Towards a comprehensive non-ergodic treatment of H-bonds and hydrophobicity in real solutions: The mobile order and disorder theory


The theory of mobile order and disorder (MOD) in H-bonded liquids is a completely new approach of the thermodynamics of H-bonds in liquids, and starts from the realistic analysis of the essential features which differentiate both the solid and liquid states. Unlike crystals, the ‘structure’ of liquids is always changing and the intermolecular contacts are never fixed: in liquids, all molecular contacts including H-bonds are transient. The continuous changes of the environment of a given molecule constitute an essential entropic characteristic of liquids which precludes, from a thermodynamic point of view, to treat them as deformed lattices. Molecular associations in crystals also differ from those in the liquid state by their stoichiometry. In the solid state, the stoichiometry of the associates is fixed and ruled by the crystal packing requirements, whereas the association state in liquids is perpetually changing. In the course of time, an amphiphilic molecule will be found in all possible states, such as monomolecule, head or tail of an open chain association, or bonded at both ends to neighbors. As a result, the thermodynamic entities to be considered at equilibrium are not the spectroscopic ones as assumed by the classical multicomponent theories. Finally, the presence of ephemeral open chain associations confers to the overall liquid system a ‘non-ergodic’ behavior: the probability in time for a molecule to escape from H-bonding is much larger than the proportion of molecules which do not form H-bonds at a given time to one or more neighbors (the time average and the ensemble average are not the same). The very anti-ergodic nature of open H-bond chains has dramatic consequences for the thermodynamics. It renders questionable almost all thermodynamic treatments on H-bonding in liquids based on the usual Boltzmann expression (which equates the thermodynamic probability of a system with the static probability of distribution of the various species at a given time). As suggested by Einstein, the classical Boltzmann equation for non-ergodic systems has to be replaced by another Boltzmann relation relating the thermodynamic probability of a state to the fraction of time during which the system is found in that state. The thermodynamics of MOD theory accordingly expresses the equilibrium condition in terms of time fractions for the time schedule that a given molecule is ‘free’ or ‘bonded’, and not in terms of the concentrations of the various associated species presumed to be present in the ensemble. These principles yield fundamental new equations for the entropy of mixing and for the effect of H-bonds on the chemical potential of dissolved substances. These equations constitute the basis of different MOD-theory-based solubility or partition models. Derived on a strictly thermodynamic basis and unspoiled by any adjustable parameter, these models enable correct predictions of solubilities in H-bonded solvents and organic solvent/water partition coefficients while providing a completely new quantitative treatment of the hydrophobic effect.

This is a preview of subscription content, access via your institution.


  1. 1.

    Bernal, J.D. and Fowler, R.H., J. Chem. Phys., 1 (1933) 515.

    Google Scholar 

  2. 2.

    Frank, H.S. and Wen, W.-Y., Discuss. Faraday Soc., 24 (1957) 133.

    Google Scholar 

  3. 3.

    Eucken, A., Die theorie der strahlung und der quanten, verhandlungen auf einer von E. Solvay einberufenen zusammenkunft 30 Oktober bis 3 November 1911, Druck und Verlag von Wilhelm Knapp, Halle, 1914.

    Google Scholar 

  4. 4.

    Pais, A., Subtle is the Lord, The Science and the Life of Albert Einstein, Oxford University Press, Oxford, 1982.

    Google Scholar 

  5. 5.

    Flory, P.J., Principles of Polymer Chemistry, Cornell University Press, Ithaca, NY, 1953.

    Google Scholar 

  6. 6.

    Szwarc, M., J. Mol. Liquids, 71 (1997) 91.

    Google Scholar 

  7. 7.

    Barthel, J., Ber. Bunsenges. Phys. Chem., 83 (1979) 252.

    Google Scholar 

  8. 8.

    Barthel, J., Pure Appl. Chem., 51 (1979) 2093.

    Google Scholar 

  9. 9.

    Lide, D.R. (Ed.) CRC Handbook of Chemistry and Physics, 78th edition, CRC Press, Boca Raton, FL, 1997, pp. 8–45.

    Google Scholar 

  10. 10.

    Luck, W.A.P., In Huyskens, P.L., Luck, W.A.P. and Zeegers-Huyskens, T. (Eds.), Intermolecular Forces. An Introduction to Modern Methods and Results, Springer, Berlin, 1991, pp. 217–249.

    Google Scholar 

  11. 11.

    Luck, W.A.P., Angew. Chem., Int. Ed. Engl., 19 (1980) 28.

    Google Scholar 

  12. 12.

    Huyskens, P.L. and Siegel, G.G., Croat. Chem. Acta, 55 (1982) 55.

    Google Scholar 

  13. 13.

    Siegel, G.G. and Huyskens, P.L., In Huyskens, P.L., Luck, W.A.P. and Zeegers-Huyskens, T. (Eds.) Intermolecular Forces. An Introduction to Modern Methods and Results, Springer, Berlin, 1991, pp. 387–395.

    Google Scholar 

  14. 14.

    Gutowsky, H.S. and Saika, A., J. Chem. Phys., 21 (1953) 1688.

    Google Scholar 

  15. 15.

    Huyskens, P.L., Zeegers-Huyskens, T. and Capart, J.J., Bull. Soc. Chim. Belg., 68 (1959) 515.

    Google Scholar 

  16. 16.

    Chastrette, M. and Crétin, D., SAR QSAR Environ. Sci., 3 (1995) 131.

    Google Scholar 

  17. 17.

    Ruelle, P. and Kesselring, U.W., J. Pharm. Sci., 87 (1998) 987.

    Google Scholar 

  18. 18.

    Huyskens, P., J. Mol. Struct., 100 (1983) 403.

    Google Scholar 

  19. 19.

    Luck, W.A.P., In Huyskens, P.L., Luck, W.A.P. and Zeegers-Huyskens, T. (Eds.) Intermolecular Forces. An Introduction to Modern Methods and Results, Springer, Berlin, 1991, pp. 157–193.

    Google Scholar 

  20. 20.

    Wolf, K.L. and Harms, H., Z. Phys. Chem., Abt. B, 44 (1939) 159.

    Google Scholar 

  21. 21.

    Kempter, H. and Mecke, R., Naturwissenschaften, 27 (1939) 853.

    Google Scholar 

  22. 22.

    Prigogine, I., Bull. Soc. Chim. Belg., 50 (1941) 153.

    Google Scholar 

  23. 23.

    Prigogine, I., Bellemans, A. and Mathot, V., The Molecular Theory of Solutions, North-Holland, Amsterdam, 1957.

    Google Scholar 

  24. 24.

    Redlich, O. and Kister, Z., J. Chem. Phys., 15 (1947) 849.

    Google Scholar 

  25. 25.

    Kretschmer, C.B. and Wiebe, R., J. Chem. Phys., 22 (1954) 425.

    Google Scholar 

  26. 26.

    Wiehe, I.A. and Bagley, E.B., Ind. Eng. Chem. Fundam., 6 (1967) 209.

    Google Scholar 

  27. 27.

    Kehiaian, H. and Treszczanowicz, A., Bull. Acad. Polon. Sci., Ser. Sci. Chim., 14 (1966) 891.

    Google Scholar 

  28. 28.

    Kehiaian, H. and Treszczanowicz, A., Bull. Soc. Chim. France, 18 (1969) 1561.

    Google Scholar 

  29. 29.

    Mullens, J., Hanssens, I. and Huyskens, P.L., J. Chim. Phys., (1971) 1417.

  30. 30.

    Nagata, I. and Kawamura, Y., Z. Phys. Chem., N.F., 107 (1977) 141.

    Google Scholar 

  31. 31.

    Abrams, D.S. and Prausnitz, J.M., AIChE J., 21 (1975) 116.

    Google Scholar 

  32. 32.

    Veytsman, B.A., J. Phys. Chem., 94 (1990) 8499.

    Google Scholar 

  33. 33.

    Huyskens, P.L., J. Mol. Struct., 297 (1993) 141.

    Google Scholar 

  34. 34.

    Huyskens, P.L., J. Am. Chem. Soc., 99 (1977) 2578.

    Google Scholar 

  35. 35.

    Nelis, K., van den Berge-Parmentier, L. and Huyskens, F., J. Mol. Liquids, 67 (1995) 157.

    Google Scholar 

  36. 36.

    Huyskens, P.L. and Haulait-Pirson, M.C., J. Mol. Liquids, 31 (1985) 135.

    Google Scholar 

  37. 37.

    Flory, P.J., J. Chem. Phys., 9 (1941) 660.

    Google Scholar 

  38. 38.

    Huggins, M.L., Ann. New York Acad. Sci., 43 Art. 1 (1942) 1.

    Google Scholar 

  39. 39.

    McAuliffe, C., J. Phys. Chem., 70 (1966) 1267.

    Google Scholar 

  40. 40.

    Ruelle, P. and Kesselring, U.W., Chemosphere, 34 (1997) 275.

    Google Scholar 

  41. 41.

    Hansch, C., Leo, A. and Hoekman, D., Exploring QSAR. Hydrophobic, Electronic, and Steric Constants, American Chemical Society, Washington, DC, 1995.

    Google Scholar 

  42. 42.

    Abraham, M.H., Chadha, H.S., Whiting, G.S. and Mitchell, R.C., J. Pharm. Sci., 83 (1994) 1085.

    Google Scholar 

  43. 43.

    Sangster, J., LOGKOW - A Databank of Evaluated Octanol-Water Partition Coefficients, Sangster Research Laboratories, Montréal, 1993.

    Google Scholar 

  44. 44.

    Nouwen, J. and Hansen, B., Quant. Struct.-Act. Relat., 15 (1996) 17.

    Google Scholar 

  45. 45.

    Ruelle, P. and Kesselring, U.W., J. Pharm. Sci., 87 (1998) 1015.

    Google Scholar 

  46. 46.

    Ruelle, P., Chemosphere, accepted.

Download references

Author information



Rights and permissions

Reprints and Permissions

About this article

Cite this article

Ruelle, P. Towards a comprehensive non-ergodic treatment of H-bonds and hydrophobicity in real solutions: The mobile order and disorder theory. Perspectives in Drug Discovery and Design 17, 61–96 (1999).

Download citation

  • aqueous solubility
  • H-bond
  • hydrophobic effect
  • mobile order and disorder theory
  • partition coefficient
  • solution thermodynamics