By Hari Singh Nalwa, Foreword by Richard E. Smalley
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Additional info for Encyclopedia of Nanoscience and Nanotechnology Volume 7
However, it opens the question of the actual wall thickness of an SWNT. At molecular-length scales, it may not be reasonable to characterize the thickness of an SWNT with the lattice spacing of MWNTs or the c-axis spacing of graphite. Consequently, the use of an elastic modulus such as E, which is, by deﬁnition, normalized to a classically deﬁned cross-sectional area, may have little meaning in that a well-deﬁned value for the NT cross-sectional area does not exist. More recently, several groups working on this problem from a simulation or theoretical perspective have stated results only in terms of the product aE to avoid the ambiguity inherent in applying a classical “wall thickness” to a structure of single-atom thickness [99–100].
HFM phase maps (10 m × 10 m scans) for tip and sample vibrations below (left) and above (right) threshold amplitude, respectively, for polymer/Al test structure. The dark regions are polymeric plugs in an Al ﬁeld. The structure was fabricated using IC processing. The reduced contrast for the polymeric regions correspond to an increase in the viscoelasticity compared to the Al. 33 Nanomechanics of Nanoscale Materials (n,0) – zig-zag ) (n,m tor vec ma2 na1 a2 a1 ( n, n) cha rm –a ir Figure 16. Schematic diagram outlining how a 2-D graphite sheet is “rolled” to form a nanotube.
Reported relatively large sample-to-sample variations of modulus measured using this method . 0x10 Time (sec) Figure 8. Experimental ultrasonic tip-deﬂection curves obtained from aluminum (upper curve) and polymer (lower curve) surfaces. Arrows denote the onset of tip deﬂection, estimating threshold amplitudes. The ramped modulation envelope for the ultrasonic sample vibration is shown at the bottom of the ﬁgure. ) In the repulsive regime of the force–displacement curve, S is related to the reduced Young’s modulus of the tip and the sample.
Encyclopedia of Nanoscience and Nanotechnology Volume 7 by Hari Singh Nalwa, Foreword by Richard E. Smalley