本文運用隨機程序模擬，將勞氏模型的方向性和長度分離，觀察兩者在單一應變後鬆弛的行為。這樣的分子鏈內部訊息一般很難甚至無法直接從傳統數學方法得到。模擬結果顯示鏈長被拉伸後，方向性鬆弛會有延遲的現象。另外我們發現，過去DE模型對勞氏鏈長度縮回的假設，會有應變相依 (strain dependent) 的情形。對此我們根據勞氏鏈模擬的結果，修改了原始DE模型的假設，得到無應變相依 (strain independent) 的長度縮回方程式。
至於高分子高濃度系統的非線性應力鬆弛行為，我們利用勞式鏈模擬長度縮回的機制，發現鬆弛分佈較狹窄的一維勞氏鏈在定量上較符合實驗數據。另外，由勞氏鏈模擬得到的長度縮回方程式，定量上的表現比DE模型佳，且無應變相依的情形。

Stochastic schemes are employed to simulate the nonlinear relaxation dynamics of the Rouse chain that lack close-form solutions. The validity of stochastic simulations is confirmed by showing excellent agreement between the simulation results and existing analytical solutions for the linear dynamics. By artificially separating the orientation and stretch retractions of a Rouse chain following single step-strain deformations, the coupling between these two molecular mechanisms can be investigated. The simulation results show that un-relaxed chain tension will lead to a general delay in the corresponding orientation relaxation. Similarly, the orientation relaxation also seems to have an important impact on the corresponding stretch relaxation. The implications of these findings are discussed. In contrast to the assumption in the Doi-Edwards model in modeling chain retraction of the primitive chain, the rate of chain retraction of a Rouse chain is found to be strain dependent. Based largely on the simulation results, we here propose a simple differential equation that describes the chain-stretch relaxation of the Rouse chain very well and applies to all strain magnitudes. The merit of the new proposal for primitive chain retraction is checked with an existing set of nonlinear relaxation data on a concentrated polystyrene solution.

誌謝…………………………Ⅰ
中文摘要… … … … … Ⅱ
英文摘要… … … … Ⅲ
本文目錄 … …… … Ⅴ
圖表目錄 … … … Ⅶ
第一章 前言
1.1 簡介 … … … … 1
1.2 文獻回顧… … 1
1.3 研究動機 … … … 4
第二章 理論背景與計算方法(一)
2.1 勞氏模型理論背景… 6
2.2 勞氏模型模擬方法 … 8
第三章 結果與討論(一)
3.1 方向性的鬆弛行為… 12
3.1 鏈長的鬆弛行為… …16
第四章 理論背景與計算方法(二)
4.1 DE模型理論背景… 22
4.2 高濃度系統模擬方法…26
第五章 結果與討論(二)
5.1 高濃度系統高分子應力鬆弛行為… 30
第六章 結論 … … … … … … … 38
參考文獻… … … … … … … … … 40

1.Bird, R. B.; Curtiss, C. F.; Hassager, O.; Armstrong, R. C. Dynamics of Polymeric Liquids; John Wiley & Sons: New York, 1987
2.Rouse, P. E. J Chem Phys 1953, 21, 1273.
3.de Gennes, P. G. J Chem Phys 1971, 55, 572.
4.Ottinger, H. C. J Chem Phys 1989, 90, 463.
5.Wedgewood, L. E. J Non-Newtonian Fluid Mech 1989, 31, 127.
6.Prakash, J.R.; Ottinger, H. C. J Non-Newtonian Fluid Mech 1997, 71, 245.
7.Prakash, J.R.; Ottinger, H. C. Macromolecules 1999, 32, 2028.
8.Doi, M.; Edwards, S. F. J Chem Soc Faraday Trans, 1978, 74, 1789.
9.Doi, M.; Edwards, S. F. J Chem Soc Faraday Trans, 1978, 74, 1802.
10.Doi, M.; Edwards, S. F. J Chem Soc Faraday Trans, 1978, 74, 1818.
11.Doi, M. J Chem. Sci Polym Lett Ed 1981, 19, 265.
12.Graesslev, W. W. Adv Polym Sci 1982, 47, 67.
13.Tsenoglou, C. Am Chem Soc Polym Preprints 1987, 28, 185.
14.des Cloizeaux, J. Europhys. Lett 1988, 5, 437.
15.Marrucci, G.; Grizzuti, N. Gazz Chim Ital 1988, 118, 179.
16.Pearson, D. S.; Herbolzheimer, E.; Grizzuti, N.; Marrucci, G. J Chem Sci Polym Phys Ed 1991 29, 1589.
17.Ianniruberto, G.; Marrucci, G. J Non-Newtonian Fluid Mech 1996, 65, 241.
18.Mead, D. W.; Larson, R. G.; Doi, M. Marcomolecules 1998, 31, 7895.
19.Hua, C. C.; Schieber, J. D. J Chem Phys 1998, 109, 10018.
20.Doi, M.; Edwards, S. F. The Theory of Polymer Dynamics; Clarendon Press: Oxford, 1986
21.Briels, W. J. Theory of polymer dynamics lecture notes, Uppsala, 1994 unpublished, The full text can be downloaded from http:// www.tn.utwente.nl/cdr/PolymeerDictaat/..
22.陳志仁，蛇行運動理論之限制釋放隨機演算法，碩士論文，中正大學，民國八十九年。
23.Venerus, D. C.; Kahvand, H. J Polym Sci Polym Phys 1994, 32, 1531.
24.Mhetar, V. R.; Archear, L. A. J Non-Newtonian Fluid Mech 1999, 81, 71.