Advertisement

Russian Journal of Electrochemistry

, Volume 54, Issue 11, pp 879–885 | Cite as

A New Approach in the Theory of Spatially-Restricted Nonlocal Dielectric Media

  • M. A. VorotyntsevEmail author
  • A. A. Rubashkin
  • A. E. Antipov
Article

Abstract

A new method for the calculation of electric field distributions in the systems with spatiallyrestricted regions filled with polar media with nonlocal dielectric characteristics is proposed. The presence of regions with different dielectric properties in the system (as exemplified by the presence of an ion-filled cavity in which there is no polar medium surrounding the ion) is automatically taken into account within this procedure. The field distribution inside a uniform and isotropic nonlocal dielectric medium outside the spherical cavity containing a spherically symmetric charge distribution (the system represents the ion inside the polar solvent) has illustrated this new approach. In contrast to the previously suggested approach (dielectric approximation), where calculations of this characteristic required complex numerical and analytical calculations, the new method requires only single integration in order to determine the distribution of the potential of the electric field inside the polar medium with an arbitrary law of spatial dispersion of its dielectric permittivity (which can be specified eithter analytically or numerically).

Keywords

spatial dispersion of dielectric permittivity volume cutting effect nonlocal electrostatics solvation energy dielectric permittivity 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Dogonadze, R.R. and Kornyshev, A.A., Polar solvent structure in the theory of ionic salvation, J. Chem. Soc., Faraday Trans. 2, 1974, vol. 70, p. 1121.CrossRefGoogle Scholar
  2. 2.
    Kornyshev, A.A., Nonlocal screening of ions in a structurized polar liquid—new aspects of solvent description in electrolyte theory, Electrochim. Acta, 1981, vol. 26, p. 1.CrossRefGoogle Scholar
  3. 3.
    Kornyshev, A.A and Volkov, A.G., On the evaluation of standard Gibbs energies of ion transfer between two solvents, J. Electroanal. Chem. Interfacial Electrochem., 1984, vol. 180, p. 363.CrossRefGoogle Scholar
  4. 4.
    Kornyshev, A.A., Vorotyntsev, M.A., Nielsen, H., and Ulstrup, J., Non-local screening effects in the longrange interionic interaction in a polar solvent, J. Chem. Soc., Faraday Trans. 2, 1982, vol. 78, p. 217.CrossRefGoogle Scholar
  5. 5.
    Vorotyntsev, M.A. and Kornyshev, A.A., Physical significance of an effective dielectric constant that depends on the distance from the electrode, Sov. Electrochem., 1979, vol. 15, p. 560.Google Scholar
  6. 6.
    Vorotyntsev, M.A., Kornyshev, A.A., and Rubinshtein, A.I., Possible mechanisms of “controlling” ionic interaction at the electrode-solution interface, Sov. Electrochem., 1980, vol. 16, p. 65.Google Scholar
  7. 7.
    Vorotyntsev, M.A. and Kornyshev, A.A., Electrostatic interaction on a metal-insulator interface, Sov. Phys.–JETP, 1980, vol. 51, p. 509.Google Scholar
  8. 8.
    Kornyshev, A.A. and Vorotyntsev, M.A., Nonlocal electrostatic approach to the double layer and adsorption at the electrode-electrolyte interface, Surf. Sci., 1980, vol. 101, p. 23.CrossRefGoogle Scholar
  9. 9.
    Kornyshev, A.A., Vorotyntsev, M. A., and Ulstrup, J., The effect of spatial dispersion of the dielectric permittivity on the capacitance of thin insulating films: Nonlinear dependence of the inverse capacitance on film thickness, Thin Solid Films, 1981, vol. 75, p. 105.CrossRefGoogle Scholar
  10. 10.
    Kornyshev, A.A. and Vorotyntsev, M.A., Nonlocal dielectric response of the electrode/solvent interface in the double layer problem, Can. J. Chem., 1981, vol. 59, p. 2031.CrossRefGoogle Scholar
  11. 11.
    Kornyshev, A.A., Schmickler, W., and Vorotyntsev, M.A., Nonlocal electrostatic approach to the problem of a double layer at a metal-electrolyte interface, Phys. Rev. B, 1982, vol. 25, p. 5244.CrossRefGoogle Scholar
  12. 12.
    Vorotyntsev, M.A., Izotov, V.Yu., and Kornyshev, A.A., Differential capacitance of the electric double layer in dilute solutions of surface-inactive electrolytes and upon the specific adsorption of ions: nonlocal and nonlinear effects, Sov. Electrochem., 1983, vol. 19, p. 364.Google Scholar
  13. 13.
    Vorotyntsev, M.A. and Kornyshev, A.A., Models to describe collective properties of the metal/solvent interface in electric double-layer theory, Sov. Electrochem., 1984, vol. 20, p. 1.Google Scholar
  14. 14.
    Vorotyntsev, M.A. and Holub, K., Image forces at the metal/electrolyte solution interface: their dependence on electrode charge and electrolyte concentration, Sov. Electrochem., 1984, vol. 20, p. 243.Google Scholar
  15. 15.
    Holub, K. and Kornyshev, A.A., Comment on the solvent structure in thermodynamics of electrolytes: anomalous behavior of activity coefficients at low concentrations, J. Electroanal. Chem. Interfacial Electrochem., 1982, vol. 142, p. 57.CrossRefGoogle Scholar
  16. 16.
    Kornyshev, A.A., Non-local dielectric response of a polar-solvent and Debye-screening in ionic solution, J. Chem. Soc., Faraday Trans. 2, 1983, vol. 79, p. 651.CrossRefGoogle Scholar
  17. 17.
    Kornyshev, A.A., Nonlocal electrostatics of salvation, in The Chemical Physics of Solvation, Dogonadze, R.R., Kalman, E., Kornyshev, A.A., and Ulstrup, J., Eds., Amsterdam: Elsevier, 1985.Google Scholar
  18. 18.
    Vorotyntsev, M.A. and Kornyshev, A.A., Elektrostatika sred s prostranstvennoi dispersiei (Electrostatics of Media with Spatial Dispersion), Moscow: Nauka, 1993.Google Scholar
  19. 19.
    Kornyshev, A.A. and Sutmann, G., The shape of the nonlocal dielectric function of polar liquids and the implications for thermodynamic properties of electrolytes: a comparative study, J. Chem. Phys., 1996, vol. 104, p. 1524.CrossRefGoogle Scholar
  20. 20.
    Rubashkin, A.A., Vorotyntsev, M.A., Antipov, E.M., and Aldoshin, S.M., Nonlocal electrostatic theory of ion solvation: A combination of the overscreening effect in the dielectric response of the medium with a smeared ion charge distribution, Dokl. Phys. Chem., 2015, vol. 464, p. 198.CrossRefGoogle Scholar
  21. 21.
    Rubashkin, A.A. and Vorotyntsev, M.A., Electrostatic contribution to the ion solvation energy: Overscreening effect in the nonlocal dielectric response of the polar medium, Curr. Phys. Chem., 2016, vol. 6, p. 120.CrossRefGoogle Scholar
  22. 22.
    Kornyshev, A.A., Rubinshtein, A.I., and Vorotyntsev, M.A., Model nonlocal electrostatics: 1, J. Phys. C: Solid State Phys., 1978, vol. 11, p. 3307.CrossRefGoogle Scholar
  23. 23.
    Vorotyntsev, M.A. Model nonlocal electrostatics: II. Spherical interface, J. Phys. C: Solid State Phys., 1978, vol. 11, p. 3323.CrossRefGoogle Scholar
  24. 24.
    Kornyshev, A.A. and Vorotyntsev, M.A., Model nonlocal electrostatics: 3. Cylindrical interface, J. Phys. C: Solid State Phys., 1979, vol. 12, p. 4939.CrossRefGoogle Scholar
  25. 25.
    Basilevsky, M.V. and Parsons, D.F., An advanced continuum medium model for treating solvation effects: nonlocal electrostatics with a cavity, J. Chem. Phys., 1996, vol. 105, p. 3734.CrossRefGoogle Scholar
  26. 26.
    Basilevsky, M.V. and Parsons, D.F., Nonlocal continuum solvation model with exponential susceptibility kernels, J. Chem. Phys., 1998, vol. 108, p. 9107.CrossRefGoogle Scholar
  27. 27.
    Hildebrandt, A., Blossey, R., Rjasanow, S., Kohlbacher, O., and Lenhof, H.-P., Novel formulation of nonlocal electrostatics, Phys. Rev. Lett., 2004, vol. 93, p. 108104–1.CrossRefGoogle Scholar
  28. 28.
    Rubinstein, A. and Sherman, S., Influence of the Solvent Structure on the Electrostatic Interactions in Proteins, Biophys. J., 2004, vol. 87, p. 1544.CrossRefGoogle Scholar
  29. 29.
    Rubinstein, A.I., Sabirianov, R.F., and Namavar, F., Effects of the dielectric properties of the ceramic-solvent interface on the binding of proteins to oxide ceramics: a non-local electrostatic approach, Nanotechnology, 2016, vol. 27, p. 415703.CrossRefGoogle Scholar
  30. 30.
    Rubinstein, A., Sabirianov, R.F., Mei, W.N., Namavar, F., and Khoynezhad, A., Effect of the ordered interfacial water layer in protein complex formation: A nonlocal electrostatic approach, Phys. Rev. E, 2010, vol. 82, p. 021915.CrossRefGoogle Scholar
  31. 31.
    Bardhan, J.P., Nonlocal continuum electrostatic theory predicts surprisingly small energetic penalties for charge burial in proteins, J. Chem. Phys., 2011, vol. 135, p. 104113–1.CrossRefGoogle Scholar
  32. 32.
    Paillusson, F. and Blossey, R., Slits, plates, and Poisson-Boltzmann theory in a local formulation of nonlocal electrostatics, Phys. Rev. E, 2010, vol. 82, p. 052501–1.CrossRefGoogle Scholar
  33. 33.
    Rubashkin, A.A., The role of spatial dispersion of the dielectric constant of spherical water cavity in the lowering of the free energy of ion transfer to the cavity, Russ. J. Electrochem., 2014, vol. 50, p. 1090.CrossRefGoogle Scholar
  34. 34.
    Vorotyntsev, M.A. and Rubashkin, A.A. Electrostatic contribution to the ion solvation energy: cavity effects, Phys. Chem. Liq., 2017, vol. 55, p. 141.CrossRefGoogle Scholar
  35. 35.
    Kharkats, Yu.I., Kornyshev, A.A., and Vorotyntsev, M.A., Electrostatic Models in the Theory of Solutions, J. Chem. Soc., Faraday Trans. 2, 1976, vol. 72, p. 361.CrossRefGoogle Scholar
  36. 36.
    Zubarev, D.N., Neravnovesnaya statisticheskaya termodinamika (Non-Equilibrium Statistical Thermodynamics), Moscow: Nauka, 1971.Google Scholar
  37. 37.
    Landau, L.D. and Lifshitz, E.M., Course of Theoretical Physics, Vol. 3: Quantum Mechanics Non-Relativistic Theory, Oxford: Pergamon, 1965, 2nd ed.Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  • M. A. Vorotyntsev
    • 1
    • 2
    • 3
    • 4
    Email author
  • A. A. Rubashkin
    • 5
  • A. E. Antipov
    • 1
    • 2
  1. 1.Department of ChemistryMoscow State UniversityMoscowRussia
  2. 2.Mendeleev Russian University of Chemical EngineeringMoscowRussia
  3. 3.Institute of Problems of Chemical PhysicsRussian Academy of SciencesChernogolovka, Moscow RegionRussia
  4. 4.ICMUB, UMR 6302 CNRSUniversité de BourgogneDijonFrance
  5. 5.Institute of CytologyRussian Academy of SciencesSt. PetersburgRussia

Personalised recommendations