Abstract
Glass-like carbon (GLC) is a complex structure with astonishing properties: isotropic 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.
Highlights
Carbon is the most versatile element of the periodic table
Thanks to the uniformisation theorem and the classification one, some amazing properties of glass-like or vitreous carbon (GLC) can be understood at first glance
Material properties are governed by mathematics and physics
Summary
Carbon is the most versatile element of the periodic table. There are nearly ten million known carbon compounds, and an entire branch of chemistry, known as organic chemistry, is devoted to their study (see Figure 1). Noda and Inakagi proposed in 1964 [9] a structural model of GLC deduced from X-ray diffraction, in which tetrahedral carbon atoms form the main part of the cross-linkages which link the graphite-like layers in a random way. Harris [17] proposed a model for the structure of non-graphitising carbons, which consists of fragments of curved carbon sheets (fullerene-like), containing pentagons and heptagons as well as hexagons. Thanks to neutron and X-ray diffraction, Jurkiewicz et al [18] showed a large proportion of curved graphitic sheets The presence of these curved elements in carbon nanomaterials can be related to the formation of topological point-type defects in non-hexagonal rings (pentagons, heptagons and higher-membered rings). Other observations predict that carbon foams contain graphite-like “sp carbon” segments, connected by sp carbon atoms, resulting in porous Kagome structures [23].
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