Henrik Jackman

Measurements of the critical strain for rippling in carbon nanotubes

We report measurements of the bending stiffness in free standing carbon nanotubes, using atomic force microscopy inside a scanning electron microscope. Two regimes with different bending stiffness were observed, indicative of a rippling deformation at high curvatures. The observed critical strains for rippling were in the order of a few percent and comparable to previous modeling predictions. We have also found indications that the presence of defects can give a higher critical strain value and a concomitant reduction in Young’s modulus.

Mechanical behavior of carbon nanotubes in the rippled and buckled phase

We have studied the mechanical behavior of multi-walled carbon nanotubes for bending strains beyond the onset for rippling and buckling. We found a characteristic drop in the bending stiffness at the rippling and buckling onset and the relative retained stiffness was dependent on the nanotube dimensions and crystallinity. Thin tubes are more prone to buckle, where some lose all of their bending stiffness, while thicker tubes are more prone to ripple and on average retain about 20% of their bending stiffness. In defect rich tubes, the bending stiffness is very low prior to rippling, but these tubes retain up to 70% of their initial bending stiffness.

Direct measurement of bending stiffness and estimation of Young's modulus of vertically aligned carbon nanofibers

The bending stiffness of individual, as-grown, vertically aligned carbon nanofibers was measured using a custom-built atomic force microscope placed inside a scanning electron microscope. The internal structure of the nanofiber was best modeled as dual-phase, composed of an inner graphitic core covered with a tapered amorphous carbon shell. It was found that the fibers have a relatively low bending stiffness, with Youngs modulus values of about 10 GPa for the inner core and 65 GPa for the outer shell. The low Youngs modulus of the inner core is attributed to a non-zero angle between the graphitic sheets and the nanofiber axis. The weak shear modulus between graphitic sheets thereby dominates the mechanical behaviour of the fibers.

Image formation mechanisms in scanning electron microscopy of carbon nanotubes, and retrieval of their intrinsic dimensions.

We present a detailed analysis of the image formation mechanisms that are involved in the imaging of carbon nanotubes with scanning electron microscopy (SEM). We show how SEM images can be modelled by accounting for surface enhancement effects together with the absorption coefficient for secondary electrons, and the electron-probe shape. Images can then be deconvoluted, enabling retrieval of the intrinsic nanotube dimensions. Accurate estimates of their dimensions can thereby be obtained even for structures that are comparable to the electron-probe size (on the order of 2 nm). We also present a simple and robust model for obtaining the outer diameter of nanotubes without any detailed knowledge about the electron-probe shape.

Large variations in the onset of rippling in concentric nanotubes

We present a detailed experimental study of the onset of rippling in highly crystalline carbon nanotubes. Modeling has shown that there should be a material constant, called the critical length, describing the dependence of the critical strain on the nanotube outer radius. Surprisingly, we have found very large variations, by a factor of three, in the critical length. We attribute this to a supporting effect from the inner walls in multiwalled concentric nanotubes. We provide an analytical expression for the maximum deflection prior to rippling, which is an important design consideration in nanoelectromechanical systems utilizing nanotubes.