Springer Nature is making Coronavirus research free. View research | View latest news | Sign up for updates

Proton dynamics in hydrogen-bonded systems

  • 39 Accesses

  • 11 Citations

Abstract

We discuss a simplified version of an ice lattice which consists of an alternating sequence of heavy and light masses. The light masses (protons) are each subject to a bistable potential caused by the heavy masses (oxygens). The protons interact with one another, as do the heavy ions. The interactions between the protons and the oxygens modulate the bistable proton potential. This system is known to exhibit kink and antikink solutions associated with mobile ionic defects accompanied by a lattice distortion. We show that at finite temperatures and in the presence of a constant external field on the protons, the defect velocity is a nonmonotonic function of the temperature, reflecting an interesting interplay of thermal effects (noise) and the constant deterministic external forcing in this nonlinear system. We discuss extensions of the model to higher dimensions, and present preliminary results for the proton motion in such networks.

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

References

  1. 1.

    M. I. Dykman, D. G. Luchinsky, R. Mannella, P. V. E. McClintock, N. D. Stein, and N. G. Stocks,J. Stat. Phys. 70:463 (1992).

  2. 2.

    V. Ya. Antonchenko, A. S. Davydov, and A. V. Zolotaryuk,Phys. Stat. Sol. (b) 115:631 (1983).

  3. 3.

    M. Peyrard, St. Pnevmatikos, and N. Flytzanis,Phys. Rev. A 36:903 (1987).

  4. 4.

    St. Pnevmatikos,Phys. Rev. Lett. 60:1534 (1988).

  5. 5.

    G. P. Tsironis and St. Pnevmatikos,Phys. Rev. B 39:7161 (1989).

  6. 6.

    A. Zolotaryuk and St. Pnevmatikos,Phys. Lett. A 143:233 (1990).

  7. 7.

    P. S. Lomdahl and W. C. Kerr,Phys. Rev. Lett. 55:1235 (1985).

  8. 8.

    K. Lindenberg and B. J. West,The Nonequilibrium Statistical Mechanics of Open and Closed Systems (VCH, New York, 1990).

  9. 9.

    E. S. Nylund and G. P. Tsironis,Phys. Rev. Lett. 66:1886 (1991).

  10. 10.

    P. B. Hobbs,Ice Physics (Clarendon, Oxford, 1974).

  11. 11.

    H. Engelheart, B. Bullemer, and N. Riehl,Physics of Ice, N. Riehl, B. Bullemer, and H. Engelheart, eds. (Plenum Press, New York, 1969).

  12. 12.

    B. Klar, B. Hingerty, and W. Saenger,Acta Cryst. B 36:1154 (1980); W. Saenger, Ch. Betzel, B. Hingerty, and G. M. Brown,Nature 296:581 (1982).

  13. 13.

    H. Morgan and R. Pethig,Int. J. Quantum Chem. Quantum Biol. Symp. 11:209 (1984).

  14. 14.

    W. Stoeckenius and W. H. Kunau,J. Cell Biol. 38:337 (1968); D. Osterhelt and W. Stoeckenius,Proc. Natl. Acad. Sci. USA 70:2853 (1973).

  15. 15.

    H. Merz and G. Zundel,Biochem. Biophys. Res. Commun. 156:86 (1981).

  16. 16.

    P. C. Jordan,J. Phys. Chem. 91:6582 (1987).

  17. 17.

    S. F. Fornili, D. P. Vercantern, and E. Clementi,Biochem. Biophys. Acta 771:151 (1984); D. H. J. Mackay, P. H. Berens, K. R. Wilson, and A. T. Hagler,Biophys. J. 46:229 (1984).

  18. 18.

    J. F. Nagle and S. Tristram-Nagle,J. Membrane Biol. 74:1 (1983).

  19. 19.

    St. Pnevmatikos, A. V. Savin, and A. V. Zolotaryuk, inNonlinear Coherent Structures, M. Barthes and J. Léon, eds. (Springer-Verlag, Berlin, 1990).

Download references

Author information

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Nylund, E., Lindenberg, K. & Tsironis, G. Proton dynamics in hydrogen-bonded systems. J Stat Phys 70, 163–181 (1993). https://doi.org/10.1007/BF01053961

Download citation

Key words

  • Hydrogen-bonded networks
  • proton dynamics
  • multidimensional effects
  • collective motion