Skip to main content
Log in

A Novel Attempt to Calculate the Velocity Correlation Coefficients in Ternary Electrolyte Solution

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

Abstract

This work gives estimated values of the velocity correlation coefficients VCCs for ternary electrolyte solutions (the system may have a tracer ion as one of the components), utilizing available measured transport coefficients. The VCCs originate from linear response theory and give a deeper insight into the microdynamic structure of complex ionic solutions. By assuming Onsager’s relation to be valid, ten sets of velocity correlation coefficients were calculated for a ternary system and were used to calculate the VCCs for 134Cs+ ion (present in trace amount) transport in aqueous solutions of CsCl and KCl at 25 ○C.

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

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Kropman, M.K., Bakkar, H.J.: Dynamics of water molecules in aqueous solvation shells. Science 291, 2118–2120 (2001)

    Article  CAS  Google Scholar 

  2. Chandra, A.: Effects of ion atmosphere on hydrogen-bond dynamics in aqueous electrolyte solutions. Phys. Rev. Lett. 85, 768–771 (2000)

    Article  CAS  Google Scholar 

  3. Barthel, J.M.G., Krienke, H., Kunz, W.: Physical Chemistry of Electrolyte Solutions. Springer, New York (1998)

    Google Scholar 

  4. Hubbard, J.B., Wolynes, P.G.: In: Dogonadze, R.R., Kalman, E., Kornyshev, A.A., Ulstrup, J. (eds.) Chemical Physics of Solvation, Part D. Elsevier, Amsterdam (1988)

    Google Scholar 

  5. Roux, B., Karplus, M.: Molecular dynamics simulations of the gramicidin channel. Ann. Rev. Biophys. Biomol. Struct. 23, 732–753 (1994)

    Google Scholar 

  6. Harned, H.S., Owen, B.B.: The Physical Chemistry of Electrolytic Solutions. Reinhold, New York (1958)

    Google Scholar 

  7. Rick, S.W.: Simulations of ice and liquid water over a range of temperatures using the fluctuating charge model. J. Chem. Phys. 114, 2276–2283 (2001)

    Article  CAS  Google Scholar 

  8. Ren, P., Ponder, J.W.: Temperature and pressure dependence of the AMOEBA water model. J. Phys. Chem. B 108, 13427–13437 (2004)

    Article  CAS  Google Scholar 

  9. Yu, H., Van Gunsteren, W.F.: Charge-on-spring polarizable water models revisited: from water clusters to liquid water to ice. J. Chem. Phys. 121, 9549–9564 (2004)

    Article  CAS  Google Scholar 

  10. Hertz, H.G., Mills, R.: Velocity correlations in aqueous electrolyte solutions from diffusion, conductance and transference data. Applications to concentrated solutions of 1:2 electrolytes. J. Phys. Chem. 82, 952–959 (1978)

    Article  CAS  Google Scholar 

  11. Dufreche, J.F., Bernard, O., Turq, P., Mukherjee, A., Bagchi, B.: Ionic self-diffusion in concentrated aqueous electrolyte solutions. Phys. Rev. Lett. 88, 095902 (2002)

    Article  Google Scholar 

  12. Onsager, L.: Reciprocal relations in irreversible processes. I. Phys. Rev. 37, 405–426 (1930)

    Article  Google Scholar 

  13. Onsager, L.: Reciprocal relations in irreversible processes. II. Phys. Rev. 38, 2265–2279 (1931)

    Article  CAS  Google Scholar 

  14. McCall, D.W., Douglass, D.C.: Diffusion in binary solute. J. Phys. Chem. 71, 987–997 (1967)

    Article  CAS  Google Scholar 

  15. Douglass, D.C., Frisch, H.L.: Isothermal diffusion in some two- and three-component systems in terms of velocity correlation functions. J. Phys. Chem. 73, 3039–3047 (1969)

    Article  CAS  Google Scholar 

  16. Steele, W.A.: In: Hanley, H.J.M. (ed.) Transport Phenomena in Fluids, p. 209. Marcel Dekker, New York (1969)

    Google Scholar 

  17. Barr, L.W., Miller, D.G., Mills, R.: Tracer (self) diffusion of potassium ion in NaCl–KCl–H2O mixtures at 25 ○C. J. Solution Chem. 9, 75–80 (1980)

    Article  CAS  Google Scholar 

  18. Phang, S., Stokes, R.H.: Density, viscosity, conductance and transference number of concentrated aqueous magnesium chloride at 25 ○C. J. Solution Chem. 9, 497–505 (1980)

    CAS  Google Scholar 

  19. Woolf, L.A., Harris, K.R.: Velocity correlation coefficients as an expression of the particle-particle interaction in (electrolyte) solutions. J. Chem. Soc. Faraday Trans. I 74, 933–959 (1978)

    Article  CAS  Google Scholar 

  20. Woolf, L.A.: Velocity correlation coefficients in multicomponent electrolyte solutions. J. Phys. Chem. 82, 959–962 (1978)

    Article  CAS  Google Scholar 

  21. Mills, R., Hertz, H.G.: Application of the velocity cross-correlation method to binary nonelectrolyte mixtures. J. Phys. Chem. 84, 220–224 (1980)

    Article  CAS  Google Scholar 

  22. Miller, D.G.: Explicit relations of velocity correlation coefficients to Onsager l ij ’s, to experimental quantities, and to infinite dilution limiting laws for binary electrolyte solutions. J. Phys. Chem. 85, 1137–1146 (1981)

    Article  CAS  Google Scholar 

  23. Friedman, H.L., Mills, R.: Velocity cross correlations in binary mixtures of simple fluids. J. Solution Chem. 10, 395–409 (1981)

    Article  CAS  Google Scholar 

  24. Geiger, A., Hertz, H.G., Mills, R.: Velocity correlations in aqueous electrolyte solutions from diffusion, conductance and transference data: application to concentrated solutions of nickel chloride and magnesium chloride. J. Solution Chem. 10, 83–94 (1981)

    Article  CAS  Google Scholar 

  25. Bastug, T., Kuyucak, S.: Temperature dependence of the transport coefficients of ions from molecular dynamics simulations. Chem. Phys. Lett. 408, 84–88 (2005)

    Article  CAS  Google Scholar 

  26. Schönert, H.: Evaluation of velocity correlation coefficients from experimental transport data in electrolytic systems. J. Phys. Chem. 88, 3359–3363 (1984)

    Article  Google Scholar 

  27. Miller, D.G.: Application of irreversible thermodynamics to electrolyte solutions. II. Ionic coefficients for isothermal vector transport processes in ternary systems. J. Phys. Chem. 71, 616–632 (1967)

    Article  CAS  Google Scholar 

  28. Chakrabarti, H.: Cation diffusion coefficients in CsCl–H2O system over the concentration range 0.009 to 10.00 mol⋅dm−3 at 25 ○C. Appl. Radiat, Isot. 45, 171–175 (1994)

    Article  CAS  Google Scholar 

  29. Anderson, J., Paterson, R.: Application of irreversible thermodynamics to isotopic diffusion. Part 1.—Isotope–isotope coupling coefficients for ions and water in concentrated aqueous solutions of alkali metal chlorides at 298.16 K. J. Chem. Soc. Faraday Trans. I 71, 1335–1351 (1975)

    Article  CAS  Google Scholar 

  30. Raineri, F.O., Timmermann, E.O.: Salt velocity correlation functions: a microscopic interpretation. Part 2.—Solution of two or more binary electrolytes with a common ion. J. Chem. Soc. Faraday Trans. 86, 1057–1065 (1990)

    Article  CAS  Google Scholar 

  31. Kirkwood, J.G., Baldwin, R.L., Dunlop, P.T., Gosting, L.J., Kegeles, G.: Flow equations and frames of reference for isothermal diffusion in liquids. J. Chem. Phys. 33, 1505–1513 (1960)

    Article  CAS  Google Scholar 

  32. Chakrabarti, H., Changdar, S.N.: Accurate measurement of tracer diffusion coefficients in aqueous solutions with sliding cell technique. Appl. Radiat. Isot. 43, 405–412 (1992)

    Article  CAS  Google Scholar 

  33. Chakrabarti, H.: Strong evidence of an isotope effect in the diffusion of a NaCl and CsCl solution. Phys. Rev. B, 12809–12812 (1995)

  34. Mills, R., Woolf, L.A.: Tracer-diffusion coefficients of cesium ion in aqueous alkali chloride solutions at 25 ○. J. Phys. Chem. 63, 2068–2069 (1959)

    Article  CAS  Google Scholar 

  35. Friedman, A.M., Kennedy, J.W.: The self-diffusion coefficients of potassium, cesium, iodide and chloride ions in aqueous solutions. J. Am. Chem. Soc. 77, 4499–4501 (1955)

    Article  CAS  Google Scholar 

  36. Chakrabarti, H., Kanjilal, B.: Measurement of the diffusivity of cesium ion in aqueous rubidium chloride solution. J. Solution Chem. 39, 409–416 (2010)

    Article  CAS  Google Scholar 

  37. Hasan, S.A.: Morphology of ion clusters in aqueous solutions. Phys. Rev. E 77, 031501 (2008)

    Article  Google Scholar 

  38. Robinson, R.A., Strokes, R.H.: Electrolyte Solutions, Appendices pp. 466, 494. Butterworths Scientific, London (1959)

    Google Scholar 

  39. Mills, R., Lobo, V.M.M.: Self diffusion in electrolyte solutions—a critical examination of data compiled from literature. In: Physical Sciences Data, vol. 36. Elsevier, Amsterdam (1989)

    Google Scholar 

  40. Miller, D.G.: Application of irreversible thermodynamics to electrolyte solutions. I. Determination of ionic transport coefficients l ij for isothermal vector transport processes in binary electrolyte systems. J. Phys. Chem. 70, 2639–2659 (1966)

    Article  CAS  Google Scholar 

  41. Supplement to Mellor’s Comprehensive Treatise on Inorganic and Theoretical Chemistry—Alkali Metals Part II, vol. 2, Supplement III. Longmans, London (1963)

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Haimanti Chakrabarti.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chakrabarti, H., Sil, S. & Kundu, S. A Novel Attempt to Calculate the Velocity Correlation Coefficients in Ternary Electrolyte Solution. J Solution Chem 39, 1278–1290 (2010). https://doi.org/10.1007/s10953-010-9586-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10953-010-9586-x

Keywords

Navigation