Journal of Solution Chemistry

, Volume 43, Issue 1, pp 93–108 | Cite as

Activity Coefficients of Aqueous Mixed Ionic Surfactant Solutions from Osmometry

  • Jennifer A. MacNeil
  • Gargi B. Ray
  • Poonam Sharma
  • Derek G. Leaist


Osmotic techniques for measuring thermodynamic activities, such as isopiestic equilibration, are well established for multicomponent solutions, especially mixed salt solutions. Surprisingly, these techniques have not yet been applied to mixed ionic surfactants, despite the numerous practical applications of these systems and the importance of the Gibbs free energy for micelle stability. In this study, mass-action equations are developed for the osmotic coefficients of solutions of ionic surfactant CA + ionic surfactant CB, with common counterion C. Extended Debye–Hückel equations are used for the ionic activity coefficients. The equilibrium constants for mixed micelle formation are evaluated by Gibbs–Duhem integration of critical micelle concentrations. Fitting the derived equations to the osmotic coefficients of aqueous sodium decanoate + sodium dodecylsulfate solutions measured by freezing-point osmometry is used to evaluate the activities of the total surfactant components. Very large departures from ideal solution behavior are indicated, including stoichiometric surfactant activity coefficients and micelle activity coefficients that drop below 0.05 and 10−8, respectively, relative to unity for ideal solutions. Osmometry offers many interesting and unexplored possibilities for studies of mixed surfactant thermodynamics.


Activity coefficients Freezing point depression Mass-action model Micelles Surfactants Osmotic coefficient 



Acknowledgment is made to the Natural Sciences and Engineering Research Council for the financial support of this work.


  1. 1.
    Blandamer, M.J., Engberts, J.B.F.N., Gleeson, P.T., Reis, J.C.R.: Activity of water in aqueous systems; a frequently neglected property. Chem. Soc. Rev. 34, 440–458 (2005)CrossRefGoogle Scholar
  2. 2.
    Elliott, J.A.W., Prickett, R.C., Elmoazzen, H.Y., Porter, K.R., McGann, L.E.: A multisolute osmotic virial equation for solutions of interest in biology. J. Phys. Chem. B 111, 1775–1785 (2007)CrossRefGoogle Scholar
  3. 3.
    Robinson, R.A., Stokes, R.H.: Electrolyte Solutions, 2nd edn. Butterworths, London (1959)Google Scholar
  4. 4.
    Pitzer, K.S., Brewer, L.: Thermodynamics, 2nd edn. McGraw-Hill, New York (1961). (revised version of 1st edn by Lewis, G. N., Randall, M.)Google Scholar
  5. 5.
    Pitzer, K.S., Mayorga, G.: Thermodynamics of electrolytes. II. Activity and osmotic coefficients for strong electrolytes with one or both ions univalent. J. Phys. Chem. 77, 2300–2308 (1973)CrossRefGoogle Scholar
  6. 6.
    Burchfield, T.E., Woolley, E.M.: Model for thermodynamics of ionic surfactant solutions. 1. Osmotic and activity coefficients. J. Phys. Chem. 88, 2149–2155 (1984)CrossRefGoogle Scholar
  7. 7.
    McKay, H.A.C., Perring, J.K.: Calculations of the activity coefficients of mixed aqueous electrolytes from vapour pressures. Trans. Faraday Soc. 49, 163–165 (1953)CrossRefGoogle Scholar
  8. 8.
    McKay, H.A.C.: Activities and activity coefficients in ternary systems. Trans. Faraday Soc. 49, 237–242 (1953)CrossRefGoogle Scholar
  9. 9.
    Pan, C.: New forms of McKay–Perring equations. J. Phys. Chem. 72, 2548–2551 (1968)CrossRefGoogle Scholar
  10. 10.
    Pitzer, K.S.: A consideration of Pitzer’s equations for activity and osmotic coefficients in mixed electrolytes. J. Chem. Soc. Faraday Trans. I 80, 3451–3454 (1984)Google Scholar
  11. 11.
    Yang, J., Pitzer, K.S.: Thermodynamics of electrolyte mixtures. Activity and osmotic coefficients consistent with the higher-order limiting law for symmetrical mixing. J. Solution Chem. 17, 909–924 (1988)CrossRefGoogle Scholar
  12. 12.
    Pitzer, K.S.: Thermodynamics of electrolytes. 1. Theoretical basis and general equations. J. Phys. Chem. 77, 268–277 (1973)CrossRefGoogle Scholar
  13. 13.
    Pitzer, K.S., Kim, J.J.: Thermodynamics of electrolytes. IV. Activity and osmotic coefficients for mixed electrolytes. J. Am. Chem. Soc. 96, 5701–5707 (1974)CrossRefGoogle Scholar
  14. 14.
    Clegg, S.L., Milioto, S., Palmer, D.A.: Osmotic and activity coefficients of aqueous (NH4)2SO4 as a function of temperature, and aqueous (NH4)2SO4–H2SO4 mixtures at 298.15 K. J. Chem. Eng. Data 41, 455–467 (1996)CrossRefGoogle Scholar
  15. 15.
    Rard, J.A., Miller, D.G.: Isopiestic determination for the osmotic and activity coefficients of aqueous mixtures of sodium chloride and magnesium chloride at 25 °C. J. Chem. Eng. Data 32, 85–92 (1987)CrossRefGoogle Scholar
  16. 16.
    Rard, J.A., Clegg, S.L., Platford, R.F.: Thermodynamics of [zNaCl + (1 − z)Na2SO4](aq) from T = 278.15 K to T = 318.15 K, and representation with an extended ion-interaction (Pitzer) model. J. Chem. Thermodyn. 35, 967–1008 (2003)CrossRefGoogle Scholar
  17. 17.
    Dearden, L.V., Woolley, E.M.: Osmotic coefficients of alkyltrimethylammonium bromides in water and aqueous sodium bromide solutions at 55 °C. J. Phys. Chem. 91, 2404–2408 (1987)CrossRefGoogle Scholar
  18. 18.
    Woolley, E.M., Burchfield, T.E.: Thermodynamics of ionic surfactant solutions containing added strong electrolytes. Fluid Phase Equilib. 20, 225–232 (1985)CrossRefGoogle Scholar
  19. 19.
    Widera, B., Neueder, R., Kunz, W.: Vapor pressures and osmotic coefficients of aqueous solutions of SDS, C6TAB, and C8TAB at 25 °C. Langmuir 19, 8226–8229 (2003)CrossRefGoogle Scholar
  20. 20.
    De Lisi, R., Inglese, A., Milioto, S., Pellerito, A.: Demixing of mixed micelles. Thermodynamics of sodium perfluorooctanoate—sodium dodecanoate mixtures in water. Langmuir 13, 192–202 (1997)CrossRefGoogle Scholar
  21. 21.
    De Lisi, R., Inglese, A., Milioto, S., Pellerito, A.: Excess free energy, enthalpy and entropy of surfactant–surfactant mixed micelle formation. Fluid Phase Equilib. 126, 273–287 (1996)CrossRefGoogle Scholar
  22. 22.
    De Lisi, R., Inglese, A., Milioto, S., Pellerito, A.: Thermodynamic studies of sodium dodecyl sulfate–sodium dodecanoate mixtures in water. J. Colloid Interface Sci. 180, 174–187 (1996)CrossRefGoogle Scholar
  23. 23.
    Crisantino, R., De Lisi, R., Milioto, S.: Energetics of sodium dodecylsulfate–dodecyldimethylamine oxide mixed micelle formation. J. Solution Chem. 23, 639–662 (1994)CrossRefGoogle Scholar
  24. 24.
    Kamrath, R.F., Franses, E.I.: Thermodynamics of mixed micellization. Pseudo-phase separation models. Ind. Eng. Chem. 22, 230–239 (1983)CrossRefGoogle Scholar
  25. 25.
    Kamrath, R.F., Franses, E.I.: Mass-action model of micellization. J. Phys. Chem. 88, 1642–1648 (1984)CrossRefGoogle Scholar
  26. 26.
    Maeda, H.: A thermodynamic analysis of charged mixed micelles in water. J. Phys. Chem. B 109, 15933–15940 (2005)CrossRefGoogle Scholar
  27. 27.
    Maeda, H.: A simple thermodynamic analysis of the stability of ionic/nonionic mixed micelles. J. Colloid Interface Sci. 172, 98–105 (1995)CrossRefGoogle Scholar
  28. 28.
    Nagarajan, R., Ruckenstein, R.: Aggregation of amphiphiles as micelles or vesicles in aqueous media. J. Colloid Interface Sci. 71, 580–604 (1979)CrossRefGoogle Scholar
  29. 29.
    Nagarajan, R.: Molecular theory for mixed micelles. Langmuir 1, 331–341 (1985)CrossRefGoogle Scholar
  30. 30.
    Roux, A.H., Hetu, D., Perron, G., Desnoyers, J.E.: Chemical equilibrium model for the thermodynamic properties of mixed aqueous micellar systems: application to thermodynamic functions of transfer. J. Solution Chem. 13, 1–25 (1984)CrossRefGoogle Scholar
  31. 31.
    Peyre, V.: Determination of activities of mixed micelles involving neutral surfactants. Langmuir 18, 1014–1023 (2002)CrossRefGoogle Scholar
  32. 32.
    Scamehorn, J.F. (ed.): Phenomena in Mixed Surfactant Systems, vol. 311. American Chemical Society, Washington, DC (1986)Google Scholar
  33. 33.
    Clint, J.H.: Micellization of mixed ionic surface active agents. J. Chem. Soc. Faraday Trans. I 71, 1327–1334 (1975)Google Scholar
  34. 34.
    Holland, P.M., Rubingh, D.N.: Nonideal multicomponent mixed micelle model. J. Phys. Chem. 87, 1984–1990 (1983)CrossRefGoogle Scholar
  35. 35.
    Holland, P.M.: Nonideal mixed micellar solutions. Adv. Colloid Interface Sci. 26, 111–129 (1986)CrossRefGoogle Scholar
  36. 36.
    Holland, P.M., Rubingh, D.N. (eds.): Phenomena in Mixed Surfactant Systems, vol. 501. ACS Symposium SeriesAmerican Chemical Society, Washington, DC (1992)Google Scholar
  37. 37.
    MacNeil, J.A., Ray, G.B., Leaist, D.G.: Activity coefficients and free energies of nonionic mixed surfactant solutions from vapor-pressure and freezing-point osmometry. J. Phys. Chem. B 115, 5947–5957 (2011)CrossRefGoogle Scholar
  38. 38.
    Sharma, P., MacNeil, J.A., Bowles, J., Leaist, D.G.: The unusual importance of activity coefficients for micelle solutions illustrated by an osmometry study of aqueous sodium decanoate and aqueous sodium decanoate + sodium chloride solutions. Phys. Chem. Chem. Phys. 13, 21333–21343 (2011)CrossRefGoogle Scholar
  39. 39.
    Scatchard, G., Prentiss, S.S.: The freezing points of aqueous solutions. IV. Potassium, sodium and lithium chlorides and bromides. J. Am. Chem. Soc. 55, 4355–4362 (1933)CrossRefGoogle Scholar
  40. 40.
    Hall, D.G.: Electrostatic effects in dilute solutions containing charged colloidal entities. J. Chem. Soc., Faraday Trans. 87, 3529–3535 (1991)CrossRefGoogle Scholar
  41. 41.
    Desnoyers, J.E., Caron, G., De Lisi, R., Roberts, D., Roux, A., Perron, G.: Thermodynamic properties of alkyldimethylamine oxides in water. Application of a mass-action model for micellization. J. Phys. Chem. 87, 1397–1406 (1983)CrossRefGoogle Scholar
  42. 42.
    Philips, J.N.: The energetics of micelle formation. Trans. Faraday Soc. 51, 561–569 (1955)CrossRefGoogle Scholar
  43. 43.
    Benjamin, L.: Calorimetric studies of the micellization of dimethyl-n-alkylamine oxides. J. Phys. Chem. Soc. 68, 3575–3581 (1964)CrossRefGoogle Scholar
  44. 44.
    MacEwan, K., Leaist, D.G.: Quaternary mutual diffusion coefficients for aqueous solutions of a cationic–anionic mixed surfactant from moments analysis of Taylor dispersion profiles. Phys. Chem. Chem. Phys. 5, 3951–3958 (2003)CrossRefGoogle Scholar
  45. 45.
    Wygnal, E., MacNeil, J.A., Bowles, J., Leaist, D.G.: Mutual diffusion with equal eigenvalues in solutions of strongly associated surfactants. A new kind of multicomponent diffusion. J. Mol. Liq. 156, 95–102 (2010)CrossRefGoogle Scholar
  46. 46.
    MacEwan, K., Leaist, D.G.: Incongruent diffusion (negative main diffusion coefficient) for a ternary mixed surfactant system. J. Phys. Chem. B 106, 10296–10300 (2002)CrossRefGoogle Scholar
  47. 47.
    Moulins, J.R., MacNeil, J.A., Leaist, D.G.: Thermodynamic stability and the origins of incongruent and strongly coupled diffusion in solutions of micelles, solubilizates, and microemulsions. J. Chem. Eng. Data 54, 2371–2380 (2009)CrossRefGoogle Scholar
  48. 48.
    Clark, W.M., Rowley, R.L.: Ternary liquid diffusion near Plait points. Int. J. Thermophys. 6, 631–642 (1985)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Jennifer A. MacNeil
    • 1
  • Gargi B. Ray
    • 1
  • Poonam Sharma
    • 1
  • Derek G. Leaist
    • 1
  1. 1.Department of ChemistrySt. Francis Xavier UniversityAntigonishCanada

Personalised recommendations