Skip to main content
SpringerLink
Log in

Topological Versus Physical and Chemical Properties of Negatively Curved Carbon Surfaces

  • Chapter
  • First Online:
Topological Modelling of Nanostructures and Extended Systems

Part of the book series: Carbon Materials: Chemistry and Physics ((CMCP,volume 7))

Abstract

Some relevant physical and chemical properties of negatively curved carbon surfaces like sp 2-bonded schwarzites can be predicted or accounted for on the basis of purely topological arguments. The general features of the vibrational spectrum of complex sp 2-carbon structures depend primarily on the topology of the bond network and can be estimated, in a first approximation and for systems with only nearest-neighbor interactions, from the diagonalization of the adjacency matrix. Examples are discussed for three- and two-periodic carbon schwarzites, where a direct comparison with ab initio calculations is possible. The spectral modifications produced by the insertion of defects can also analyzed on pure topological grounds. Two-periodic (planar) schwarzites can be viewed as regular arrays of Y-shaped nanojunctions, which are basic ingredients of carbon-based nano-circuits. A special class of planar schwarzites is obtained from a modification of a graphene bilayer where the two sheets are linked by a periodic array of hyperboloid necks with a negative Gaussian curvature. Ab initio density functional calculations for some structures among the simplest planar schwarzites – (C18)2, (C26)2, and (C38)2 – are presented and discussed in light of the structural stability predictions derived from a topological graph-theory analysis based on the Wiener index. A quantum-mechanical justification is provided for the effectiveness of the Wiener index in ranking the structural stability of different sp 2-conjugated structures.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    The universe (that others call the Library) is composed by an undefined, sometimes infinite number of hexagonal tunnels.

References

  • Agarwal S, Zhou X, Ye F, He Q, Chen GCK, Soo J, Boey F, Zhang H, Chen P (2010) Langmuir Lett 26:2244

    Article  CAS  Google Scholar 

  • Arcon D, Jaglicic Z, Zorko A, Rode AV, Christy AG, Madsen NR, Gamaly EG, Luther-Davies B (2006) Phys Rev B 74:014438

    Article  Google Scholar 

  • Bandaru PR, Daraio C, Jin S, Rao AM (2005) Nat Mater 4:663

    Article  CAS  Google Scholar 

  • Barborini E, Piseri P, Milani P, Benedek G, Ducati C, Robertson J (2002) Appl Phys Lett 81:3359; highlighted by E Gerstner, Nature, Materials Update, 7 Nov 2002. http://wwwnaturecom/materials/news/news/021107/portal/m021107-1html

  • Benedek G, Milani P, and Ralchenko VG (eds) (2001) Nanostructured carbon for advance applications. Kluwer, Dordrecht and papers therein

    Google Scholar 

  • Benedek G, Vahedi-Tafreshi H, Barborini E, Piseri P, Milani P, Ducati C, Robertson J (2003) Diamond Relat Mater 12:768

    Article  CAS  Google Scholar 

  • Benedek G, Vahedi-Tafreshi H, Milani P, Podestà A (2005) Fractal growth of carbon schwarzites. In: Beck C et al (eds) Complexity, metastability and non-extensivity. World Scientific, Singapore, pp 146–155

    Google Scholar 

  • Benedek G, Bernasconi M, Cinquanta E, D’Alessio L, De Corato M (2011) The topological background of schwarzite physics. In: Cataldo F, Graovac A, Ottorino O (eds) Mathematics and topology of fullerenes, Springer series on carbon materials chemistry and physics. Springer, Heidelberg/Berlin, Chap 12

    Google Scholar 

  • Bogana M, Donadio D, Benedek G, Colombo L (2001) Europhys Lett 54:72

    Article  CAS  Google Scholar 

  • Bongiorno G, Lenardi C, Ducati C, Agostino RG, Caruso T, Amati M, Blomqvist M, Barborini E, Piseri P, La Rosa S, Colavita E, Milani P (2005) J Nanosci Nanotechnol 10:1

    Google Scholar 

  • Boscolo I, Milani P, Parisotto M, Benedek G, Tazzioli F (2000) J Appl Phys 87:4005

    Article  CAS  Google Scholar 

  • Bühl M, Hirsch A (2001) Chem Rev 101:1153

    Article  Google Scholar 

  • Cappelletti RL, Copley JRD, Kamitakahara WA, Li F, Lannin JS, Ramage D (1991) Phys Rev Lett 66:3261

    Article  CAS  Google Scholar 

  • Castro Neto AH, Guinea F, Peres NMR, Novoselov KS, Geim AK (2009) Rev Mod Phys 81:109

    Article  CAS  Google Scholar 

  • Chernozatonskii LA (1993) Phys Lett A 172:173

    Article  Google Scholar 

  • De Corato M, Benedek G (2012) Dynamics and spectral properties of free-standing negatively curved carbon surfaces. In: Proceedings of the 49th course of the international school of solid state physics. Edited by: Antonio Cricenti (Istituto di Struttura della Materia, Italy). World Scientific, New York

    Google Scholar 

  • De Corato M, Benedek G, Ori O, Putz MV (2012) Int J Chem Model 4:105–114

    Google Scholar 

  • Deepak FL, Govindaraj A, Rao CNR (2001) Chem Phys Lett 345:5

    Article  CAS  Google Scholar 

  • Diederich L, Barborini E, Piseri P, Podestà A, Milani P, Scheuwli A, Gallay R (1999) Appl PhysLett 75:2662

    CAS  Google Scholar 

  • Donadio D, Colombo L, Milani P, Benedek G (1999) Phys Rev Lett 84:776

    Article  Google Scholar 

  • Ferrari AC, Satyanarayana BS, Robertson J, Milne WI, Barborini E, Piseri P, Milani P (1999) Europhys Lett 46:245

    Article  CAS  Google Scholar 

  • Gaito S, Colombo L, Benedek G (1998) Europhys Lett 44:525

    Article  CAS  Google Scholar 

  • Geim AK, Novoselov KS (2007) Nat Mater 6:183

    Article  CAS  Google Scholar 

  • Genechten KA van, Mortier WJ, Geerlings P (1987) J Chem Phys 86:5063

    Article  Google Scholar 

  • Gersten JI, Smith FW (2001) The physics and chemistry of materials. Wiley, New York, 176

    Google Scholar 

  • Giannozzi P, Baroni S, Bonini N, Calandra M, Car R, Cavazzoni C, Ceresoli D, Chiarotti GL, Cococcioni M, Dabo I, Dal Corso A, Fabris S, Fratesi G, de Gironcoli S, Gebauer R, Gerstmann U, Gougoussis C, Kokalj A, Lazzeri M, Martin-Samos L, Marzari N, Mauri F, Mazzarello R, Paolini S, Pasquarello A, Paulatto L, Sbraccia C, Scandolo S, Sclauzero G, Seitsonen AP, Smogunov A, Umari P, Wentzcovitch RM (2009) QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials. J Phys Condens Matter 21:395502

    Article  Google Scholar 

  • Iijima S (1991) Nature 324:56

    Article  Google Scholar 

  • Kroto HW, Heath JR, O’Brien SC, Curl RF, Smalley RE (1985) Nature 318:162

    Article  CAS  Google Scholar 

  • Làszlò I, Rassat A, Fowler PW, Graovac A (2001) Chem Phys Lett 342:369

    Article  Google Scholar 

  • Lenosky T, Gonze X, Teter M, Elser V (1992) Nature 355:333

    Article  CAS  Google Scholar 

  • Manolopoulos DE, Fowler PW (1992) J Chem Phys 96:7603

    Article  CAS  Google Scholar 

  • McKay AL (1985) Nature 314:604

    Article  Google Scholar 

  • McKay AL, Terrones H (1991) Nature 352:762

    Article  Google Scholar 

  • Monkhorst HJ, Pack JD (1976) Phys Rev B 13:5188

    Article  Google Scholar 

  • Novoselov KS, Geim AK, Morozov SV, Jiang D, Zhang Y, Dubonos SV, Grigorieva IV, Firsov AA (2004) Science 30:666

    Article  Google Scholar 

  • Novoselov KS, Geim AK, Morozov SV, Jiang D, Katsnelson MI, Grigorieva IV, Dubonos SV, Firsov A (2005a) Nature 438:197

    Article  CAS  Google Scholar 

  • Novoselov KS, Jiang D, Booth T, Khotkevich VV, Morozov SM, Geim AK (2005b) Proc Natl Acad Sci USA 102:10451

    Article  CAS  Google Scholar 

  • O’Keeffe M, Adams GB, Sankey OF (1992) Phys Rev Lett 68:2325

    Article  Google Scholar 

  • Ori O, Cataldo F, Graovac A (2009) Fuller Nanotub Carbon Nanostruct 17(3):308–323

    Article  CAS  Google Scholar 

  • Perdew JP, Burke K, Ernzerhof M (1996) Phys Rev Lett 77:3865

    Article  CAS  Google Scholar 

  • Pintschovius L (1996) Rep Prog Phys 59:473, and references therein

    Google Scholar 

  • Putz MV (2010) MATCH Commun Math Comput Chem 64:391–418

    CAS  Google Scholar 

  • Putz MV (2011) In: Putz MV (ed) Carbon bonding and structures: advances in physics and chemistry. Series of carbon materials: chemistry and physics. Springer, London, pp 1–32

    Google Scholar 

  • Rode V, Gamaly EG, Christy AG, Fitz Gerald JG, Hyde ST, Elliman RG, Luther-Davies B, Veinger AI, Androulakis J, Giapintzakis J (2004) Phys Rev B 70:054407, highlighted by R F Service (2004) Science 304:42

    Google Scholar 

  • Romo-Herrera JM, Terrones M, Terrones H, Dag S, Meunier V (2007) Nano Lett 7:570

    Article  CAS  Google Scholar 

  • Rosato V, Celino M, Gaito S, Benedek G (1999) Phys Rev B 60:16928

    Article  CAS  Google Scholar 

  • Satishkumar BC, John Thomas P, Govindaraj A, Rao CNR (2000) Appl Phys Lett 77:2530

    Article  CAS  Google Scholar 

  • Schwarz HA (1990) Gesammelte Mathematische Abhandlungen, 11. Springer, Berlin

    Google Scholar 

  • Spadoni S, Colombo L, Milani P, Benedek G (1997) Europhys Lett 39:269

    Article  CAS  Google Scholar 

  • Spagnolatti I, Bernasconi M, Benedek G (2003) Eur Phys J B 32(2):181–187

    Article  CAS  Google Scholar 

  • Terrones H, McKay AL (1993) In: Kroto HW, Fisher JE, Cox DE (eds) The fullerenes. Pergamon Press, Oxford, p 113

    Chapter  Google Scholar 

  • Terrones M, Banhart F, Grobert N, Charlier JC, Terrones H, Ajayan PM (2002) Phys Rev Lett 89:075505

    Article  CAS  Google Scholar 

  • Townsend SJ, Lenosky T, Muller DA, Nichols CS, Elser V (1992) Phys Rev Lett 69:921

    Article  CAS  Google Scholar 

  • Vanderbilt D (1990) Phys Rev B 41:7892

    Article  Google Scholar 

  • Vanderbilt D, Tersoff J (1992) Phys Rev Lett 68:511

    Article  CAS  Google Scholar 

  • Vukicevic D, Cataldo F, Ori O, Graovac A (2011) Chem Phys Lett 501(4–6):442

    Article  CAS  Google Scholar 

  • Wiener H (1947) J Am Chem Soc 1(69):17

    Article  Google Scholar 

  • Zakharchenko KV, Fasolino A, Los JH, Katsnelson MI (2011) J Phys Condens Matter 23:202202

    Article  CAS  Google Scholar 

Download references

Acknowledgements

We thank Prof. Antonio Papagni and Dr. Gabriele Cesare Sosso (University of Milano-Bicocca), and Dr. Fabio Petrucci (EPFL, Lausanne) for many stimulating discussions. One of us (GB) acknowledges Ikerbasque (ABSIDES project) and the Donostia International Physics Center (DIPC) for support. MVP thanks Romanian Ministry of Education and Research for support through the CNCS-UEFISCDI project Code TE-16/2010-2013.

Author information

Authors and Affiliations

  1. Dipartimento di Scienza dei Materiali, Universitá di Milano-Bicocca, Via R. Cozzi 53, 20125, Milan, Italy

    Marzio De Corato, Marco Bernasconi & Giorgio Benedek

  2. Centro S3, CNR-Istituto Nanoscienze, I-41125, Modena, Italy

    Marzio De Corato

  3. Dipartimento di Fisica, Università di Modena e Reggio Emilia, I-41125, Modena, Italy

    Marzio De Corato

  4. Donostia International Physics Center (DIPC), Paseo M. de Lardizábal 4, 20018, Donostia/San Sebastián, Spain

    Marco Bernasconi & Giorgio Benedek

  5. Department of Physics, Boston University, 590 Commonwealth Av., Boston, MA, 02215, USA

    Luca D’Alessio

  6. Actinium Chemical Research, Via Casilina 1626/A, 00133, Rome, Italy

    Ottorino Ori

  7. Laboratory of Computational and Structural Physical Chemistry, Biology-Chemistry Department, West University of Timişoara, Pestalozzi Street No.16, Timişoara, RO-300115, Romania

    Mihai V. Putz

Authors
  1. Marzio De Corato
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Marco Bernasconi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Luca D’Alessio
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ottorino Ori
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Mihai V. Putz
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Giorgio Benedek
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Marzio De Corato .

Editor information

Editors and Affiliations

  1. , Department of Mathematics, University of Kashan, Kashan, Iran

    Ali Reza Ashrafi

  2. , Department of Materials Science, Tor Vergata University, Rome, Italy

    Franco Cataldo

  3. , Department of Mathematics, Tarbiat Modares University, Tehran, Iran

    Ali Iranmanesh

  4. Actinium Chemical Research, Rome, Italy

    Ottorino Ori

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

De Corato, M., Bernasconi, M., D’Alessio, L., Ori, O., Putz, M.V., Benedek, G. (2013). Topological Versus Physical and Chemical Properties of Negatively Curved Carbon Surfaces. In: Ashrafi, A., Cataldo, F., Iranmanesh, A., Ori, O. (eds) Topological Modelling of Nanostructures and Extended Systems. Carbon Materials: Chemistry and Physics, vol 7. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-6413-2_4

Download citation

Publish with us

Policies and ethics

Search

Navigation