Topological Defects and Morphology of Graphitic Carbon Materials: An Approach Based on Differential Geometry

TL;DR

This paper explores how topological defects like pentagons and heptagons induce quantized curvature in graphitic carbon materials, using differential geometry to understand their structural effects and limitations.

Contribution

It introduces a differential geometric approach, particularly the Gauss-Bonnet theorem, to analyze the impact of curvature quantization on graphitic carbon structures.

Findings

Curvature in graphitic materials is quantized due to symmetry.

The structure of graphitic carbon is restricted by curvature quantization.

Differential geometry provides insights into the morphology of these materials.

Abstract

It has been known that pentagons and heptagons in hexagonal graphitic network give rise to a certain amount of curvature in the three dimensional structure of graphitic carbon materials. The amount of curvature is quantized due to the symmetry of graphite and, as a result, the structure formed by the network is also restricted. We clarify the effects of curvature quantization on the forms of graphitic carbon materials, employing the knowledge of differential geometry, especially the Gauss-Bonnet theorem.