Journal of Materials Science

, Volume 50, Issue 7, pp 2973–2983 | Cite as

A 2D percolation-based model for characterizing the piezoresistivity of carbon nanotube-based films

  • Bo Mi Lee
  • Kenneth J. Loh
Original Paper


Carbon nanotubes (CNTs) have attracted considerable attention due to their unique electrical, mechanical, and electromechanical properties. In particular, thin films formed by embedding CNTs in polymer matrices have been shown to exhibit strain-sensitive electromechanical properties, which can serve as an alternative to traditional strain sensors. Although numerous experimental studies have characterized their electrical properties and piezoresistivity, it remains unclear as to what nano-scale mechanisms dominate to govern nanocomposite electromechanical properties. Therefore, the objective of this study is to create a two-dimensional (2D) percolation-based numerical model to understand the electrical and coupled electromechanical behavior of CNT-based thin films. First, a percolation-based model with randomly dispersed straight nanotubes was generated. Second, the percolation and unstrained electrical properties of the model were evaluated as a function of CNT density and length. Next, uniaxial tensile–compressive strains were applied to the model for characterizing their electromechanical response and piezoresistivity. In addition, the effects of different intrinsic strain sensitivities of individual nanotubes were also considered. The results showed that bulk film strain sensitivity was strongly related to CNT density, length, and its intrinsic strain sensitivity. In particular, it was found that strain sensitivity decreased with increasing CNT density. While these strain sensitivity trends were consistent for different intrinsic CNT gage factors, the results were more complicated near the percolation threshold. These results were also compared to other experimental research so as to understand how different nano-scale parameters propagate and affect bulk film response.


Percolation Threshold Strain Sensitivity Gage Factor Electromechanical Property Bulk Film 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The authors thank the U.S. National Science Foundation (NSF), under Grant number CMMI-CAREER 1253564, for the support of this research.


  1. 1.
    Coleman JN, Khan U, Gun’ko YK (2006) Mechanical reinforcement of polymers using carbon nanotubes. Adv Mater 18:689–706CrossRefGoogle Scholar
  2. 2.
    Tsukagoshi K, Yoneya N, Uryu S, Aoyagi Y, Kanda A, Ootuka Y, Alphenaar BW (2002) Carbon nanotube devices for nanoelectronics. Physica B 323:107–114CrossRefGoogle Scholar
  3. 3.
    Baughman RH, Zakhidov AA, de Heer WA (2002) Carbon nanotubes-the route toward applications. Science 297:787–792CrossRefGoogle Scholar
  4. 4.
    De Volder MFL, Tawfick SH, Baughman RH, Hart AJ (2013) Carbon nanotubes: present and future commercial applications. Science 339:535–539CrossRefGoogle Scholar
  5. 5.
    Javey A, Guo J, Wang Q, Lundstrom M, Dai H (2003) Ballistic carbon nanotube field-effect transistors. Nature 424:654–657CrossRefGoogle Scholar
  6. 6.
    Bandaru PR (2007) Electrical properties and applications of carbon nanotube structures. J Nanosci Nanotechnol 7:1–29CrossRefGoogle Scholar
  7. 7.
    Tombler TW, Zhou C, Alexseyev L, Kong J, Dai H, Liu L, Jayanthi CS, Tang M, Wu S-Y (2000) Reversible electromechanical characteristics of carbon nanotubes under local-probe manipulation. Nature 405:769–772CrossRefGoogle Scholar
  8. 8.
    Li QW, Li Y, Zhang XF, Chikkannanavar SB, Zhao YH, Dangelewicz AM, Zheng LX, Doorn SK, Jia QX, Peterson DE, Arendt PN, Zhu YT (2007) Structure-dependent electrical properties of carbon nanotube fibers. Adv Mater 19:3358–3363CrossRefGoogle Scholar
  9. 9.
    Vaisman L, Wagner HD, Marom G (2006) The role of surfactants in dispersion of carbon nanotubes. Adv Colloid Interface Sci 128–130:37–46CrossRefGoogle Scholar
  10. 10.
    Loh KJ-H (2008) Development of multifunctional carbon nanotube nanocomposite sensors for structural health monitoring. PhD Dissertation, University of MichiganGoogle Scholar
  11. 11.
    Breuer O, Sundararaj U (2004) Big returns from small fibers: a review of polymer/carbon nanotube composites. Polym Compos 25:630–645CrossRefGoogle Scholar
  12. 12.
    Blanco J, García EJ, Guzmán de Villoria R, Wardle BL (2009) Limiting mechanisms of mode I interlaminar toughening of composites reinforced with aligned carbon nanotubes. J Compos Mater 43:825–841CrossRefGoogle Scholar
  13. 13.
    Gojny FH, Wichmann MHG, Köpke U, Fiedler B, Schulte K (2004) Carbon nanotube-reinforced epoxy-composites: enhanced stiffness and fracture toughness at low nanotube content. Compos Sci Technol 64:2363–2371CrossRefGoogle Scholar
  14. 14.
    Qian D, Dickey EC, Andrews R, Rantell T (2000) Load transfer and deformation mechanisms in carbon nanotube-polystyrene composites. Appl Phys Lett 76:2868–2870CrossRefGoogle Scholar
  15. 15.
    Dharap P, Li Z, Nagarajaiah S, Barrera EV (2004) Nanotube film based on single-wall carbon nanotubes for strain sensing. Nanotechnol 15:379–382CrossRefGoogle Scholar
  16. 16.
    Li Z, Dharap P, Nagarajaiah S, Barrera EV, Kim JD (2004) Carbon nanotube film sensors. Adv Mater 16:640–643CrossRefGoogle Scholar
  17. 17.
    Kang I, Schulz MJ, Kim JH, Shanov V, Shi D (2006) A carbon nanotube strain sensor for structural health monitoring. Smart Mater Struct 15:737–748CrossRefGoogle Scholar
  18. 18.
    Loh KJ, Kim J, Lynch JP, Kam NWS, Kotov NA (2007) Multifunctional layer-by-layer carbon nanotube–polyelectrolyte thin films for strain and corrosion sensing. Smart Mater Struct 16:429–438CrossRefGoogle Scholar
  19. 19.
    Loh KJ, Lynch JP, Shim BS, Kotov NA (2008) Tailoring piezoresistive sensitivity of multilayer carbon nanotube composite strain sensors. JIMSS 19:747–764Google Scholar
  20. 20.
    Pham GT, Park YB, Liang Z, Zhang C, Wang B (2008) Processing and modeling of conductive thermoplastic/carbon nanotube films for strain sensing. Compos B 39:209–216CrossRefGoogle Scholar
  21. 21.
    Park M, Kim H, Youngblood JP (2008) Strain-dependent electrical resistance of multi-walled carbon nanotube/polymer composite films. Nanotechnol 19:055705CrossRefGoogle Scholar
  22. 22.
    Loyola B, La Saponara V, Loh KJ (2010) In situ strain monitoring of fiber-reinforced polymers using embedded piezoresistive nanocomposites. JMSC 45:6786–6798. doi: 10.1007/s10853-010-4775-y Google Scholar
  23. 23.
    Kumar S, Murthy JY, Alam MA (2005) Percolating conduction in finite nanotube networks. Phys Rev Lett 95:066802CrossRefGoogle Scholar
  24. 24.
    Behnam A, Ural A (2007) Computational study of geometry-dependent resistivity scaling in single-walled carbon nanotube films. Phys Rev B 75:125432CrossRefGoogle Scholar
  25. 25.
    Li C, Thostenson ET, Chou T-W (2008) Effect of nanotube waviness on the electrical conductivity of carbon nanotube-based composites. Compos Sci Technol 68:1445–1452CrossRefGoogle Scholar
  26. 26.
    Du F, Fischer JE, Winey KI (2005) Effect of nanotube alignment on percolation conductivity in carbon nanotube/polymer composites. Phys Rev B 72:121404CrossRefGoogle Scholar
  27. 27.
    Bao WS, Meguid SA, Zhu ZH, Meguid MJ (2011) Modeling electrical conductivities of nanocomposites with aligned carbon nanotubes. Nanotechnol 22:485704CrossRefGoogle Scholar
  28. 28.
    Hu N, Karube Y, Yan C, Masuda Z, Fukunaga H (2008) Tunneling effect in a polymer/carbon nanotube nanocomposite strain sensor. Acta Mater 56:2929–2936CrossRefGoogle Scholar
  29. 29.
    Hu N, Karube Y, Arai M, Watanabe T, Yan C, Li Y, Liu Y, Fukunaga H (2010) Investigation on sensitivity of a polymer/carbon nanotube composite strain sensor. Carbon 48:680–687CrossRefGoogle Scholar
  30. 30.
    Rahman R, Servati P (2012) Effects of inter-tube distance and alignment on tunnelling resistance and strain sensitivity of nanotube/polymer composite films. Nanotechnol 23:055703CrossRefGoogle Scholar
  31. 31.
    Amini A, Bahreyni B (2012) Behavioral model for electrical response and strain sensitivity of nanotube-based nanocomposite materials. J Vac Sci Technol B 30(2):022001CrossRefGoogle Scholar
  32. 32.
    Wang Z, Ye X (2013) A numerical investigation on piezoresistive behaviour of carbon nanotube/polymer composites: mechanism and optimizing principle. Nanotechnol 24:265704CrossRefGoogle Scholar
  33. 33.
    Stampfer C, Jungen A, Linderman R, Obergfell D, Roth S, Hierold C (2006) Nano-electromechanical displacement sensing based on single-walled carbon nanotubes. Nano Lett 6:1449–1453CrossRefGoogle Scholar
  34. 34.
    Cullinan MA, Culpepper ML (2010) Carbon nanotubes as piezoresistive microelectromechanical sensors: theory and experiment. Phys Rev B 82:115428CrossRefGoogle Scholar
  35. 35.
    Broadbent SR, Hammersley JM (1957) Percolation processes. MPCPS 53:629–641Google Scholar
  36. 36.
    Hammersley JM (1957) Percolation processes: lower bounds for the critical probability. Ann Math Stat 28:790–795CrossRefGoogle Scholar
  37. 37.
    Kirkpatrick S (1973) Percolation and conduction. Rev Mod Phys 45:574–588CrossRefGoogle Scholar
  38. 38.
    Lee BM, Loh KJ, Burton A, Loyola BR (2014) Modeling the electromechanical and strain response of carbon nanotube-based nanocomposites. Paper presented at the SPIE, San DiegoGoogle Scholar
  39. 39.
    Odegard G (2009) Multiscale modeling of nanocomposite materials. In: Farahmand B (ed) Virtual testing and predictive modeling. Springer, New York, pp 221–245. doi: 10.1007/978-0-387-95924-5_8Google Scholar
  40. 40.
    Harper LT, Qian C, Turner TA, Li S, Warrior NA (2012) Representative volume elements for discontinuous carbon fibre composites—Part 1: boundary conditions. Compos Sci Technol 72:225–234CrossRefGoogle Scholar
  41. 41.
    Kanit T, Forest S, Galliet I, Mounoury V, Jeulin D (2003) Determination of the size of the representative volume element for random composites: statistical and numerical approach. IJSS 40:3647–3679Google Scholar
  42. 42.
    Hill R (1963) Elastic properties of reinforced solids: some theoretical principles. J Mech Phys Solids 11:357–372CrossRefGoogle Scholar
  43. 43.
    Alamusi, Hu N, Fukunaga H, Atobe S, Liu Y, Li J (2011) Piezoresistive strain sensors made from carbon nanotubes based polymer nanocomposites. Sensors 11:10691–10723CrossRefGoogle Scholar
  44. 44.
    Berhan L, Sastry AM (2007) Modeling percolation in high-aspect-ratio fiber systems. I. Soft-core versus hard-core models. Phys Rev E 75:041120CrossRefGoogle Scholar
  45. 45.
    McEuen PL, Park JY (2004) Electron transport in single-walled carbon nanotubes. MRS Bull 29:272–275CrossRefGoogle Scholar
  46. 46.
    Fuhrer MS, Nygård J, Shih L, Forero M, Yoon Y-G, Mazzoni MSC, Choi HJ, Ihm J, Louie SG, Zettl A, McEuen PL (2000) Crossed nanotube junctions. Science 288:494–497CrossRefGoogle Scholar
  47. 47.
    Nirmalraj PN, Lyons PE, De S, Coleman JN, Boland JJ (2009) Electrical connectivity in single-walled carbon nanotube networks. Nano Lett 9:3890–3895CrossRefGoogle Scholar
  48. 48.
    Jang H-S, Lee Y-H, Na H-J, Nahm SH (2008) Variation in electrical resistance versus strain of an individual multiwalled carbon nanotube. JAP 104(11):114304Google Scholar
  49. 49.
    Cao J, Wang Q, Dai H (2003) Electromechanical properties of metallic, quasimetallic, and semiconducting carbon nanotubes under stretching. Phys Rev Lett 90:157601CrossRefGoogle Scholar
  50. 50.
    Zeng X, Xu X, Shenai PM, Kovalev E, Baudot C, Mathews N, Zhao Y (2011) Characteristics of the electrical percolation in carbon nanotubes/polymer nanocomposites. J Phys Chem C 115:21685–21690CrossRefGoogle Scholar
  51. 51.
    Bauhofer W, Kovacs JZ (2009) A review and analysis of electrical percolation in carbon nanotube polymer composites. Compos Sci Technol 69:1486–1498CrossRefGoogle Scholar
  52. 52.
    Lee D, Hong HP, Lee CJ, Park CW, Min NK (2011) Microfabrication and characterization of spray-coated single-wall carbon nanotube film strain gauges. Nanotechnol 22:455301CrossRefGoogle Scholar
  53. 53.
    Li X, Levy C, Elaadil L (2008) Multiwalled carbon nanotube film for strain sensing. Nanotechnol 19:045501CrossRefGoogle Scholar
  54. 54.
    Jang JE, Cha SN, Choi Y, Amaratunga Gehan AJ, Kang DJ, Hasko DG, Jung JE, Kim JM (2005) Nanoelectromechanical switches with vertically aligned carbon nanotubes. Appl Phys Lett 87:163114Google Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Department of Civil & Environmental EngineeringUniversity of CaliforniaDavisUSA

Personalised recommendations