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Nanomechanics of Graphene Sheets

Registry Matrix Analysis and Interfacial Sliding

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Trends in Nanoscale Mechanics

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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.

Dr. V. Harik, f. ICASE Staff Scientist at the NASA Langley Research Center (Hampton, VA), Principal Scientist at Nanodesign Consulting, author of a monograph and a short course entitled “Mechanics of Carbon Nanotubes” © (2001) presented at the Annual ASME Congress (2001 and 2004) and a co-editor of Kluwer volumes: “Trends in Nanoscale Mechanics” (2003) and “Micromechanics and Nanoscale Effects” (2004).

Nanodesigns Consulting is a 2004 spin-off from the NASA Langley Research Center, Hampton, Virginia. Its Staff consulted for the Princeton-based NASA-funded URETI Institute for Nanostructured Bio-inspired Materials (http://bimat.org), National Institute of Aerospace (Hampton, VA), University Space Research Association (USRA) and NASA NAIC (Atlanta, GA). Nanodesigns Consulting also works on safety of nanotechnology.

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Notes

  1. 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. 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. 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. 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. 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. 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.”

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    Vasyl Harik

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    Vasyl Harik

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Harik, V. (2014). Nanomechanics of Graphene Sheets. In: Harik, V. (eds) Trends in Nanoscale Mechanics. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-9263-9_6

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

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