PACKING OF MOLECULES AND HOLE FORMATION IN LYOTROPIC SYSTEMS

A vector field q (the order parameter of the molecular packing) descri bing the packing (specifically, the orientation) of membrane-forming a mphiphilic molecules is introduced to describe the structures of lyotr opic phases constructed from membranes. In the general case q . n not equal 0 (where n is the unit normal vector) and therefore the singular ities of the vector field q are not determined uniquely by the topolog y 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 uni t 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 lambda of the hole boundary is small compa red with the deformation energy of the field q: lambda h/K much less t han 1 (K is the modulus of the orientational elasticity of the held q and h is the thickness of the membrane). The radius of the hole which is formed equals L approximate to 2.52(K/lambda h)(1/3) and the energy E approximate to 59.79K(lambda h/K)(1/3). (C) 1996 American Institute of Physics.