Novel mathematical description of surfactants macroaggregates

Molecular organization of surfactants in aqueous media is a key element in biochemical research and provides furthermore novel application in biomolecular materials design. Here is shown a novel mathematical representation for the interconversions within very complex and huge aggregates like vesicles, liquid crystals and colloidal dispersions. The resulting equations are able to fully represent the morphology, the symmetry and the topology of extended lipid bilayer. Furthermore, only one parameter is needed to describe the whole transition, regardless of changes in symmetry or topology. The existence of a unique parameter is the most important property of this mathematical treatment. In fact the Gaussian and the mean curvature can be easily derived and consequently bending energy and several geometrical properties can be derived by this ancestor parameter. This parameter, describing curvature and symmetry for the whole transition can be considered as a sort of natural intrinsic indication of the transformation evolution. The mathematical description of these transformations can highlight new aspects of the dynamics of colloidal systems.