Fractal Growth of Carbon Schwarzites

Benedek, G.; Tafreshi, H. Vahedi; Podestà, Alessandro; Milani, P.

doi:10.1142/9789812701558_0017

Cited by 3 publications

(4 citation statements)

References 15 publications

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“…where dS is the surface element, and the integral extends over the entire surface, supposed to be closed as explained above. The total energy of a curved single-walled graphene can be expressed in the form suggested by Helfrich for membranes and foams [23,[24][25][26]:…”

Section: Where Quantum Physics Meets Topologymentioning

confidence: 99%

“…The initial relative values of k and  k which determine whether the growth process of sp 2 carbon preferentially leads to fullerenes, nanotubes or schwarzites, define the three topological domains shown in Fig. 6 [17,23]: schwarzites are favoured for  k<¼k, nanotubes for ¼k < k<¾k and fullerenes for  k>¾k.…”

Section: Where Quantum Physics Meets Topologymentioning

confidence: 99%

“…Topological domains for the growth of sp 2 carbon graphenic structures as functions of the incipient elastic constants. The  k and k values for free-standing graphenes (red cross) favour the growth of nanotubes [16,23].…”

Section: Where Quantum Physics Meets Topologymentioning

confidence: 99%

“…5. The simulation of the TEM images of carbon schwarzites with a self-affine fractal minimal surface growing in the z-direction (a) provides a faithful visual representation of experimental TEM pictures (b)[15,23].…”

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Graphene as a Quantum Playground

Benedek¹

2018

INCONTRI

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The modern triathlon “heat-electricity-mechanics” has an indisputable champion, graphene, as a recordman, among all materials in normal conditions, in all three specialties: thermal conductivity, electrical mobility and mechanical strength. On the other hand graphene, being perfectly planar, is the simplest of all possible sp2 pure carbon structures. The graphene family includes curved forms like fullerenes, having gaussian curvature G >0, nanotubes, with G=0 like graphene, and schwarzites with G <0 and vanishing mean curvature. The conjugation of carbon-carbon sp2 bonds makes several global electronic and vibrational properties of graphenes to primarily depend upon the structure topology. Global properties which can be estimated on topological grounds are the growth process, the isomer hierarchy, the vibrational spectrum, the elastic constants, the porosity as a function of the deposition energy, etc. The dynamics of free electrons in graphene is well described by the Dirac quantum-relativistic equation, and some of its consequences like the Zitterbewegung and Klein’s paradox have been proved in graphene. Thus graphene allows for the simulation and validation of fundamental theories in fields hardy accessible to experiments like high-energy physics and cosmology. With some surprising prediction! It is a fact that since the late XIX century topology has become a reference paradigm in many branches of fundamental physics, from Hermann Weyl’s topological theory of electricity and cosmological wormholes, to string theory and present topological field theories in high-energy physics.

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Section: Where Quantum Physics Meets Topologymentioning

confidence: 99%

Section: Where Quantum Physics Meets Topologymentioning

confidence: 99%

Section: Where Quantum Physics Meets Topologymentioning

confidence: 99%

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confidence: 99%

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