Radial compression studies of nanotubes in the elastic regimea)
(A) Scanning electron micrograph of a sample electrode used to trap nanotube. (B) Zoom of (A), width of gap between electrodes is .
(Color online) (A) Typical experimental deformation curve (dots) and the FEA fitting (solid line) for nanotube using a 100 nm radius tip. (B) Comparison of raw data curves of sensor deflection vs vertical movement of the nanotube against the tip with a reference curve on the silicon wafer substrate on a 20 nm diameter nanotube. For consistency and to account for any adhesion forces, unloading curves were used for the analysis.
(Color online) Definitions of the elastic constants used in this work. (A) Definition of the axes in the cylindrical coordinate system, with the directions 1, 2, and 3 corresponding to radial, tangential, and axial, respectively. (B) Zoom of box in (A), showing definition of layers for FEA model, indicating distribution of soft and stiff shells, and the inner core structure. (C) Zoom of unit cell in (B), showing the shear components.
(Color online) (A) Force curves at different lateral positions on a nanotube and representative force curve made on the substrate. Each curve represents an average of over 15 individual curves at same spot. Measurements made on a nanotube with diameter of 20 nm, 3 nm radius tip, and cantilever spring constant . Stiffness evaluated for the different positions from fit to upper 50% of curves: 5.0, 5.5, 5.0, 3.2, and 1.6 N/m for positions 1–5, respectively. (B) AFM micrograph showing the nanotube topography and the measurement positions on the nanotube. Curve on substrate in (A) taken at position far away from the nanotube and free of debris.
Radial modulus (GPa) for the different nanotubes measured using small and large indenters for indentation depth of 15% of nanotube diameter. The value from the analytical model is the input to the FEA measurement. Values in parentheses represent standard deviation for values obtained on the fit for different experimental curves. Between 5 and 10 curves were fit for each case.
Input to the FEA calculations. Values in first two columns were fixed from previous work as noted in text. values for the shells were allowed to vary and best fit required assigning a different value for large and small tips. The values for the soft gap were held constant.
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