0
Research Papers

Interlayer Attraction Force in Concentric Carbon Nanotubes

[+] Author and Article Information
Hai Zhou

Shanghai Institute of Applied Mathematics and Mechanics,
Shanghai Key Laboratory of Mechanics in Energy Engineering,
Shanghai University,
Shanghai 200072, China
e-mail: zhouhaiasme@outlook.com

Jiantao Leng

Shanghai Institute of Applied Mathematics and Mechanics,
Shanghai Key Laboratory of Mechanics in Energy Engineering,
Shanghai University,
Shanghai 200072, China
e-mail: jtleng@foxmail.com

Zhengrong Guo

Shanghai Institute of Applied Mathematics and Mechanics,
Shanghai Key Laboratory of Mechanics in Energy Engineering,
Shanghai University,
Shanghai 200072, China
e-mail: guozhengrong@shu.edu.cn

Jianxin Li

State Key Laboratory of Ocean Engineering,
School of Naval Architecture,
Ocean and Civil Engineering,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: jianxin.li@sjtu.edu.cn

Zhanlei Huo

Shanghai Institute of Applied Mathematics and Mechanics,
Shanghai Key Laboratory of Mechanics in Energy Engineering,
Shanghai University,
Shanghai 200072, China
e-mail: Huozhanlei@shu.edu.cn

Jiaxing Qu

State Key Laboratory of Ocean Engineering,
School of Naval Architecture,
Ocean and Civil Engineering,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: qujiaxing@sjtu.edu.cn

Tienchong Chang

Shanghai Institute of Applied Mathematics and Mechanics,
Shanghai Key Laboratory of Mechanics in Energy Engineering,
Shanghai University,
Shanghai 200072, China
e-mail: tchang@staff.shu.edu.cn

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the Journal of Applied Mechanics. Manuscript received May 5, 2019; final manuscript received May 26, 2019; published online June 10, 2019. Assoc. Editor: Yonggang Huang.

J. Appl. Mech 86(9), 091004 (Jun 10, 2019) (6 pages) Paper No: JAM-19-1222; doi: 10.1115/1.4043890 History: Received May 05, 2019; Accepted May 26, 2019

The interlayer attraction force between concentric carbon nanotubes (CNTs) plays an important role in CNT-based nanodevices. However, the precise measurement of the interlayer attraction force remains to date a challenge. Although theoretical investigations have identified the dependence of the interlayer attraction force on the tube radius, no explicit relation for such dependence has been established so far. Here, based on an analytical model, we find that the interlayer attraction force between two telescoping concentric CNTs is proportional to the mean (but not the inner nor the outer) radius of the contacting two tubes and consequently propose an explicit expression that relates the interlayer attraction force with the mean radius as well as the interlayer spacing. We also implement the effect of temperature in the present expression based on the linear dependence of the attraction force on temperature. The present expression can be compared with the existing theoretical and experimental results, offering an efficient way to evaluate the interlayer attraction force in the nanodevices composed of concentric CNTs.

FIGURES IN THIS ARTICLE
<>
Copyright © 2019 by ASME
Your Session has timed out. Please sign back in to continue.

References

Iijima, S., 1991, “Helical Microtubules of Graphitic Carbon,” Nature, 354(6348), pp. 56–58. [CrossRef]
Novoselov, K. S., Geim, A. K., Morozov, S. V., Jiang, D., Zhang, Y., Dubonos, S. V., Grigorieva, I. V., and Firsov, A. A., 2004, “Electric Field Effect in Atomically Thin Carbon Films,” Science, 306(5696), p. 666. [CrossRef] [PubMed]
Dai, H., Hafner, J. H., Rinzler, A. G., Colbert, D. T., and Smalley, R. E., 1996, “Nanotubes as Nanoprobes in Scanning Probe Microscopy,” Nature, 384(6605), pp. 147–150. [CrossRef]
Moore, K. E., Tune, D. D., and Flavel, B. S., 2015, “Double-Walled Carbon Nanotube Processing,” Adv. Mater., 27(20), pp. 3105–3137. [CrossRef] [PubMed]
Maslov, L., 2006, “Concept of Nonvolatile Memory Based on Multiwall Carbon Nanotubes,” Nanotechnology, 17(10), pp. 2475–2482. [CrossRef] [PubMed]
Bunch, J. S., Verbridge, S. S., Alden, J. S., van der Zande, A. M., Parpia, J. M., Craighead, H. G., and McEuen, P. L., 2008, “Impermeable Atomic Membranes From Graphene Sheets,” Nano Lett., 8(8), pp. 2458–2462. [CrossRef] [PubMed]
Koenig, S. P., Boddeti, N. G., Dunn, M. L., and Bunch, J. S., 2011, “Ultrastrong Adhesion of Graphene Membranes,” Nat. Nanotechnol., 6(9), pp. 543–546. [CrossRef] [PubMed]
Fang, H., and Xu, J., 2013, “Stick-Slip Effect in a Vibration-Driven System With Dry Friction: Sliding Bifurcations and Optimization,” ASME J. Appl. Mech., 81(5), p. 051001. [CrossRef]
Feng, X., Kwon, S., Park, J. Y., and Salmeron, M., 2013, “Superlubric Sliding of Graphene Nanoflakes on Graphene,” ACS Nano, 7(2), pp. 1718–1724. [CrossRef] [PubMed]
Luo, M., Zhang, Z., and Yakobson, B. I., 2013, “Tunable Gigahertz Oscillators of Gliding Incommensurate Bilayer Graphene Sheets,” ASME J. Appl. Mech., 80(4), p. 040906. [CrossRef]
Tuzun, R. E., Noid, D. W., and Sumpter, B. G., 1995, “The Dynamics of Molecular Bearings,” Nanotechnology, 6(2), pp. 64–74. [CrossRef]
Damnjanović, M., Milošević, I., Vuković, T., and Sredanović, R., 1999, “Full Symmetry, Optical Activity, and Potentials of Single-Wall and Multiwall Nanotubes,” Phys. Rev. B, 60(4), pp. 2728–2739. [CrossRef]
Papadakis, S. J., Hall, A. R., Williams, P. A., Vicci, L., Falvo, M. R., Superfine, R., and Washburn, S., 2004, “Resonant Oscillators With Carbon-Nanotube Torsion Springs,” Phys. Rev. Lett., 93(14), p. 146101. [CrossRef] [PubMed]
Feng, X. L., White, C. J., Hajimiri, A., and Roukes, M. L., 2008, “A Self-Sustaining Ultrahigh-Frequency Nanoelectromechanical Oscillator,” Nat. Nanotechnol., 3(7), pp. 342–346. [CrossRef] [PubMed]
Ru, C. Q., 2000, “Effect of Van Der Waals Forces on Axial Buckling of a Double-Walled Carbon Nanotube,” J. Appl. Phys., 87(10), pp. 7227–7231. [CrossRef]
Chang, T., Li, G., and Guo, X., 2005, “Elastic Axial Buckling of Carbon Nanotubes Via a Molecular Mechanics Model,” Carbon, 43(2), pp. 287–294. [CrossRef]
Liew, K. M., Wong, C. H., He, X. Q., Tan, M. J., and Meguid, S. A., 2004, “Nanomechanics of Single and Multiwalled Carbon Nanotubes,” Phys. Rev. B, 69(11), p. 115429. [CrossRef]
Chang, T., 2008, “Dominoes in Carbon Nanotubes,” Phys. Rev. Lett., 101(17), p. 175501. [CrossRef] [PubMed]
Cheng, Y., Maria Pugno, N., Shi, X., Chen, B., and Gao, H., 2013, “Surface Energy-Controlled Self-Collapse of Carbon Nanotube Bundles With Large and Reversible Volumetric Deformation,” ASME J. Appl. Mech., 80(4), p. 040902. [CrossRef]
Zheng, Q., and Liu, Z., 2014, “Experimental Advances in Superlubricity,” Friction, 2(2), pp. 182–192. [CrossRef]
Guo, W., Yin, J., Qiu, H., Guo, Y., Wu, H., and Xue, M., 2014, “Friction of Low-Dimensional Nanomaterial Systems,” Friction, 2(3), pp. 209–225. [CrossRef]
Kis, A., and Zettl, A., 2008, “Nanomechanics of Carbon Nanotubes,” Philos. T. Roy. Soc. A, 366(1870), pp. 1591–1611. [CrossRef]
Zhang, S., Ma, T., Erdemir, A., and Li, Q., 2018, “Tribology of Two-Dimensional Materials: From Mechanisms to Modulating Strategies,” Mater. Today. in press.
Kolmogorov, A. N., and Crespi, V. H., 2000, “Smoothest Bearings: Interlayer Sliding in Multiwalled Carbon Nanotubes,” Phys. Rev. Lett. 85(22), pp. 4727–4730. [CrossRef] [PubMed]
Yu, M.-F., Lourie, O., Dyer, M. J., Moloni, K., Kelly, T. F., and Ruoff, R. S., 2000, “Strength and Breaking Mechanism of Multiwalled Carbon Nanotubes Under Tensile Load,” Science, 287(5453), p. 637. [CrossRef] [PubMed]
Cumings, J., and Zettl, A., 2000, “Low-Friction Nanoscale Linear Bearing Realized From Multiwall Carbon Nanotubes,” Science, 289(5479), p. 602. [CrossRef] [PubMed]
Zheng, Q., and Jiang, Q., 2002, “Multiwalled Carbon Nanotubes as Gigahertz Oscillators,” Phys. Rev. Lett., 88(4), p. 045503. [CrossRef] [PubMed]
Jensen, K., Girit, Ç, Mickelson, W., and Zettl, A., 2006, “Tunable Nanoresonators Constructed From Telescoping Nanotubes,” Phys. Rev. Lett., 96(21), p. 215503. [CrossRef] [PubMed]
Cumings, J., and Zettl, A., 2004, “Localization and Nonlinear Resistance in Telescopically Extended Nanotubes,” Phys. Rev. Lett., 93(8), p. 086801. [CrossRef] [PubMed]
Deshpande, V. V., Chiu, H. Y., Postma, H. W. C., Mikó, C., Forró, L., and Bockrath, M., 2006, “Carbon Nanotube Linear Bearing Nanoswitches,” Nano Lett., 6(6), pp. 1092–1095. [CrossRef] [PubMed]
Leng, J., Guo, Z., Zhang, H., Chang, T., Guo, X., and Gao, H., 2016, “Negative Thermophoresis in Concentric Carbon Nanotube Nanodevices,” Nano Lett., 16(10), pp. 6396–6402. [CrossRef] [PubMed]
Girifalco, L. A., and Lad, R. A., 1956, “Energy of Cohesion, Compressibility, and the Potential Energy Functions of the Graphite System,” J. Chem. Phys., 25(4), pp. 693–697. [CrossRef]
Kis, A., Jensen, K., Aloni, S., Mickelson, W., and Zettl, A., 2006, “Interlayer Forces and Ultralow Sliding Friction in Multiwalled Carbon Nanotubes,” Phys. Rev. Lett., 97(2), p. 025501. [CrossRef] [PubMed]
Moore, K. E., Cretu, O., Mitome, M., and Golberg, D., 2016, “In Situ Cyclic Telescoping of Multi-Walled Carbon Nanotubes in a Transmission Electron Microscope,” Carbon, 107, pp. 225–232. [CrossRef]
Zhang, R., Ning, Z., Xu, Z., Zhang, Y., Xie, H., Ding, F., Chen, Q., Zhang, Q., Qian, W., Cui, Y., and Wei, F., 2016, “Interwall Friction and Sliding Behavior of Centimeters Long Double-Walled Carbon Nanotubes,” Nano Lett., 16(2), pp. 1367–1374. [CrossRef] [PubMed]
Jiang, L. Y., Huang, Y., Jiang, H., Ravichandran, G., Gao, H., Hwang, K. C., and Liu, B., 2006, “A Cohesive Law for Carbon Nanotube/Polymer Interfaces Based on the Van Der Waals Force,” J. Mech. Phys. Solids, 54(11), pp. 2436–2452. [CrossRef]
Liu, P., Zhang, Y. W., and Lu, C., 2006, “Analysis of the Oscillatory Behavior of Double-Walled Carbon Nanotube-Based Oscillators,” Carbon, 44(1), pp. 27–36. [CrossRef]
Zhao, J., Jiang, J.-W., Jia, Y., Guo, W., and Rabczuk, T., 2013, “A Theoretical Analysis of Cohesive Energy Between Carbon Nanotubes, Graphene and Substrates,” Carbon, 57, pp. 108–119. [CrossRef]
Hill, J. M., Thamwattana, N., and Cox, B. J., 2007, “Mechanics of Atoms and Fullerenes in Single-Walled Carbon Nanotubes. I. Acceptance and Suction Energies,” Proc. R. Soc. A, 463(2078), pp. 461–476. [CrossRef]
Zhu, C., Chen, Y., Liu, R., and Zhao, J., 2018, “Buckling Behaviors of Single-Walled Carbon Nanotubes Inserted With a Linear Carbon-Atom Chain,” Nanotechnology, 29(33), p. 335704. [CrossRef] [PubMed]
Plimpton, S., 1995, “Fast Parallel Algorithms for Short-Range Molecular Dynamics,” J. Comput. Phys., 117(1), pp. 1–19. [CrossRef]
Brenner, D. W., Shenderova, O. A., Harrison, J. A., Stuart, S. J., Ni, B., and Sinnott, S. B., 2002, “A Second-Generation Reactive Empirical Bond Order (REBO) Potential Energy Expression for Hydrocarbons,” J. Phys.: Condens. Matter., 14(4), pp. 783–802. [CrossRef]
Evans, D. J., and Holian, B. L., 1985, “The Nose–Hoover Thermostat,” J. Chem. Phys., 83(8), pp. 4069–4074. [CrossRef]
Bichoutskaia, E., Heggie, M. I., Popov, A. M., and Lozovik, Y. E., 2006, “Interwall Interaction and Elastic Properties of Carbon Nanotubes,” Phys. Rev. B, 73(4), p. 045435. [CrossRef]
Rivera, J. L., McCabe, C., and Cummings, P. T., 2003, “Oscillatory Behavior of Double-Walled Nanotubes Under Extension: A Simple Nanoscale Damped Spring,” Nano Lett., 3(8), pp. 1001–1005. [CrossRef]
Ren, W., Li, F., Chen, J., Bai, S., and Cheng, H.-M., 2002, “Morphology, Diameter Distribution and Raman Scattering Measurements of Double-Walled Carbon Nanotubes Synthesized by Catalytic Decomposition of Methane,” Chem. Phys. Lett., 359(3), pp. 196–202. [CrossRef]
Kharissova, O. V., and Kharisov, B. I., 2014, “Variations of Interlayer Spacing in Carbon Nanotubes,” RSC Adv., 4(58), pp. 30807–30815. [CrossRef]
Legoas, S. B., Coluci, V. R., Braga, S. F., Coura, P. Z., Dantas, S. O., and Galvão, D. S., 2003, “Molecular-Dynamics Simulations of Carbon Nanotubes as Gigahertz Oscillators,” Phys. Rev. Lett., 90(5), p. 055504. [CrossRef] [PubMed]
Legoas, S. B., Coluci, V. R., Braga, S. F., Coura, P. Z., Dantas, S. O., and Galvao, D. S., 2004, “Gigahertz Nanomechanical Oscillators Based on Carbon Nanotubes,” Nanotechnology, 15(4), pp. S184–S189. [CrossRef]
Ansari, R., Sadeghi, F., and Ajori, S., 2017, “Oscillation Characteristics of Carbon Nanotori Molecules Along Carbon Nanotubes Under Various System Parameters,” Eur. J. Mech. A-Solid, 62, pp. 67–79. [CrossRef]
Budrikis, Z., and Zapperi, S., 2016, “Temperature-Dependent Adhesion of Graphene Suspended on a Trench,” Nano Lett., 16(1), pp. 387–391. [CrossRef] [PubMed]
Guo, Z., Zhang, H., Li, J., Leng, J., Zhang, Y., and Chang, T., 2018, “An Intrinsic Energy Conversion Mechanism Via Telescopic Extension and Retraction of Concentric Carbon Nanotubes,” Nanoscale, 10(10), pp. 4897–4903. [CrossRef] [PubMed]
Guo, Z., Chang, T., Guo, X., and Gao, H., 2017, “Gas-like Adhesion of Two-Dimensional Materials Onto Solid Surfaces,” Sci. Rep., 7(1), p. 159. [CrossRef] [PubMed]
Guo, Z., Chang, T., Guo, X., and Gao, H., 2012, “Mechanics of Thermophoretic and Thermally Induced Edge Forces in Carbon Nanotube Nanodevices,” J. Mech. Phys. Solids, 60(9), pp. 1676–1687. [CrossRef]
Guo, Z., Chang, T., Guo, X., and Gao, H., 2011, “Thermal-Induced Edge Barriers and Forces in Interlayer Interaction of Concentric Carbon Nanotubes,” Phys. Rev. Lett., 107(10), p. 105502. [CrossRef] [PubMed]
Li, J., Zhang, H., Guo, Z., Chang, T., and Gao, H., 2015, “Edge Forces in Contacting Graphene Layers,” ASME J. Appl. Mech., 82(10), p. 101011. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Continuum model of a DWCNT with an infinitely long inner tube and a half infinitely long outer tube, where l and L are, respectively, the distances from the origin to a point on the inner tube and a point on the outer tube, R is the radius of the outer tube, r is the radius of the inner tube, w is the circumference of the inner tube section, and t = Rr is the interlayer spacing between the inner and the outer tubes

Grahic Jump Location
Fig. 2

Comparison between the results for the interlayer attraction force from the analytical model, the empirical equation, MD simulations, and those from others: (a) the linear density of the attraction force as a function of the inner tube radius and (b) the attraction force as a function of the mean radius

Grahic Jump Location
Fig. 3

The interlayer attraction force as a function of the interlayer spacing of a DWCNT, with comparison to the results from others. The shaded area represents the range in which the structure of a DWCNT becomes eccentric.

Grahic Jump Location
Fig. 4

Dependence of the linear density of the interlayer attraction force on temperature: (a) the linear density as a function of temperature. The circles represent Fane, the squares represent Fawe, and the lines represent the results from the empirical equation; (b) the attraction force Fane as a function of the mean radius; (c) the attraction force Fawe as a function of the mean radius; and (d) the temperature coefficients.

Grahic Jump Location
Fig. 5

Illustration of the two interlayer attraction forces in DWCNTs at different scenarios: (a) a half infinitely long outer tube and an infinitely long inner tube and (b) a half infinitely long outer tube and a finitely long inner tube

Tables

Errata

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In