Abstract
This chapter reviews basic models and new effects in the still emerging field of Nanoscale Mechanics and one of its essential parts: Mechanics of Carbon Nanotubes . Experiments with carbon nanotubes, theoretical models and modeling (i.e., molecular dynamics simulations), classification of carbon nanotubes into four classes (i.e., thin and thick lattice shells , long high-aspect-ratio nanotubes and beam-like carbon nanotube crystals of small radii) have been reviewed. Classification of carbon nanotubes is important for the safety of nanotechnology and evaluation of health effects. Interfacial sliding of the adjacent lattice shells in the multi wall carbon nanotubes (MWNT) has been discussed along with a nanoscale analog of the Newton’s friction law and the effect of spatial exclusion of electrons (ESEE) at the interface , which effectively can be viewed as a nanoscale analog of the Pauli’s exclusion principle. Examples of lattice waves, i.e., phonons, in carbon nanotubes have been presented. Ranges of applicability of estimates for the effective thickness of carbon nanotubes varying between 0.66 and 3.4 Å have been examined along with their dependence on the balance between the elastic interactions and van der Waals forces.
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Notes
- 1.
Classification of new types of materials is important in any field of science, especially, for the highly promising carbon nanotubes, which can be separated into four distinct classes associated with quite distinct geometric parameters and some similarities with asbestos though.
- 2.
This research results have been first published at NASA and its ICASE Institute; see Harik, V.M., 2001. Ranges of applicability for the continuum-beam model in the constitutive analys is of carbon nanotubes: nanotubes or nano-beams? (NASA/CR-2001-211013, NASA Langley Research Center), Hampton, Virginia, USA. Harik, V.M., 2001. Mechanics of carbon nanotubes © 2001. ASME Education Institute (Notes for a Short Course, a 2002 CD and a 2001 video), American Society of Mechanical Engineers, New York, NY.
- 3.
For more historical perspectives and some epistemological notes about the concepts of emerging Nanoscale Mechanics see author’s footnotes for the references cited in this chapter.
- 4.
Nanoscale homogenization itself and nanoscale homogenization criteria [11, 12], in particular, are very important for the application of continuum concepts (e.g., continuous surface or a properly-defined number of representative volume elements for the volume-averaging for the uniquely-defined material properties of any material having a discrete atomic lattice structure) to the CNT lattice structures (for more details, see the next part of this chapter).
- 5.
V.M. Harik et al. 2002. Applicability of the Continuum-shell Theories to the Mechanics of Carbon Nanotubes. (NASA/CR-2002-211460/ICASE Report No. 2002–2007, ICASE Institute) NASA Langley Research Center, Hampton, Virginia. In this NASA report model applicability map [12] for the continuum shell models has been presented.
- 6.
V.M. Harik, New Trends in Mechanics of Carbon Nanotubes and Applications, Technical Report TR-2012-2, Nanodesigns Consulting, Newark, Delaware, 2012.
- 7.
Initiation of the so called SEE effect is associated with the need of at least one π-electron to overcome the registry potential of an opposing C–C bond and the associated Coulomb repulsion within the so called spatial exclusion zone (SEZ) for electrons. The size of the spatial exclusion zone depends on the local atomic lattice configuration (e.g., orientation of C–C bonds), 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-repulsion for electrons stems from the quantum Pauli principle for the identical electrons, i.e. 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 analog of Pauli repulsion and the quantum Pauli principle for the electrons both affect the precise dimensions of the spatial exclusion zone for interfacial electrons.
- 8.
S. Iijima was awarded the 1996 Nobel Prize in Chemistry for “discovering fullerenes”, which also include carbon nanotubes.
- 9.
V.M. Harik, Mechanics of Carbon Nanotubes © (2001), a short course, the Annual ASME Congress (2001, 2004) and the 2002 Nanosystems Conference (Berkeley, Califormia).
- 10.
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 [76].
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Harik, V. (2014). Mechanics of Carbon Nanotubes. In: Harik, V. (eds) Trends in Nanoscale Mechanics. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-9263-9_2
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