Geometry of Films of Amphiphile Molecules: A Curved Space Approach

  • J.-F. Sadoc
  • J. Charvolin
Part of the NATO ASI Series book series (NSSB, volume 229)


Periodical organizations of two fluid media separated by interfaces are very common in liquid crystals where they most often occur under the forms of periodical stackings along one dimension of fluid layers of molecules . In lamellar phases of lyotropic liquid crystals , built by amphiphilic molecules in presence of water [1] , paraffinic bilayers of amphiphiles and polar layers of water are alternatively stacked with flat interfaces defined by the polar heads of the amphiphiles , as shown in fig. la . Besides these phases with periodicity along one dimension the phase diagrams of liquid crystalline systems may present other ordered phases with periodicities along two or three dimensions , curved interfaces and various topologies [1,2,3] . For instance consider the particular case of phases with cubic symmetry and bicontinuous topology . They are of the type shown in fig. 1b where a film of water without self-intersection separates two identical labyrinths of amphiphilic molecules . We wonder if the complex geometry of such structures could not rely upon the same principle than that which is easily discernable in the much simpler lamellar and smectic phases.


Gaussian Curvature Curve Space Middle Surface Amphiphilic Molecule Hyperbolic Surface 
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Copyright information

© Springer Science+Business Media New York 1990

Authors and Affiliations

  • J.-F. Sadoc
    • 1
  • J. Charvolin
    • 1
  1. 1.Laboratoire de Physique des SolidesUniversité Paris-SudOrsayFrance

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