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The Topological Background of Schwarzite Physics

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The Mathematics and Topology of Fullerenes

Part of the book series: Carbon Materials: Chemistry and Physics ((CMCP,volume 4))

Abstract

About 10 years ago the synthesis of random carbon schwarzites by supersonic cluster beam deposition has endowed the rich sp2 carbon family with its three-dimensional member. Its reluctance to grow as a three-periodic minimal surface according to topological and physical predictions still prevents schwarzites from being a hot topic, although spongy carbon is already having countless applications. Understanding the links between topology and quantum structure, possibly with the help of large-scale quantum molecular dynamics simulations should trace the route to the synthesis of periodic schwarzites. In this perspective, after a brief account on the growth and characterization of spongy carbon, we review the elementary topology of schwarzites, their stability and growth conditions as derived from pure topological arguments, the electronic structure and the electron-phonon interaction of the smallest periodic schwarzites and what can be learnt by the topological monitoring of quantum molecular dynamics.

You see things and you say “Why?”

But I dream things that never were and I say “Why not?”

(George Bernard Shaw, Back to Mathusalem)

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Acknowledgement

One of us (GB) gratefully acknowledges the Ikerbasque Foundation for support within the project ABSIDES. We acknowledge many stimulating discussions with Prof. Paolo Milani (University of Milano).

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Authors and Affiliations

  1. Donostia International Physics Centre (DIPC), 20018, Donostia-San Sebastián, Spain

    Giorgio Benedek

  2. Dipartimento di Scienza dei Materiali, Universitá di Milano-Bicocca, Via Roberto Cozzi 53, 20125, Milano, Italy

    Giorgio Benedek, Marco Bernasconi, Eugenio Cinquanta, Luca D’Alessio & Marzio De Corato

  3. Department of Physics, Boston University, Boston, MA, 02215, USA

    Luca D’Alessio

Authors
  1. Giorgio Benedek
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  2. Marco Bernasconi
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  3. Eugenio Cinquanta
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  4. Luca D’Alessio
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  5. Marzio De Corato
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Correspondence to Giorgio Benedek .

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Editors and Affiliations

  1. , Dept. of Materials Science, Tor Vergata University, Rome, Italy

    Franco Cataldo

  2. Faculty of Science, University of Split, Nikole Tesle 12, Split, HR–21000, Croatia

    Ante Graovac

  3. Actinium Chemical Research, Via Casilina 1626-A, Rome, 00133, Italy

    Ottorino Ori

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Benedek, G., Bernasconi, M., Cinquanta, E., D’Alessio, L., De Corato, M. (2011). The Topological Background of Schwarzite Physics. In: Cataldo, F., Graovac, A., Ori, O. (eds) The Mathematics and Topology of Fullerenes. Carbon Materials: Chemistry and Physics, vol 4. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0221-9_12

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