The NN group was the first to report on a reliable and practical method for the measurement of the elastic moduli of nanofilaments ( nanotubes, nanowires, nanobundle) by Atomic Force Microscopy (AFM) [1, 2]. The method involves depositing individual nanofilaments over holes or trenches, and then to deflect the suspended structures vertically using an AFM cantilever. Once deposited, the adhesion of a nanotube on the substrate is much stronger than the normal force applicable by the AFM cantilever, so the suspended nanotube is modeled as a doubly clamped beam (suspended length L of the tube) of circular and uniform cross section (diameter D). The Young´s modulus is calculated from the midpoint deflection δ of the tube and the loading force F. The procedure is illustrated below:

AFM image of the nanotube suspended over a hole. .of a suspended nanotube. The measured deflection on varying loading force is plotted

From the slope pf the F-δ relation the  Young’s modulus E is calculated.

We have  studied the mechanical properties of numerous nanofilaments including inorganic materials like MoS2, V2O5 etc. [3, 4].  In the case of composite nanostructures, not only the Young´s modulus, but the shear modulus G was also extracted like it is shown in the case of single-walled carbon nanotube (SWNT) bundle.

For arc-discharge MWNTs the Young modulus was found to be close to 1 TPa. For the SWNTs beyond the very high E, a shear modulus G of roughly 5 GPa was also extracted from the measurements.

The low shear modulus is disadvantegeous in the case of composite preparation with SWNTs bundles as reinforcment fibers. We have shown that under electron beam irradiation of carbon nanotube ropes, their mechanical properties can be dramatically improved due to intertube bridging [5, 6]. Furthermore, we have studied the mechanical properties of carbon nanotubes as a function of their diameter. The strong decrease of E with increasing diameter suggested a metastable state of the catalyst particle during the carbon nanotubes growth by CCVD [7].
This method works also for the characterization of the mechanical properties of biological structures like microtubules [8,10] or intermediate filaments [9] composants of the cytoskeleton.


[1] J.P. Salvetat, A.J. Kulik, J.M. Bonard, G.A.D. Briggs, T. Stockli, K. Metenier, S. Bonnamy, F. Beguin, N. A. Burnham and L. Forró, Adv. Mat. 11, 161 (1999).
[2] J.P. Salvetat, G.A.D. Briggs, J.M. Bonard, R.R. Bacsa, A.J. Kulik, T. Stöckli, N.A. Burnham and L. Forró, Phys. Rev. Lett. 82, 944 (1999).
[3] A. Kis, D. Mihailovic, M. Remskar, A. Mrzel, A. Jesih, I. Piwonski, A.J. Kulik, W. Benoit and L. Forro, Adv. Mater. 15, 733 (2003).
[4] B. Sipos, M. Duchamp, A. Magrez, L. Forró, N. Barisic, A. Kis, J.W. Seo, F. Bieri, F. Krumeich, R. Nesper and G.R. Patzke, J. Appl. Phys., 105, 074317 (2009).
[5] A. Kis, G. Csanyi, J.P. Salvetat, T.N. Lee, E. Couteau, A.J. Kulik, W. Benoit, J. Brugger and L. Forro, Nat. Mater. 3, 153 (2004).
[6] M. Duchamp, R. Meunier, R. Smajda, M. Mionic, A. Magrez, JW. Seo, L. Forró, Bo Song, D. Tománek, J. Appl. Phys. 108, 084314 (2010).
[7] K.M. Lee, B. Lukic, A. Magrez, J.W. Seo, G.A.D. Briggs, A.J. Kulik, and L. Forró, Nano Lett. 7, 1598 (2007).
[8] A. Kis, S. Kasas, B. Babic, A.J. Kulik, W. Benoit, G.A.D. Briggs, C. Schonenberger, S. Catsicas and L. Forró, Phys. Rev. Lett, 89, 248101 (2002).
[9] C. Guzman, S. Jeney, L. Kreplak, S. Kasas, A.J. Kulik, U. Aebi, L. Forró, J. Mol. Biol. 360, 623 (2006).
[10] A. Kis, S. Kasas, A. Kulik, S. Catsicas, L. Forró, Langmuir, 24. 6176 (2008).