Negative stiffness and enhanced damping of individual multiwalled carbon nanotubes

The mechanical instabilities and viscoelastic response of individual multiwalled carbon nanotubes and nanofibers (MWCNTs/Fs) under uniaxial compression are studied with atomic force microscopy. Specific buckling events are evident by regimes of negative stiffness, i.e., marked drops in force with increasing compression. Uniaxial cyclic loading can be repeatedly executed even in initially postbuckled regimes, where the CNTs/Fs display incremental negative stiffness. Increases in mechanical damping of $145\text{–}600\%$ in these initially postbuckled regimes, as compared to the linear prebuckled regimes, are observed. Increased damping is attributed to frictional energy dissipation of walls in buckled configurations of the MWCNTs/Fs. This represents the extension of the concept of negative stiffness to the scale of nanostructures and opens up possibilities for designing nanocomposites with high stiffness and high damping simultaneously.

Figure 1

(Color online) (a) AFM-MWCNT configurations (schemes I and II) used in this study, resembling qualitatively the Reuss (series) composite (scheme R) model. Scheme I: AFM tip-mounted MWCNT configuration. Scheme II: AFM tip on AAO-grown MWCNT/F configuration. (b) SEM image of an AFM tip-mounted MWCNT. (c) AFM topographic image of the vertically aligned MWCNT/Fs grown from AAO pores. (d) TEM image of one of these MWCNTs/Fs, showing a thick wall structure and the nickel catalyst at the tip.

Figure 2

(Color online) AFM Axial force versus relative vertical sample displacement and strain. (a) On an AFM tip-mounted MWCNT. (b) On an AAO-grown MWCNT/F. All tests were performed cyclically to large displacements multiple times at room temperature and at $1–2\mathrm{Hz}$.

Figure 3

(Color online) Higher resolution and magnification of cyclic axial loading for scheme II. (a) In the prebuckled regime, the CNT exhibits positive stiffness and the energy dissipation is minimal (negligible hysteresis). (b) In the initial postbuckled, the CNT exhibits negative stiffness regime and the energy dissipation is considerable (large hysteresis). All controlled cyclic loadings were performed within linear regimes, at $\sim 1\mathrm{Hz}$. Purple lines are least-squares curve fits to the raw data points. The insets identify the location of these controlled oscillations with respect to the force-displacement characteristics of Fig. 2a. The mean displacement $d_{\mathrm{av}}$ is $\sim 75\mathrm{nm}$ for (a) and $\sim 227\mathrm{nm}$ for (b).

Figure 4

(Color online) Linear viscoelastic properties of the AFM tip-mounted MWCNT (scheme I). (a) Absolute values of the storage and loss moduli (multiplied by the cross-sectional area) at different average sample displacements $d_{\mathrm{av}}$ in both prebuckled and initial postbuckled regimes. The inset shows the absolute value of $\tan \delta$ at different average sample displacements $d_{\mathrm{av}}$. Marked increases in $\tan \delta$ and the moduli are observed immediately after buckling. (b) Energy dissipation per cycle at various strain amplitudes in both the prebuckled (brown) and initial postbuckled (purple) regimes. More energy is dissipated in the initial postbuckled negative stiffness regime than in the prebuckled positive stiffness regime at roughly the same strain amplitudes (green boxed region). Error bars are within the size of the symbols for certain data points.

Figure 5

(Color online) Viscoelastic properties of the AFM tip on an AAO-grown MWCNT/F (scheme II). (a) Absolute values of storage and loss moduli (multiplied by the cross-sectional area) at different displacements $d_{\mathrm{av}}$ in both prebuckled and initial postbuckled regimes. The inset shows the absolute value of $\tan \delta$ at different average sample displacements $d_{\mathrm{av}}$. Once again, marked increases in $\tan \delta$ and moduli are observed immediately after buckling. (b) Energy dissipation per cycle at various strain amplitudes in both the prebuckled (brown) and initial postbuckled (purple) regimes. More energy is dissipated in the initial postbuckled negative stiffness regime than in the prebuckled positive stiffness regime at the same strain amplitudes (green boxed region). However, percentage increases are less than those for the AFM tip-mounted MWCNT. Error bars are all within the size of the symbols.