Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Published in:
New Trends in Nanoscale Mechanics of Carbon Nanotubes Read chapter Read first chapter

2014 | OriginalPaper | Chapter

Nanomechanics of Graphene Sheets

Registry Matrix Analysis and Interfacial Sliding

Author : Vasyl Harik

Published in: Trends in Nanoscale Mechanics

Publisher: Springer Netherlands

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

This chapter reviews basic structure of graphene sheets, interfacial sliding between adjacent graphene sheets, a nanoscale analog of the Newton’s friction law, registry effects between adjacent graphene sheets and their atomic lattices, registry matrices to describe interfacial registry in graphene stacking and the registry matrix analysis for the sliding of graphene sheets in nanoscale electronic devices. Interfacial sliding of graphene sheets depends on the interfacial registry potentials and the so called effect of the spatial exclusion of electrons (ESEE) at the interface of two graphene sheets, which can be viewed as the nanoscale analog of Pauli’s exclusion principle. Understanding of nanoscale sliding phenomena is critical for improving manufacturing technology for the single layer graphene sheets in nanoelectronic devices. Interfacial sliding between adjacent graphene sheets has been also described by a nanoscale analog of the Newton’s friction law for the nanoscale surface sliding mechanics and the associated stiction effects. Understanding of nanoscale sliding helps nanoscale cleaning and safety.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now
previous chapter New Trends in Nanoscale Mechanics of Nanostructures, Graphene Sheets and Nanocomposites
next chapter Molecular Mechanics of Polymer Nanocomposites
Footnotes
1
The so called Brillouin zone is used to schematically represent the energy dispersion relation for the energy of states of the graphene lattice vibration waves, i.e., phonons, and the energy of states of the oscillating electrons.
 
2
The Bohr radius, a 0 = 0.529 Å is the most probable distance between a proton and an electron in the Hydrogen atom according to the Bohr’s planetary model of an atom.
 
3
The onset of the Ψ-registry configuration (Fig. 6a) is associated with the need of a π-electron to overcome the registry potential of the C–C bond and the associated Coulomb repulsion within the electron spatial exclusion (ESE) zone (see Harik [16]). The size of the ESE zone depends on the local atomic lattice configuration, the registry potential barriers, the nanoscale Coulomb repulsion proportional to 1/r2, and the nanoscale repulsion proportional to 1/r12. The combined effect results in the so called SEE effect. The nanoscale analog of Pauli exclusion of electrons is similar to the quantum Pauli principle for the identical particles with the spin ½ (fermions); the two identical particles cannot occupy the same energy state, as their combined wave function, ψ, is anti-symmetric. The nanoscale Coulomb repulsion, the nanoscale SEE repulsion and the quantum Pauli principle for the electrons all affect precise dimensions of the ESE zone.
 
4
This fundamental research was partially supported by the Princeton-based NASA-funded URETI Institute (http://​bimat.​org) for the Bio-inspired Nanostructured Multifunctional Materials (award No. NCC-1-02037).
 
5
In the late 15th century Leonardo da Vinci had identified the three important parts of friction as follows. “Friction is divided into three parts: these are simple, compound and disordered.” Simple friction is due to the motion and dragging; the compound friction is “between two immovable things” and the irregular friction is associated with the “corners of different sides.” For more details see the notebooks of Leonardo da Vinci [51], p. 527, and the following footnote.
 
6
The momentum of moving “things” has been also analyzed by Leonardo da Vinci [51], p. 543: “No impulse can end immediately but proceeds to consume itself through stages of movement.”
 
Literature
1.
A.K. Geim, K.S. Novoselov, The rise of graphene. Nature 6, 183 (2007)
2.
A. Bostwick, T. Ohta, T. Seyller, K. Horn, E. Rotenberg, Nature 3, 36 (2006)
3.
H. Raza, J. Phys.: Condens. Matter, 23, 382203 (2011)
4.
S. Ihnatsenka, I.V. Zozoulenko, G. Kirczenow, Phys. Rev. B 80, 155415 (2009)
5.
H. Raza, Graphene Nanoelectronics: Metrology, Synthesis, Properties and Applications (Springer, Berlin, 2011)
6.
7.
V.M. Harik, Ranges of Applicability for the Continuum- Beam Model in the Constitutive Analysis of Carbon Nanotubes: Nanotubes or Nano-beams? (NASA/CR-2001-211013, NASA Langley Research Center) (Hampton, Virginia, 2001)
8.
V.M. Harik, Mechanics of Carbon Nanotubes (A Short Course Notes) (ASME Education Institute, American Society of Mechanical Engineers, New York, 2001)
9.
10.
V.M. Harik, M. Salas (eds.), Trends in Nanoscale Mechanics (Kluwer Academic Publishers, The Netherlands, 2003)
11.
A.N. Cleland, Foundations of Nanomechanics (Springer, Berlin, 2003)
12.
V.M. Harik, L.-S. Luo (eds.), Micromechanics and Nanoscale Effects (Kluwer Academic Publishers, The Netherlands, 2004)
13.
A.N. Kolmogorov, V.H. Crespi, Phys. Rev. Lett. 85(22), 4727 (2000)
14.
K. Liao, S. Li, Appl. Phys. Lett. 79(25), 4225 (2001)
15.
A.N. Kolmogorov, V.H. Crespi, Phys. Rev. B 71, 235415 (2005)
16.
N. Marom, J. Bernstein, J. Garel, A. Tkatchenko, E. Joselevich, L. Kronik, O. Hod, Phys. Rev. Lett. 105, 046801 (2010)
17.
R. Saito, G. Dresselhaus, M.S. Dresselhaus, Physical Properties of Carbon Nanotubes (Imperial College Press, London, 1998)CrossRef
13.
S.J.V. Frankland, A. Caglar, D.W. Brenner, M. Griebel, J. Phys. Chem. B 106, 3046 (2002)CrossRef
19.
S.J.V. Frankland, V.M. Harik, Surf. Sci. Lett. 525, L103 (2003)
20.
S.J.V. Frankland, V.M. Harik, Mat. Res. Soc. Symp. Proc. 733 E, T6.2.1 (2002)
21.
V.M. Harik, R.A. Cairncross, Mech. Mater. 32, 807 (2000)
22.
S.J.V. Frankland, V.M. Harik, Mat. Res. Soc. Symp. Proc. 740, I12.1.1 (2002)
23.
V.M. Harik, Mechanics of Carbon Nanotubes (Nanodesigns Press, Newark, Delaware, 2011)
24.
B.N.J. Persson, Sliding Friction: Physical Principles and Applications (Springer, Berlin, 1999)
25.
B.N.J. Persson, Surf. Sci. Reports, 33, 83 (1999)
26.
Q.Y. Li, K.-S. Kim, Proc. Roy. Soc. A 464, 1319 (2008)
27.
28.
P. Tangney, M.L. Cohen, S.G. Louie, Phys. Rev. Lett. 97(19), 195901 (2006)
29.
X.H. Zhang, G.E. Santoro, U. Tartaglino, E. Tosatti, Phys. Rev. Lett. 102(12), 125502 (2009)
30.
M.J. Yang, V. Koutsos, M. Zaiser, J. Phys. Chem. B 109, 10009 (2005)
31.
Q.B. Zheng, Q.Z. Xue, K.Y. Yan, L.Z. Hao, Q. Li, X.L. Gao, J. Phys. Chem. C 111, 4628 (2007)
32.
M. Foroutan, A.T. Nasrabadi, J. Phys. Chem. B 114, 5320 (2010)
33.
J. Krim, A. Widom, Phys. Rev. B 38, 12184 (1998)
34.
C. Daly, J. Krim, Phys. Rev. Lett. 76, 803 (1996)
35.
S. Morita, S. Fujisawa, Y. Sugawara, Surf. Sci. Reports 23, 1 (1996)
36.
S. Okita, M. Ishikawa, K. Miura, Surf. Sci. 442, L959 (1999)
37.
M.R. Falvo, R.M. Taylor, A. Helser, V. Chi, F.P. Brooks, S. Washburn, S. Superfine, Nature 397, 236 (1999)CrossRef
38.
H.D. Wagner, O. Lourie, Y. Feldman, R. Tenne, Appl. Phys. Lett. 72, 188 (1998)
39.
P.M. Ajayan, L.S. Schadler, C. Giannaris, A. Rubio, Adv. Mater. 12, 750 (1998)
40.
A.H. Barber, S.R. Cohen, H.D. Wagner, Phys. Rev. Lett. 92, 186103 (2004)
41.
A. Kis, K. Jensen, S. Aloni, W. Mickelson, A. Zettl, Phys. Rev. Lett. 97(2), 025501 (2006)
42.
B. Bhushan, J. Phys.: Condens. Matter. 20, 365214 (2008)
43.
J. Servantie, P. Gaspard, Phys. Rev. Lett. 91, 185503 (2003)
44.
J. Servantie, P. Gaspard, Phys. Rev. B 73, 125428 (2006)
45.
Z. Xia, W.A. Curtin, Phys. Rev. B 69, 233408 (2004)
46.
L. Li, Z.H. Xia, W.A. Curtin, Y.Q. Yang, Am. Ceram. Soc. 92(10), 2331 (2009)
47.
A. Garg, S.B. Sinnott, Chem. Phys. Lett. 295, 273 (1998)
48.
S.-J. Heo, S.B. Sinnott, J. Appl. Phys. 102, 064307 (2007)
49.
50.
M.S. Dresselhaus, P.C. Eklund, Adv. Phys. 49(6), 705 (2000)
51.
E. MacCurdy (ed.), The Notebooks of Leonardo Da Vinci (Konecky and Konecky printing, Duckworth & Co., London, 1906)
Metadata
Title
Nanomechanics of Graphene Sheets
Author
Vasyl Harik
Copyright Year
2014
Publisher
Springer Netherlands
Book
Trends in Nanoscale Mechanics

Print ISBN: 978-94-017-9262-2

Electronic ISBN: 978-94-017-9263-9

Copyright Year: 2014

DOI
https://doi.org/10.1007/978-94-017-9263-9_6

Premium Partners

    Image Credits