Vitreous Carbon, Geometry and Topology: A Hollistic Approach

Abstract

Glass-like carbon (GLC) is a complex structure with astonishing properties: isotropic sp2 structure, low density and chemical robustness. Despite the expanded efforts to understand the structure, it remains little known. We review the different models and a physical route (pulsed laser deposition) based on a well controlled annealing of the native 2D/3D amorphous films. The many models all have compromises: neither all bad nor entirely satisfactory. Properties are understood in a single framework given by topological and geometrical properties. To do this, we present the basic tools of topology and geometry at a ground level for 2D surface, graphene being the best candidate to do this. With this in mind, special attention is paid to the hyperbolic geometry giving birth to triply periodic minimal surfaces. Such surfaces are the basic tools to understand the GLC network architecture. Using two theorems (the classification and the uniformisation), most of the GLC properties can be tackled at least at a heuristic level. All the properties presented can be extended to 2D materials. It is hoped that some researchers may find it useful for their experiments.

Discrimination of different amorphous carbon by low fluence laser irradiation

“…amorphous carbon films can be seen as randomly distributed hexagon rings in a matrix of sp 3 -hybridized carbon and that can be transformed to glassy carbon structure by laser irradiation by converting the sp 3 sites to the sp 2 ones and forming curved graphene sheets interlinked between all dispersed hexagonal rings [19,35]. fs-PLD under vacuum produces the same carbon films after laser irradiation, regardless of the sp 2 nature of the target.…”

Reconfiguring Hard Carbons with Emerging Sodium‐Ion Batteries: A Perspective

“…Graphitic carbons are typically comprised of planar hexagonal networks of atoms, while non‐graphitic carbons contain curved hexagonal networks of atoms together with non‐hexagonal components. [ 3,38,39 ]…”

“…Graphitic carbons are typically comprised of planar hexagonal networks of atoms, while non-graphitic carbons contain curved hexagonal networks of atoms together with non-hexagonal components. [3,38,39] Non-graphitic carbons are usually divided into graphitizable carbons (soft carbons) and non-graphitizable carbons (hard carbons) depending on whether they can be readily graphitized at a temperature of ≈3000 °C. [40,41] Both soft carbons and hard car-bons lack a long-range periodic structure, and sp 2 and sp 3 hybridization co-exist in the structure as shown in Figure 2a.…”

“…Carbon materials are abundant and inexpensive and have a higher electrochemical activity than other materials, making them useful for commercial use in energy storage devices. [1][2][3] Hard carbons are nongraphitizable and have amorphous structures that mainly consist of curved and irregularly distributed graphene nanosheets. Even at temperatures above 2800 °C, they are difficult to graphitize.…”

Electrophysical Properties and Structure of Natural Disordered sp2 Carbon

“…The process of graphitization of hydrocarbon compounds is irreversible, but it is not always terminated with the formation of graphite, both in terms of structure ordering and in terms of removal of hydrogen, oxygen, nitrogen, and sulfur heterocompounds. Condensation of carbonaceous matter can occur at the stage of formation of graphite-like nanostructures of various degrees of order and sizes [ 6 ] and can also end with the formation of structures such as multilayer ribbons and fullerenes [ 7 , 8 ]. In the sequence of carbonization (dehydrogenation) of hydrocarbon compounds, according to their physicochemical properties, a class of substances of the highest degree of transformation (carbonization) was distinguished, which was characterized by the so-called pre-graphite structural stage [ 9 , 10 , 11 ].…”