本論文利用分子動力學的方法(Molecular Dynamics，MD)模擬水團簇在不同溫度及大小下之結構分佈，例如氧原子之密度分佈、氫鍵和偶極矩等特性行為等，而所採用的勢能為F3C水勢能模型（flexible three-centered water model）。文中分析水團簇的結果發現，隨著溫度的增加，氧原子密度分佈與平均一顆水分子所形成的氫鍵數目逐漸遞減，而在水團簇大小效應下，對於水團簇內水分子間之相互影響則較少。

另外更進一步研究介於水團簇外部範圍及內部範圍不同的結構特性，可以發現當溫度增加時，平均一顆水分子所形成的氫鍵數目將逐漸遞減，但是外部水分子比例卻逐漸增加。而文中發現水團簇大小的效應，對於內部範圍的水分子，密度分佈和平均氫鍵數並沒有太大的影響，然而水團簇外部範圍的水分子對於水團簇尺寸大小的效應下確有很大的改變。

Structure properties of water clusters are investigated in this study by means of molecular dynamics simulations. The oxygen density profile, dipole moment and hydrogen bond properties of water clusters are all examined. The temperature dependence and size dependence of the structure properties are also explored in the present study. Upon the molecular dynamics simulations, the flexible three-centered (F3C) water potential is used to model the inter- and intra-actions of the water molecule. It is found that as the temperature rises, the density of the oxygen and the average number of hydrogen bonds per water molecule will decrease. The effect of cluster size, however, is less significant on the structure properties.
The differences between the structural properties for the surface region and those for the interior region of the cluster are also investigated. It is found that as the temperature rises, the average number of hydrogen bonds per water molecule decreases, but the ratio of surface water molecules increases. After comparing the water densities in interior regions and the average number of hydrogen bonds in those regions, we find there is no apparent size effect on water molecules in the interior region, whereas the size of the water cluster has a significant influence on the behavior of water molecules at the surface region.

中文摘要............................................ 1

ABSTRACT............................................ 2

第1 章 緒論......................................... 3

1.1 研究動機........................................ 3
1.2 文獻回顧........................................ 6
1.3 本文架構.........................................9

第2 章 分子動力學理論..............................10
2.1 勢能函數...................................... 12
2.2 運動方程...................................... 15
2.3 溫度修正方法...................................16
2.4 週期性邊界條件................................ 19
2.5 徑向分佈函數.................................. 21

第3 章 分子動力學數值方法......................... 23

3.1 鄰近原子表列法................................ 23
3.1.1 Verlet List 表列法................................................23
3.1.2 Cell Link 表列法........................... 25
3.1.3 Verlet List 表列法結合Cell Link 表列法...... 25
3.2 無因次化...................................... 27

第4 章 結果分析與討論..............................29

4.1 水團簇..................................... 29
4.1.1 物理模型.................................... 29
4.1.2 氫鍵、偶極矩、氫鍵鍵長、O-H鍵長............. 30


4.2 外部與內部水分子之比較......................35

4.2.1 模擬系統................................35
4.2.2 密度分佈.....................................36
4.2.3 氫鍵.........................................36
4.2.4 外部水分子比例..............................37
4.2.5 徑向分佈函數.................................38

4.3 外部與內部水分子氫鍵動態特性之比較.............46
4.3.1 氫鍵動態特性...................... ..........46
4.3.2 氫鍵動態特性之定義...........................46
4.3.3 氫鍵動態特性之驗證...........................47
4.3.4 水團簇外部與內部之氫鍵動態特性...............48

第5 章 結論與建議................................. 54

5.1 結論.......................................... 54
5.2 建議與未來展望................................ 56

1. 川和知二編著/工研院奈米中心編校，圖解奈米科技，全華科技圖書，2003年。

2. 大泊巖/王建義，圖解奈米技術，全華圖書公司，2003年。

3. 呂宗昕編著，圖解奈米科技與光觸媒，商周出版社出版，2003年。

4. P. G . de Gennes, “Wetting: Static and dynamics”, Reviews of Modern Physics, Vol.57, pp.827 ,(1985).

5. J. Charvolin, J. F. Joanny, and J. Zinn-Justin, “Liquids at Interfaces” (North-Holland, New York) , pp.371,(1990).

6. F. Bouchard-Wyart and P. G. de Gennes, “Dynamics of partial wetting”, Advance in Colloid Interface Science, Vol.39, pp.1-11, (1992).

7. A . M . Cazabat , “How does a droplet spread”, Contemp. Phys. Vol.28, pp.347 (1987).
8. F. Heslot, A.M.Cazabat, and N. Fraysse, “Diffusion-controlled wetting films”, Journal of Physics : Condens. Matterl, pp.5793-5798 .(1989).

9. C.C.Hwang, Y.R. Jeng, Y.L. Hsu and J.G.. Chang , “Molecular Dynamics Simulation of Microscopic Droplet Spread on Rough Surfaces”, Journal of the Physical Society of Japan,Vol.70, pp.2626-2632,(2001).

10. S. Maruyama, T. Kimura and M. Lu, “Molecular Scale Aspects of Liquid Contact on a Solid Surface”, Thermal Science & Engineering Vol.10, (2002).

11. J.S. Rowlinson, B. Widom, “Molecular Theory of Capillarity”, Clarendon Press, Oxford, (1982).

12. N.T. Kirkman, T. Stirner , W.E. Hagston, “A new method for investigating the surface tension from molecular dynamics simulations applied to liquid droplets”, Computational Materials Science 30, pp.126-130 ,(2004).

13. S. Subramaniam, D.R. White, D.J. Scholl, and W.H. Weber, “In situ optical measurement of liquid drop surface tension in gas metal arc welding”, Journal of Physics D: Applied Physics. Vol.31 ,pp.1963-1965. (1998).

14. E.N. Brodskaya, J.C. Eriksson, A. Laaksonen, A.I. Rusanov, “Local Structure and Work of Formation of Water Clusters Studied by Molecular Dynamics Simulations”, Journal of Colloid and Interface Science,Vol.180,pp.86-97(12), (1996).

15. A.D. Shere, Walton , J.P.R.B.Walton, and K.E Gubbins, “Liquid drops of polar molecules” ,Journal of Chemical Physical . Vol.85,pp.2178,(1986).

16. V. V. Zakharov , E. N. Brodskaya and A. Laaksonen, “Surface tension of water droplets: A molecular dynamics study of model and size dependencies” , Journal of Chemical Physical. Vol.107 ,(24),(1997).

17. J.S. Rowlinson, B. Widom, “Molecular Theory of Capillarity”, Oxford University Press, London(Books: JS Rowlinson), (1982).

18. P. G . de Gennes, “Wetting: Static and dynamics”, Reviews of Modern Physics, Vol.57, pp.827 ,(1985).

19. V.E. Dussan, S. Davis, “On the Motion of Fluid-Fluid Interface along a Solid

Surface ”, Journal of Fluid Mechanics ,Vol.65, pp.71. (1974).

20. A. W. Adamson, “The Physical Chemistry of Surfaces, 4th Edition”. (Wiley, New York, 1985).

21. J.D. Coninck, M.J de Ruijter, and M. Voue, “Dynamics of wetting”, Current Opinion in Colloid & Interface Science ,Vol. 6, pp.49, (2001).

22. S. Tan , “Spreading of a droplet on a solid in the partial wetting and non wetting regime by Monte-Carlo simulation”, Physicochemical and Engineering Aspects ,Vol.148 ,pp.223–230,(1999).

23. T. Kimura and S. Maruyama , “Molecular dynamics simulation of heterogeneous nucleation of liquid droplet on solid surface” , Proceedings of the 4th Jsme-Ksme Thermal Engineering Conference October 1-6 , (2000).

24. M.S. Kurashige, T. Matsumoto, S.Yamaguchi, and T.Kimura, “Liquid Droplet in Contact with a Solid Surface”, Microscale Thermophysical Engineering, Vol. 2, No. 1, pp. 49-62. (1998).

25. X.Wu, N. N.Thien, X.J. Fan, and T. Y. Ng, “A molecular dynamics study of drop spreading on a solid surface”, Physics of Fluids, Vol.15, No.6, (2003).

26. J. Irving, J. Kirkwood, “The statistical mechanical theorey of transport properties. IV. The equations of hydrodynamics”, Journal of Chemical Physical, Vol. 18, pp. 817-829. (1950).

27. R. A. Atkinson and V. Saudek, “The direct determination of protein structure by NMR without assignment”, Febs Letters, Vol.510, pp.1-4, (2002).

28. R.A. Venters, R. Thompson and J. Cavanagh, “Current approaches for the study of large proteins by NMR”, Journal of molecular Structure ,Vol.602, pp.275-292, (2002).

29. C. anfinsen, “Principles that govern the folding of protein chains”, Science, Vol.181, pp.223, (1973).

30. W.J. Browne, A. C. North, D.C. Phillips, K.V, Drew, T. C.,and R. L. Hill, “A possible three-dimensional structure of bovine alpha-lactalbumin based on that of hen’s egg-white lysozyme”, Journal of Moleculae Biology, Vol.42, pp.65-86, (1969).

31. C. Chothia, A.M. Lesk, “Relationship between the divergence of sequence and structure in proteins” , The EMBO Journal, Vol.5, pp.823-827, (1986).

32. J. Moult, “The current state of the art in protein structure prediction” , Current Opinion in Biotechnology, Vol.7, pp.422-427, (1996).

33. T. Cardozo, S. Batalov, R. Abagyan, “Estimating local backbone structural deviation in homology models” , Computers and Chemistry, Vol.24, pp.13-31, (2000).

34. C. Sander and R. Schneider, “Database of similarity-derived protein structures and the structural meaning of. sequence alignment” Proteins : Struct. Funct. Genet, Vol .9, pp.56-68, (1991).


35. B. Rost, R. Schneider and C. Sander, “Protein Fold Recognition by Prediction-based Threading”, Journal of Molecular Biolog , Vol .270, pp.471-480, (1997).

36. B. Rost, “Protein structures sustain evolutionary drift”, Folding & Design, 2, S19-S24, (1997).

37. J. H. Irving, and J. G. Kirkwood, “The statistical mechanical theory of transport processes. IV. The equations of hydrodynamics”, Journal of Chemical Physical, Vol.18 , pp.817-829, (1950).

38.W.A. Wallqvist, and O. Teleman, “Properties of flexible water models” Molecular Physics, Vol .74, pp.515 (1991).

39. Y. Dou, N. Winograd, B. Garrison , and L.V. Zhigilei, “Substrate-Assisted Laser -Initiated Ejection of Proteins Embedded in Water Films”, Journal of Physical Chemistry B, Vol.107, pp.2362-2365, (2003).

40.T. I. Mizan et al, “Comparison of rigid and flexible simple point charge water
models at supercritical conditions”, Journal of Computational Chemistry , Vol .17, pp.1757 (1996).

41.M. Levitt et al, “Calibration and Testing of a Water Model for Simulation of
the Molecular Dynamics of Proteins and Nucleic Acids in Solution”, Journal of Physical Chemistry B , Vol.101, pp.5051,(1997).

42.J. Bocker et al, “Molecular dynamics simulation studies of the mercury-water
interface” ,Surface Science Vol.335,pp.372, (1995).


43.M.Levitt, M. Hirshberg, R.Sharon, K. E. Laidig, and V.Daggett,
“Calibration and Testing of a Water Model for Simulation of the Molecular Dynamics of Proteins and Nucleic Acids in Solution”, Journal of Physical Chemistry B, Vol.101, pp.5051-5061, (1997).

44. S. Nose, “A unified formulation of the constant temperature molecular dynamics methods”, Journal of Chemical Physical, Vol.81,pp.511,(1984).

45. W. Hoover, “Canonical dynamics: Equilibrium phase-spacedistributions” , Physical Review A, Vol.31,1695,(1985).

46. J. Haile, “Molecular Dynamics Simulation: Elementary Methods”, John Wiley & Sons, Inc., New York, (1997).

47. Rapaport, “The Art of Molecular Dynamics Simulation”, Cambridge University Press, London. (1997).

48. J. Goodfellow et al.,” Molecular dynamics”, CRC Press, Boston. (1990).

49. M. Allen, D. Tildesley, “Computer Simulation of Liquids”, Oxford Science, London.80, (1991).

50. D. Frenkel, B. Smit, “Understanding Molecular Simulation”, Academic Press, San Diego. (1996).

51. D. Heermann,“Computer Simulation Method”, Springer-Verlag, Berlin,( 1990).

52.D. C. Rapaport, “The Art of Molecular dynamics Simulation”,Cambridge university press, (1995).

53. M. Tuckerman and B. J. Berne , “Reversible multiple time scale molecular dynamics”,Journal of Chemical Physical,Vol. 97, pp.1990 (1992).

54. J. M. Haile, “Molecular dynamics simulation elementary methods”, John Wiley and Sons, New York,(1992).

55. J. Haile, “Molecular Dynamics Simulation: Elementary Methods”, John Wiley & Sons, Inc., New York. , (1997).

56. D. Rapaport, “The Art of Molecular Dynamics Simulation”, CambridgeUniversity Press, London. , (1997).

57. Bitsanis and G. Hadziioannou, “Molecular dynamics simulations of the structure and dynamics of confined polymer melts”, Journal of Chemical Physical. Vol.92, pp.3827,(1990).

58. M.C. Gordillo, J. Marti, “Hydrogen bond structure of liquid water confined in nanotubes”, Chemical Physics Letters ,Vol.329 ,pp.341-345,(2000).

59. H.Y. Wong ,and S.Y. Lo, “Possible mechanism of formation and stability of anomalous states of water”, Journal of Moleculae Biology, Vol.42, pp.1-14. (1998).

60. V. V. Zakharov; E. N. Brodskaya , “Surface tension of water droplets: A molecular dynamics study of model and size dependencies”, Journal of Chemical Physical., Vol.107, pp.10675. (1997).

61. C. L. Brint; J. J. Burton, “Molecular dynamics study of water microclusters”,
Journal of Chemical Physical., Vol.63, pp.3327. (1975).

62. S Erkoc, “Stability of Gold Clusters: Molecular-Dynamics Simulations”,Physica E ,Vol.8, pp.210. (2000).

63. S. T .Lin , P. K. Maiti ,W. A. Goddard , “Dynamics and Thermodynamics of Water in PAMAM Dendrimers at Subnanosecond Time Scales”, Journal of Physial Chemistry B. Vol.109, pp.8663. (2005).

64. S. P. Ju , J. G. Chang , J. S. Lin , Y. S. Lin, “The effects of confinement on the behavior of water molecules between parallel Au plates of (001) planes”, Journal of Chemical Physical. Vol.122, pp.154707. (2005).

65. D. Bertolini, M. Cassettari, M. Ferrario, P. Grigolini, and G. Salvetti, “Dynamical Properties of Hydrogen Bonded Liquids”,Adv. Chem Phys.Vol.62, pp.277 .(1985).

66. H. Chen and J. Teixeira, “Structure and hydrogen bond dynamics of water-dimethyl sulfoxide mixtures by computer simulations” ,Adv. Chem Phys, Vol.64, (1986).

67. E.W. Castner, Y.J. Chang, Y.C. Chu, and G.E. Walrafen, “The intermolecular dynamics of liquid water”, Journal of Chemical Physical, Vol.102, pp.653 .(1995).

68.M.F. Kropman and H.J. Bakker, “Dynamics of water molecules in aqueous solvation shells”, Science, Vol.291, pp.2118 (2001).

69.H.J. Bakker, H.K. Nienhuys, G. Gallot, N. Lascoux, G.M. Gale, J.-C. Leicknam,
and S. Bratos, “Transient absorption of vibrationally excited water”, Journal of Chemical Physical,Vol.116, pp.2592 ,(2002).

70.A. Luzar and D. Chandler, “Hydrogen-bond kinetics in liquid water”, Nature,
Vol.379, pp.53 ,(1996).

71.A. Luzar, “Resolving the hydrogen bond dynamics conundrum”, Journal of Chemical Physical., Vol.113, pp.10663 ,(2000).

72.H. Xu, H.A. Stern, and B.J. Berne,“Can water polarizability be ignored in hydrogen bond kinetics”, Journal of Physical Chemistry B, Vol.106, pp. 2054 , (2002).

73.G.. Sutmann and R. Vallauri, “Dynamics of the hydrogen bond network in liquid water”, Journal of Molecular Liquids, Vol.213 ,pp.98–99, (2002).

74.F. Starr, J. Nielsen, and H.E. Stanley, “Hydrogen-bond dynamics for the extended simple point-charge model of water” Physics Review E ,Vol.62, pp.579 .(2000).

75.A. Chandra, “Dynamical Behavior of Anion-Water and Water-Water Hydrogen Bonds in Aqueous Electrolyte Solutions: A Molecular Dynamics Study”, Journal of Physical Chemistry B, Vol.107, pp.3899. (2003).

76.J. Marti, J.A. Padro, and E. Guardia, “Molecular dynamics simulation of liquid
water along the coexistence curve:Hydrogen bonds and vibrational spectra”, Journal of Chemical Physical ,Vol.105, pp.639 .(1996).


77. S.H. Chen and J. Teixeira, “Structure and dynamics of low temperature water as studied by scattering techniques”, Advances in Chemical Physics., Vol.64. (1986).

78.M.F. Kropman and H.J. Bakker, “Femtosecond mid-infrared spectroscopy of
aqueous solvation shells”, Journal of Chemical Physical,Vol.115, pp.8942 .(2001).

79.A. Chandra, “Effects of Ion Atmosphere on Hydrogen-Bond Dynamics in Aqueous Electrolyte Solutions”, Physical Review Letters., Vol.85, pp.768 .(2000).

80. S. Paul and A. Chandra, “Hydrogen bond dynamics at vapour–water and metal–water interfaces”, Chemical Physics Letters, Vol.386, pp.218 .(2004)