Packing of molecules and hole formation in lyotropic systems

  • V. L. Golo
  • E. I. Kats
  • G. Porte


A vector field q (the order parameter of the molecular packing) describing the packing (specifically, the orientation) of membrane-forming amphiphilic molecules is introduced to describe the structures of lyotropic phases constructed from membranes. In the general case q·n≠0 (where n is the unit normal vector) and therefore the singularities of the vector field q are not determined uniquely by the topology of the surface. The condition q·n=0 signifies disruption of the packing of the molecules. This corresponds to holes, which can form in membranes when lyotropic systems are diluted. As an illustration, the simplest type of such singularities, in which the distribution of the field q around a hole is described by a part of an instanton with unit topological charge, is studied. It is shown that such a distribution guarantees the existence of a local minimum under the condition that the tension per unit length λ of the hole boundary is small compared with the deformation energy of the field q:λh/K≪l (K is the modulus of the orientational elasticity of the field q and h is the thickness of the membrane). The radius of the hole which is formed equals L≈2.52(K/λh)1/3 and the energy E≈59.79K(λh/K)1/3.

PACS numbers



Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    M. Filali, G. Porte, J. Appell, and P. Pfeuty, J. Phys. 2 France 4, 349 (1994).Google Scholar
  2. 2.
    G. Porte, J. Appell, P. Basserean et al., Physica A 176, 168 (1991).CrossRefADSGoogle Scholar
  3. 3.
    S. T. Hyde, J. Phys. Chem. 93, 1458 (1989).Google Scholar
  4. 4.
    M. C. Holmes and J. Charvolin, J. Phys. Chem. 88, 810 (1984).CrossRefGoogle Scholar
  5. 5.
    J. Burgoyne, M. C. Holmes, and G. J. T. Tiddy, J. Phys. Chem. 99, 6054 (1995).CrossRefGoogle Scholar
  6. 6.
    P. G. de Gennes, C. R. Acad. Sci. Paris 304, Ser. II, 259 (1987).Google Scholar
  7. 7.
    D. Roux, M. E. Cates, U. Olsson et al., Europhys. Lett. 11, 229 (1990).ADSGoogle Scholar
  8. 8.
    D. Huse and S. Leibler, Phys. Rev. Lett. 66, 1709 (1991).CrossRefGoogle Scholar
  9. 9.
    W. Helfrich, Z. Naturforsch. B 103, 67 (1975).Google Scholar
  10. 10.
    A. M. Polyakov, Gauge Fields and Strings, Harwood Academic Publishers, 1987.Google Scholar
  11. 11.
    E. A. Dubrovin, S. P. Novikov, and A. E. Fomenko, Modern Geometry — Methods and Applications, Parts I–III, Springer-Verlag, New York, 1984, 1985, 1990 [Russian original, Parts I–III, Nauka, Moscow, 1979].Google Scholar
  12. 12.
    A. M. Polyakov and A. A. Belavin, JETP Lett. 22, 114 (1975).Google Scholar
  13. 13.
    R. Rajaraman, Solitons and Instantons, North-Holland, Amsterdam, 1989.Google Scholar
  14. 14.
    J. Park, T. C. Lubensky, and F. C. MacKintosh, Europhys. Lett. 20, 279 (1992).ADSGoogle Scholar
  15. 15.
    Y. Imry and S. Ma, Phys. Rev. Lett. 35, 1399 (1975).CrossRefADSGoogle Scholar
  16. 16.
    M. E. Cates, P. van der Schoot, and C. Y. Lu, Europhys. Lett. 29, 669 (1995).Google Scholar

Copyright information

© MAIK "Nauka/Interperiodica" 1996

Authors and Affiliations

  • V. L. Golo
    • 1
    • 2
  • E. I. Kats
    • 3
  • G. Porte
    • 4
  1. 1.M. V. Lomonosov Moscow State UniversityMoscowRussia
  2. 2.Université Montpellier-2MontpellierFrance
  3. 3.L. D. Landau Institute of Theoretical PhysicsRussian Academy of SciencesMoscowRussia
  4. 4.Université Montpellier-2MontpellierFrance

Personalised recommendations