Bicontinuous surfaces in self-assembling amphiphilic systems

U. S. Schwarz and G. Gompper

In: Morphology of Condensed Matter: Physics and Geometry of 
Spatially Complex Systems, Eds. K. R. Mecke and D. Stoyan,
Springer Lecture Notes in Physics Vol. 600, pp. 107-151, 2002.

Amphiphiles are molecules which have both hydrophilic and hydrophobic
parts. In water- and/or oil-like solvent, they self-assemble into
extended sheet-like structures due to the hydrophobic effect. The free
energy of an amphiphilic system can be written as a functional of its
interfacial geometry, and phase diagrams can be calculated by
comparing the free energies following from different geometries.  Here
we focus on bicontinuous structures, where one highly convoluted
interface spans the whole sample and thereby divides it into two
separate labyrinths. The main models for surfaces of this class are
triply periodic minimal surfaces, their constant mean curvature and
parallel surface companions, and random surfaces. We discuss the
geometrical properties of each of these types of surfaces and how they
translate into the experimentally observed phase behavior of
amphiphilic systems.