Nonlinear dynamics of localized structures and proton transfer in a hydrogen-bonded chain model including dipole interactions

  • I. Chochliouros
  • J. Pouget
Part III: Lattice Excitations and Localised Modes
Part of the Lecture Notes in Physics book series (LNP, volume 393)


The transport of energy in H-bonded chains is really an extremely important problem, because of its close connection with basic phenomena in biological systems. We consider a lattice model which is made of two one-dimensional harmonically coupled sublattices corresponding to the oxygens and protons, the two sublattices being coupled. The study becomes more interesting when we introduce the dipole-dipole interactions. As a microscopic dipole is created by the proton motion, it may affect the response of the nonlinear excitations propagating along the chain. We are looking for a solution for which the motion of oxygen ions can be neglected. A ϕ6 equation is found, which admits nonlinear excitations of solitary wave type. We distinguish different classes of solutions for the description of the proton motion. Analytical expressions and the necessary conditions for the existence of these types of solutions are given. The introduction of the dipole interaction produces an influence on the electric field of the system which means that the proton motion is also affected and this makes the proton conductivity much easier. Numerical simulations are presented for special cases. Finally, possible further extensions of the work are discussed.


Proton Conductivity Nonlinear Excitation Proton Motion Orientational Defect Supersonic Wave 
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  1. [1]
    A. S. DAVYDOV, Biology and Quantum Mechanics (Pergamon, New York, 1982).Google Scholar
  2. [2]
    J. F. NAGLE and H. J. MOROWITZ, Proc. Nat. Acad. Sci. USA 75, 298 (1978).PubMedGoogle Scholar
  3. [3]
    V. Ya. ANTONCHENKO, A. S. DAVYDOV and A. V. ZOLOTARYUK, Phys. Status Solidi B 115, 631 (1983).Google Scholar
  4. [4]
    E. W. LAEDKE, K. H. SPATSCHEK, M. WILKENS Jr. and A. V. ZOLOTARYUK, Phys. Rev. A 32, 1161 (1985).PubMedGoogle Scholar
  5. [5]
    J. D. BERNAL and R. H. FOWLER, J. Chem. Phys. 1, 515 (1933).Google Scholar
  6. [6]
    M. PEYRARD, St. PNEVMATIKOS and N. FLYTZANIS, Phys. Rev. A 36, 903 (1987).CrossRefPubMedGoogle Scholar
  7. [7]
    D. HOCHSTRASSER, H. BUTTNER, H. DESFONTAINES and M. PEYRARD, Phys. Rev. A 38, 5332 (1988).PubMedGoogle Scholar
  8. [8]
    H. WEBERPALS and K. H. SpATSCHEK, Phys. Rev. A 36, 2946 (1981).CrossRefGoogle Scholar
  9. [9]
    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
  10. [10]
    N. BJERRUM, Science 115, 385 (1952).Google Scholar
  11. [11]
    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
  12. [12]
    E. WHALLEY, Journal of Glaciology, Vol. 21, 13 (1978).Google Scholar

Copyright information

© Springer-Verlag 1991

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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