Defect-related hysteresis in nanotube-based nano-electromechanical systems
© Tsetseris and Pantelides; licensee Springer. 2011
Received: 18 December 2010
Accepted: 22 March 2011
Published: 22 March 2011
The electronic properties of multi-walled carbon nanotubes (MWCNTs) depend on the positions of their walls with respect to neighboring shells. This fact can enable several applications of MWCNTs as nano-electromechanical systems (NEMS). In this article, we report the findings of a first-principles study on the stability and dynamics of point defects in double-walled carbon nanotubes (DWCNTs) and their role in the response of the host systems under inter-tube displacement. Key defect-related effects, namely, sudden energy changes and hysteresis, are identified, and their relevance to a host of MWCNT-based NEMS is highlighted. The results also demonstrate the dependence of these effects on defect clustering and chirality of DWCNT shells.
The presence of point defects, namely, vacancies and self-interstitials (SI), in modern carbonbased nano-materials has been the subject of intense research investigations [1–5]. These defects correspond to high-energy configurations which are not energetically favorable under thermal equilibrium. Nonetheless, they can be formed as metastable structures because of non-equilibrium conditions during growth or under irradiation. Though they are typically harmful to device performance, control over their formation can lead to defect engineering of novel structures with enhanced functionalities.
One particular class of materials where point defects are expected to play an important role are nano-electromechanical systems (NEMS) that are based on multi-walled carbon nanotubes (MWCNTs) [6–12]. The relative displacement of MWCNT shells causes variation in the overlap of electronic states associated with neighboring tubes and change MWCNT properties. This fact, combined with the ultra-low friction for inter-shell displacement in the so-called incommensurate MWCNTs, has opened the way for a host of proposals toward novel MWCNT-based NEMS, such as nano-motors , nano-switches , or GHz oscillators [10–12].
For many types of vacancy and SI configurations, structural properties resemble those described in previous extended studies [13, 14] for their counterparts on single-walled carbon nanotubes (SWC-NTs). The possibility, however, of defect-induced linking of vicinal tubes is a key difference between MWCNTs and SWCNTs and gives rise to important features in the dynamics of defects in the former systems. Evidence for the role of point defects has appeared in experiments [15–18] and molecular dynamics simulations [19–24]. Distinct defect-related features that have been discussed in past computational studies are the mechanical load transfer and oscillation damping in MWCNT-based NEMS [19–24]. Recently, we discussed  other important effects associated with point defects in MWCNTs. In particular, we identified the atomic-scale mechanisms that induce hysteresis and energy dissipation in NEMS-related response of double-walled carbon nanotubes (DWCNTs) with zig-zag moving shells.
In this article, we report the results of ab initio calculations that explore additional key aspects of defect dynamics in DWCNTs. First, we address the possibility of defect clustering and its effect on NEMS-related response of the zig-zag DWCNTs. We find that formation of defect complexes is energetically favorable and limits hysteresis during inter-tube displacement of DWCNTs. Second, we analyze the stability of point defects in arm-chair DWCNTs and their response during inter-tube sliding or inter-tube rotation. We find that hysteresis is a common tract for zig-zag and arm-chair DWCNTs, but its relative importance differs for sliding and rotation in these two classes of nano-materials. Overall, the results show that the chirality of MWCNT shells and the interactions between defects are the key factors for the employment of these systems in NEMS applications.
The results presented in this article are based on the first-principles density-functional theory calculations. We used a plane wave basis with an energy cutoff of 300 eV, and ultrasoft-pseudopotentials  for the interactions between valence electrons and the ionic cores, as implemented in the code VASP . The exchange and correlation effects were described with a local-density approximation  functional. Large supercells were employed to ensure convergence of total energy differences with respect to the size of the periodic simulation box. In particular, the results presented in this article for a (9,0)@(18,0) DWCNT are based on supercells with 144 (288) atoms in the inner (outer) tube. The corresponding numbers for the (6,6)@(11,11) DWCNTs are 144 and 264 for the inner and outer shells, respectively.
Results and discussion
As for SIs, clustering is energetically favorable also for vacancies. The lowest-energy structure is the di-vacancy on the inner (9,0) shell. The energy of a di-vacancy on the outer (18,0) tube is 0.8 eV higher, while the vacancy-induced inter-tube bridge formation increases the energy by more than 5.5 eV. The results of Figure 3 show that the presence of the di-vacancy affects the response of the (9,0)@(18,0) DWCNT under inter-tube sliding in a similar way as SI pairs. In particular, the formation of the di-vacancy does not introduce any hysteretic effects, but limits corrugation by about 0.24 eV.
The energy curves of Figures 5 and 6 share some key features, namely sudden changes and hysteresis, with the corresponding diagrams for energy variation  during inter-tube sliding and rotation in zig-zag DWCNTs. There are, however, also important differences between the two types of nanotubes. In particular, the energy corrugation during inter-shell sliding is significant for a (9,0)@(18,0) DWCNT with no defects or with vacancies, but small in the case of the (6,6)@(111,11) DWCNT. Moreover, as we noted above, the (6,6)@(11,11) SI defect moves along with the inner-tube during rotation, but stays at the same site during sliding. The reverse is true for a (9,0)@(18,0) DWCNT defect under sliding and rotation.
Owing to the SI-related effects described above, the performance of many types of MWCNT-based NEMS may degrade in the presence of even small numbers of defects. Nevertheless, there also scenarios in which the defects can enable new features. For example, because of the sudden drops in energy during inter-tube displacement, the inter-shell bridges may be used to convert the mechanical energy supplied for sliding or rotation to thermal energy. Given that carbon nanotubes have high thermal conductivity, this excess thermal energy can be transferred to the other end of the nanotube and, thus, cause local heating of restricted spots.
In summary, we showed using the first-principles calculations that defect formation can lead to the appearance of inter-tube bridges and significant hysteretic effects in MWCNT during inter-tube displacement. The extent of these effects, however, depends strongly on the chirality of nanotube shells, and on the creation of defect complexes, which favors elimination of the inter-shell links.
double-walled carbon nanotube
multi-walled carbon nanotube
single-walled carbon nanotube.
The study was supported by the McMinn Endowment at Vanderbilt University and by Grant No HDTRA 1-10-10016. The calculations were performed at ORNL's Center for Computational Sciences.
- Orlikowski D, Buongiorno Nardelli M, Bernholc J, Roland C: Ad-dimers on strained carbon nanotubes: A new route for quantum dot formation? Phys Rev Lett 1999, 83: 4132. 10.1103/PhysRevLett.83.4132View ArticleGoogle Scholar
- Telling RH, Ewels CP, El-Barbary AA, Heggie MI: Wigner defects bridge the graphite gap. Nat Mater 2003, 2: 333. 10.1038/nmat876View ArticleGoogle Scholar
- Krasheninnikov AV, Nordlund K: Ion and electron irradiation-induced effects in nanostruc-tured materials. J Appl Phys 2010, 107: 071301. 10.1063/1.3318261View ArticleGoogle Scholar
- Tsetseris L, Pantelides ST: Adatom complexes and self-healing mechanisms on graphene and single-wall carbon nanotubes. Carbon 2009, 47: 901. 10.1016/j.carbon.2008.12.002View ArticleGoogle Scholar
- Tsetseris L, Pantelides ST: Adsorbate-induced defect formation and annihilation on graphene and single-walled carbon nanotubes. J Phys Chem B 2009, 113: 941. 10.1021/jp809228pView ArticleGoogle Scholar
- Lozovik YE, Minogin AV, Popov AM: Nanomachines based on carbon nanotubes. Phys Lett A 2003, 313: 112. 10.1016/S0375-9601(03)00649-2View ArticleGoogle Scholar
- Bourlon B, Glattli DC, Miko C, Forro L, Bachtold A: Carbon nanotube based bearing for rotational motions. Nano Lett 2004, 4: 709. 10.1021/nl035217gView ArticleGoogle Scholar
- Bailey SWD, Amanatidis I, Lambert CJ: Carbon nanotube electron windmills: A novel design for nanomotors. Phys Rev Lett 2008, 100: 256802. 10.1103/PhysRevLett.100.256802View ArticleGoogle Scholar
- Deshpande VV, Chiu HY, Postma HWC, Miko C, Forro L, Bockrath M: Carbon nanotube linear bearing nanoswitches. Nano Lett 2006, 6: 1092. 10.1021/nl052513fView ArticleGoogle Scholar
- Zheng Q, Jiang Q: Multiwalled carbon nanotubes as gigahertz oscillators. Phys Rev Lett 2002, 88: 045503. 10.1103/PhysRevLett.88.045503View ArticleGoogle Scholar
- Legoas SB, Coluci VR, Braga SF, Coura PZ, Dantas SO, Galvao DS: Molecular-dynamics simulations of carbon nanotubes as gigahertz oscillators. Phys Rev Lett 2005, 90: 055504. 10.1103/PhysRevLett.90.055504View ArticleGoogle Scholar
- Rivera JL, McCabe C, Cummings PT: Oscillatory behavior of double-walled nanotubes under extension: A simple nanoscale damped spring. Nano Lett 2003, 3: 1001. 10.1021/nl034171oView ArticleGoogle Scholar
- Krasheninnikov AV, Nordlund K, Lehtinen PO, Foster AS, Ayuela A, Nieminen RM: Adsorption and migration of carbon adatoms on zigzag carbon nanotubes. Carbon 2004, 42: 1021. 10.1016/j.carbon.2003.12.025View ArticleGoogle Scholar
- Krasheninnikov AV, Lehtinen PO, Foster AS, Nieminen RM: Bending the rules: Contrasting vacancy energetics and migration in graphite and carbon nanotubes. Chem Phys Lett 2006, 418: 132. 10.1016/j.cplett.2005.10.106View ArticleGoogle Scholar
- Kolmogorov AN, Crespi VH: Smoothest bearings: Interlayer sliding in multiwalled carbon nanotubes. Phys Rev Lett 2000, 85: 4727. 10.1103/PhysRevLett.85.4727View ArticleGoogle Scholar
- Peng B, Locascio M, Zapol P, Li S, Mielke SL, Schatz GC, Espinosa HD: Measurements of near-ultimate strength for multiwalled carbon nanotubes and irradiation-induced crosslinking improvements. it Nat Nanotechnol 2008, 3: 626. 10.1038/nnano.2008.211View ArticleGoogle Scholar
- Kis A, Jensen K, Aloni S, Mickelson W, Zettl A: Interlayer forces and ultralow sliding friction in multiwalled carbon nanotubes. Phys Rev Lett 2006, 97: 025501. 10.1103/PhysRevLett.97.025501View ArticleGoogle Scholar
- Papadakis SJ, Hall AR, Williams PA, Vicci L, Falvo MR, Superfine R, Washburn S: Resonant oscillators with carbon-nanotube torsion springs. Phys Rev Lett 2004, 93: 146101. 10.1103/PhysRevLett.93.146101View ArticleGoogle Scholar
- Huhtala M, Krasheninnikov AV, Aittonieni J, Stuart SJ, Nordlund K, Kaski K: Improved mechanical load transfer between shells of multiwalled carbon nanotubes. Phys Rev B 2004, 70: 045404. 10.1103/PhysRevB.70.045404View ArticleGoogle Scholar
- Xia Z, Curtin WA: Pullout forces and friction in multiwall carbon nanotubes. Phys Rev B 2004, 69: 233408. 10.1103/PhysRevB.69.233408View ArticleGoogle Scholar
- Guo W, Zhong W, Dai Y, Li S: Coupled defect-size effects on interlayer friction in multiwalled carbon nanotubes. Phys Rev B 2005, 72: 075409. 10.1103/PhysRevB.72.075409View ArticleGoogle Scholar
- Wong LH, Zhao Y, Chen GH, Chwang AT: Grooving the carbon nanotube oscillators. Appl Phys Lett 2006, 88: 183107. 10.1063/1.2199471View ArticleGoogle Scholar
- Liu P, Gao HJ, Zhang YW: Effect of defects on oscillation characteristics and instability of carbon nanotube-based oscillators. Appl Phys Lett 2008, 93: 083107. 10.1063/1.2976127View ArticleGoogle Scholar
- Lebedeva IV, Knizhnik AA, Popov AM, Lozovik YE, Potapkin BV: Dissipation and fluctuations in nanoelectromechanical systems based on carbon nanotubes. Nanotechnology 2009, 20: 105202. 10.1088/0957-4484/20/10/105202View ArticleGoogle Scholar
- Tsetseris L, Pantelides ST: Defect formation and hysteretic inter-tube displacement in multi-wall carbon nanotubes. Carbon 2011, 49: 581. 10.1016/j.carbon.2010.09.061View ArticleGoogle Scholar
- Vanderbilt D: Soft self-consistent pseudopotentials in a generalized eigenvalue formalism. Phys Rev B 1990, 41: 7892. 10.1103/PhysRevB.41.7892View ArticleGoogle Scholar
- Kresse G, Furthmuller J: Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys Rev B 1996, 54: 11169. 10.1103/PhysRevB.54.11169View ArticleGoogle Scholar
- Perdew JP, Zunger A: Self-interaction correction to density-functional approximations for many-electron systems. Phys Rev B 1981, 23: 5048. 10.1103/PhysRevB.23.5048View ArticleGoogle Scholar
- Mills G, Jónsson H, Schenter GK: Reversible work transition-state theory - application to dissociative adsorption of hydrogen. Surf Sci 1995, 324: 305. 10.1016/0039-6028(94)00731-4View ArticleGoogle Scholar
- Tsetseris L, Kalfagiannis N, Logothetidis S, Pantelides ST: Role of N defects on thermally induced atomic-scale structural changes in transition-metal nitrides. Phys Rev Lett 2007, 99: 125503. 10.1103/PhysRevLett.99.125503View ArticleGoogle Scholar
- Tsetseris L, Pantelides ST: Vacancies, interstitials and their complexes in titanium carbide. Acta Mater 2008, 56: 2864. 10.1016/j.actamat.2008.02.020View ArticleGoogle Scholar
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