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完整後設資料紀錄
DC 欄位 | 值 | 語言 |
---|---|---|
dc.contributor.advisor | 金必耀(Bih-Yaw Jin) | |
dc.contributor.author | Chern Chuang | en |
dc.contributor.author | 莊宸 | zh_TW |
dc.date.accessioned | 2021-06-15T04:28:37Z | - |
dc.date.available | 2011-08-20 | |
dc.date.copyright | 2009-08-20 | |
dc.date.issued | 2009 | |
dc.date.submitted | 2009-08-20 | |
dc.identifier.citation | [1] H. W. Kroto, J. R. Heath, S. C. OBrien, R. F. Curl, and R. E. Smalley.
C-60 - Buckyminsterfullerene. Nature, 318(6042):162{163, 1985. [2] S Iijima. Helical microtubules of graphitic carbon. Nature, 354(6348):56{58, NOV 7 1991. [3] A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim. The electronic properties of graphene. Reviews of Modern Physics, 81(1):109, 2009. [4] R. Saito, G. Dresselhaus, and M. S. Dresselhaus. Physical Properties of Carbon Nanotubes. World Scienti‾c Publishing Company, ‾rst edition, 1998. [5] Sigeo Ihara, Satoshi Itoh, and Jun-ichi Kitakami. Toroidal forms of graphitic carbon. Phys. Rev. B, 47(19):12908{12911, May 1993. [6] Satoshi Itoh and Sigeo Ihara. Toroidal forms of graphitic carbon. ii. elongated tori. Phys. Rev. B, 48(11):8323{8328, Sep 1993. [7] X. F. Zhang and Z. Zhang. Polygonal spiral of coil-shaped carbon nanotubes. Phys. Rev. B, 52(7):5313{5317, Aug 1995. 451 452 BIBLIOGRAPHY [8] A. Krishnan1, E. Dujardin, M. M. J. Treacy, J. Hugdahl, S. Lynum, and T. W. Ebbesen. Graphitic cones and the nucleation of curved carbon surfaces. Nature, 388:451{454, Jul 1997. [9] T. Lenosky, X. Gonze, M Teter, and V Elser. Energetics of negatively curved graphitic carbon. Nature, 355:333, 1992. [10] Kazuto Akagi, Ryo Tamura, Masaru Tsukada, Satoshi Itoh, and Sigeo Ihara. Electronic structure of helically coiled cage of graphitic carbon. Phys. Rev. Lett., 74(12):2307{2310, Mar 1995. [11] K. Akagi, R. Tamura, M. Tsukada, S Itoh, and S Ihara. Electronic structure of helically coiled carbon nanotubes: relation between the phason lines and energy band features. Phys. Rev. B, 53:2114, 1996. [12] Florentino Lopez-Urias, Mauricio Terrones, and Humberto Terrones. Electronic properties of giant fullerenes and complex graphitic nanos- tructures with novel morphologies. Chem. Phys. Lett., 381(5-6):683 { 690, 2003. [13] Humberto Terrones and Mauricio Terrones. Quasiperiodic icosahedral graphite sheets and high-genus fullereneswith nonpositive gaussian cur- vature. Phys. Rev. B, 55(15):9969{9974, Apr 1997. [14] JL RicardoChavez, J DorantesDavila, M Terrones, and H Terrones. Electronic properties of fullerenes with nonpositive Gaussian curvature: Finite zeolites. Phys. Rev. B, 56(19):12143{12146, NOV 15 1997. BIBLIOGRAPHY 453 [15] H Terrones and AL Mackay. The geometry of hypothetical curved graphite structures. Carbon, 30(8):1251{1260, 1992. [16] H Terrones and AL Mackay. Triply periodic minimal-surfaces decorated with curved graphite. Chem. Phys. Lett., 207(1):45{50, MAY 14 1993. [17] S. Ihara, S. Itoh, K. Akagi, R. Tamura, and M. Tsukada. Struc- ture of polygonal defects in graphitic carbon sheets. Phys. Rev. B, 54(20):14713{14719, Mar 1996. [18] Ryo Tamura and Masaru Tsukada. Disclinations of monolayer graphite and their electronic states. Phys. Rev. B, 49(11):7697{7708, Mar 1994. [19] S. Lijima, T Ichihashi, and Y Ando. Pentagons, heptagons and negative curvature in graphite microtubule growth. Nature, 356:776, 1992. [20] A. Hashimoto, K. Suenaga, A. Gloter, K. Urita, and S. Iijima. Direct evidence for atomic defects in graphene layers. Nature, 430:870{873, Aug 2004. [21] A. Sarkar, H. W. Kroto, and M. Endo. Hemi-toroidal networks in pyrolytic carbon nanotubes. Carbon, 33(1):51{55, 1995. [22] K. Suenaga, H. Wakabayashi, M. Koshino, Y. Sato, K. Urita, and S. Iijima. Imaging active topological defects in carbon nanotubes. Na- ture Nanotechnology, 2:358{360, May 2007. [23] M. Ahlskoga, E. Seynaevea, R. J. M. Vullersa, C. Van Haesendoncka, A. Fonsecab, K. Hernadib, and J. B. Nagy. Ring formations from 454 BIBLIOGRAPHY catalytically synthesized carbon nanotubes. Chemical Physics Letters, 300:202{206, 1999. [24] Ryo Tamura, Mitsuhiro Ikuta, Toru Hirahara, and Masaru Tsukada. Positive magnetic susceptability in polygonal nanotube tori. Phys. Rev. B, 71(4):045418, Jan 2005. [25] C. C. Tsai, F. L. Shyu, C. W. Chiu, C. P. Chang, R. B. Chen, and M. F. Lin. Magnetization of armchair carbon tori. Phys. Rev. B, 70:075411, 2004. [26] L. Liu, G. Y. Guo, C. S. Jayanthi, and S. Y.Wu. Colossal paramagnetic moments in metallic carbon nanotori. Phys. Rev. Lett., 88:217206, 2002. [27] S. Latil, S. Roche, and A. Rubio. Persistent currents in carbon nan- otube based rings. Phys. Rev. B, 67, 2003. [28] F. L. Shyu. Magneto-optical properties of carbon toroids.. in°uence of geometry and magnetic ‾eld. Phys. Rev. B, 72, 2005. [29] C. G. Rocha, M. Pacheco, Z. Barticevic, and A. Latge. Carbon nan- otube tori under external ‾elds. Phys. Rev. B, 70, 2004. [30] K. Sasaki. Vacuum structure of toroidal carbon nanotubes. Phys. Rev. B, 65, 2002. [31] M. F. Lin. Magnetic properties of toroidal carbon nanotubes. Journal of the Physical Society of Japan, 67, Apr 1998. BIBLIOGRAPHY 455 [32] J. E. Avron and J. Berger. Tiling rules for toroidal molecules. Phys. Rev. A, 51(2):1146{1149, Feb 1995. [33] J. Berger and J. E. Avron. Classi‾cation scheme for toroidal molecules. J. Chem. Soc. Faraday Trans., 91(22):4037{4045, 1995. [34] Satoshi Itoh, Sigeo Ihara, and Jun-ichi Kitakami. Toroidal form of carbon c360. Phys. Rev. B, 47(3):1703{1704, Jan 1993. [35] Satoshi Itoh and Sigeo Ihara. Isomers of the toroidal forms of graphitic carbon. Phys. Rev. B, 49(19):13970{13974, May 1994. [36] R. Setton and N. Setton. Carbon nanotubes.. iii. toroidal structures and limits of a model for the construction of helical and s-shaped nanotubes. Carbon, 35(4):497{505, 1997. [37] B. I. Dunlap. Connecting carbon tubules. Phys. Rev. B, 46(3):1933{ 1936, Jul 1992. [38] A. J. Stone and D. J. Wales. Theoretical studies of icosahedral c60 and some related species. Chem. Phys. Lett., 128:501, 1986. [39] A. Ceulemans, L. F. Chibotaru, and P. W. Fowler. Molecular anapole moments. Phys. Rev. Lett., 80:1861, 1998. [40] I. L¶aszl¶o and A. Rassat. The geometric structure of deformed nan- otubes and the topological coordinates. Journal of Chemical Informa- tion and Computer Science, 43:519{524, 2003. [41] M. Goldberg. A class of multi-symmetric polyhedra. Tohoku Math. J., 43:104{108, 1937. 456 BIBLIOGRAPHY [42] S. Iijima, P. M. Ajayan, and T Ichihashi. Growth model for carbon nanotubes. Phys. Rev. Lett., 69(21):3100{3103, Aug 1992. [43] D. H. Oh, J. M. Park, and K. S. Kim. Structures and electronic prop- erties of small carbon nanotube tori. Phys. Rev. B, 62(3):1600{1603, Apr 2000. [44] A. T. Balaban, editor. From Chemical Topology to Three-Dimensional Geometry. Springer, ‾rst edition, 1997. [45] Chern Chuang, Yuan-Chia Fan, and Bih-Yaw Jin. Generalized classi- ‾cation scheme of toroidal and helical carbon nanotubes. Journal of Chemical Information and Modeling, 49(2):361{368, 2009. [46] H. S. M. Coxeter. A Spectrum of Mathematics. [47] P. W. Fowler. How unusual is c60? magic numbers for carbon clusters. Chem. Phys. Lett., 131(6):444 { 450, 1986. [48] A Maritan, C Micheletti, A Trovato, and JR Banavar. Optimal shapes of compact strings. NATURE, 406(6793):287{290, JUL 20 2000. [49] P. Pieranski and S. Przybyl. Ideal trefoil knot. Phys. Rev. E, 64(3):031801, Aug 2001. [50] E. C. Kirby. On toroidal azulenoids and other shapes of fullerene cage. Fullerene Sci. Technol., 42:395{404, 1994. [51] B. I. Dunlap. Constraints on small graphitic helices. Phys. Rev. B, 50(11):8134{8137, Sep 1994. BIBLIOGRAPHY 457 [52] H Terrones and M Terrones. Fullerenes with non-positive Gaussian cur- vature: holey-balls and holey-tubes. Fullerene Sci. Technol., 6(5):751{ 767, 1998. [53] H Terrones and M Terrones. Fullerenes and nanotubes with non- positive Gaussian curvature. Carbon, 36(5-6):725{730, 1998. [54] H Terrones and A. L. Mackay. Negatively curved graphite and triply periodic minimal-surfaces. J. Math. Chem., 15(1-2):183{195, 1994. [55] D Vanderbilt and J TersoR. Negative-curvature fullerene analog of C60. Phys. Rev. Lett., 68(4):511{513, JAN 27 1992. [56] M Fujita, M Yoshida, and E Osawa. Morphology of new fullerene families with negative curvature. Fullerene Sci. Technol., 3(1):93{105, 1995. [57] H Terrones, J Fayos, and JL Aragon. Geometrical and physical- properties of hypothetical periodic and aperiodic graphitic structures. Acta Metall. Mater., 42(8):2687{2699, AUG 1994. [58] H Terrones. Curved graphite and its mathematical transformations. J. Math. Chem., 15(1-2):143{156, 1994. [59] P. W. Fowler and D. E. Manolopoulos. An Atlas of Fullerenes. Dover Publications, ‾rst edition, 2007. [60] J. M. Romo-Herrera, M. Terrones, H. Terrones, S. Dag, and V. Meu- nier. Covalent 2D and 3D networks from 1D nanostructures: Designing new materials. NANO LETTERS, 7(3):570{576, MAR 2007. 458 BIBLIOGRAPHY [61] Jose M. Romo-Herrera, Mauricio Terrones, Humberto Terrones, and Vincent Meunier. Guiding Electrical Current in Nanotube Circuits Using Structural Defects: A Step Forward in Nanoelectronics. ACS NANO, 2(12):2585{2591, DEC 2008. [62] J. M. Romo-Herrera, M. Terrones, H. Terrones, and Vincent Meunier. Electron transport properties of ordered networks using carbon nan- otubes. NANOTECHNOLOGY, 19(31), AUG 6 2008. [63] AL Mackay and H Terrones. Diamond from graphite. Nature, 352(6338):762, AUG 29 1991. [64] T Lenosky, X Gonze, M Teter, and V Elser. Energetics of negatively curved graphitic carbon. Nature, 355(6358):333{335, JAN 23 1992. [65] SJ Townsend, TJ Lenosky, DA Muller, CS Nichols, and V Elser. Neg- atively curved graphitic sheet model of amorphous-carbon. Phys. Rev. Lett., 69(6):921{924, AUG 10 1992. [66] B. GrAunbaum and G. C. Shephard. Tilings and Patterns. W. H. Free- man and Company, ‾rst edition, 1987. [67] Chern Chuang and Bih-Yaw Jin. Systematics of high-genus fullerenes. J. Chem. Inf. Model., 49(7):1664{1668, 2009. [68] Chern Chuang, Yuan-Chia Fan, and Bih-Yaw Jin. Dual space approach to the classi‾cation of toroidal carbon nanotubes. J. Chem. Inf. Model., 49(7):1679{1686, 2009. BIBLIOGRAPHY 459 [69] P Fowler and T Pisanski. Leapfrog transformations and polyhedra of Clar type. J. Chem. Soc. Faraday Trans., 90(19):2865{2871, OCT 7 1994. [70] J. F. Stoddart. The master of chemical topology. Chem. Soc. Rev., 38:1521{1529, 2009. [71] D. Bonchev and D. R. Rouvray, editors. Chemical Topology: Appli- cations and Techniques. Gordon and Breach Science Publishers, ‾rst edition, 2000. [72] C. C. Adams, editor. The Knot Book. Henry Holt and Company, LLC, ‾rst edition, 2002. [73] C. P. Liu. Zeeman eRect on the electronic structure of carbon nanotori in a strong ‾eld. Int. J. Mod. Phys. B, 22(27):4845{4852, OCT 30 2008. [74] C. P. Liu and N. Xu. Magnetic response of chiral carbon nanotori: The dependence of torus radius. Physica B-Cond. Matt., 403(17):2884{ 2887, AUG 1 2008. [75] C. P. Liu, H. B. Chen, and J. W. Ding. Magnetic response of carbon nanotori: the importance of curvature and disorder. J. Phys.-Cond. Matt., 20(1), JAN 9 2008. [76] F. L. Shyu. In°uence of electric ‾elds on magnetization of achiral carbon tori. Physica E-Low Dim. Sys. & Nanostruct., 41(4):537{542, FEB 2009. 460 BIBLIOGRAPHY [77] N. Xu, J. W. Ding, H. B. Chen, and M. M. Ma. Curvature and external electric ‾eld eRects on the persistent current in chiral toroidal carbon nanotubes. Euro. Phys. J. B, 67(1):71{75, JAN 2009. [78] E. C. Kirby, R. B. Mallion, and P Pollak. Toroidal polyhexes. J. Chem. Soc. Faraday Trans., 89(12):1945{1953, JUN 21 1993. [79] D. J. Klein. Elemental benzenoids. J. Chem. Inf. Comput. Sci., 34(2):453{459, MAR-APR 1994. [80] Okuma Y. Tsukano Y. Hosoya, H. and K. Nakada. Multilayered cyclic fence graphs: novel cubic graphs related to the graphite network. J. Chem. Inf. Comput. Sci., 35(3):351{356, MAY-JUN 1995. [81] John P. E. Fowler, P. W. and H. Sachs. (3,6)-Cages, hexagonal toroidal cages, and their spectra. DIMACS Series in Discrete Mathematics and Theoretical Computer Science 2000, 51():139{174, 2000. [82] M. V. Diudea and P. E. John. Covering polyhedral tori. MATCH Commum. Math. Comput. Chem., 44():103{116, 2001. [83] Parv B. Diudea, M. V. and E. C. Kirby. Azulenic tori. MATCH Commum. Math. Comput. Chem., 47():53{70, 2003. [84] Fowler P. W. Rassat A. Deza, M. and K. M. Rogers. Fullerenes as tilings of surfaces. J. Chem. Inf. Comput. Sci., 40(3):550{558, MAY- JUN 2000. [85] P. E. John and H. Sachs. Spectra of toroidal graphs. Discret. Math., 309(9):2663{2681, MAY 6 2009. BIBLIOGRAPHY 461 [86] J Liu, HJ Dai, JH Hafner, DT Colbert, RE Smalley, SJ Tans, and C Dekker. Fullerene `crop circles'. Nature, 385(6619):780{781, FEB 27 1997. [87] V. Meunier, Ph. Lambin, and A. A. Lucas. Atomic and electronic structures of large and small carbon tori. Phys. Rev. B, 57(23):14886{ 14890, Jun 1998. [88] B. Borstnik and D. Lukman. Molecular mechanics of toroidal carbon molecules. Chem. Phys. Lett., 228(4-5):312{316, OCT 7 1994. [89] Michael J. S. Dewar, Eve G. Zoebisch, Eamonn F. Healy, and James J. P. Stewart. Development and use of quantum mechanical molecular models. 76. am1: a new general purpose quantum mechanical molecular model. J. Amer. Chem. Soc., 107(13):3902{3909, 1985. [90] J. TersoR. Energies of fullerenes. Phys. Rev. B, 46(23):15546{15549, Dec 1992. [91] ST Hyde and M OKeeRe. Elastic warping of graphitic carbon sheets: Relative energies of some fullerenes, schwarzites and buckytubes. Phi. Trans. Roy. Soc. London A, 354(1715):1999{2008, SEP 16 1996. [92] Shoaib Ahmad. Continuum elastic model of fullerenes and the spheric- ity of the carbon onion shells. J. Chem. Phys., 116(8):3396{3400, 2002. [93] Antonio ·Siber and Rudolf Podgornik. Stability of elastic icosadelta- hedral shells under uniform external pressure: Application to viruses under osmotic pressure. Phys. Rev. E, 79(1):011919, 2009. 462 BIBLIOGRAPHY [94] Ilia A. Solov'yov, Maneesh Mathew, Andrey V. Solov'yov, and Walter Greiner. Liquid surface model for carbon nanotube energetics. Phys. Rev. E, 78(5):051601, 2008. [95] A. Siber. Shapes and energies of giant icosahedral fullerenes - Onset of ridge sharpening transition. Euro. Phys. J. B, 53(3):395{400, OCT 2006. [96] Antonio Siber. Energies of sp(2) carbon shapes with pentagonal discli- nations and elasticity theory. Nanotech., 17(14):3598{3606, JUL 28 2006. [97] JA Rodriguez-Manzo, F Lopez-Urias, M Terrones, and H Terrones. Magnetism in corrugated carbon nanotori: The importance of sym- metry, defects, and negative curvature. Nano Lett., 4(11):2179{2183, NOV 2004. [98] Julio A. Rodriguez-Manzo, Florentino Lopez-Urias, Mauricio Terrones, and Humberto Terrones. Anomalous paramagnetism in doped carbon nanostructures. Small, 3(1):120{125, JAN 2007. [99] A. Maritan, C. Micheletti, A. Trovato, and J. R. Banavar. Optimal shapes of compact strings. Nature, 406:287{290, 2000. [100] S. Przybyl and P. Pieranski. Helical close packings of ideal ropes. Eur. Phys. J. E, 68(4):445, 2001. [101] J. E. Graver. Counting on Frameworks. The Mathematical Association of America, ‾rst edition, 2001. BIBLIOGRAPHY 463 [102] R. J. Gillespie and R. S. Nyholm. Inorganic stereochemistry. Quart. Rev. Chem. Soc., 11:339{380, 1957. [103] R. J. Gillespie. The electron-pair repulsion model for molecular geom- etry. J. Chem. Educ., 40:295, 1963. [104] R. J. Gillespie. The electron-pair repulsion model for molecular geom- etry. J. Chem. Educ., 47:18, 1970. [105] R. J. Gillespie. The vsepr model revisited. Chem. Soc. Rev., page 59, 1992. [106] V. G. S. Box. The molecular mechanics of quantized valence bonds. J. Mol. Modell., 3:124{141, 1997. [107] L. A. Girifalco, Miroslav Hodak, and Roland S. Lee. Carbon nanotubes, buckyballs, ropes, and a universal graphitic potential. Phys. Rev. B, 62(19):13104{13110, Nov 2000. [108] J. P. Stewart. MOPAC2009. Stewart Computational Chemistry, Col- orado Springs, CO, USA, 2008. [109] L. D. Landau. Theory of Elasticity. Butterworth-Heinemann (A Di- vision of Reed Educational and Professional Publishing Ltd.), thrid edition, 1999. [110] Ou-Yang Zhong-can, Zhao-Bin Su, and Chui-Lin Wang. Coil forma- tion in multishell carbon nanotubes: Competition between curvature elasticity and interlayer adhesion. Phys. Rev. Lett., 78(21):4055{4058, May 1997. 464 BIBLIOGRAPHY [111] Shengli Zhang, Shumin Zhao, Minggang Xia, Erhu Zhang, Xianjun Zuo, and Tao Xu. Optimum diameter of single-walled carbon nan- otubes in carbon nanotube ropes. Phys. Rev. B, 70(3):035403, Jul 2004. | |
dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/45583 | - |
dc.description.abstract | 在本篇論文中,我們有系統地探討了sp2碳共軛體系可能的幾何、拓樸,其中包括環型碳管(Toroidal Carbon NanoTube, TCNT)、螺旋型碳管(Helical CNT, HCNT)、環結型碳管(CNT Torus Knot)、週期性最小曲面石墨(TPMS graphite, Schwartzite)、高虧格富勒烯(High-Genus Fullerene, HGF)等。對於高對稱的環型碳管我們進行了AM1量子化學的計算,並以此結果探討其幾何結構與化學穩定性的關係,並進一步利用彈性力學理論分析之。對於螺旋型碳管的幾何構型我們亦進行了數值實驗與結果分析,發現其幾何參數的相圖(phase diagram)相較於文獻中連續模型所得之結果大為不同。
本篇論文附有二附錄,一為本實驗室所開發之電腦程式,二則為一些在本篇論文中所探討的純碳分子之分子圖。 | zh_TW |
dc.description.abstract | In this thesis I present a rather different aspect to the classification of complex graphitic structures. Among them numerous novel structures are proposed for the fist time. And new approaches to some complex molecules that had been discussed in the literature are also presented, which I believe are much easier for chemists to grasp since they contain minimal mathematics. In addition to the discussion of molecular structures, which is included in the part one of the thesis, the energetic of the proposed molecules is also analyzed both in traditional quantum chemical computational approach and by the theory of elastic membrane, which are presented in the second part of the thesis.
In part one, I first make a thorough examination on the problem of finding possible isomers of highly symmetric toroidal carbon nanotubes (TCNT), which are isomorphic to torus. And the problem is attacked in two different ways each having its own advantages and drawbacks, namely the real space and the dual space approaches. The two different schemes are discussed in chapter 2 and 3, respectively. Starting from TCNT, complex graphitic structures with diverse geometries and topologies can be obtained by applying certain manipulations on the structure of parent TCNT, as shown in the following illustration. Note that the shown molecular structures are categorized into two major groups: ones derived from the topological manipulations (LHS) and from the geometrical manipulations (RHS) of TCNT. In chapter 4 I address the construction of helically coiled carbon nanotube (HCCNT). Since the HCCNTs have helical symmetry, they are singly periodic extended structures contrary to their TCNT parent molecules. Along the line on the RHS of the above figure, tubular structures as complicated as carbon nanotube torus knot can be obtained by altering the nonhexagon distribution on the molecular surface. In general, carbon nanotubes with any desired geometry (space curve) can be approached with the geometric manipulation schemes discussed herein, where in chapter 6 I focus on torus knot in particular. Turning our attention to the LHS of the figure, a large family of porous graphitic structures, either closed (0D) or extended (2D, 3D), can be classified by assembling suitable sets of neck-like structures. The neck structure is obtained by peeling the outer-rim of a TCNT off leaving the central hole unchanged. Depending on the occasion, necks with different geometric features are used and the resulting porous molecules can be high-genus fullerenes (0D), doubly periodic supergraphene (2D), or triply periodic quasi-minimal surfaces (3D). These constitute chapter 5 of the thesis. The second part of the thesis is divided into two chapters. In chapter 7 I discuss the use of three different molecular mechanical (MM) potential forms in the context of graphitic molecules. The first two of them are new to the literature and are both derived from simple theories of structural stability, namely the framework rigidity theory and the valence-shell electron-pair repulsion (VSEPR) theory. By applying these MM potentials to the geometry optimization of above mentioned graphitic molecules, it is shown that they are essentially efficient and robust to give reliable results while costing minimal computational effort. Concerning the thermodynamic stability of these molecules more rigorously, a thorough AM1 quantum chemical computation on a large family (over 1,000) of TCNTs was carried out. The results are certainly more reliable than ones obtained by utilizing potentials in chapter 7, nevertheless are difficult and somewhat tedious to follow. Thus in chapter 8 I first review some of the key features of the calculation results, then I turn to a unique application of the theory of elastic membrane. In stead of continualizing the molecular structure and thereby obtaining a 3D surface for the analysis, here a discretized version of elasticity theory for membrane is proposed. By suitably defining Gaussian and mean curvature values for each face of a graphitic structure, the formation energy can be split into three parts: elastic bending energy of graphene sheet, formation energies of the nonhexagonal defects, and the residual energy originated from quantum effects. The main advantage of this approach is that it bypasses the complex arithmetic required to fit the molecular shapes into continuous surfaces, which is exclusively used in the literature, while gives us maximal information about the distribution of strain energy. In addition to the above mentioned, there are two appedices attached in the end of the thesis. One enclosing the computer codes (mainly Matlab) that are developed during the study. And the other includes numerous molecular figures of the molecular structures discussed in the thesis. | en |
dc.description.provenance | Made available in DSpace on 2021-06-15T04:28:37Z (GMT). No. of bitstreams: 1 ntu-98-R96223127-1.pdf: 29514562 bytes, checksum: 373ee5059c5dfbfda8a2d407d21ce2dd (MD5) Previous issue date: 2009 | en |
dc.description.tableofcontents | 1 Introduction 25
I Geometric Classification of Graphitic Structures 29 2 Toroidal Carbon Nanotube: Real Space Approach 37 2.1 Basic Construction Scheme . . . . . . . . . . . . . . . . . . . . 39 2.1.1 Achiral TCNTs . . . . . . . . . . . . . . . . . . . . . . 40 2.1.2 Chiral TCNTs . . . . . . . . . . . . . . . . . . . . . . . 42 2.1.3 Inner- and Outer-RimRotation . . . . . . . . . . . . . 45 2.1.4 Stability . . . . . . . . . . . . . . . . . . . . . . . . . . 46 2.1.5 Special Cases: Quadrilateral and Octagon . . . . . . . 48 2.2 Isomerizations of TCNTs . . . . . . . . . . . . . . . . . . . . . 49 2.2.1 Horizontal Shifting: Dnd Isomers . . . . . . . . . . . . 49 2.2.2 Generalized Stone-Wales Transformation: Induced Chirality and Edge Transformation . . . . . . . . . . . . . 51 2.3 Helically Coiled Carbon Nanotubes . . . . . . . . . . . . . . . 57 2.4 Correspondence to Existing Classification Schemes . . . . . . . 59 2.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 3 Toroidal Carbon Nanotube: Dual Space Approach 63 3.1 Basic Construction Scheme . . . . . . . . . . . . . . . . . . . . 65 3.1.1 Chirality: Goldberg Inclusion . . . . . . . . . . . . . . 67 3.1.2 Inner- and Outer-RimRotation . . . . . . . . . . . . . 69 3.2 Isomerizations . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 3.2.1 Horizontal Shifting: Dnd Isomers . . . . . . . . . . . . 77 3.2.2 Generalized Stone-Wales Transformation . . . . . . . . 78 3.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 4 Helically Coiled Carbon Nanotube 87 4.1 Horizontal Shifting . . . . . . . . . . . . . . . . . . . . . . . . 87 4.1.1 Relation between HSP and the Pitch Angle of HCCNT 89 4.2 Vertical Shifting . . . . . . . . . . . . . . . . . . . . . . . . . . 99 4.2.1 Limiting Values for V SP and nV S . . . . . . . . . . . . 101 5 High-Genus Fullerenes 107 5.1 H-Type Neck Structure . . . . . . . . . . . . . . . . . . . . . . 108 5.2 High-Genus Fullerene Platonic Polyhedra . . . . . . . . . . . . 110 5.2.1 Dodecahedron . . . . . . . . . . . . . . . . . . . . . . . 111 5.2.2 Cube . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 5.2.3 Tetrahedron, Octahedron, and Icosahedron . . . . . . . 113 5.3 High-Genus Fullerene Archimedean Polyhedra . . . . . . . . . 119 5.4 High-Genus Fullerene General Polyhedra: Superfullerenes . . . 120 5.5 D-Type Neck Structure . . . . . . . . . . . . . . . . . . . . . . 124 5.6 Stabilities of High-Genus Fullerene Polyhedra . . . . . . . . . 127 6 Periodic Porous Structures 129 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 6.2 Neck Structures . . . . . . . . . . . . . . . . . . . . . . . . . . 130 6.3 Planar Tilings of Necks . . . . . . . . . . . . . . . . . . . . . . 132 6.3.1 Platonic Tilings . . . . . . . . . . . . . . . . . . . . . . 132 6.3.2 Archimedean Tilings . . . . . . . . . . . . . . . . . . . 133 6.4 Coloring of the Regular Tilings: Triply Periodic Structures . . 135 6.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 7 Special Topics 141 7.1 Carbon Nanotube Torus Knot . . . . . . . . . . . . . . . . . . 141 7.1.1 The Geometry of Torus Knot . . . . . . . . . . . . . . 142 7.1.2 Construction of Helically Coiled Carbon Nanotube . . 145 7.1.3 Carbon Nanotube Torus Knot . . . . . . . . . . . . . . 149 7.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 7.3 Buckytori . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 7.4 One-Dimensional Analogs of C60 . . . . . . . . . . . . . . . . . 159 7.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170 II Stability and Physical Properties 171 8 Simple Empirical Interatomic Potentials 175 8.1 Geometry Optimization of Graphitic Structures in Dual Space: Rigidity Theory . . . . . . . . . . . . . . . . . . . . . . . . . . 176 8.2 VSEPR Potential: An Efficient and Robust Empirical MolecularMechanics Potential . . . . . . . . . . . . . . . . . . . . . 179 8.3 Lenosky Potential with Lennard-Jones Type van der Waals Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183 9 Stability of Toroidal Carbon Nanotubes 187 9.1 AM1 QuantumChemical Calculation . . . . . . . . . . . . . . 187 9.2 Stability Analysis by Classical Elasticity Theory . . . . . . . . 192 9.2.1 Elasticity Theory ofMembrane . . . . . . . . . . . . . 192 9.2.2 Curvature in DiscreteMembranous Structures . . . . . 194 9.2.3 Application to the Stability of Toroidal Carbon Nanotube199 III Appendix 201 A Computational Toolkits: Implementations in Matlab 203 A.1 Demo Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204 A.1.1 Toroidal Carbon Nanotubes . . . . . . . . . . . . . . . 204 A.1.2 High-Genus Fullerenes . . . . . . . . . . . . . . . . . . 205 A.1.3 Doubly Periodic Graphitic Porous Structures . . . . . . 205 A.1.4 Triply Periodic Graphitic Porous Structures . . . . . . 206 A.1.5 Carbon Nanotube Torus Knot . . . . . . . . . . . . . . 206 A.2 C Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 A.2.1 Connectivity Calculation . . . . . . . . . . . . . . . . . 207 A.2.2 Ring Indices Calculation . . . . . . . . . . . . . . . . . 210 A.3 Main Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221 A.3.1 TCNT Related Codes . . . . . . . . . . . . . . . . . . 221 A.3.2 HGF Related Codes . . . . . . . . . . . . . . . . . . . 241 A.3.3 Extended Periodic Porous Structures . . . . . . . . . . 254 A.3.4 Codes for CNTTKs . . . . . . . . . . . . . . . . . . . . 263 A.4 Basic Functions . . . . . . . . . . . . . . . . . . . . . . . . . . 264 A.4.1 Codes Involved in the Dual Space Construction Scheme 265 A.4.2 Modular Pieces Composing HGFs . . . . . . . . . . . . 266 A.4.3 Codes Involved in Geometry Optimization . . . . . . . 270 A.4.4 Symmetry Operation Subroutines . . . . . . . . . . . . 283 A.5 Functions for Illustration Purposes . . . . . . . . . . . . . . . 290 A.5.1 Basic Plotting Functions . . . . . . . . . . . . . . . . . 290 A.5.2 Plotting Functions for the Dual Space Representation . 292 A.5.3 Plotting Functions for General Fullerenes . . . . . . . . 294 A.5.4 Plotting Functions of Special Purposes . . . . . . . . . 298 A.5.5 Plotting Functions with Fancy Output Illustrations . . 302 A.5.6 Illustrative Tool Functions . . . . . . . . . . . . . . . . 310 A.6 Codes Constructing HCCNTs and BCNTs . . . . . . . . . . . 324 A.6.1 HCCNTs Deriving fromHS-TCNTs . . . . . . . . . . . 324 A.6.2 HCCNTs Deriving fromVS-TCNTs . . . . . . . . . . . 333 A.6.3 BCNTs Deriving fromTCNTs . . . . . . . . . . . . . . 339 A.7 Miscellaneous . . . . . . . . . . . . . . . . . . . . . . . . . . . 357 B Atlas of Toroidal Carbon Nanotubes and Other Exotic Carbon Nanostructures 371 B.1 TCNT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371 B.2 HS-HCCNT . . . . . . . . . . . . . . . . . . . . . . . . . . . . 389 B.3 VS-HCCNT . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395 B.4 HGF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404 B.5 Periodic Porous Structures . . . . . . . . . . . . . . . . . . . . 435 B.5.1 Doubly Periodic Porous Structures . . . . . . . . . . . 435 B.5.2 Triply Periodic Porous Structures . . . . . . . . . . . . 436 B.6 CNTTK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 440 B.7 BCNT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445 | |
dc.language.iso | en | |
dc.title | 純碳共軛系統之幾何、拓樸與物理性質的理論研究 | zh_TW |
dc.title | Theoretical Studies of Geometries, Topologies, and Physical Properties of Conjugated Graphitic Structures | en |
dc.type | Thesis | |
dc.date.schoolyear | 97-2 | |
dc.description.degree | 碩士 | |
dc.contributor.oralexamcommittee | 王瑜(Yu Wang),王伯昌(Bo-Cheng Wang),陸駿逸(David Chun-Yi Lu) | |
dc.subject.keyword | 純碳,共軛,幾何,拓樸,虧格,螺旋, | zh_TW |
dc.subject.keyword | graphitic,conjugated,geometry,topology, | en |
dc.relation.page | 464 | |
dc.rights.note | 有償授權 | |
dc.date.accepted | 2009-08-20 | |
dc.contributor.author-college | 理學院 | zh_TW |
dc.contributor.author-dept | 化學研究所 | zh_TW |
顯示於系所單位: | 化學系 |
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