Vitreous Carbon, Geometry and Topology: A Hollistic Approach

Area of Science:

• Materials Science
• Condensed Matter Physics
• Nanotechnology

Background:

• Glass-like carbon (GLC) exhibits remarkable properties like an isotropic sp2 structure, low density, and chemical robustness.
• Despite extensive research, the precise atomic structure of GLC remains largely unknown.
• Existing models for GLC structure often present limitations.

Purpose of the Study:

• To review current models of glass-like carbon structure.
• To introduce topological and geometrical frameworks for understanding GLC properties.
• To explore the application of hyperbolic geometry and minimal surfaces in elucidating GLC network architecture.

Main Methods:

• Review of existing structural models for glass-like carbon.
• Introduction to topological and geometrical concepts for 2D surfaces and networks.
• Application of hyperbolic geometry and theorems (classification, uniformization) to analyze GLC structure.
• Consideration of pulsed laser deposition and controlled annealing for film preparation.

Main Results:

• No single existing model fully explains GLC structure; all have compromises.
• Topological and geometrical properties provide a unified framework for understanding GLC characteristics.
• Hyperbolic geometry and triply periodic minimal surfaces are key to understanding GLC network architecture.
• The proposed framework can heuristically explain most GLC properties.

Conclusions:

• A topological and geometrical approach, particularly using hyperbolic geometry, offers a powerful framework for understanding glass-like carbon structure and properties.
• The presented concepts can be extended to other 2D materials.
• This work aims to guide future experimental investigations into glass-like carbon and related materials.