Dynamics of Nonlinear Coherent Structures in a Hydrogen-Bonded Chain Model: The Role of the Dipole-Dipole Interactions

  • I. Chochliouros
  • J. Pouget
Part of the NATO ASI Series book series (NSSB, volume 291)

Abstract

The problem of the energy transport along H-bonded chains has recently attracted a renewal of interest due to the close connection with basic biological processes. In our study we consider a lattice model consisting of two one-dimensional harmonically coupled sublattices corresponding to the oxygens and protons, the two sublattices being coupled. We also introduce the dipole-dipole interactions which are present as a result of the existence of microscopic dipoles created by the proton motion. This kind of interaction may affect the response of the nonlinear excitations propagating along the chain. We are looking for a solution for which the heavy-ion sublattice can be considered as “frozen”, that is the oxygens “stay” at rest and do not participate in motion. A phi-6 equation is found, which admits nonlinear excitations of solitary wave type. We have different classes of localized solutions for the proton motion and analytical expressions of these types are also given. A parallel study of the problem based on the potential is additionally presented, in a way to discuss a physical interpretation of the previous mathematical results. The proton motion is affected by the influence of the dipole interactions and the proton conductivity becomes much easier. Numerical simulations are presented for special cases. Finally, possible further extensions of the work are envisaged.

Keywords

Hydroxyl Soliton Hydroxonium 

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References

  1. [1]
    V. Ya. Antonchenko, A. S. Davydov and A. V. Zolotaryuk, Phys. Status Solidi B 115, 631 (1983).CrossRefGoogle Scholar
  2. [2]
    A. V. Zolotaryuk, K. H. Spatschek, and E. W. Laedke, Phys. Lett. A 101, 517 (1983).CrossRefGoogle Scholar
  3. [3]
    J. D. Bernal and R. H. Fowler, J. Chem. Phys. 1, 515 (1933).CrossRefGoogle Scholar
  4. [4]
    J. F. Nagle, M. Mille, and H. J. Morowitz, J. Chem. Phys. 72, 3959 (1980).CrossRefGoogle Scholar
  5. [5]
    N. Bjerrum, Science 115, 385 (1952).CrossRefGoogle Scholar
  6. [6]
    R. Janoschek,in The Hydrogen Bond: Recent Developments in Theory and Experiments, edited by P. Schuster, G. Zundel and C. Sandforty (North Holland, Amsterdam, 1976), p. 165.Google Scholar
  7. [7]
    E. W. Laedke, K. H. Spatschek, M. Wilkens, Jr. and A. V. Zolotaryuk, Phys. Rev. A 32, 1161 (1985).CrossRefGoogle Scholar
  8. [8]
    M. Peyrard, St. Pnevmatikos, and N. Flytzanis, Phys. Rev. A 36, 903 (1987).CrossRefGoogle Scholar
  9. [9]
    A. S. Davydov, Solitons in Molecular Systems (Dreidel Publishing Company, Dordrecht, Holland 1985).Google Scholar
  10. [10]
    A. V. Zolotaryuk, Theor. Math. Phys. 68, 916 (1986).CrossRefGoogle Scholar
  11. [11]
    G. P. Johari and S. J. Jones, Journal de Chimie Physique, 82, Nº11/12, 1019, 1985.Google Scholar
  12. [12]
    E. Whalley, Journal of Glaciology, Vol. 21, 13 (1978).Google Scholar
  13. [13]
    L. Onsager,in Physics and Chemistry of Ice edited by E. Whalley, S. J. Jones and L. W. Crold (Royal Society of Canada, Ottawa, 1973) pp. 7–12.Google Scholar
  14. [14]
    D. Hochstrasser, H. Buttner, H. Desfontaines and M. Peyrard, Phys. Rev. A 38, 5332 (1988).CrossRefGoogle Scholar
  15. [15]
    H. Weberpals and K. H. Spatschek, Phys. Rev. A 36, 2946 (1981).CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1992

Authors and Affiliations

  • I. Chochliouros
    • 1
  • J. Pouget
    • 1
  1. 1.Laboratoire de Modélisation en Mécanique (associé au CNRS)Université Pierre et Marie CurieParis, Cédex 05France

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