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On the Calculation of the Dielectric Properties of Liquid Ionic Systems

  • Marcello Sega
  • Sofia S. Kantorovich
  • Axel Arnold
  • Christian Holm
Conference paper
Part of the NATO Science for Peace and Security Series B: Physics and Biophysics book series (NAPSB)

Abstract

The calculation of dielectric properties of fluids, which is straightforward for homogeneous dipolar liquids, presents several intricacies when applied to ionic liquids. We investigate, for a model sodium chloride aqueous solution, three different methods which could provide an estimate of the static permittivity, namely (a) the Einstein-Helfand approach, (b) the first moment of the current-current correlation functions, and (c) the analysis of the low frequency limit of the dielectric spectrum. The contribution to the static permittivity of the sodium chloride solution coming from the ion-ion correlations, often neglected in simulation studies but implicitly taken into account in experimental measurements, are shown to be important, although particularly hard to measure. In the case of our model sodium chloride solutions, we find these dynamic contributions to be the main cause of the saturation of the dielectric constant with increasing salt concentration.

Keywords

Dielectric Permittivity Dielectric Response Static Permittivity Increase Salt Concentration Dielectric Spectrum 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Berendsen HJC, Postma JPM, van Gunsteren WF, Hermans J (1981) Intermolecular forces. Reidel, Dordrecht, pp 331–342Google Scholar
  2. 2.
    Berendsen HJC, Postma JPM, van Gunsteren WF, DiNola A, Haak JR (1984) Molecular dynamics with coupling to a heat bath. J Chem Phys 81:3684–3690CrossRefADSGoogle Scholar
  3. 3.
    Bopp PA, Kornyshev AA, Sutmann G (1998) Frequency and wave-vector dependent dielectric function of water: collective modes and relaxation spectra. J Chem Phys 109:1939–1958CrossRefADSGoogle Scholar
  4. 4.
    Buchner R, Hefter GT, May PM (1999), Dielectric relaxation of aqueous NaCl solutions. J Phys Chem A 103:1–9CrossRefGoogle Scholar
  5. 5.
    Caillol J-M (1994) Comments on the numerical simulation of electrolytes in periodic boundary conditions. J Chem Phys 101(7):6080–6090. doi: 10.1063/1.468422 CrossRefADSGoogle Scholar
  6. 6.
    Caillol JM, Levesque D, Weis JJ (1986) Theoretical calculation of ionic solution properties. J Chem Phys 85(11):6645–6657CrossRefADSGoogle Scholar
  7. 7.
    de Leeuw SW, Perram JW, Smith ER (1980) Simulation of electrostatic systems in periodic boundary conditions. I. Lattice sums and dielectric constants. Proc R Soc Lond Ser A 373(1752):27–56ADSGoogle Scholar
  8. 8.
    de Leeuw SW, Perram JW, Smith ER (1980) Simulation of electrostatic systems in periodic boundary conditions. II. Equivalence of boundary conditions. Proc R Soc Lond Ser A 373(1752):57–66ADSGoogle Scholar
  9. 9.
    Essmann U, Perera L, Berkowitz ML, Darden T, Lee H, Pedersen L (1995), A smooth Particle Mesh Ewald method. J Chem Phys 103:8577CrossRefADSGoogle Scholar
  10. 10.
    Felderhof B (1979) Fluctuation theorems for dielectrics. Physica A 95:572Google Scholar
  11. 11.
    Frigo M, Johnson SG (2005) The design and implementation of FFTW3. Proc IEEE 93(2):216–231. Special issue on “Program Generation, Optimization, and Platform Adaptation”Google Scholar
  12. 12.
    Fulton RL (1978) Long and short range correlations in the Brownian motion of charged particles. J Chem Phys 68:3089CrossRefADSGoogle Scholar
  13. 13.
    Hansen JP, McDonald IR (1986) Theory of simple liquids. Academic, LondonGoogle Scholar
  14. 14.
    Hess B, Holm C, van der Vegt N (2006) Osmotic coeffcients of atomistic NACl (aq) force-fields. J Chem Phys 124:164509CrossRefADSGoogle Scholar
  15. 15.
    Hess B, Kutzner C, van der Spoel D, Lindahl E (2008) Gromacs 4: algorithms for highly efficient, load-balanced, and scalable molecular simulation. J Chem Theory Comput 4(3):435–447CrossRefGoogle Scholar
  16. 16.
    Hoover WG (1985) Canonical dynamics: equilibrium phase-space distributions. Phys Rev A 31(3):1695–1697CrossRefADSGoogle Scholar
  17. 17.
    Hubbard JB, Colonomos P, Wolynes PG (1979) Molecular theory of solvated ion dynamics. iii. J Chem Phys 71:2652–2661CrossRefADSGoogle Scholar
  18. 18.
    Jackson JD (1999) Classical electrodynamics, 3rd edn. Wiley, New YorkzbMATHGoogle Scholar
  19. 19.
    Kaatze U (1997) The dielectric properties of water in its different states of interaction. J Solut Chem 26(11):1049–1112CrossRefGoogle Scholar
  20. 20.
    Kremer F, Schönhals A (eds) (2003), Broadband dielectric spectroscopy. Springer, BerlinGoogle Scholar
  21. 21.
    Kubo R. (1957) Statistical mechanical theory of irreversible processes. I. J Phys Soc Jpn 12:570–586MathSciNetCrossRefADSGoogle Scholar
  22. 22.
    Marquardt D (1963) An algorithm for least-squares estimation of nonlinear parameters. SIAM J Appl Math 11:431–441MathSciNetzbMATHCrossRefGoogle Scholar
  23. 23.
    Miyamoto S, Kollman PA (1992) Settle: an analytical version of the shake and rattle algorithm for rigid water models. J Comput Chem 13(8):952–962CrossRefGoogle Scholar
  24. 24.
    Neumann M, Steinhauser O (1983) On the calculation of the dielectric constant using the ewald-kornfeld tensor. Chem Phys Lett 95:417CrossRefADSGoogle Scholar
  25. 25.
    Nosé S (1984) A molecular dynamics method for simulations in the canonical ensemble. Mol Phys 52(2):255–268CrossRefADSGoogle Scholar
  26. 26.
    Parrinello M, Rahman A (1981) Polymorphic transitions in single crystals: a new molecular dynamics method. J Appl Phys 52(12):7182–7190CrossRefADSGoogle Scholar
  27. 27.
    Resta R (1998) Quantum-mechanical position operator in extended systems. Phys Rev Lett 80:1800CrossRefADSGoogle Scholar
  28. 28.
    Resta R, Vanderbilt D (2007) Theory of polarization: a modern approach, vol 105. Springer, Berlin, p 31Google Scholar
  29. 29.
    Schröder C, Steinhauser O (2010) Using fit functions in computational dielectric spectroscopy. J Chem Phys 132(24):244109–244116CrossRefADSGoogle Scholar
  30. 30.
    Schröder C, Rudas T, Steinhauser O (2006) Simulation studies of ionic liquids: orientational correlations and static dielectric properties. J Chem Phys 125:244506CrossRefADSGoogle Scholar
  31. 31.
    Schröder C, Haberler M, Steinhauser O (2008) On the computation and contribution of conductivity in molecular ionic liquids. J Chem Phys 128(13):134501CrossRefADSGoogle Scholar
  32. 32.
    Schröeder C, Hunger J, Stoppa A, Buchner R, Steinhauser O (2008) On the collective network of ionic liquid/water mixtures. II. Decomposition and interpretation of dielectric spectra. J Chem Phys 129:184501Google Scholar
  33. 33.
    Scott WRP, Hünenberger PH, Tironi IG, Mark AE, Billeter SR, Fennen J, Torda AE, Huber T, Krüger P, van Gunsteren WF (1999) The gromos biomolecular simulation program package. J Phys Chem A 103(19):3596–3607CrossRefGoogle Scholar
  34. 34.
    van der Spoel D, van Maaren PJ, Berendsen HJC (1998) A systematic study of water models for molecular simulation: derivation of water models optimized for use with a reaction field. J Chem Phys 108:10220–10230CrossRefGoogle Scholar
  35. 35.
    Weerasinghe S, Smith PE (2003) A kirkwood–buff derived force field for sodium chloride in water. J Chem Phys 119(21):11342–11349CrossRefADSGoogle Scholar
  36. 36.
    Wolynes PG (1980) Dynamics of electrolyte solutions. Annu Rev Phys Chem 31:345–376CrossRefADSGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Marcello Sega
    • 1
  • Sofia S. Kantorovich
    • 1
    • 2
  • Axel Arnold
    • 1
  • Christian Holm
    • 1
  1. 1.ICP, Universität StuttgartStuttgartGermany
  2. 2.URFUEkaterinburgRussia

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