壓力分佈圖

我們從壓力分佈圖發現，Case1 獲得了最大的瞬間壓力將近 300MPa，Case2 獲得最大的瞬間壓力不到 200 MPa，Case3 所獲得的 壓力曲線最溫和都不超過100MPa，如圖 5.16。

case1

case2

case3

圖 5.16 壓力分佈圖

5.3.4 分子個數分佈圖

我們想更了解此噴印究竟有多少水分子抵達板子上，所以做了水 分子個數對位置的做圖，如圖5.17

case1

case2

case3

圖5.17 水分子分佈圖

我們可以發現噴嘴吸附的分子明顯變少，且數量在 case1 約有 80 個水分子，在 case2 約有 120 個水分子，在 case3 約有 100 個水分 子，沒有特別的規律性；但板子上的水分子，就幾乎與活塞前進距離 成正比，如圖5.18，在 case1 約有 4153 個水分子於板子上，在 case2 約有1913 個水分子於板子上，在 case3 約有 903 個水分子於板子上，

這是一個極大的好消息，表示藉由這次模擬我們能做到定量的掌控，

但要注意越多的量，需要越大的瞬間壓力給予分子飛行的能量。

圖5.18 水分子個數與推進距離作圖

第六章、結論與未來展望

研究中探討不同溫度噴流過程及不同瞬時推速的噴印過程，由實 驗結果可知，我們由瞬時圖中液滴的形成、液滴形狀、分子蒸發現象、

衛星液滴的產生、打在板子上的圖形、及流場，各項分析顯示出，在 溫度較低時，是最適合做精密計算的奈米噴流加工。

當 噴 流 系 統 溫 度 為 T=278(K) 時 ， 可 看 出 其 蒸 發 現 象 較 T=298,348(K)時相對較低。此外液滴打在板子上的情況也是最優良。

且較不易產生衛星液滴，十分利於精密加工。

所以接著噴印的模擬過程就選定溫度為 278K，重大發現，只要 有足夠的趨動壓力，抵達板子上的水分子會幾乎與活塞前進距離成正 比，因分子於噴頭吸附的量變少。

期待在未來利用噴墨的加工技術越來越高科技且微小化，可以經 由本研究中的模擬系統預先嘗試，降低成本，減少失誤及錯誤估計的 損失，在研究中假設噴流系統中成分為純水，實際上噴流系統中成分 都較為複雜，所以希望未來可以模擬出更多樣化的物質，讓我們的模 擬系統更加接近實際情況，得到更加準確的訊息。

希望我們能在未來全球都全力投入奈米科技的研發時，給予人 類對微加工的摸索及了解能有所幫助。

參考文獻

1. Rayleigh, Lord. 1945 The Theory of Sound, Volume II (2nd ed.).

New York: Dover.

2. M.C. Yuen, "Non-Linear capillary instability of liquid jet", J. Fluid Mech. Volume 33, pp.151-163, 1968.

3. A. H. Nayfeh, "Nonlinear stability of a liquid jet", Phys. Fluids, Volume 13, pp.841-847, 1970.

4. E.F. Goedde, M.C. Yuen, "Experiments on liquid jet instability", J.

Fluid Mech., Volume 40, pp.495-511, 1970.

5. D.F. Rutland, G.J. Jameson, "A nonlinear effect in the capillary instability of liquid jets", J. Fluid Mech., Volume 46, pp.267-271, 1971.

6. W.T. Pimbley, H.C. Lee, "Satellite droplet formation in a liquid jet", IBM J. Res. Dev., Volume 21, pp.21-30, 1977.

7. H. C. Lee, "Drop formation in a liquid jet", IBM Journal of Research and Development, July, pp.364-369, 1974.

8. J. Eggers, and T. F. Dupont, "Drop formation in a one-dimensional approximation of the Navier-Stokes equation", J. Fluid Mech., Volume 262, p.205, 1994.

9. E. L. Kyser, L. F. Collins, and N. Herbert, "Design of an impulse ink jet", J. Appl. Photogr. Eng., Volume 7, pp.73-79.

10. J. E. Fromm, "A numerical study of drop-on-demand jets", in Proceedings of the Second International Colloquium on Drops and Bubbles, pp.54-82, 1982.

11. J. E. Fromm, "Numerical calculation of the fluid dynamics of

drop-on-demand jets", IBM J. Res. Develop., Volume 28, pp.322-333, 1984

12. D. B. Bogy, and F. E. Talke, "Experimental and theoretical study of wave propagation phenomena in drop-on demand ink jet devices", IBM J. Res. Develop., Volume 28, pp.314-321, 1984.

13. R. R. Allen, J. D. Meyer, and W. R. Knight, "Thermodynamics and hydrodynamics of thermal ink jets", Hewlett-Packard J., Volume 36, pp.21-27, 1985.

14. A. Asai, "Three-dimensional calculation of bubble growth and drop ejection in a bubble jet printer", Transactions of the ASME, Volume 114, pp.638-641, 1992.

15. F. G. Tseng, C. J. Kim, and C. M. Ho, "A novel microinjector with virtual chamber neck", in Proc. IEEE MEMS Workshop, Heidelberg, Germany, Jan. pp.25-29, 1998.

16. F. G. Tseng, C. J. Kim, and C. M. Ho, "A microinjection free of satellite drops and characterization of the ejected droplets", ASME Int. Mechanical Engineering Congress and Exposition, Anaheim, CA.

Nov. 1998.

17. Ping-Hei Chen, Hsin-Yah Peng, Hsin-Yi Liu, S.-L Chang, T.-I Wu, Chiang-Ho Cheng, "Pressure response and droplet ejection of a piezoelectric inkjet printhead", Int. J. Mech. Sci., Volume 41,

pp.235-248, 1999.

18. T.M. Liou, K.C. Shih, S.W. Chau, S.C. Chen, "Three-dimensional simulations of the droplet formation during the inkjet printing process", Int. Comm. Heat Mass Transfer, Volume 29, pp.1109-1118, 2002.

19. J.Brünahl, Alex M. Grishin, "Piezoelectric shear mode drop-on-demand inkjet actuator", Sensors and Actuators A, Volume 101, pp.317-382, 2002.

20. J. Koplik, J. R. Banavar, "Molecular dynamics of interface rupture", Phys. Fluids A, Volume 5, pp.521-536, 1993.

21. S. Kawano, "Molecular dynamics of rupture phenomena in a liquid thread", Phys. Rev. E, Volume 58, pp.4468-4472, 1998.

22. M. Moseler, U. Landman, "Formation, stability, and breakup of nanojets", Science, Volume 289, pp.1165-1169, 2000.

23. M. Goto, L.V. Zhigilei, J. Hobley, M. Kishimoto, B.J. Garrison, H.

Fukumura, "Laser expulsion of an organic molecular nanojet from a spatially confined domain", J. Appl. Phys., Volume 90, pp.4755-4760, 2001.

24. J. Voigt, B. Reinker, I.W. Rangelow, "NANOJET：Nanostructuring via a downstream plasmajet", J. Vac. Sci. Technol. B, Volume 17, pp.2764-2767, 1999.

25. J. Voigt, F. Shi, P. Hudek, I.W. Rangelow, "Progress on

nanostructuring with Nanojet", J. Vac. Sci. Technol. B, Volume 18, pp.3525-3529, 2000.

26. I.W. Rangelow, J. Voigt, "”NANOJET”：Tool for the nanofabrication", J. Vac. Sci. Technol. B, Volume 19, pp.2723-2726, 2001.

27. J. Voigt, F. Shi, K. Edinger, P. Güthner, I.W. Rangelow,

"Nanofabrication with scanning nanonozzle ‘Nanojet’", Microelectronic Engineering, Volume 57-58, pp.1035-1042, 2001.

28. G. S. Heffelfinger, "Parallel atomistic simulations", Computer Physics Communications, vol.128(2000), pp.219-237.

29. J.N. Israelachvili, "Intermolecular and Surface Force, 2nd ed. "

Academic, New York (1992).

30. W.G.. Hoover, "Canonical dynamics: Equilibrium phase-space distributions", Physical Review A, vol.31(1985), pp.1695-1697.

31. S. Nosé, "A unified formulation of the constant temperature molecular dynamics methods", Journal of Chemical Physics, vol.81(1984), pp.511-519.

32. D.D. Humphreys, R.A. Friesner, B.J. Berne, "A Multiple-Time-Step Molecular Dynamics Algorithm for Macromolecules", Journal of Physics Chemical, vol.98(1994), pp.6885-6892.

33. Stephen Harrington,Peter H. Poole,Francesco Sciortino,H. Eugene Stanley,” Equation of state of supercooled water simulated using the extended simple point charge intermolecular potential”, 1997 American Institute of Physics

34. www.cas.ac.cn/Images/ 2003/07/04/46742_1.jpg 35. goldenswamp.com/ blogImages05/pled.jpg 36. www.yikst.com/ photo/pt/tb3.gif

37. www.u-nano.com/ images/cataloge_9.gif 38. www.candocom.com/ img/p-04.jpg

39. www.taifer.com.tw/.../ 043010/pictures/aa11.gif 40. www.lsbu.ac.uk/water/ images/h2omodels.gif

41. Masakazu Matsumoto, Shinji Saito, Iwao Ohmine ,” Molecular

dynamics simulation of the ice nucleation and growth process leading to water freezing ”, 2002 nature

42. 卓志哲，"奈米噴流之分子動力學模擬"，碩士論文，國立清華大 學，2003

43. 顏詠弘，"以分子動力學模擬高分子鏈在縫合線上之排向行為"，

碩士論文，國立清華大學，2003。

44. 林弘凡，"運用分子動力學與平行運算於奈米流場之研究"，碩士 論文，國立清華大學，2004。

45. 林俊儀，"以分子動力學模擬奈米壓印的加工行為"，碩士論文，

國立清華大學，2006

46. 曾煥錩，以分子動力學模擬高分子的擠出加工行為，博士研究，

國立交通大學，2006

47. Huan-Chuang Tseng, Jiann-Shing Wu, Rong-Yeu Chang ,”Surface phenomena of nano-extrusion flow behavior of a polyethylene melt by molecular dynamics simulation “, 41st International Symposium on Macromolecules, Macro 2006, Av. Sernambetiba, 2630 Barra da Tijuca - CEP 22620-170 - Rio de Janeiro (Brazil)

48. Jenn-Jye Wang, Rong-Yeu Chang, “The Study of the Application of Molecular Dynamics On Contraction-Expansion Flow “ , 41st International Symposium on Macromolecules, Macro 2006, Av.

Sernambetiba, 2630 Barra da Tijuca - CEP 22620-170 - Rio de Janeiro (Brazil)

49. Rong-Yeu Chang, Chi-Fu Dai “ The Fractional Phenomenon of nano

Polymer Thin Films by Shear Deformation”, 41st International Symposium on Macromolecules, Macro 2006, Av. Sernambetiba, 2630 Barra da Tijuca - CEP 22620-170 - Rio de Janeiro (Brazil)

50. Rong-Yeu Chang, Chun-I Lin, Chi-Fu Dai, “Molecular Dynamics Simulation of Nanoimprinting at Different Process Condition”, pp2556-2560, Annual Technical Conference Proceedings, SPE Antec 2006, Charlotte, North Carolina, May 7-11, 2006 (USA)

51. Huan-Chuang Tseng, Jiann-Shing Wu, Rong-Yeu Chang, ,

“Application of Parallel Computing on Die Swell of Nano-scale Polymer Extrusion”, pp2325-2329, Annual Technical Conference Proceedings, SPE Antec 2006, Charlotte, North Carolina, May 7-11, 2006(USA)

52. Rong-Yeu Chang, Chi-Fu Dai, “Analyze Rheology of Polymer Thin Film by Nano-Rheometrics Simulation”, pp1258-1264, vol1, ANTEC 2005, SPE’s 63th Annual Technical Conference, Boston, U.S.A., 2005

Appendix A 減縮單位轉換

由於防止計算數值過小而造成電腦計算溢位的問題，因此通常都 會採用減縮單位來處理計算數值。

本研究中模擬的基本單位為水分子中的O，因此所有減縮單位皆 以此為基本單位，主要設定的部分為氧分子的質量、特徵長度與能 量，以及其他衍生的參數性質，如表A.1 所示。

表A.1 減縮單位換算表 減縮單位相關參數數值 SI 制單位

Mass m 1.8x10^-2(kg/mole) Length σ 3.166x10^-10(m)

Energy ε 648.923(J/mole) Time τ 1.667x10^-12(s)

Density 1(g/cm³)

Pressure 2.04966x10³²(Pa/mole) Temperature 78.113(K)