ABSTRACT
Te-Chien Hou, Chin-Hung Liu, and Yu-Lun Chueh Department of Materials Science and Engineering National Tsing Hua University, 101, Sec. 2, Kuang-Fu Road, Hsinchu 30013, Taiwan, People’s Republic of China ylchueh@mx.nthu.edu.tw
to many existing, testing, and measuring techniques due to the following limitations. First, their dimensions (diameter and length) are relatively small so that it is impossible to apply them to well-established testing techniques. Second, the small size of nanotubes or NWs makes their manipulation rather difficult. Thus, new approaches and methodologies must be developed to quantify the properties of these individual nanostructures [1]. The objective of this section is to introduce how to characterize nanomechanical properties based on two experimental methods. Briefly, one is based on dynamic resonance, which uses electric-field-induced resonant excitation; another is to quantify the static axial tensile by stretching the 1D nanostructure using an atomic force microscope (AFM) tip. 23.2.1 Electrostatic Deflections and Electromechanical
Resonances of Carbon NanotubesTransmission electron microscopy (TEM) is a powerful tool for characterizing the materials in atomic scale. Modern TEM is a versatile technique that can provide real-space resolution better than 0.2 nm and also can provide information of quantitative chemical and electronic analysis from a region as small as 1 nm. A powerful and unique approach could be developed if we can integrate the structural information of a nanostructure provided by TEM with the properties measured in situ from the same nanostructure [1]. To carry out the property measurement of a nanotube, a specimen holder for a 100 kV transmission electron microscope was built to apply a voltage across a nanotube and its counterelectrode. This setup is similar to the integration of the scanning probe technique with TEM. The static and dynamic properties of the nanotubes can be obtained by applying an electric field [1]. When a static potential Vs was applied to the wire, the carbon nanotubes that protruded from the fiber became electrically charged and were attracted to the counterelectrode. The nanotubes that were not perpendicular to the counterelectrode bent toward it (Fig. 23.1) [1]. The shape of the dynamically deflected nanotube (which is independent of the force distribution on the nanotube) corresponds to the shape, which is predicted by a resonantly excited cantilevered beam. The frequencies are found from the following equation:
( )2 2 2218j bj Ev D DiLb p r= + (23.1)
Figure 23.1 Electron micrographs of the electromechanical deflections of a carbon nanotube. (a) Uncharged nanotube (Vs = 0), (b) charged nanotube (Vs = 20 V), and (c) measured static deflections as a function of Vs for two nanotubes (solid circles: D = 18 nm, L = 4.6 mm; open circles: D = 41 nm, L = 1.5 mm), showing the quadratic dependence on Vs. Reproduced from Science, 283, pp. 1513-1516 (1999). Copyright © 1999, American Association for the Advancement of Science [2].where D is the outer diameter, Di is the inner diameter, Eb is the elastic modulus, ρ is the density, and bj is a constant for the jth harmonic at b1 = 1.875 and b2 = 4.694. This equation originated from the Bernoulli-Euler analysis of cantilevered elastic beams . If the beam is bent by elongation of the outer arc and a compression
of the inner arc of the bend, Eb can be identified with the Young’s modulus E of the material. Higher modes can be excited, such as the second harmonic of the same nanotube (Fig. 23.1c). The frequency of this vibration is n2 = 3.01 MHz = 5.68 n1. For a uniform cantilevered beam, the theoretical ratio n2/n1 = 6.2. The position of the node in the n2 mode is found at 0.76 L, which is very close to the theoretical value of 0.8 L (Fig. 23.2) [2].
