Polycontinuous morphologies and interwoven helical networks
Department of Applied Mathematics,
Research School of Physical Sciences Australian
National University, Canberra, ACT 0200, Australia
Accepted: 27 January 2000
We describe a construction procedure for polycontinuous structures, giving generalisations of bicontinuous morphologies to more than two equivalent, continuous and interwoven sub-volumes. The construction gives helical windings of disjoint graphs on triply periodic hyperbolic surfaces, whose universal cover in the hyperbolic plane consists of packed, parallel trees. The simplest tri-, quadra- and octa-continuous morphologies consist of three , four and eight interwoven networks, respectively. The quadra- and octa-continuous cases are chiral. A novel chiral bicontinuous structure is also derived, closely related to the well-known cubic gyroid mesophase.
PACS: 02.40.Sf – Manifolds and cell complexes / 61.25.Em – Molecular liquids / 61.30.Cz – Theory and models of liquid crystal structure
© EDP Sciences, 2000