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Extrapolation Methods for AC Impedance Measurements Made with a Concentric Cylinder Cell on Solutions of High Ionic Strength

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Abstract

Different extrapolation methods of AC impedance spectra measured in a conductance cell with concentric cylinder geometry have been evaluated at room temperature. This was undertaken because previous high temperature studies showed that the extrapolation method was one of the largest contributors to the uncertainty for molar conductivities at high concentrations: these high concentrations are needed to determine ion-pairing formation constants under hydrothermal conditions. This was done by measuring the impedance spectrum of sodium chloride solutions with ionic strengths up to 0.49 mol·kg−1 and comparing different extrapolation methods to accurate molar conductivity results reported by other authors using cells designed for concentrated solutions at ambient conditions. The most accurate extrapolation method at high concentrations was found to be the method based on the expression \( Z_{\text{Re}} \left( \omega \right) = R_{s} + b_{0} \cdot \omega^{{ - b_{1} }} \), where Z Re(ω) is the real component of the angular frequency-dependent impedance, and R s, b 0 and b 1 are fitting parameters.

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References

  1. Noyes, A.A.: The Electrical Conductivity of Aqueous Solutions. Carnegie Institution of Washington, Publication No. 63 (1907)

  2. Franck, E.U.: Hochverdichteter Wasserdampf I. Elektrolytische Leitfähigkeit in KCl–H2O–Lösungen bis 750 °C. Z. Phys. Chem., Neue Folge 8, 92–105 (1956)

    CAS  Google Scholar 

  3. Franck, E.U., Savolainen, J.E., Marshall, W.L.: Electrical conductance assembly for use with aqueous solutions up to 800 °C and 4000 bar. Rev. Sci. Instruments 33, 115–117 (1962)

    CAS  Google Scholar 

  4. Ho, P.C., Palmer, D.A., Mesmer, R.E.: Electrical conductivity measurements of aqueous sodium chloride solutions to 600 °C and 300 MPa. J. Solution Chem. 23, 997–1017 (1994)

    CAS  Google Scholar 

  5. Zimmerman, G.H., Gruskiewicz, M.S., Wood, R.H.: New apparatus for conductance measurements at high temperatures: conductance of aqueous solutions of LiCl, NaCl, NaBr, and CsBr at 28 MPa and water densities from 700 to 260 kg m−3. J. Phys. Chem. 99, 11612–11625 (1995)

    CAS  Google Scholar 

  6. Ho, P.C., Bianchi, H., Palmer, D.A., Wood, R.H.: Conductivity of dilute aqueous electrolyte solutions at high temperatures and pressures using a flow cell. J. Solution Chem. 29, 217–235 (2000)

    CAS  Google Scholar 

  7. Hnedkovsky, L., Wood, R.H., Balashov, V.N.: Electrical conductances of aqueous Na2SO4, H2SO4, and their mixtures: limiting equivalent ion conductances, dissociation constants, and speciation to 673 K and 28 MPa. J. Phys. Chem. B 109, 9034–9046 (2005)

    CAS  Google Scholar 

  8. Zimmerman, G.H., Scott, P.W., Greynolds, W.: A new flow instrument for conductance measurements at elevated temperatures and pressures: measurements on NaCl(aq) to 458 K and 1.4 MPa. J. Solution Chem. 36, 767–786 (2007)

    CAS  Google Scholar 

  9. Chialvo, A., Gruszkiewicz, M.S., Simonson, J.M., Palmer, D.A., Cole, D.R.: Ion-pair association in extreme aqueous environments: molecular-based and electrical conductance approaches. J. Solution Chem. 38, 827–841 (2009)

    CAS  Google Scholar 

  10. Fogo, J.K., Copeland, C.S., Benson, S.W.: A pressure counterbalancing apparatus for the measurement of the electrical conductivity of aqueous solutions above their critical temperatures. Rev. Sci. Instrum. 22, 765–769 (1951)

    CAS  Google Scholar 

  11. Nichol, J.C., Fuoss, R.M.: A new cell design for precision conductimetry. J. Phys. Chem. 58, 696–699 (1954)

    CAS  Google Scholar 

  12. Zimmerman, G.H., Arcis, H., Tremaine, P.R.: Limiting conductivities and ion association constants of aqueous NaCl under hydrothermal conditions: experimental data and correlations. J. Chem. Eng. Data 57, 2415–2429 (2012)

    CAS  Google Scholar 

  13. Zimmerman, G.H., Arcis, H., Tremaine, P.R.: Limiting conductivities and ion association in aqueous NaCF3SO3 and Sr(CF3SO3)2 from 298 to 623 K at 20 MPa. Is triflate a non-complexing anion in high-temperature water? J. Chem. Eng. Data 57, 3180–3197 (2012)

    CAS  Google Scholar 

  14. Sharygin, A.V., Wood, R.H., Zimmerman, G.H., Balashov, V.N.: Multiple ion association versus redissociation in aqueous NaCl and KCl at high temperatures. J. Phys. Chem. B 106, 7121–7134 (2002)

    CAS  Google Scholar 

  15. Fisher, F.H., Fox, A.P.: Conductance of aqueous NaCl solutions at pressures up to 2000 atm. J. Solution Chem. 10, 871–879 (1981)

    CAS  Google Scholar 

  16. Chambers, J.F., Stokes, J.M., Stokes, R.H.: Conductances of concentrated aqueous sodium and potassium chloride solutions at 25 °C. J. Phys. Chem. 60, 985–986 (1956)

    CAS  Google Scholar 

  17. Shedlovsky, T.: The electrolytic conductivity of some uni-univalent electrolytes in water at 25 °C. J. Am. Chem. Soc. 54, 1411–1428 (1932)

    CAS  Google Scholar 

  18. Robinson, R.A., Stokes, R.H.: Electrolyte Solutions, 2nd edn. Butterworths, London (1965)

    Google Scholar 

  19. Bester-Rogac, M., Neueder, R., Barthel, J.: Conductivity of sodium chloride in water + 1,4-dioxane mixtures at temperatures from 5 to 35 °C. I. Dilute solutions. J. Solution Chem. 28, 1071–1086 (1999)

    CAS  Google Scholar 

  20. Bester-Rogac, M., Neueder, R., Barthel, J.: Conductivity of sodium chloride in water + 1,4-dioxane mixtures at temperatures from 5 to 35 °C. II. Concentrated solutions. J. Solution Chem. 29, 51–61 (2000)

    CAS  Google Scholar 

  21. De Leo, Méndez, Wood, R.H.: Conductance study of association in aqueous CaCl2, Ca(CH3COO)2, and Ca(CH3COO)2·nCH3COOH from 348 to 523 K at 10 MPa. J. Phys. Chem. B 109, 14243–14250 (2005)

    Google Scholar 

  22. Bard, A.J., Faulkner, L.R.: Electrochemical Methods: Fundamentals and Applications. John Wiley & Sons, New York (2001)

    Google Scholar 

  23. Balashov, V.N., Fedkin, M.V., Lvov, S.N.: Experimental system for electrochemical studies of aqueous corrosion at temperatures above 300 °C. J. Electrochem. Soc. 156, C209–C213 (2009)

    CAS  Google Scholar 

  24. MacDonald, J.R., Johnson, W.B.: Fundamentals of Impedance Spectroscopy. In: Barsoukov, E., MacDonald, J.R. (eds.) Impedance Spectroscopy Theory, Experiment and Applications, pp. 1–26. Wiley-Interscience, New York (2005)

    Chapter  Google Scholar 

  25. Orazem, M.E., Tribollet, B.: Electrochemical Impedance Spectroscopy. Wiley, Hoboken (2008)

    Book  Google Scholar 

  26. Ragheb, T., Geddes, L.A.: The polarization impedance of common electrode metals operated at low current density. Ann. Biomed. Eng. 19, 151–163 (1991)

    CAS  Google Scholar 

  27. Raistruck, I.D., Franceschetti, D.R., MacDonald, J.R.: The Electrical Analogs of Physical and Chemical Processes. In: Barsoukov, E., MacDonald, J.R. (eds.) Impedance Spectroscopy Theory, Experiment and Applications, pp. 27–75. Wiley, New York (2005)

    Chapter  Google Scholar 

  28. Madekufamba, M., Tremaine, P.R.: Ion association in dilute aqueous magnesium sulfate and nickel sulfate solutions under hydrothermal conditions by flow conductivity measurements. J. Chem. Eng. Data 56, 889–898 (2011)

    CAS  Google Scholar 

  29. Erickson, K.M., Arcis, H., Raffa, D., Zimmerman, G.H., Tremaine, P.R.: Deuterium isotope effects on the ionization constant of acetic acid in H2O and D2O by AC conductance from 368 to 548 K at 20 MPa. J. Phys. Chem. B 115, 3038–3051 (2011)

    CAS  Google Scholar 

  30. Gruszkiewicz, M.S., Wood, R.H.: Conductance of dilute LiCl, NaCl, NaBr, and CsBr solutions in supercritical water using a flow conductance cell. J. Phys. Chem. B 101, 6549–6559 (1997)

    CAS  Google Scholar 

  31. Zimmerman, G.H., Wood, R.H.: Conductance of dilute sodium acetate solutions to 469 K and of acetic acid and sodium acetate/acetic acid mixtures to 548 K and 20 MPa. J. Solution Chem. 31, 995–1017 (2002)

    CAS  Google Scholar 

  32. Barthel, J., Feuerlein, F., Neuder, R., Wachter, R.: Calibration of conductance cells at various temperatures. J. Solution Chem. 9, 209–219 (1980)

    CAS  Google Scholar 

  33. Fisher, F.H., Fox, A.P.: Electrical conductance of aqueous solutions of KCl solutions at pressures up to 2000 atm. J. Solution Chem. 8, 627–634 (1979)

    CAS  Google Scholar 

  34. Archer, D.G.: Thermodynamic properties of the NaCl+H2O system. II. Thermodynamic properties of NaCl(aq), NaCl·2H2O(cr), and phase equilibria. J. Phys. Chem. Ref. Data 21, 793–829 (1992)

    CAS  Google Scholar 

  35. Adams, L.H., Hall, R.E.: The effect of pressure on the electrical conductivity of solutions of sodium chloride and of other electrolytes. J. Phys. Chem. 35, 2145–2163 (1931)

    CAS  Google Scholar 

  36. Franceschetti, D.R., MacDonald, J.R.: Physical and Electrochemical Models. In: Barsoukov, E., MacDonald, J.R. (eds.) Impedance Spectroscopy Theory, Experiment and Applications, pp. 91–95. Wiley, New York (2005)

    Google Scholar 

  37. Bonanos, N., Steele, B.C.H., Butler, E.P.: Measuring Techniques and Data Analysis. In: Barsoukov, E., MacDonald, J.R. (eds.) Impedance Spectroscopy Theory, Experiment and Applications, pp. 232–234. Wiley, New York (2005)

    Google Scholar 

  38. Primdahl, S., Hendriksen, P.V.: Pitfalls in solid electrode characterization. In: Poulsen, F.W., Bonanos, N., Linderoth, S., Mogensen, M., Zachau-Christiansen, B. (eds.) Proceedings of the 17th Riso International Symposium on Materials Science: High Temperature Electrochemistry; Ceramics and Metals, pp. 403–410. Riso National Laboratory, Roskilde, Denmark (1996)

  39. Zimmerman, G.H., Scott, P.W., Greynolds, W.: Conductance of dilute hydrochloric acid solutions to 458 K and 1.4 MPa. J. Solution Chem. 38, 499–512 (2009)

    CAS  Google Scholar 

  40. MacDonald, J.R.: Data Analysis. In: Barsoukov, E., MacDonald, J.R. (eds.) Impedance Spectroscopy Theory, Experiment and Applications, pp. 199–204. Wiley, New York (2005)

    Google Scholar 

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Acknowledgments

The authors express deep gratitude to Professor Robert H. Wood, University of Delaware, for donating the AC conductance cell to the Hydrothermal Chemistry Laboratory at the University of Guelph, for providing us with the benefit of his extensive operating experience, and for many productive discussions. We also thank Professor Peter Tremaine for many fruitful discussions and his helpful, insightful comments on this manuscript. We are also grateful to Mr. Ian Renaud and Mr. Case Gielen of the electronics shop and machine shop in the College of Physical and Engineering Science at the University of Guelph, for their very considerable expertise in maintaining and modifying the instrument and its data acquisition system. We also thank Mr. Conor Flynn, Bloomsburg University (B. S. Chemistry, 2014) for performing simulation calculations of the equivalent electrical circuit. This research was supported by the Natural Science and Engineering Research Council of Canada (NSERC), Ontario Power Generation Ltd. (OPG), the University Network of Excellence in Nuclear Engineering (UNENE), and Bloomsburg University for sabbatical leave (G.H.Z.). G.H.Z. would like to express appreciation for the financial support provided by Fulbright Canada, and gratitude for the support of the governments of Canada and the United States in making this program possible.

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Authors and Affiliations

  1. Department of Chemistry and Biochemistry, Bloomsburg University, Bloomsburg, PA, 17815, USA

    G. H. Zimmerman

  2. Department of Chemistry, University of Guelph, Guelph, ON, N1G 2W1, Canada

    H. Arcis

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  1. G. H. Zimmerman
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Correspondence to G. H. Zimmerman.

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Zimmerman, G.H., Arcis, H. Extrapolation Methods for AC Impedance Measurements Made with a Concentric Cylinder Cell on Solutions of High Ionic Strength. J Solution Chem 44, 912–933 (2015). https://doi.org/10.1007/s10953-014-0208-x

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