Chemical Applications of Topology and GroupTheory.29.Low Density PolymericCarbon Allotropes Based on Negative CurvatureStructures

Abstract

The construction of graphite and fullerene structures from networks of trigonal sp2 carbon atoms of zero and positive curvature can be extended to a fourth form of carbon, provisionally called schwarzites, consisting of networks of trigonal sp2 carbon atoms decorating infinite periodic minimal surfaces (IPMS's) of negative curvature and topological genus 3 such as the so-called D and P surfaces. The carbon networks of the simplest schwarzite structures contain only six- and seven-membered rings analogous to the fullerene networks containing only six- and five-membered rings. The stable structures of both fullerenes and schwarzites contain enough six-membered rings so that no two five-membered rings in the fullerene structures or no two seven-membered rings in the schwarzite structures share edges leading to unstable pentalene and heptalene units, respectively. The smallest unit cell of a viable schwarzite structure of this type contains 168 carbon atoms and is constructed by applying a leapfrog transforma...