摘 要
　　奈米碳管可視為空間中的構架結構，而相應的構架元素之截面參數可透過分子結構力學法求得。本論文基於連體力學的觀點，研究不同結構下，奈米碳管的振動行為。內容包含對兩種不同結構的奈米碳管之靜態分析，以及在不同邊界條件下的自然振動頻率及其相應振型的探討，最後將奈米碳管應用於感測原子力的元件上，探討此微小結構作為原子力顯微鏡探針懸臂樑與傳統探針之差異。
　　本篇論文所使用的方法可對不同螺旋性的奈米碳管分別做討論，經數值模擬的結果顯示，在不同結構下碳管的靜態反應及動態行為會有所不同；在應用為原子力顯微鏡探針懸臂樑的探討上，自然振動頻率高的奈米碳管會有較大的頻率偏移量，並因其有優良的撓曲性及較高的自然頻率，雜訊量會比傳統探針小很多。

Abstract
　　This thesis presents a structural mechanics approach to modeling vibrational behaviors of carbon nanotubes. The tube wall is treated as frame-like structures and simulated by the molecular-structural-mechanics method. The analyses of static and vibrational behaviors of carbon nanotubes under different helicity are discussed. In addition, we applied carbon nanotube as the cantilever of the atomic force microscope probe and discussed the difference between carbon nanotube cantilever and conventional probe.
　　Numerical simulations show that the static and vibrational behaviors of carbon nanotubes are affected by their helicity. Nanotube cantilever as atomic force microscopy probe has higher frequency shift the conventional AFM cantilevers. Further more, it has smaller value of noise than that of conventional probe, because it exhibits superior flexibility and higher natural frequencies.

參考文獻

[ 1]Saito, S., Dresselhaus, D., and Dresselhaus, M.S., Physical Properties of Carbon Nanotubes, Imperical College Press, London (1998).

[ 2]Iijima, S., Brabec, C., Maiti, A., and Bernholc, J., “Structural flexibility of carbon nanotubes,” Journal of Chemical Physics, Vol.104, pp.2089-2092 (1996).

[ 3]Yakobson, B.I., Campbell, M.P., Brabec, C.J., and Bernholc, J., “High strain rate fracture and C-chain unraveling in carbon nanotubes,” Computational Materials Science, Vol.8, pp.341-348 (1997).

[ 4]Hernandez, E., Goze, C., Bernier, P., and Rubio, A., “Elastic properties of C and BxCyNz composite nanotubes,” Physical Review Letters, Vol.80, pp.4502-4505 (1998).

[ 5]Sanchez-Portal, D. et al., “Ab initio structural, elastic, and vibrational properties of carbon nanotubes,” Physical Review B, Vol.59, pp.12678- 12688 (1999).

[ 6]Tersoff, J., “Energies of fullerenes,” Physical Review B, Vol.46, pp.15546-15549 (1992).

[ 7]Yakobson, B.I., Brabec, C.J., and Bernholc, J., “Nanomechanics of carbon tubes: instabilities beyond linear range,” Physical Review Letters, Vol.76, pp.2511-2514 (1996).

[ 8]Ru, C.Q., “Effective bending stiffness of carbon nanotubes,” Physical Review B, Vol.62, pp.9973-9976 (2000).

[ 9]Ru, C.Q., “Elastic buckling of single-walled carbon nanotube ropes under high pressure,” Physical Review B, Vol.62, pp.10405-10408 (2000).

[10]Li, C., and Chou, T.W., “A structural mechanics approach for the analysis of carbon nanotubes,” International Journal of Solids and Structures Vol.40 pp.2487-2499 (2003).

[11]Li, C., and Chou, T.W., “Single-walled carbon nanotubes as ultrahigh frequency nanomechanical resonators,” Physical Review B, Vol.68, pp.073405 (2003).

[12]De Los Santos, H.J., Introduction to Microelectromechanical Microwave Systems, Artech House Publishers, London (1999).

[13]Wong, E.W., Sheehan, P.E., and Lieber, C.M., “Nanobeam mechanics: elasticity, strength, and toughness of nanorods and nanotubes,” Science, Vol.277, pp.1971-1975 (1997).

[14]Poncharal, P., Wang, Z.L., Ugarte, D., and de Heer, W.A., “Electrostatic deflections and electromechanical resonances of carbon nanotubes,” Science Vol.283, pp.1513-1516 (1999).

[15]Baughman, R.H., Cui, C., Zakhidov, A.A., Iqbal, Z., Barisci, N., Spinks, G.M., Wallace, G.G., Mazzoldi, A., Rossi, D.D., Rinzler, A.G., Jaschinski, O., Roth, S., and Kertesz, M., “Carbon nanotubes actuators,” Science, Vol. 284, pp.1340-1344 (1999).

[16]Craighead, H.G., “Nanoelectromechanical systems,” Science, Vol. 290, pp.1532-1535 (2000).

[17]Zheng, Q., and Jiang, Q., “Multiwalled carbon nanotubes as gigahertz oscillators,” Physical Review Letters, Vol. 88, pp. 045503 (2002).

[18]Iijima, S., “Helical microtubules of graphitic carbon,” Nature, Vol. 354, pp.56-58 (1991).

[19]Service, R.F., “Materials science: Superstrong nanotubes show they are smart, too,” Science, Vol. 281, pp.940-942 (1998).

[20]Kratschmer, W., Lamb, L.D., Fostiropulos, K., and Huffman, D.R., “Solid C60: A new form of carbon,” Nature, Vol. 347, pp.354-358 (1990).

[21]Iijima. S., and Ichihashi. T., “Single-shell carbon nanotubes of 1-nm diameter,” Nature, Vol. 363, pp.603-605 (1993).

[22]Bethune, D.S., Kiang, C.H., de Veries, M.S., Gorman, G., Saroy, R., Vazguez, J., and Beyers, R., “Cobalt-catalyzed growth of carbon nanotubes with single-atomic-layer walls,” Nature, Vol. 363, pp.605-607 (1993).

[23]Guo, T., Nikolaev, P., Thess, A., Colbert, D.T., and Smalley, R.E., “Catalytic growth of single-walled nanotubes by laser vaporization,” Chemical Physics Letters, Vol. 243, pp.49-54 (1995).

[24]deHeer, W.A., Chatelain, A., and Ugarte, D., “A carbon nanotube field emission electron source,” Science, Vol. 270, pp.1179-1180 (1995).

[25]Jin, L., Bower, C., and Zhou, O., “Alignment of carbon nanotubes in a polymer matrix by mechanical stretching,” Applied Physics Letters, Vol. 73, pp.1197-1199 (1998).

[26]Liu, C., Fan, Y.Y., Liu, M., Cong, H.T., Cheng, H.M., and Dresselhaus, M.S., “Hydrogen storage in single-walled carbon nanotubes at room temperature,” Science, Vol. 286, pp.1127-1129 (1999).

[27]Nagy, G., Levy, M., and Scarmozzino, R., et al., “Carbon nanotube tipped atomic force microscopy for measurement of <100nm etch morphology on semiconductors,” Applied Physics Letters, Vol. 73, pp.529-531 (1998).

[28]Machida, K., Principles of Molecular Mechanics, Kodansha and John Wiley & Sons Co-publication, Tokyo (1999).

[29]Rappe, A.K., Casewit, C.J., Colwell, K.S., et al., “UFF, A full periodic-table force-field for molecular mechanics and molecular dynamics simulations,” Journal of American Chemical Society, Vol.114, pp.10024-10035 (1992).

[30]Gelin, B.R., Molecular Modeling of Polymer Structures and Properties, Hanser/Gardner Publishers, Cincinnati (1994).

[31]Cornell, W.D., Cieplak, P., and Bayly, C.I., et al., “A second generation force-field for the simulation of proteins, nucleic-acids, and organic-molecules,” Journal of American Chemical Society, Vol. 117, pp.5179-5197 (1995).

[32]Dresselhaus, M.S., Dresselhaus, G., and Saito, R., “Physics of carbon nanotubes,” Carbon, Vol. 33, pp.883 (1995).

[33]Kelly, B.T., Physics of Graphite, Applied Science, London (1981).

[34]Popov, V.N., Van Doren, V.E., and Balkanski, M., “Elastic properties of single-walled carbon nanotubes,” Physical Review B, Vol. 61, pp.3078-3084 (2000).

[35]Li, C., and Chou, T.W., “Vibrational behaviors of multiwalled carbon nanotube based nanomechanical resonators,” Applied Physics Letters, Vol. 84, pp.121-123 (2003).

[36]Lennard-Jones, J.E., “The determination of molecular fields: from the variation of the viscosity of a gas with temperature,” Proc Roy Soc, Vol. 106A, pp.441 (1924).

[37]Girifalco, L.A., and Weizer, V.G., “Application of the Morse potential function to cubic metals,” Physical Review, Vol. 114, No. 3, pp.687-690 (1959).

[38]Hölscher, H., Schwarz, U.D., and Wiesendanger, R., “Calculation of the frequency shift in dynamic force microscopy,” Applied Surface Science, Vol. 140, pp.344-351 (1999).

[39]Giessibl, F.J., Bielefeldt, H., Hembacher. S., and Mannhart. J., “Calculation of the optimal imaging parameters for frequency modulation atomic force microscopy,” Applied Surface Science, Vol. 140, pp.352-357 (1999).

[40]Giessibl, F.J., “Forces and frequency shifts in atomic-resolution dynamic-force microscopy,” Physical Review B, Vol. 56, pp.16010- 16015 (1997).

[41]Albrecht, T.R., Grütter. P., Horne. D., and Rugar. D., “Frequency modulation detection using high-Q cantilevers for enhanced force microscope sensitivity,” Journal of Applied Physics, Vol. 69, pp.668-673 (1991).