Research Papers

Wrinkling Instability of Graphene on Substrate-Supported Nanoparticles

[+] Author and Article Information
Shuze Zhu

Department of Mechanical Engineering,
University of Maryland,
College Park, MD 20742

Teng Li

Department of Mechanical Engineering,
University of Maryland,
College Park, MD 20742
e-mail: LiT@umd.edu

1Corresponding author.

Manuscript received December 30, 2013; final manuscript received January 27, 2014; accepted manuscript posted February 20, 2014; published online February 20, 2014. Editor: Yonggang Huang.

J. Appl. Mech 81(6), 061008 (Feb 20, 2014) (5 pages) Paper No: JAM-13-1525; doi: 10.1115/1.4026638 History: Received December 30, 2013; Revised January 27, 2014; Accepted February 20, 2014

Wrinkles in graphene with desirable morphology have practical significance for electronic applications. Here we carry out a systematic molecular dynamics study of the wrinkling instability of graphene on substrate-supported nanoparticles (NPs). At a large NP dispersion distance, a monolayer graphene adheres to the substrate and bulges out locally to wrap around individual NPs, forming isolated dome-shaped protrusions. At a small NP dispersion distance, tunneling wrinkles form in graphene to bridge the NP-induced protrusions. A critical NP dispersion distance for the onset of tunneling wrinkle instability of graphene is determined as a function of the NP size. The prediction from the modeling study agrees well with recent experimental observations. Results from the present study offer further insights into the formation of desirable wrinkles in graphene deposited on a substrate with engineered protrusions and, thus, can potentially enable novel design of graphene-based electronics.

Copyright © 2014 by ASME
Your Session has timed out. Please sign back in to continue.


Geim, A., and Novoselov, K., 2007, “The Rise of Graphene,” Nature Mater., 6(3), pp. 183–191. [CrossRef]
Klimov, N. N., Jung, S., Zhu, S., Li, T., Wright, C. A., Solares, S. D., Newell, D. B., Zhitenev, N. B., and Stroscio, J. A., 2012, “Electromechanical Properties of Graphene Drumheads,” Science, 336(6088), pp. 1557–1561. [CrossRef] [PubMed]
Lee, C., Wei, X., Kysar, J., and Hone, J., 2008, “Measurement of the Elastic Properties and Intrinsic Strength of Monolayer Graphene,” Science, 321(5887), pp. 385–388. [CrossRef] [PubMed]
Fasolino, A., Los, J., and Katsnelson, M., 2007, “Intrinsic Ripples in Graphene,” Nature Mater., 6(11), pp. 858–861. [CrossRef]
Zhu, S., Galginaitis, J., and Li, T., 2012, “Critical Dispersion Distance of Silicon Nanoparticles Intercalated Between Graphene Layers,” J. Nanomater., 2012, p. 375289. [CrossRef]
Li, T., 2011, “Extrinsic Morphology of Graphene,” Modelling Simul. Mater. Sci. Eng., 19(5), p. 054005. [CrossRef]
Kim, K., Lee, Z., Malone, B., Chan, K., Aleman, B., Regan, W., Gannett, W., Crommie, M., Cohen, M., and Zettl, A., 2011, “Multiply Folded Graphene,” Phys. Rev. B, 83(24), p. 245433. [CrossRef]
Patra, N., Wang, B., and Kral, P., 2009, “Nanodroplet Activated and Guided Folding of Graphene Nanostructures,” Nano Lett., 9(11), pp. 3766–3771. [CrossRef] [PubMed]
Zhang, Z., Liu, B., Hwang, K., and Gao, H., 2011, “Surface-Adsorption-Induced Bending Behaviors of Graphene Nanoribbons,” Appl. Phys. Lett., 98(12), p. 121909. [CrossRef]
Xu, R., Wang, Y., Liu, B., and Fang, D., 2013, “Mechanics Interpretation on the Bending Stiffness and Wrinkled Pattern of Graphene,” ASME J. Appl. Mech., 80(4), p. 040910. [CrossRef]
Boddeti, N., Koenig, S., Long, R., Xiao, J., Bunch, J., and Dunn, M., 2013, “Mechanics of Adhered, Pressurized Graphene Blisters,” ASME J. Appl. Mech., 80(4), p. 040909. [CrossRef]
Zhang, Z., and Li, T., 2010, “Carbon Nanotube Initiated Formation of Carbon Nanoscrolls,” Appl. Phys. Lett., 97(8), p. 081909. [CrossRef]
Zhu, S., and Li, T., 2013, “Hydrogenation Enabled Scrolling of Graphene,” J. Phys. D Appl. Phys., 46(7), p. 075301. [CrossRef]
Yu, D., and Liu, F., 2007, “Synthesis of Carbon Nanotubes by Rolling Up Patterned Graphene Nanoribbons Using Selective Atomic Adsorption,” Nano Lett., 7(10), pp. 3046–3050. [CrossRef] [PubMed]
Zhang, Z., and Li, T., 2011, “Ultrafast Nano-Oscillators Based on Interlayer-Bridged Carbon Nanoscrolls,” Nanoscale Res. Lett., 6, p. 470. [CrossRef] [PubMed]
Shi, X., Pugno, N., and Gao, H., 2010, “Tunable Core Size of Carbon Nanoscrolls,” J. Comp. Theor. Nanosci., 7(3), pp. 517–521. [CrossRef]
Xie, X., Ju, L., Feng, X., Sun, Y., Zhou, R., Liu, K., Fan, S., Li, Q., and Jiang, K., 2009, “Controlled Fabrication of High-Quality Carbon Nanoscrolls From Monolayer Graphene,” Nano Lett., 9(7), pp. 2565–2570. [CrossRef] [PubMed]
Braga, S., Coluci, V., Legoas, S., Giro, R., Galvao, D., and Baughman, R., 2004, “Structure and Dynamics of Carbon Nanoscrolls,” Nano Lett., 4(5), pp. 881–884. [CrossRef]
Martins, B., and Galvao, D., 2010, “Curved Graphene Nanoribbons: Structure and Dynamics of Carbon Nanobelts,” Nanotechnology, 21(7), p. 075710. [CrossRef]
Hicks, J., Tejeda, A., Taleb-Ibrahimi, A., Nevius, M., Wang, F., Shepperd, K., Palmer, J., Bertran, F., Le Fevre, P., Kunc, J., de Heer, W., Berger, C., and Conrad, E., 2013, “A Wide-Bandgap Metal-Semiconductor-Metal Nanostructure Made Entirely From Graphene,” Nature Phys., 9(1), pp. 49–54. [CrossRef]
Guo, Y., and Guo, W., 2013, “Electronic and Field Emission Properties of Wrinkled Graphene,” J. Phys. Chem. C, 117(1), pp. 692–696. [CrossRef]
Yan, H., Sun, Y., He, L., Nie, J., and Chan, M., 2012, “Observation of Landau-Level-Like Quantization at 77 K Along a Strained-Induced Graphene Ridge,” Phys. Rev. B, 85(3), p. 035422. [CrossRef]
Yamamoto, M., Pierre-Louis, O., Huang, J., Fuhrer, M., Einstein, T., and Cullen, W., 2012, “‘The Princess and the Pea' at the Nanoscale: Wrinkling and Delamination of Graphene on Nanoparticles,” Phys. Rev. X, 2(4), p. 041018. [CrossRef]
Castro Neto, A., Guinea, F., Peres, N., Novoselov, K., and Geim, A., 2009, “The Electronic Properties of Graphene,” Rev. Mod. Phys., 81(1), pp. 109-162. [CrossRef]
Zhang, Z., and Li, T., 2010, “Graphene Morphology Regulated by Nanowires Patterned in Parallel on a Substrate Surface,” J. Appl. Phys., 107(10), p. 103519. [CrossRef]
Zhang, Z., and Li, T., 2011, “A Molecular Mechanics Study of Morphologic Interaction Between Graphene and Si Nanowires on a SiO2 Substrate,” J. Nanomater., 2011, p. 374018. [CrossRef]
Li, T., and Zhang, Z., 2010, “Snap-Through Instability of Graphene on Substrates,” Nanoscale Res. Lett., 5(1), pp. 169–173. [CrossRef]
Li, T., and Zhang, Z., 2010, “Substrate-Regulated Morphology of Graphene,” J. Phys. D Appl. Phys., 43(7), p. 075303. [CrossRef]
Aitken, Z., and Huang, R., 2010, “Effects of Mismatch Strain and Substrate Surface Corrugation on Morphology of Supported Monolayer Graphene,” J. Appl. Phys., 107(12), p. 123531. [CrossRef]
Scharfenberg, S., Rocklin, D., Chialvo, C., Weaver, R., Goldbart, P., and Mason, N., 2011, “Probing the Mechanical Properties of Graphene Using a Corrugated Elastic Substrate,” Appl. Phys. Lett., 98(9), p. 091908. [CrossRef]
Jiang, L., Huang, Y., Jiang, H., Ravichandran, G., Gao, H., Hwang, K., 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]
Plimpton, S., 1995, “Fast Parallel Algorithms for Short-Range Molecular-Dynamics,” Journal of Computational Physics, 117(1), pp. 1–19. [CrossRef]
Stuart, S., Tutein, A., and Harrison, J., 2000, “A Reactive Potential for Hydrocarbons With Intermolecular Interactions,” J. Chem. Phys., 112(14), pp. 6472–6486. [CrossRef]
Koenig, S., Boddeti, N., Dunn, M., and Bunch, J., 2011, “Ultrastrong Adhesion of Graphene Membranes,” Nature Nanotech., 6(9), pp. 543–546. [CrossRef]
Zong, Z., Chen, C., Dokmeci, M., and Wan, K., 2010, “Direct Measurement of Graphene Adhesion on Silicon Surface by Intercalation of Nanoparticles,” J. Appl. Phys., 107(2), p. 026104. [CrossRef]
Tomori, H., Kanda, A., Goto, H., Ootuka, Y., Tsukagoshi, K., Moriyama, S., Watanabe, E., and Tsuya, D., 2011, “Introducing Nonuniform Strain to Graphene Using Dielectric Nanopillars,” Appl. Phys. Express, 4(7), p. 075102. [CrossRef]
Li, G., Yilmaz, C., An, X., Somu, S., Kar, S., Jung, Y., Busnaina, A., and Wan, K., 2013, “Adhesion of Graphene Sheet on Nano-Patterned Substrates With Nano-Pillar Array,” J. Appl. Phys., 113(24), p. 244303. [CrossRef]
Neek-Amal, M., Covaci, L., and Peeters, F., 2012, “Nanoengineered Nonuniform Strain in Graphene Using Nanopillars,” Phys. Rev. B, 86(4), p. 041405. [CrossRef]


Grahic Jump Location
Fig. 3

(a) MD simulation model. Inset shows the cross-sectional view of the initial configuration. Periodical boundary condition (PBC) is applied in y direction, so that the length of the simulation box along the PBC direction represents the NP dispersion distance S. (b) The typical equilibrium morphology of graphene on a small and isolated NP on the substrate. (c)–(e) Variation of wrinkling morphology of graphene on an isolated NP with increasing size.

Grahic Jump Location
Fig. 2

A schematic of a flat graphene monolayer on a substrate with a separation distance of h

Grahic Jump Location
Fig. 1

(a) Schematics of graphene covering a substrate with dispersed NPs (not to scale). (b) Atomic force microscopy image of the wrinkled morphology of a monolayer graphene covering a SiO2 substrate with dispersed SiO2 NPs. Three representative types of wrinkling morphology (highlighted by red circles) can be observed: (1) wrinkling of graphene on isolated NP; (2) wrinkling of graphene bridging two neighboring NPs; (3) wrinkling of graphene on quasi-isolated NPs. The atomic force microscopy image is reprinted from Ref. 23, under the terms of the Creative Commons Attribution 3.0 License.

Grahic Jump Location
Fig. 4

Wrinkling morphology of graphene on NPs with relatively small dispersion distance. For visual guidance, two periodical images are combined along the PBC direction. For dNP = 2 nm, (a) the two NP-intercalated graphene domes remain isolated when dispersion distance S = 25 nm. (b) A tunneling wrinkle forms between two NPs when S = 21 nm. For dNP = 6 nm, (c) two long tipped wrinkles run in parallel between neighboring NPs and terminate in the middle with a short overlap but their tips remain distinct from each other (inset) when S = 110 nm. (d) When S = 100 nm, a tunneling wrinkle forms between two neighboring NPs.

Grahic Jump Location
Fig. 5

A diagram of the wrinkling instability of graphene morphology on substrate-supported NPs in the space of NP dispersion distance and diameter




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