz, J.M.: Computerized design of multicomponent distillation columns using the UNIFAC group contribution method for calculation of activity coefficients. Ind. Eng. Chem. Process Des. Dev. 16, 450–462 (1977)

    CAS  Google Scholar 

  136. Lohmann, J., Joh, R., Gmehling, J.: From UNIFAC to modified UNIFAC (Dortmund). Ind. Eng. Chem. Res. 40, 957–964 (2001)

    CAS  Google Scholar 

  137. Gmehling, J., Constantinescu, D., Schmid, B.: Group contribution methods for phase equilibrium calculations. Annu. Rev. Chem. Biomol. Eng. 6, 267–292 (2015)

    CAS  PubMed  Google Scholar 

  138. Constantinescu, D., Gmehling, J.: Further development of modified UNIFAC (Dortmund): revision and extension. J. Chem. Eng. Data 61, 2738–2748 (2016)

    CAS  Google Scholar 

  139. Lyckman, E.W., Eckert, C.A., Prausnitz, J.M.: Generalized liquid volumes and solubility parameters for regular solution application. Chem. Eng. Sci. 20, 703–706 (1965)

    CAS  Google Scholar 

  140. Majer, V., Svoboda, V., Pick, J.: Heats of Vaporization of Fluids. Studies in Modern Thermodynamics 9. Elsevier, Amsterdam (1989)

    Google Scholar 

  141. Frenkel, M.L., Gadzhiev, S.N., Lebedev, Yu.A. (eds.): Thermochemistry and Equilibria of Organic Compounds. Wiley, New York (1993)

    Google Scholar 

  142. Sarge, S.M., Höhne, G.W.H., Hemminger, W.: Calorimetry: Fundamentals, Instrumentation and Applications. Wiley-VCH, Weinheim (2014)

    Google Scholar 

  143. Zaitsau, D.H., Paulechka, E.: Calorimetric determination of enthalpies of vaporization. In: Wilhelm, E., Letcher, T.M. (eds.) Enthalpy and Internal Energy: Liquids, Solutions and Vapours, pp. 133–158. The Royal Society of Chemistry/IACT, Cambridge (2018)

    Google Scholar 

  144. Wagner, W.: New vapour pressure measurements for argon and nitrogen and a new method for establishing rational vapour pressure equations. Cryogenics 13, 470–482 (1973)

    CAS  Google Scholar 

  145. Ambrose, D.: The correlation and estimation of vapour pressures IV. Observations on Wagner’s method of fitting equations to vapour pressures. J. Chem. Thermodyn. 18, 45–51 (1986)

    CAS  Google Scholar 

  146. Velasco, S., Román, F.L., White, J.A., Mulero, A.: A predictive vapor-pressure equation. J. Chem. Thermodyn. 40, 789–797 (2008)

    CAS  Google Scholar 

  147. Forero, G.L.A., Velásquez, J.J.A.: Wagner liquid–vapour pressure equation constants from a simple methodology. J. Chem. Thermodyn. 43, 1235–1251 (2011)

    Google Scholar 

  148. Srinivasan, K., Ng, K.C., Velasco, S., White, J.A.: A corresponding states treatment of the liquid–vapor saturation line. J. Chem. Thermodyn. 44, 97–101 (2012)

    CAS  Google Scholar 

  149. Velasco, S., Santos, M.J., White, J.A.: The Miller function, a sensitive test for equations of state and theoretical vapor pressure data. J. Chem. Thermodyn. 58, 263–268 (2013)

    CAS  Google Scholar 

  150. Velasco, S., White, J.A.: Some empirical rules concerning the vapor pressure curve revisited. J. Chem. Thermodyn. 68, 193–198 (2014)

    CAS  Google Scholar 

  151. Leibovici, C.F., Nichita, D.V.: New basis functions for the representation of vapor pressure data. Fluid Phase Equilib. 361, 1–15 (2014)

    CAS  Google Scholar 

  152. Velasco, S., Santos, M.J., White, J.A.: Extended corresponding states expressions for the changes in enthalpy, compressibility factor and constant-volume heat capacity at vaporization. J. Chem. Thermodyn. 85, 68–76 (2015)

    CAS  Google Scholar 

  153. Planck, M.: Ueber das Princip der Vermehrung der Entropie. Ann. Phys. Chem. Neue Folge 30, 562–582 (1887)

    Google Scholar 

  154. Wilhelm, E.: What you always wanted to know about heat capacities, but were afraid to ask. J. Solution Chem. 39, 1777–1818 (2010)

    CAS  Google Scholar 

  155. Levelt Sengers, J.M.H.: Thermodynamics of solutions near the solvent’s critical point. In: Bruno, T.J., Ely, J.F. (eds.) Supercritical Fluid Technology: Reviews in Modern Theory and Applications, pp. 1–56. CRC Press, Boca Raton (1991)

    Google Scholar 

  156. Binney, J.J., Dowrick, N.J., Fisher, A.J., Newman, M.E.J.: The Theory of Critical Phenomena. Oxford University Press, Oxford (1992)

    Google Scholar 

  157. Guggenheim, E.A.: The principle of corresponding states. J. Chem. Phys. 13, 253–261 (1945)

    CAS  Google Scholar 

  158. Magee, J.W.: Molar heat capacity (C V) for saturated and compressed liquid and vapor nitrogen from 65 to 300 K at pressures to 35 MPa. J. Res. Natl. Inst. Stand. Technol. 96, 725–740 (1991)

    CAS  PubMed  PubMed Central  Google Scholar 

  159. Perkins, A.R., Magee, J.W.: Molar heat capacity at constant volume for isobutane at temperatures from (114 to 345) K and at pressures to 35 MPa. J. Chem. Eng. Data 54, 2646–2655 (2009)

    CAS  Google Scholar 

  160. Polikhronidi, N.G., Abdulagatov, I.M., Batyrova, R.G., Stepanov, G.V., Wu, J.T., Ustuzhanin, E.E.: Experimental study of the isochoric heat capacity of diethyl ether (DEE) in the critical and supercritical regions. Int. J. Thermophys. 33, 185–219 (2012)

    CAS  Google Scholar 

  161. Yang, C.N., Yang, C.P.: Critical point in liquid–gas transitions. Phys. Rev. Lett. 13, 303–305 (1964)

    CAS  Google Scholar 

  162. Fisher, M.E.: Renormalization group theory: its basis and formulation in statistical physics. Rev. Mod. Phys. 70, 653–681 (1998)

    Google Scholar 

  163. Anisimov, M.A., Sengers, J.V.: Critical region. In: Sengers, J.V., Kayser, R.F., Peters, C.J., White, H.J. (eds.) Equations of State for Fluids and Fluid Mixtures. Experimental Thermodynamics, vol. 5, pp. 381–434. Elsevier/IUPAC, Amsterdam (2000)

    Google Scholar 

  164. Widom, B., Rowlinson, J.S.: New model for the study of liquid–vapor phase transitions. J. Chem. Phys. 52, 1670–1684 (1970)

    CAS  Google Scholar 

  165. Mermin, N.D.: Lattice gas with short-range pair interactions and a singular coexistence-curve diameter. Phys. Rev. Lett. 26, 957–959 (1971)

    Google Scholar 

  166. Rice, O.K., Chang, D.R.: Some thermodynamic relations at the critical point in liquid–vapor systems. Proc. Nat. Acad. Sci. USA 69, 3436–3439 (1972)

    CAS  PubMed  Google Scholar 

  167. Fisher, M.E., Orkoulas, G.: The Yang-Yang anomaly in fluid criticality: experiment and scaling theory. Phys. Rev. Letters 85, 696–699 (2000)

    CAS  Google Scholar 

  168. Kim, Y.C., Fisher, M.E., Orkoulas, G.: Asymmetric fluid criticality. I. Scaling with pressure mixing. Phys. Rev. E 67, 061506 (2003)

    Google Scholar 

  169. Orkoulas, G., Fisher, M.E., Üstün, C.: The Yang-Yang relation and the specific heats of propane and carbon dioxide. J. Chem. Phys. 113, 7530–7545 (2000)

    CAS  Google Scholar 

  170. Orkoulas, G., Fisher, M.E., Panagiotopoulos, A.Z.: Precise simulation of criticality in asymmetric fluids. Phys. Rev. E 63, 051507 (2001)

    CAS  Google Scholar 

  171. Wang, J., Anisimov, M.A.: Nature of vapor–liquid asymmetry in fluid criticality. Phys. Rev. E 75, 051107 (2007)

    Google Scholar 

  172. Anisimov, M.A.: Universality versus nonuniversality in asymmetric fluid criticality. Cond. Matter Phys. 16, 23603 (2013)

    Google Scholar 

  173. Cerdeiriña, C.A., Orkoulas, G., Fisher, M.E.: Soluble model fluids with complete scaling and Yang-Yang features. Phys. Rev. Lett. 116, 040601 (2016)

    PubMed  Google Scholar 

  174. Abdulagatov, I.M., Polikhronidi, N.G., Batyrova, R.G.: Yang-Yang critical anomaly strength parameter from the direct two-phase isochoric heat capacity measurements near the critical point. Fluid Phase Equil. 415, 144–157 (2016)

    CAS  Google Scholar 

  175. Losada-Pérez, P., Cerdeiriña, C.A.: Coexisting densities and critical asymmetry between gas and liquid. J. Chem. Thermodyn. 109, 56–60 (2017)

    Google Scholar 

  176. Behnejad, H., Sengers, J.V., Anisimov, M.A.: Thermodynamic behaviour of fluids near critical points. In: Goodwin, A.R.H., Sengers, J.V., Peters, C.J. (eds.) Applied Thermodynamics of Fluids, pp. 321–367. The Royal Society of Chemistry/IUPAC & IACT, Cambridge (2010)

    Google Scholar 

  177. Wilhelm, E., Letcher, T.M. (eds.): Heat Capacities: Liquids, Solutions and Vapours. The Royal Society of Chemistry/IUPAC & IACT, Cambridge (2010)

    Google Scholar 

  178. Wilhelm, E., Letcher, T.M. (eds.): Volume Properties: Liquids, Solutions and Vapours. The Royal Society of Chemistry/IUPAC & IACT, Cambridge (2015)

    Google Scholar 

  179. Wilhelm, E., Letcher, T.M. (eds.): Enthalpy and Internal Energy: Liquids, Solutions and Vapours. The Royal Society of Chemistry/IACT, Cambridge (2018)

    Google Scholar 

  180. Thoen, J., Glorieux, C.: Photothermal techniques for heat capacities. In: Wilhelm, E., Letcher, T.M. (eds.) Heat Capacities: Liquids, Solutions and Vapours, pp. 264–286. The Royal Society of Chemistry/IUPAC & IACT, Cambridge (2010)

    Google Scholar 

  181. Thoen, J.: High resolution adiabatic scanning calorimetry and heat capacities. In: Wilhelm, E., Letcher, T.M. (eds.) Heat Capacities: Liquids, Solutions and Vapours, pp. 287–306. The Royal Society of Chemistry/IUPAC & IACT, Cambridge (2010)

    Google Scholar 

  182. Anisimov, M.A., Thoen, J.: Heat capacities in the critical region. In: Wilhelm, E., Letcher, T.M. (eds.) Heat Capacities: Liquids, Solutions and Vapours, pp. 307–328. The Royal Society of Chemistry/IUPAC & IACT, Cambridge (2010)

    Google Scholar 

  183. Cerdeiriña, C.A., Losada-Pérez, P., Pérez-Sánchez, G., Troncoso, J.: Critical behaviour: pure fluids and mixtures. In: Wilhelm, E., Letcher, T.M. (eds.) Volume Properties: Liquids, Solutions and Vapours, pp. 326–344. The Royal Society of Chemistry/IUPAC & IACT, Cambridge (2015)

    Google Scholar 

  184. Losada-Pérez, P., Leys, J., Cordoyiannis, G., Glorieux, C., Thoen, J.: Temperature dependence of the enthalpy near critical and tricritical second-order and weakly first-order transitions. In: Wilhelm, E., Letcher, T.M. (eds.) Enthalpy and Internal Energy: Liquids, Solutions and Vapours, pp. 364–379. The Royal Society of Chemistry/IACT, Cambridge (2018)

    Google Scholar 

  185. Abdulagatov, I.M., Magee, J.W., Polikhronidi, N.G., Batyrova, R.G.: Yang-Yang critical anomaly. In: Wilhelm, E., Letcher, T.M. (eds.) Enthalpy and Internal Energy: Liquids, Solutions and Vapours, pp. 380–410. The Royal Society of Chemistry/IACT, Cambridge (2018)

    Google Scholar 

  186. Watson, K.M.: Thermodynamics of the liquid state. Ind. Eng. Chem. 35, 398–406 (1943)

    CAS  Google Scholar 

  187. Thek, R.E., Stiel, L.I.: A new reduced vapor pressure equation. AIChE J. 12, 599–602 (1966). Erratum: AIChE J. 13, 626 (1967)

    CAS  Google Scholar 

  188. Sterbacek, A., Biskup, B., Tausk, P.: Calculation of Properties Using Corresponding States Methods. Elsevier, Amsterdam (1979)

    Google Scholar 

  189. Pitzer, K.S.: The volumetric and thermodynamic properties of fluids. I. Theoretical basis and virial coefficients. J. Am. Chem. Soc. 77, 3427–3433 (1955)

    CAS  Google Scholar 

  190. Pitzer, K.S., Lippmann, D.Z., Curl Jr., R.F., Huggins, C.M., Peterson, D.E.: The volumetric and thermodynamic properties of fluids. II. Compressibility factor, vapor pressure and entropy of vaporization. J. Am. Chem. Soc. 77, 3433–3440 (1955)

    CAS  Google Scholar 

  191. Carruth, G.F., Kobayashi, R.: Extension to low reduced temperatures of three-parameter corresponding states: vapor pressures, enthalpies and entropies of vaporization, and liquid fugacity coefficients. Ind. Eng. Chem. Fundam. 11, 509–517 (1972)

    CAS  Google Scholar 

  192. Sivaraman, A., Magee, J., Kobayashi, R.: Correlation for prediction of latent heat of pure components incorporating renormalization group formulations with corresponding-states principle. Fluid Phase Equilib. 16, 1–12 (1984)

    CAS  Google Scholar 

  193. Pitzer, K.S., Curl Jr., R.F.: The volumetric and thermodynamic properties of fluids. III. Empirical equation for the second viral coefficient. J. Am. Chem. Soc. 79, 2369–2370 (1957)

    CAS  Google Scholar 

  194. Curl Jr., R.F., Pitzer, K.S.: Volumetric and thermodynamic properties of fluids—enthalpy, free energy, and entropy. Ind. Eng. Chem. 50, 265–274 (1958)

    CAS  Google Scholar 

  195. Pitzer, K.S.: Origin of the acentric factor. In: Storvick, T.S., Sandler, S.I. (eds.) Phase Equilibria and Fluid Properties in the Chemical Industry: Estimation and Correlation, ACS Symposium Series 60, pp. 1–10. American Chemical Society, Washington, D. C. (1977)

    Google Scholar 

  196. Edmister, W.C.: Applied Hydrocarbon Thermodynamics. Gulf Publishing Company, Houston (1961)

    Google Scholar 

  197. Lee, B.I., Kesler, M.G.: A generalized thermodynamic correlation based on three-parameter corresponding states. AIChE J. 21, 510–527 (1975). Erratum. AIChE J. 21, 1040 (1975); Erratum. AIChE J. 21, 1237 (1975)

    CAS  Google Scholar 

  198. Benedict, M., Webb, G.B., Rubin, L.C.: An empirical equation for thermodynamic properties of light hydrocarbons and their mixtures I. Methane, ethane, propane and n-butane. J. Chem. Phys. 8, 334–345 (1940)

    CAS  Google Scholar 

  199. Benedict, M., Webb, G.B., Rubin, L.C.: An empirical equation for thermodynamic properties of light hydrocarbons and their mixtures II. Methane, ethane, propane, and n-butane. J. Chem. Phys. 10, 747–758 (1942)

    CAS  Google Scholar 

  200. Benedict, M., Webb, G.B., Rubin, L.C.: An empirical equation for thermodynamic properties of light hydrocarbons and their mixtures. Constants for twelve hydrocarbons. Chem. Eng. Progress 47, 419–422 (1951)

    CAS  Google Scholar 

  201. Benedict, M., Webb, G.B., Rubin, L.C.: An empirical equation for thermodynamic properties of light hydrocarbons and their mixtures. Fugacities and liquid–vapor equilibria. Chem. Eng. Progress 47, 449–454 (1951)

    CAS  Google Scholar 

  202. Wilhelm, E.: Heat capacities: introduction, concepts and selected applications. In: Wilhelm, E., Letcher, T.M. (eds.) Heat Capacities: Liquids, Solutions and Vapours, pp. 1–27. The Royal Society of Chemistry/IUPAC & IACT, Cambridge (2010)

    Google Scholar 

  203. Růžička Jr., V., Domalski, E.S.: Estimation of the heat capacities of organic liquids as a function of temperature using group additivity. I. Hydrocarbon compounds. J. Phys. Chem. Ref. Data 22, 597–618 (1993)

    Google Scholar 

  204. Růžička Jr., V., Domalski, E.S.: Estimation of the heat capacities of organic liquids as a function of temperature using group additivity II. Compounds of carbon, hydrogen, halogens, nitrogen, oxygen, and sulfur. J. Phys. Chem. Ref. Data 22, 619–657 (1993)

    Google Scholar 

  205. Zábranský, M., Růžička Jr., V.: Estimation of the heat capacities of organic liquids as a function of temperature using group additivity: an amendment. J. Phys. Chem. Ref. Data 33, 1071–1081 (2004)

    Google Scholar 

  206. Constantinou, L., Gani, R.: New group contribution method for estimating properties of pure compounds. AIChE J. 40, 1697–1710 (1994)

    CAS  Google Scholar 

  207. Marrero, J., Gani, R.: Group-contribution based estimation of pure component properties. Fluid Phase Equilib. 183–184, 183–208 (2001)

    Google Scholar 

  208. Kolská, Z., Kukal, J., Zábranský, M., Růžička, V.: Estimatiom of the heat capacity of organic liquids as a function of temperature by a three-level group contribution method. Ind. Eng. Chem. Res. 47, 2075–2085 (2008)

    Google Scholar 

  209. Jovanović, J.D., Knežević-Stevanović, A.B., Grozdanić, D.K.: Prediction of high pressure liquid heat capacities of organic compounds by a group contribution method. J. Serb. Chem. Soc. 76, 417–423 (2011)

    Google Scholar 

  210. Randzio, S.L.: Scanning transitiometry and its use to determine heat capacities of liquids at high pressures. In: Wilhelm, E., Letcher, T.M. (eds.) Heat Capacities: Liquids, Solutions and Vapours, pp. 153–184. The Royal Society of Chemistry/IUPAC & IACT, Cambridge (2010)

    Google Scholar 

  211. Benson, S.W., Cruickshank, F.R., Golden, D.M., Haugen, G.R., O’Neal, H.E., Rodgers, A.S., Shaw, R., Walsh, R.: Additivity rules for the estimation of thermochemical properties. Chem. Rev. 69, 279–324 (1969). There are a number of references to Benson’s work, and Poling et al. in Ref. 88 adopted the notation of the CHETAH program (version 7.2) from ASTM, distributed by NIST as Special Data Base 16. This differs from Benson’s original and also from that of previous editions of The Properties of Gases and Liquids

    CAS  Google Scholar 

  212. Joback, K.G., Reid, R.C.: Estimation of pure-component properties from group-contributions. Chem. Eng. Commun. 57, 233–243 (1987)

    CAS  Google Scholar 

  213. Shi, C., Borchardt, T.B.: JRgui: a Python program of Joback and Reid method. ACS Omega 2, 8682–8688 (2017)

    CAS  Google Scholar 

  214. Herzfeld, K.F., Litovitz, T.A.: Absorption and Disperion of Ultrasonic Waves. Academic Press, New York (1959)

    Google Scholar 

  215. Bhatia, A.B.: Ultrasonic Absorption. Oxford University Press, London (1967)

    Google Scholar 

  216. Goodwin, A.R.H., Trusler, J.P.M.: Speed of sound. In: Goodwin, A.R.H., Marsh, K.N., Wakeham, W.A. (eds.) Experimental Thermodynamics, Vol. VII: Measurement of the Thermodynamic Properties of Single Phases, pp. 237–323. Elsevier/IUPAC, Amsterdam (2003)

    Google Scholar 

  217. Wilhelm, E., Asenbaum, A.: Heat capacities and Brillouin scattering in liquids. In: Wilhelm, E., Letcher, T.M. (eds.) Heat Capacities: Liquids, Solutions and Vapours, pp. 238–263. The Royal Society of Chemistry/IUPAC & IACT, Cambridge (2010)

    Google Scholar 

  218. Asenbaum, A., Pruner, Ch., Wilhelm, E.: Ultrasonics 1: speed of ultrasound, isentropic compressibility and related properties of liquids. In: Wilhelm, E., Letcher, T.M. (eds.) Volume Properties: Liquids, Solutions and Vapours, pp. 345–394. The Royal Society of Chemistry/IUPAC & IACT, Cambridge (2015)

    Google Scholar 

  219. Takagi, T., Wilhelm, E.: Speed-of-sound measurements and heat capacities of liquid sysrems at high pressure. In: Wilhelm, E., Letcher, T.M. (eds.) Heat Capacities: Liquids, Solutions and Vapours, pp. 218–237. The Royal Society of Chemistry/IUPAC & IACT, Cambridge (2010)

    Google Scholar 

  220. Takagi, T.: Ultrasonics 2: high pressure speed of sound, isentropic compressibility. In: Wilhelm, E., Letcher, T.M. (eds.) Volume Properties: Liquids, Solutions and Vapours, pp. 395–413. The Royal Society of Chemistry/IUPAC & IACT, Cambridge (2015)

    Google Scholar 

  221. Wilhelm, E.: Chemical thermodynamics: a journey of many vistas. J. Solution Chem. 43, 525–576 (2014)

    CAS  Google Scholar 

  222. Wilhelm, E.: Pressure dependence of the isothermal compressibility and a modified form of the Tait equation. J. Chem. Phys. 63, 3379–3381 (1975)

    CAS  Google Scholar 

  223. Wilhelm, E.: Precision methods for the determination of the solubility of gases in liquids. CRC Crit. Rev. Analyt. Chem. 16, 129–175 (1985)

    CAS  Google Scholar 

  224. Bruno, T.J., Ely, J.F. (eds.): Supercritical Fluid Technology: Reviews in Modern Theory and Applications. CRC Press, Boca Raton (1991)

    Google Scholar 

  225. McHugh, M.A., Krukonis, V.J.: Supercritical Fluid Extraction: Principles and Practice, 2nd edn. Butterworth-Heinemann, Boston (1994)

    Google Scholar 

  226. Brunner, G.: Gas Extraction: An Introduction to Fundamentals of Supercritical Fluids and the Application to Separation Processes. Springer, Berlin (1994)

    Google Scholar 

  227. Brunner, G. (ed.): Supercritical Fluids as Solvents and Reaction Media. Elsevier, Amsterdam (2004)

    Google Scholar 

  228. Clifford, A.: Fundamentals of Supercritical Fluids. Oxford University Press, Oxford (1999)

    Google Scholar 

  229. Kiran, E., Debenedetti, P.G., Peters, C.J. (eds.): Supercritical Fluids: Fundamentals and Applications. Kluwer, Dordrecht (2000)

    Google Scholar 

  230. Mukhopadhyay, M.: Natural Extracts Using Supercritical Carbon Dioxide. CRC Press, Boca Raton (2000)

    Google Scholar 

  231. Arai, Y., Sako, T., Takebayashi, Y. (eds.): Supercritical Fluids. Molecular Interactions, Physical Properties and New Applications. Springer, Berlin (2002)

    Google Scholar 

  232. Martinez, J.L. (ed.): Supercritical Fluid Extraction of Nutraceuticals and Bioactive Compounds. CRC Press, Boca Raton (2008)

    Google Scholar 

  233. Osborne, J. (ed.): Handbook on Supercritical Fluids: Fundamentals, Properties and Applications. Nova Science Publishers, New York (2014)

    Google Scholar 

  234. Souyoul, S.A., Saussy, K.P., Lupo, M.P.: Nutraceuticals: a review. Dermatol. Ther. (Heidelb.) 8, 5–16 (2018)

    Google Scholar 

  235. Turner, C., King, J.W., Mathiasson, L.: Supercritical fluid extraction and chromatography for fat-soluble vitamin analysis. J. Chromatogr. A 936, 215–237 (2001)

    CAS  Google Scholar 

  236. Williams, J.R., Clifford, A.A., Al-Saidi, S.H.R.: Supercritical fluids and their applications in biotechnology and related areas. Mol. Biotechn. 22, 263–286 (2002)

    CAS  Google Scholar 

  237. York, P., Kompella, U.B., Shekunov, B.V. (eds.): Drug Delivery and Supercritical Technology. Marcel Dekker, New York (2004)

    Google Scholar 

  238. Brunner, G.: Supercritical fluids: technology and application to food processing. J. Food Eng. 67, 21–33 (2005)

    Google Scholar 

  239. Reverchon, E., De Marco, I.: Supercritical fluid extraction and fractionation of natural matter. J. Supercrit. Fluids 38, 146–166 (2006)

    CAS  Google Scholar 

  240. King, J.W., Srinivas, K.: Multiple unit processing sub-and supercritical fluids. J. Supercrit. Fluids 47, 598–610 (2009)

    CAS  Google Scholar 

  241. Herrero, M., Mendiola, J.A., Cifuentes, A., Ibáñez, E.: Supercritical fluid extraction: recent advances and applications. J. Chromatogr. A 1217, 2495–2511 (2010)

    CAS  PubMed  Google Scholar 

  242. King, J.W., Srinivas, K., Zhang, D.: Advances in critical fluid processing. In: Proctor, A. (ed.) Alternatives to Conventional Food Processing, pp. 93–144. The Royal Society of Chemistry, Cambridge (2011)

    Google Scholar 

  243. Azmir, J., Zaidul, I.S.M., Rahman, M.M., Sharif, K.M., Mohamed, A., Sahena, F., Jahurul, M.H.A., Ghafoor, K., Norulaini, N.A.N., Omar, A.K.M.: Techniques for extraction of bioactive compounds from plant materials: a review. J. Food Eng. 117, 426–436 (2013)

    CAS  Google Scholar 

  244. King, J.W.: Modern supercritical fluid technology for food applications. Annu. Rev. Food Sci. Technol. 5, 215–238 (2014)

    CAS  PubMed  Google Scholar 

  245. Da Silva, R.P.F.F., Rocha-Santos, T.A.P., Duarte, A.C.: Supercritical fluid extraction of bioactive compounds. Trends Analyt. Chem. 76, 40–51 (2016)

    Google Scholar 

  246. Giddings, J.C., Myers, M.N., McLaren, L., Keller, R.A.: High pressure gas chromatography of nonvolatile species. Science 162, 67–73 (1968)

    CAS  PubMed  Google Scholar 

  247. Giddings, J.C., Myers, M.N., King, J.W.: Dense gas chromatography at pressures to 2000 atmospheres. J. Chromatogr. Sci. 7, 276–283 (1969)

    CAS  Google Scholar 

  248. Giddings, J.C., Czubryt, J.J., Myers, M.N.: Solubility phenomena in dense carbon dioxide gas in the range 270–1900 atmospheres. J. Phys. Chem. 74, 4260–4266 (1970)

    CAS  Google Scholar 

  249. Eissler, R.L., Friedrich, J.P.: Estimation of supercritical fluid–liquid solubility parameter differences for vegetable oils and other liquids from data taken with a stirred autoclave. J. Am. Oil Chem. Soc. 65, 764–767 (1988)

    CAS  Google Scholar 

  250. Mishra, V.K., Temelli, F., Ooraikul, B.: Modeling binary phase behavior of supercritical carbon dioxide and fatty acid esters. J. Supercrit. Fluids 6, 51–57 (1993)

    CAS  Google Scholar 

  251. Marcus, Y.: Are solubility parameters relevant to supercritical fluids? J. Supercrit. Fluids 38, 7–12 (2006)

    CAS  Google Scholar 

  252. Soave, G.: Equilibrium constants from a modified Redlich-Kwong equation of state. Chem. Eng. Sci. 27, 1197–1203 (1972)

    CAS  Google Scholar 

  253. Peng, D.-Y., Robinson, D.B.: A new two-constant equation of state. Ind. Eng. Chem. Fundam. 15, 59–64 (1976)

    CAS  Google Scholar 

  254. Johnston, K.P.: New directions in supercritical fluid science and technology. In: Johnston, K.P., Penninger, J.M.L. (eds.) Supercritical Fluid Science and Technology, ACS Symposium Series 406, pp. 1–12. American Chemical Society, Washington, D. C. (1989)

    Google Scholar 

  255. Allada, S.R.: Solubility parameters of supercritical fluids. Ind. Eng. Chem. Process Des. Dev. 23, 344–348 (1984)

    CAS  Google Scholar 

  256. Hougen, O.A., Watson, K.M., Ragatz, R.A.: Chemical Process Principles, Part II, 2nd edn. Asia Publishing House, Bombay (1960)

    Google Scholar 

  257. Marcus, Y.: Solubility parameter of carbon dioxide—an enigma. ACS Omega 3, 524–528 (2018)

    CAS  Google Scholar 

  258. Span, R., Wagner, W.: A new equation of state for carbon dioxide covering the fluid region from the triple point temperature to 1100 K at pressures up to 800 MPa. J. Phys. Chem. Ref. Data 25, 1509–1596 (2007)

    Google Scholar 

  259. Franck, E.U.: Water and aqueous solutions at high pressures and temperatures. Pure Appl. Chem. 24, 13–30 (1970)

    CAS  Google Scholar 

  260. Franck, E.U.: Supercritical water. In: Tremaine, P.R., Hill, P.G., Irish, D.E., Balakrishnan, P.V. (eds.) Steam, Water, and Hydrothermal Systems: Physics and Chemistry Meeting the Needs of Industry. In: Proceedings of the 13th International Conference on the Properties of Water and Steam. NRC Research Press, Ottawa (2000)

  261. Weingärtner, H., Franck, E.U.: Supercritical water as a solvent. Angew. Chem. Int. Ed. 44, 2672–2692 (2005)

    Google Scholar 

  262. Wagner, W., Kretzschmar, H.-J.: International Steam Tables—Properties of Water and Steam Based on the Industrial Formulation IAPWS-IF97, 2nd edn. Springer, Berlin (2008)

    Google Scholar 

  263. Meija, J., Coplen, T.B., Berglund, M., Brand, W.A., De Bièvre, P., Gröning, M., Holden, N.E., Irrgeher, J., Loss, R.D., Walczyk, T., Prohaska, T.: Atomic weights of the elements 2013 (IUPAC Technical Report). Pure Appl. Chem. 88, 265–291 (2016)

    CAS  Google Scholar 

  264. Fernández, D.P., Goodwin, A.R.H., Lemmon, E.W., Levelt-Sengers, J.M.H., Williams, R.C.: A formulation for the static permittivity of water and steam at temperatures from 238 K to 873 K at pressures up to 1200 MPa, including derivatives and Debye–Hückel coefficients. J. Phys. Chem. Ref. Data 26, 1125–1166 (1997)

    Google Scholar 

  265. Harris, F.E., Alder, B.J.: Dielectric polarization in polar substances. J. Chem. Phys. 21, 1031–1038 (1953)

    CAS  Google Scholar 

  266. Kirkwood, J.G.: The dielectric polarization of polar liquids. J. Chem. Phys. 7, 911–919 (1939)

    CAS  Google Scholar 

  267. Kutney, M.C., Dodd, V.S., Smith, K.A., Herzog, H.J., Tester, J.W.: Tester, J.W.: A hard-sphere volume-translated van der Waals equation of state for supercritical process modeling. 1. Pure components. Fluid Phase Equil. 128, 149–171 (1997)

    CAS  Google Scholar 

  268. Marcus, Y.: Supercritical Water, a Green Solvent: Properties and Uses. Wiley, Hoboken (2012)

    Google Scholar 

  269. Pang, T.-H., McLaughlin, E.: Supercritical extraction of aromatic hydrocarbon solids and tar sand bitumens. Ind. Eng. Chem. Process Des. Dev. 24, 1027–1032 (1985)

    CAS  Google Scholar 

  270. Clausius, R.: Über das Verhalten der Kohlensäure in Bezug auf Druck, Volumen und Temperatur. Ann. Phys. Chem. Neue Folge 9, 337–357 (1880)

    Google Scholar 

  271. Berthelot, D.: Sur les thermomètres à gaz et sur la réduction de leurs indications à l’échelle absolue des températures. Trav. Mém. Bureau Int. Poids et Més. XIII, (B) 1–113 (1907). The equation of state known as the Berthelot EOS is introduced on p. 26 of this article with the follwing original quotation:L’équation caractéristic que nous désignerons sous le nom d’équation de Van der Waals modifiée, devient \( \left( {p + \frac{a}{{Tv^{2} }}} \right)\left( {v - b} \right) = RT \).”

  272. Redlich, O., Kwong, J.N.S.: On the thermodynamics of solution. V. An equation of state. Fugacities of gaseous solutions. Chem. Rev. 44, 233–244 (1949)

    CAS  PubMed  Google Scholar 

  273. Martin, J.J.: Cubic equations of state—which? Ind. Eng. Chem. Fundam. 18, 81–97 (1979)

    CAS  Google Scholar 

  274. Kumar, K.H., Starling, K.E.: Comments on: “Cubic equations of state—which?”. Ind. Eng. Chem. Fundam. 19, 128–129 (1980)

    CAS  Google Scholar 

  275. Martin, J.J.: Comments on: “Cubic equations of state – which?”. Ind. Eng. Chem. Fundam. 19, 130–131 (1980)

    CAS  Google Scholar 

  276. Peneloux, A., Rauzy, E., Freze, R.: A consistent correction for Redlich–Kwong–Soave volumes. Fluid Phase Equilib. 8, 7–23 (1982)

    CAS  Google Scholar 

  277. Chen, C.-C., Mathias, P.M.: Applied thermodynamics for process modeling. AIChE J. 48, 194–200 (2002)

    CAS  Google Scholar 

  278. Valderama, J.O.: The state of the cubic equations of state. Ind. Eng. Chem. Res. 42, 1603–1618 (2003)

    Google Scholar 

  279. Prausnitz, J.M., Tavares, F.W.: Thermodynamics of fluid-phase equilibria for standard chemical engineering operations. AIChE J. 50, 739–761 (2004)

    CAS  Google Scholar 

  280. Wilczek-Vera, G., Vera, J.H.: Understanding cubic equations of state: a search for the hidden clues of their success. AIChE J. 61, 2824–2831 (2015)

    CAS  Google Scholar 

  281. Fuller, G.G.: A modified Redlich–Kwong–Soave equation of state capable of representing the liquid state. Ind. Eng. Chem. Fundam. 15, 254–257 (1976)

    CAS  Google Scholar 

  282. Graboski, M.S., Daubert, T.E.: A modified Soave equation of state for phase equilibrium calculations. 1. Hydrocarbon systems. Ind. Eng. Chem. Process Des. Dev. 17, 443–448 (1978)

    CAS  Google Scholar 

  283. Graboski, M.S., Daubert, T.E.: A modified Soave equation of state for phase equilibrium calculations. 2. Systems containing CO2, H2S, N2, and CO. Ind. Eng. Chem. Process Des. Dev. 17, 448–454 (1978)

    CAS  Google Scholar 

  284. Graboski, M.S., Daubert, T.E.: A modified Soave equation of state for phase equilibrium calculations. 3. Systems containing hydrogen. Ind. Eng. Chem. Process Des. Dev. 18, 300–306 (1979)

    CAS  Google Scholar 

  285. Lopez-Echeverry, J.S., Reif-Acherman, S., Araujo-Lopez, E.: Peng-Robinson equation of state: 40 years through cubics. Fluid Phase Equil. 447, 39–71 (2017)

    CAS  Google Scholar 

  286. Privat, R., Visvonte, M., Zazoua-Khames, A., Jaubert, J.-N., Gani, R.: Analysis and prediction of the alpha-function parameters used in cubic equations of state. Chem. Eng. Sci. 126, 584–603 (2015)

    CAS  Google Scholar 

  287. Le Guennec, Y., Lasala, S., Privat, R., Jaubert, J.-N.: A consistency test for α-functions of cubic equations of state. Fluid Phase Equilib. 427, 513–538 (2016)

    Google Scholar 

  288. Le Guennec, Y., Privat, R., Lasala, S., Jaubert, J.-N.: On the imperative need to use a consistent α-function for the prediction pure-compound supercritical properties with a cubic equation of state. Fluid Phase Equilib. 445, 45–53 (2017)

    Google Scholar 

  289. Colina, C.M., Santos, J., Olivera-Fuentes, C.: High-temperature behaviour of the cohesion parameter of cubic equations of state. High Temp.–High Press. 29, 525–532 (1997)

    CAS  Google Scholar 

  290. Mahmoodi, P., Sedigh, M.: Soave alpha function at supercritical temperatures. J. Supercrit. Fluids 112, 22–36 (2016)

    CAS  Google Scholar 

  291. Mahmoodi, P., Sedigh, M.: Second derivative of alpha functions in cubic equations of state. J. Supercrit. Fluids 120, 191–206 (2017)

    CAS  Google Scholar 

  292. Mahmoodi, P., Sedigh, M.: A consistent and precise alpha function for cubic equations of state. Fluid Phase Equilib. 436, 69–84 (2017)

    CAS  Google Scholar 

  293. Wang, F., Threatt, T.J., Vargas, F.M.: Determination of solubility parameters from density measurements for non-polar hydrocarbons at temperatures from (298–433) K and pressures up to 137 MPa. Fluid Phase Equilib. 430, 19–32 (2016)

    CAS  Google Scholar 

  294. Majer, V., Pádua, A.A.H.: Measurement of density with vibrating bodies. In: Goodwin, A.R.H., Marsh, K.N., Wakeham, W.A. (eds.) Experimental Thermodynamics, Vol. VII: Measurement of the Thermodynamic Properties of Single Phases, pp. 149–168. Elsevier/IUPAC, Amsterdam (2003)

    Google Scholar 

  295. González-Salgado, D., Troncoso, J., Romani, L.: Experimental techniques 2: vibrating tube densimetry. In: Wilhelm, E., Letcher, T.M. (eds.) Volume Properties: Liquids, Solutions and Vapours, pp. 100–114. The Royal Society of Chemistry/IUPAC & IACT, Cambridge (2015)

    Google Scholar 

  296. Chapman, W.G., Gubbins, K.E., Jackson, G., Radosz, M.: SAFT: equation-of-state solution model for associating fluids. Fluid Phase Equil. 52, 31–38 (1989)

    CAS  Google Scholar 

  297. Gross, J., Sadowski, G.: Perturbed-Chain SAFT: an equation of state based on a perturbation theory for chain molecules. Ind. Eng. Chem. Res. 40, 1244–1260 (2001)

    CAS  Google Scholar 

  298. Michelsen, M.L., Hendriks, E.M.: Physical properties from association models. Fluid Phase Equilib. 180, 147–165 (2001)

    Google Scholar 

  299. Gross, J., Sadowski, G.: Application of the Perturbed-Chain SAFT equation of state to associating systems. Ind. Eng. Chem. Res. 41, 5510–5515 (2002)

    CAS  Google Scholar 

  300. Karakatsani, E.K., Spyriouni, T., Economou, I.G.: Extended statistical associating fluid theory (SAFT) equations of state for dipolar fluids. AIChE J. 51, 2328–2342 (2005)

    CAS  Google Scholar 

  301. Dufal, S., Lafitte, T., Galindo, A., Jackson, G., Haslam, A.J.: Developing intermolecular-potential models for use with the SAFT-VR Mie equation of state. AIChE J. 61, 2891–2912 (2015)

    CAS  Google Scholar 

  302. Oliveira, M.B., Llovell, F., Coutinho, J.A.P., Vega, L.F.: New procedure for enhancing the transferability of statistical associating fluid theory (SAFT) molecular parameters: the role of derivative properties. Ind. Eng. Chem. Res. 55, 10011–10024 (2016)

    CAS  Google Scholar 

  303. Fuenzalida, M., Cuevas-Valenzuela, J., Pérez-Correa, J.R.: Improved estimation of PC-SAFT equation of state parameters using a multi-objective variable-weight cost function. Fluid Phase Equil. 427, 308–319 (2016)

    CAS  Google Scholar 

  304. Zeng, Z.-Y., Xu, Y.-Y., Li, Y.-W.: Calculation of solubility parameter using perturbed-chain SAFT and cubic-plus-association equations of state. Ind. Eng. Chem. Res. 47, 9663–9669 (2008)

    CAS  Google Scholar 

  305. Kontogeorgis, G.M., Voutsas, E.C., Yakoumis, I.V., Tassios, D.P.: An equation of state for associating fluids. Ind. Eng. Chem. Res. 35, 4310–4318 (1996)

    CAS  Google Scholar 

  306. Kontogeorgis, G.M., Michelsen, M.L., Folas, G.K., Derawi, S., von Solms, N., Stenby, E.H.: Ten years with the CPA (cubic-plus-association) equation of state. Part 1. Pure compounds and self-associating systems. Ind. Eng. Chem. Res. 45, 4855–4868 (2006)

    CAS  Google Scholar 

  307. Kontogeorgis, G.M., Michelsen, M.L., Folas, G.K., Derawi, S., von Solms, N., Stenby, E.H.: Ten years with the CPA (cubic-plus-association) equation of state. Part 2. Ind. Eng. Chem. Res. 45, 4869–4878 (2006)

    CAS  Google Scholar 

  308. Stefanis, E., Tsivintzelis, I., Panayiotou, C.: The partial solubility parameters: an equation-of-state approach. Fluid Phase Equilib. 240, 144–154 (2006)

    CAS  Google Scholar 

  309. Panayiotou, C.: Partial solvation parameters and LSER molecular descriptors. J. Chem. Thermodyn. 51, 172–189 (2012)

    CAS  Google Scholar 

  310. Panayiotou, C., Mastrogeorgopoulos, S., Aslanidou, D., Avgidou, M., Hatzimanikatis, V.: Redefining solubility parameters: bulk and surface properties from unified molecular descriptors. J. Chem. Thermodyn. 111, 207–220 (2017)

    CAS  Google Scholar 

  311. Tsivintzelis, I., Panayiotou, C.: Molecular thermodynamics of solutions. In: Wilhelm, E., Letcher, T.M. (eds.) Enthalpy and Internal Energy: Liquids, Solutions and Vapours, pp. 569–589. The Royal Society of Chemistry/IACT, Cambridge (2018)

    Google Scholar 

  312. Chapman, W.G., Gubbins, K.E., Jackson, G., Radosz, M.: New reference equation of state for associating liquids. Ind. Eng. Chem. Res. 29, 1709–1721 (1990)

    CAS  Google Scholar 

  313. Magoulas, K., Tassios, D.: Thermophysical properties of n-alkanes from C1 to C20 and their prediction for higher ones. Fluid Phase Equilib. 56, 119–140 (1990)

    CAS  Google Scholar 

  314. Zabaloy, M.S., Brignole, E.A.: On volume translations in equations of state. Fluid Phase Equilib. 140, 87–95 (1997)

    CAS  Google Scholar 

  315. Tsai, J.-C., Chen, Y.-P.: Application of a volume-translated Peng-Robinson equation of state on vapor–liquid equilibrium calculations. Fluid Phase Equilib. 145, 193–215 (1998)

    CAS  Google Scholar 

  316. Yelash, L.V., Kraska, T.: Volume-translated equations of state: empirical approach and physical relevance. AIChE J. 49, 1569–1579 (2003)

    CAS  Google Scholar 

  317. Frey, K., Augustine, C., Ciccolini, R.P., Paap, S., Modell, M., Tester, J.: Volume translation in equations of state as a means of accurate property estimation. Fluid Phase Equilib. 260, 316–325 (2007)

    CAS  Google Scholar 

  318. Abudour, A.M., Mohammad, S.A., Robinson Jr., R.L., Gasem, K.A.M.: Volume-translated Peng-Robinson equation of state for saturated and single-phase liquid densities. Fluid Phase Equilib. 335, 74–87 (2012)

    CAS  Google Scholar 

  319. Abudour, A.M., Mohammad, S.A., Robinson Jr., R.L., Gasem, K.A.M.: Volume-translated Peng-Robinson equation of state for liquid densities of diverse binary mixtures. Fluid Phase Equilib. 349, 37–55 (2013)

    CAS  Google Scholar 

  320. Jaubert, J.-N., Privat, R., Le Guennec, Y., Coniglio, L.: Note on the properties altered by application of a Péneloux-type volume translation to an equation of state. Fluid Phase Equilib. 419, 88–95 (2016)

    CAS  Google Scholar 

  321. Hekayati, J., Roosta, A., Javanmardi, J.: Volumetric properties of supercritical carbon dioxide from volume-translated and modified Peng-Robinson equations of state. Korean J. Chem. Eng. 33, 3231–3244 (2016)

    CAS  Google Scholar 

  322. Shi, J., Li, H.A.: Criterion for determining crossover phenomenon in volume-translated equation of states. Fluid Phase Equilib. 430, 1–12 (2016)

    CAS  Google Scholar 

  323. Shi, J., Li, H.A., Pang, W.: An improved volume translation strategy for PR EOS without crossover issue. Fluid Phase Equilib. 470, 164–175 (2018)

    CAS  Google Scholar 

  324. Tihic, A., Kontogeorgis, G.M., von Solms, N., Michelsen, M.L.: A predictive group-contribution simplified PC-SAFT equation of state: application to polymer systems. Ind. Eng. Chem. Res. 47, 5092–5101 (2008)

    CAS  Google Scholar 

  325. Rai, N., Wagner, A.J., Ross, R.B., Siepmann, J.I.: Application of the TraPPE force field for predicting the Hildebrand solubility parameters of organic solvents and monomer units. J. Chem. Theory Comput. 4, 136–144 (2008)

    CAS  PubMed  Google Scholar 

  326. Belmares, M., Blanco, M., Goddard III, W.A., Ross, R.B., Caldwell, G., Chou, S.-H., Pham, J., Olofson, P.M., Thomas, C.: Hildebrand and Hansen solubility parameters from molecular dynamics with applications to electronic nose polymer sensors. J. Comput. Chem. 25, 1814–1826 (2004)

    CAS  PubMed  Google Scholar 

  327. Rai, N., Siepmann, J.I., Schultz, N.E., Ross, R.B.: Pressure dependence of the Hildebrand solubility parameter and the internal pressure: Monte Carlo simulations for external pressures up to 300 MPa. J. Phys. Chem. C 111, 15634–15641 (2007)

    CAS  Google Scholar 

  328. Shahamat, M., Rey, A.D.: Characterization of pressure effects on the cohesive properties and structure of hexane and polyethylene using molecular dynamics simulations. Macromol. Theory Simul. 21, 535–543 (2012)

    CAS  Google Scholar 

  329. Meunier, M. (ed.): Industrial Applications of Molecular Simulations. CRC Press, Taylor & Francis Group, Boca Raton (2012)

    Google Scholar 

  330. Gupta, J., Nunes, C., Vyas, S., Jonnalagadda, S.: Prediction of solubility parameters and miscibility of pharmaceutical compounds by molecular dynamics simulations. J. Phys. Chem. B 115, 2014–2023 (2011)

    CAS  PubMed  Google Scholar 

  331. Huynh, L., Neale, C., Pomès, R., Allen, C.: Computational approaches to the rational design of nanoemulsions, polymeric micelles, and dendrimers for drug delivery. Nanomedicine 8, 20–36 (2012)

    CAS  PubMed  Google Scholar 

  332. Smith, W.R., Jirsák, J., Nezbeda, I., Qi, W.: Molecular simulation of caloric properties of fluids modelled by force fields with intramolecular contributions: application to heat capacities. J. Chem. Phys. 147, 034508 (2017)

    PubMed  Google Scholar 

  333. McQuarrie, D.A.: Statistical Mechanics. Harper & Row, New York (1976)

    Google Scholar 

  334. Katayama, T.: Heats of mixing, liquid heat capacities and enthalpy—concentration charts for methanol–water and iso-propanol–water systems. Chem. Eng. (Japan) 26, 361–372 (1962)

    Google Scholar 

  335. Rayer, A.V., Henni, A., Tontiwachwuthikul, P.: Molar heat capacities of solvents used in CO2 capture: a group additivity and molecular connectivity analysis. Can. J. Chem. Eng. 90, 367–376 (2012)

    CAS  Google Scholar 

  336. Yaws, C.L.: Chemical Properties Handbook. McGraw–Hill Education, New York (1999)

    Google Scholar 

  337. Yoon, T.J., Lee, Y.-W.: Current theoretical opinions and perspectives on the fundamental description of supercritical fluids. J. Supercrit. Fluids 134, 21–27 (2018)

    CAS  Google Scholar 

  338. Vega, L.F.: Perspectives on molecular modeling of supercritical fluids: from equations of state to molecular simulation. Recent advances, remaining challenges and opportunities. J. Supercrit. Fluids 134, 41–50 (2018)

    CAS  Google Scholar 

  339. Wilson, K.G.: Renormalization group and critical phenomena. I. Renormalization group and the Kadanoff scaling picture. Phys. Rev. B 4, 3174–3183 (1971)

    Google Scholar 

  340. Wilson, K.G.: Renormalization group and critical phenomena. II. Phase-space cell analysis of critical behavior. Phys. Rev. B 4, 3184–3205 (1971)

    Google Scholar 

  341. Llovell, F., Vega, L.F.: Global fluid phase equilibria and critical phenomena of selected mixtures using the crossover soft-SAFT equation. J. Phys. Chem. B 110, 1350–1362 (2006)

    CAS  PubMed  Google Scholar 

  342. Forte, E., Llovell, F., Vega, L.F., Trusler, J.P.M., Galindo, A.: Application of a renormalization-group treatment to the statistical associating fluid theory for potentials of variable range (SAFT-VR). J. Chem. Phys. 134, 154102 (2011)

    PubMed  Google Scholar 

  343. Bymaster, A., Emborsky, C., Dominik, A., Chapman, W.G.: Renormalization-group corrections to a perturbed-chain statistical associating fluid theory for pure fluids near to and far from the critical region. Ind. Eng. Chem. Res. 47, 6264–6274 (2008)

    CAS  Google Scholar 

  344. Barton, A.F.M.: Internal pressure: a fundamental liquid property. J. Chem. Educ. 48, 156–162 (1971)

    CAS  Google Scholar 

  345. Barton, A.F.M.: Solubility parameters. Chem. Rev. 75, 731–753 (1975)

    CAS  Google Scholar 

  346. Dack, M.R.J.: The importance of solvent internal pressure and cohesion to solution phenomena. J. Chem. Soc. Rev. 4, 211–229 (1975)

    CAS  Google Scholar 

  347. Marcus, Y.: The Properties of Solvents. Wiley Series in Solution Chemistry, vol. 4. Wiley, Chichester (1998)

    Google Scholar 

  348. Marcus, Y.: Internal pressure of liquids and solutions. Chem. Rev. 113, 6536–6551 (2013)

    CAS  PubMed  Google Scholar 

  349. Whalley, E.: The compression of liquids. In: Le Neindre, B., Vodar, B. (eds.) Experimental Thermodynamics, Volume II: Experimental Thermodynamics of Non-reacting Fluids, pp. 421–500. Butterworths/IUPAC, London (1975)

    Google Scholar 

  350. McLinden, M.O.: Experimental techniques 1: direct methods. In: Wilhelm, E., Letcher, T.M. (eds.) Volume Properties: Liquids, Solutions and Vapours, pp. 73–99. The Royal Society of Chemistry/IUPAC & IACT, Cambridge (2015)

    Google Scholar 

  351. Randzio, S.L., Grolier, J.-P.E., Chorazewski, M.: High-pressure “Maxwell relations” measurements. In: Wilhelm, E., Letcher, T.M. (eds.) Volume Properties: Liquids, Solutions and Vapours, pp. 414–438. The Royal Society of Chemistry/IUPAC & IACT, Cambridge (2015)

    Google Scholar 

  352. Lafuente, C., Gascón, I., Cerdeiriña, C.A., Gonzáles-Salgado, D.: Volumetric properties and thermodynamic response functions of liquids and liquid mixtures. In: Wilhelm, E., Letcher, T.M. (eds.) Volume Properties: Liquids, Solutions and Vapours, pp. 439–456. The Royal Society of Chemistry/IUPAC & IACT, Cambridge (2015)

    Google Scholar 

  353. Lemmon, E.W., Huber, M.L., McLinden, M.O.: NIST Standard Reference Database 23. REFPROP, Reference Fluid Thermodynamic and Transport Properties (2003)

    Google Scholar 

  354. Frank, H.S.: Free volume and entropy in condensed systems II. Entropy of vaporization in liquids and the pictorial theory of the liquid state. J. Chem. Phys. 13, 493–507 (1945)

    CAS  Google Scholar 

  355. Benninga, H., Scott, R.L.: Internal pressure of carbon tetrachloride between –7° and 70°. J. Chem. Phys. 23, 1911–1914 (1955)

    CAS  Google Scholar 

  356. Smith, E.B., Hildebrand, J.H.: Liquid isochores and derived functions of n-C7F16, c-C6F11CF3, c-C4Cl2F6, n-2,2,3-C4Cl3F7, CCl2F-CCl2F, and CCl4. J. Chem. Phys. 31, 145–147 (1959)

    CAS  Google Scholar 

  357. Allen, G., Gee, G., Wilson, G.J.: Intermolecular forces and chain flexibilities in polymers: I. Internal pressures and cohesive energy densities of simple liquids. Polymer 1, 456–466 (1960)

    CAS  Google Scholar 

  358. Allen, G., Gee, G., Mangaraj, D., Sims, D., Wilson, G.J.: Intermolecular forces and chain flexibilities in polymers: II. Internal pressures of polymers. Polymer 1, 467–476 (1960)

    CAS  Google Scholar 

  359. Bianchi, U., Agabio, G., Turturro, A.: Internal pressure of simple liquids. J. Phys. Chem. 69, 4392–4395 (1965)

    CAS  Google Scholar 

  360. Fried, V., Schneier, G.B.: Some comments on cohesion energies of liquids. J. Phys. Chem. 72, 4688–4690 (1968)

    CAS  Google Scholar 

  361. Bagley, E.B., Nelson, T.P., Barlow, J.W., Chen, S.-A.: Internal pressure measurements and liquid-state energies. Ind. Eng. Chem. Fundam. 9, 93–97 (1970)

    CAS  Google Scholar 

  362. Bagley, E.B., Nelson, T.P., Chen, S.-A., Barlow, J.W.: Internal pressure measurements and external molecular vibrational modes in the liquid state. Ind. Eng. Chem. Fundam. 10, 27–32 (1970)

    Google Scholar 

  363. Bagley, E.B., Nelson, T.P., Scigliano, J.M.: Internal pressures of liquids and their relationship to the enthalpies and entropies of mixing in nonelectrolyte solutions. J. Phys. Chem. 77, 2794–2798 (1973)

    CAS  Google Scholar 

  364. Amoros, J., Solana, J.R., Villar, E.: Behaviour of the internal pressure of liquids in accordance with variations in temperature, volume and cohesive energy density. Mater. Chem. Phys. 10, 557–578 (1984)

    CAS  Google Scholar 

  365. Westwater, W., Frantz, H.W., Hildebrand, J.H.: The internal pressure of pure and mixed liquids. Phys. Rev. 31, 135–144 (1928)

    CAS  Google Scholar 

  366. Hildebrand, J.H.: The compressibility and thermal pressure coefficients of certain liquids. Phys. Rev. 34, 649–651 (1929)

    CAS  Google Scholar 

  367. Hildebrand, J.H.: Intermolecular forces in liquids. Phys. Rev. 34, 984–993 (1929)

    CAS  Google Scholar 

  368. Hildebrand, J.H., Carter, J.M.: A study of van der Waals forces between tetrahalide molecules. J. Am. Chem. Soc. 54, 3592–3603 (1932)

    CAS  Google Scholar 

  369. Randzio, S.L., Grolier, J.-P.E., Quint, J.R.: An isothermal scanning calorimeter controlled by linear pressure variations from 0.1 to 400 MPa. Calibration and comparison with the piezothermal technique. Rev. Sci. Instrum. 65, 960–965 (1994)

    CAS  Google Scholar 

  370. Randzio, S.L., Grolier, J.-P.E., Quint, J.R., Eatough, D.J., Lewis, E.A., Hansen, L.D.: n-Hexane as a model for compressed simple liquids. Int. J. Thermophys. 15, 415–441 (1994)

    CAS  Google Scholar 

  371. Randzio, S.L., Grolier, J.-P.E., Quint, J.R.: Thermophysical properties of 1-hexanol over the temperature range from 303 to 503 K and at pressures from the saturation line to 400 MPa. Fluid Phase Equilib. 110, 341–359 (1995)

    CAS  Google Scholar 

  372. Randzio, S.L.: Scanning transitiometry. Chem. Soc. Rev. 25, 383–392 (1996)

    CAS  Google Scholar 

  373. Chorążewski, M., Grolier, J.-P.E., Randzio, S.L.: Isobaric thermal expansivities of toluene measured by scanning transitiometry at temperatures from (243 to 423) K and pressures up to 200 MPa. J. Chem. Eng. Data 55, 5489–5496 (2010)

    Google Scholar 

  374. Dávila, M.J., Alcalde, R., Atilhan, M., Aparicio, S.: PρT measurements and derived properties of liquid 1-alkanols. J. Chem. Thermodyn. 47, 241–259 (2012)

    Google Scholar 

  375. Ihmels, E.C., Gmehling, J.: Densities of tolouene, carbon dioxide, carbonyl sulfide, and hydrogen sulfide over a wide temperature and pressure range in the sub- and supercritical state. Ind. Eng. Chem. Res. 40, 4470–4477 (2001)

    CAS  Google Scholar 

  376. Spencer, F.C., Danner, R.P.: Improved equation for prediction of saturated liquid density. J. Chem. Eng. Data 17, 236–241 (1972)

    CAS  Google Scholar 

  377. Dymond, J.H., Malhotra, R.: The Tait equation: 100 years on. Int. J. Thermophys. 9, 941–951 (1988)

    Google Scholar 

  378. Haward, R.N., Parker, B.M.: The internal pressure of simple liquids. J. Phys. Chem. 72, 1842–1844 (1968)

    CAS  Google Scholar 

  379. Lugo, L., Comuñas, M.J.P., López, E.R., Fernández, J.: (p, V m, T, x) measurements of dimethyl carbonate + octane binary mixtures I. Experimental results, isothermal compressibilities, isobaric expansivities and internal pressures. Fluid Phase Equilib. 186, 235–255 (2001)

    CAS  Google Scholar 

  380. Gibson, R.E., Loeffler, O.H.: Pressure–volume–temperature relations in solution. V. The energy–volume coefficients of carbon tetrachloride, water and ethylene glycol. J. Am. Chem. Soc. 63, 898–906 (1941)

    CAS  Google Scholar 

  381. Wilhelm, E., Zettler, M., Sackmann, H.: Molwärmen binärer Systeme aus Cyclohexan, Kohlenstofftetrachlorid, Siliziumtetrachlorid und Zinntetrachlorid. Ber. Bunsenges. Phys. Chem. 78, 795–804 (1974)

    CAS  Google Scholar 

  382. Muringer, M.J.P., Trappeniers, N.J., Biswas, S.N.: The effect of pressure on the sound velocity and density of toluene and n-heptane up to 2600 bar. Phys. Chem. Liq. 14, 273–296 (1985)

    CAS  Google Scholar 

  383. Asenbaum, A., Wilhelm, E., Soufi-Siavoch, P.: Brillouin scattering in liquid toluene at high pressures. Acustica 68, 131–141 (1989)

    CAS  Google Scholar 

  384. Wilhelm, E.: The fascinating world of pure and mixed nonelectrolytes. Pure Appl. Chem. 77, 1317–1330 (2005)

    CAS  Google Scholar 

  385. Staveley, L.A.K., Hart, K.R., Tupman, W.I.: The heat capacities and other thermodynamic properties of some binary liquid mixtures. Disc. Faraday Soc. 15, 130–142 (1953)

    Google Scholar 

  386. Staveley, L.A.K., Tupman, W.I., Hart, K.R.: Some thermodynamic properties of the systems benzene + ethylene dichloride, benzene + carbon tetrachloride, acetone + chloroform, and acetone + carbon disulphide. Trans. Faraday Soc. 51, 323–343 (1955)

    CAS  Google Scholar 

  387. Harrison, D., Moelwyn-Hughes, E.A.: The heat capacities of certain liquids. Proc. Roy. Soc. A 239, 230–246 (1957)

    Google Scholar 

  388. Wilhelm, E., Schano, R., Becker, G., Findenegg, G.H., Kohler, F.: Molar heat capacity at constant volume. Binary mixtures of 1,2-dichloroethane and 1,2-dibromoethane with cyclohexane. Trans. Faraday Soc. 65, 1443–1455 (1969)

    CAS  Google Scholar 

  389. Verdier, S., Andersen, S.I.: Determination of isobaric thermal expansivity of organic compounds from 0.1 to 30 MPa at 30 °C with an isothermal pressure scanning microcalorimeter. J. Chem. Eng. Data 48, 892–897 (2003)

    CAS  Google Scholar 

  390. Verdier, S., Andersen, S.I.: Internal pressure and solubility parameter as a function of pressure. Fluid Phase Equilib. 231, 125–137 (2005)

    CAS  Google Scholar 

  391. Kaplan, I.G.: Intermolecular Interactions: Physical Picture, Computational Methods and Model Potentials. Wiley, Chichester (2006)

    Google Scholar 

  392. Lucas, K.: Molecular Models for Fluids. Cambridge University Press, New York (2007)

    Google Scholar 

  393. Wu, J.Z.: Density functional theory for liquid structure and thermodynamics. In: Lu, X., Hu, Y. (eds.) Molecular Thermodynamics of Complex Systems. Structure and Bonding, vol. 131, pp. 1–73. Springer, Berlin (2009)

    Google Scholar 

  394. Tuckerman, M.E.: Statistical Mechanics: Theory and Molecular Simulation. Oxford University Press, New York (2010)

    Google Scholar 

  395. Goodwin, A.R.H., Sengers, J.V., Peters, C.J. (eds.): Applied Thermodynamics of Fluids. The Royal Society of Chemistry/IUPAC & IACT, Cambridge (2010)

    Google Scholar 

  396. Gray, C.G., Gubbins, K.E.: Theory of Molecular Fluids. Vol. 1: Fundamentals. Clarendon Press, Oxford (1984)

    Google Scholar 

  397. Gray, C.G., Gubbins, K.E., Joslin, C.G.: Theory of Molecular Fluids. Vol. 2. Applications. Oxford University Press, Oxford (2011)

    Google Scholar 

  398. Deiters, U.K., Kraska, T.: High-Pressure Fluid Phase Equilibria: Phenomenology and Computation. Elsevier, Oxford (2012)

    Google Scholar 

  399. Hansen, J.-P., McDonald, I.R.: Theory of Simple Liquids, 4th edn. Academic Press, Oxford (2013)

    Google Scholar 

  400. Assael, M.J., Goodwin, A.R.H., Vesovic, V., Wakeham, W.A. (eds.): Experimental Thermodynamics Volume IX: Advances in Transport Properties of Fluids. The Royal Society of Chemistry/IUPAC, Cambridge (2014)

    Google Scholar 

  401. Allen, M.P., Tildesley, D.J.: Computer Simulation of Liquids, 2nd edn. Oxford University Press, Oxford (2017)

    Google Scholar 

  402. Mie, G.: Zur kinetischen Gastheorie der einatomigen Körper. Ann. Phys. 11, 657–697 (1903)

    Google Scholar 

  403. Hergert, W., Wried, T. (eds.): The Mie Theory. Basics and Applications. Springer Series in Optical Sciences, vol. 169. Springer, Berlin (2012)

    Google Scholar 

  404. Lennard-Jones, J.E.: Cohesion. Proc. Phys. Soc. 43, 461–482 (1931)

    CAS  Google Scholar 

  405. Jäger, B., Hellmann, R., Bich, E., Vogel, E.: Ab initio virial equation of state for argon using a new nonadditive three-body potential. J. Chem. Phys. 135, 084308 (2011)

    PubMed  Google Scholar 

  406. International Union of Pure and Applied Chemistry: Quantities, Units and Symbols in Physical Chemistry. RSC Publishing/IUPAC, Cambridge (2007)

    Google Scholar 

  407. Grabowski, S.J. (ed.): Hydrogen Bonding—New Insights. Springer, Dordrecht (2006)

    Google Scholar 

  408. Marechal, Y.: The Hydrogen Bond and the Water Molecule: The Physics and Chemistry of Water, Aqueous and Bio Media. Elsevier, Amsterdam (2007)

    Google Scholar 

  409. Gilli, G., Gilli, P.: The Nature of the Hydrogen Bond. Outline of a Comprehensive Hydrogen Bond Theory. Oxford University Press, Oxford (2009)

    Google Scholar 

  410. Dolezalek, F.: Zur Theorie der binären Gemische und konzentrierten Lösungen. Z. Phys. Chem. 64, 727–747 (1908)

    Google Scholar 

  411. Wertheim, M.S.: Fluids with highly directional attractive forces. I. Statistical thermodynamics. J. Stat. Phys. 35, 19–34 (1984)

    Google Scholar 

  412. Wertheim, M.S.: Fluids with highly directional attractive forces. II. Thermodynamic perturbation theory and integral equations. J. Stat. Phys. 35, 35–47 (1984)

    Google Scholar 

  413. Wertheim, M.S.: Fluids with highly directional attractive forces. III. Multiple attraction sites. J. Stat. Phys. 42, 459–476 (1986)

    Google Scholar 

  414. Wertheim, M.S.: Fluids with highly directional attractive forces. IV. Equilibrium polymerization. J. Stat. Phys. 42, 477–492 (1986)

    Google Scholar 

  415. Wertheim, M.S.: Fluids of dimerizing hard spheres, and fluid mixtures of hard spheres and dispheres. J. Chem. Phys. 85, 2929–2936 (1986)

    CAS  Google Scholar 

  416. Wertheim, M.S.: Thermodynamic perturbation theory of polymerization. J. Chem. Phys. 87, 7323–7331 (1986)

    Google Scholar 

  417. Carlson, H.C., Colburn, A.P.: Vapor–liquid equilibria of nonideal solutions. Utilization of theoretical methods to extend data. Ind. Eng. Chem. 34, 581–589 (1942)

    CAS  Google Scholar 

  418. Griffith, R.B., Wheeler, J.C.: Critical points in multicomponent systems. Phys. Rev. A 2, 1047–1064 (1970)

    Google Scholar 

  419. Rowlinson, J.S., Swinton, F.L.: Liquids and Liquid Mixtures, 3rd edn. Butterworth Scientific, London (1982)

    Google Scholar 

  420. Mohr, J.P., Newell, D.B., Taylor, B.N.: CODATA recommended values of the fundamental physical constants: 2014. Rev. Mod. Phys. 88, 035009-1–035009-73 (2016)

    Google Scholar 

  421. Mohr, J.P., Newell, D.B., Taylor, B.N., Tiesinga, E.: Data and analysis for the CODATA 2017 special fundamental constants adjustment. Metrologia 55, 125–146 (2018)

    Google Scholar 

  422. Newell, D.B., Cabiati, F., Fischer, J., Fujii, K., Karshenboim, S.G., Margolis, H.S., de Mirandés, E., Mohr, J.P., Nez, F., Pachucki, K., Quinn, T.J., Taylor, B.N., Wang, M., Wood, B.M., Zhang, Z.: The CODATA 2017 values of h, e, k, and N A for the revision of the SI. Metrologia 55, L13–L16 (2018)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Materials Chemistry & Research/Institute of Physical Chemistry, University of Wien, Währinger Straße 42, 1090, Vienna, Austria

    Emmerich Wilhelm

Authors
  1. Emmerich Wilhelm
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Emmerich Wilhelm.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wilhelm, E. Mitigating Complexity: Cohesion Parameters and Related Topics. I: The Hildebrand Solubility Parameter. J Solution Chem 47, 1626–1709 (2018). https://doi.org/10.1007/s10953-018-0821-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10953-018-0821-1

Keywords

Search

Navigation