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Activity Coefficients of Aqueous Mixed Ionic Surfactant Solutions from Osmometry

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Abstract

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.

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References

  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)

    Article  CAS  Google Scholar 

  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)

    Article  CAS  Google Scholar 

  3. Robinson, R.A., Stokes, R.H.: Electrolyte Solutions, 2nd edn. Butterworths, London (1959)

    Google Scholar 

  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. 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)

    Article  CAS  Google Scholar 

  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)

    Article  CAS  Google Scholar 

  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)

    Article  CAS  Google Scholar 

  8. McKay, H.A.C.: Activities and activity coefficients in ternary systems. Trans. Faraday Soc. 49, 237–242 (1953)

    Article  CAS  Google Scholar 

  9. Pan, C.: New forms of McKay–Perring equations. J. Phys. Chem. 72, 2548–2551 (1968)

    Article  CAS  Google Scholar 

  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. 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)

    Article  CAS  Google Scholar 

  12. Pitzer, K.S.: Thermodynamics of electrolytes. 1. Theoretical basis and general equations. J. Phys. Chem. 77, 268–277 (1973)

    Article  CAS  Google Scholar 

  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)

    Article  CAS  Google Scholar 

  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)

    Article  CAS  Google Scholar 

  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)

    Article  CAS  Google Scholar 

  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)

    Article  CAS  Google Scholar 

  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)

    Article  CAS  Google Scholar 

  18. Woolley, E.M., Burchfield, T.E.: Thermodynamics of ionic surfactant solutions containing added strong electrolytes. Fluid Phase Equilib. 20, 225–232 (1985)

    Article  CAS  Google Scholar 

  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)

    Article  CAS  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  23. Crisantino, R., De Lisi, R., Milioto, S.: Energetics of sodium dodecylsulfate–dodecyldimethylamine oxide mixed micelle formation. J. Solution Chem. 23, 639–662 (1994)

    Article  CAS  Google Scholar 

  24. Kamrath, R.F., Franses, E.I.: Thermodynamics of mixed micellization. Pseudo-phase separation models. Ind. Eng. Chem. 22, 230–239 (1983)

    Article  CAS  Google Scholar 

  25. Kamrath, R.F., Franses, E.I.: Mass-action model of micellization. J. Phys. Chem. 88, 1642–1648 (1984)

    Article  CAS  Google Scholar 

  26. Maeda, H.: A thermodynamic analysis of charged mixed micelles in water. J. Phys. Chem. B 109, 15933–15940 (2005)

    Article  CAS  Google Scholar 

  27. Maeda, H.: A simple thermodynamic analysis of the stability of ionic/nonionic mixed micelles. J. Colloid Interface Sci. 172, 98–105 (1995)

    Article  CAS  Google Scholar 

  28. Nagarajan, R., Ruckenstein, R.: Aggregation of amphiphiles as micelles or vesicles in aqueous media. J. Colloid Interface Sci. 71, 580–604 (1979)

    Article  CAS  Google Scholar 

  29. Nagarajan, R.: Molecular theory for mixed micelles. Langmuir 1, 331–341 (1985)

    Article  CAS  Google Scholar 

  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)

    Article  CAS  Google Scholar 

  31. Peyre, V.: Determination of activities of mixed micelles involving neutral surfactants. Langmuir 18, 1014–1023 (2002)

    Article  CAS  Google Scholar 

  32. Scamehorn, J.F. (ed.): Phenomena in Mixed Surfactant Systems, vol. 311. American Chemical Society, Washington, DC (1986)

    Google Scholar 

  33. Clint, J.H.: Micellization of mixed ionic surface active agents. J. Chem. Soc. Faraday Trans. I 71, 1327–1334 (1975)

    Google Scholar 

  34. Holland, P.M., Rubingh, D.N.: Nonideal multicomponent mixed micelle model. J. Phys. Chem. 87, 1984–1990 (1983)

    Article  CAS  Google Scholar 

  35. Holland, P.M.: Nonideal mixed micellar solutions. Adv. Colloid Interface Sci. 26, 111–129 (1986)

    Article  CAS  Google Scholar 

  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. 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)

    Article  CAS  Google Scholar 

  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)

    Article  CAS  Google Scholar 

  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)

    Article  CAS  Google Scholar 

  40. Hall, D.G.: Electrostatic effects in dilute solutions containing charged colloidal entities. J. Chem. Soc., Faraday Trans. 87, 3529–3535 (1991)

    Article  CAS  Google Scholar 

  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)

    Article  CAS  Google Scholar 

  42. Philips, J.N.: The energetics of micelle formation. Trans. Faraday Soc. 51, 561–569 (1955)

    Article  Google Scholar 

  43. Benjamin, L.: Calorimetric studies of the micellization of dimethyl-n-alkylamine oxides. J. Phys. Chem. Soc. 68, 3575–3581 (1964)

    Article  CAS  Google Scholar 

  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)

    Article  CAS  Google Scholar 

  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)

    Article  CAS  Google Scholar 

  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)

    Article  CAS  Google Scholar 

  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)

    Article  CAS  Google Scholar 

  48. Clark, W.M., Rowley, R.L.: Ternary liquid diffusion near Plait points. Int. J. Thermophys. 6, 631–642 (1985)

    Article  CAS  Google Scholar 

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Acknowledgments

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

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Correspondence to Derek G. Leaist.

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This paper is dedicated to Donald G. Miller in recognition and appreciation of his outstanding contributions to research on the transport properties and thermodynamics of solutions.

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MacNeil, J.A., Ray, G.B., Sharma, P. et al. Activity Coefficients of Aqueous Mixed Ionic Surfactant Solutions from Osmometry. J Solution Chem 43, 93–108 (2014). https://doi.org/10.1007/s10953-013-0043-5

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