Geometrical Foundation of Mesomorphic Polymorphism

Abstract

The aggregation of amphiphilic molecules in water, and in particular the growth and first steps of micellar organization in the dilute region of their phase diagrams, were discussed in earlier chapters of this book, primarily the first two. In these diluted regions the problem of the formation of structures by amphiphilic molecules in aqueous solution could be treated within a rather simple geometrical framework which can be summarized as follows. First, the “micellar” topology of the organization—an infinite number of finite aggregates separated by a connected film of water—does not change during aggregation and growth. The aggregation and growth processes were therefore described as continuous deformations of aggregates of simple shapes. Second, the aggregates are sufficiently diluted for the solution of micelles to be treated as ideal, except for steric interactions in first order, so that the only interaction present between interfaces takes place within the aggregates and constrains their size along one direction to stay constant, with a value of about twice the length of a molecule. The deformations of the aggregates under concentration changes, or the evolution of their interfacial curvature, were then considered to occur subject to this one spatial constraint only.KeywordsCurve SpaceStereographic ProjectionHyperbolic PlaneMiddle SurfaceSpatial ConstraintThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.