二維柱狀液體中之Tetratic 整齊因子及慢動力行為

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蘇彥碩(Yen-Shuo Su) 查詢紙本館藏

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論文名稱

二維柱狀液體中之Tetratic 整齊因子及慢動力行為
(Tetratic Order and Slow Dynamics of 2D Rodlike Liquids)

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摘要(中)

急速冷卻液體至熔點以下可防止結晶程序的發生。此過程稱為焠火。焠火液體的動力行為不但慢並且顯露出異質性。過去十年間，藉由分子動力行為以及膠體粒子實驗，焠火液體的異質運動的微觀起源被廣泛的研究，然而為了防止結晶程序的發生，普遍將粒子尺寸控制為不均勻。考慮到真實液體分子間的交互作用多半非均向，是否非均向交互作用可以取代粒子尺寸的不均勻性以防止結晶化的發生是一重要的開放問題。在此工作中，藉由 Langevin 動力模擬，我們研究了二維柱狀液體在暫態及穩態下的動力及相行為。在均向液體及結晶態之間的過渡tetratic態在降溫下被辨識。雖然此狀態下之位能高於結晶態，穩定的區域tetratic整齊結構提供了高度能量障蔽以防止結晶行為的發生。類似於典型過冷液體，在此tetratic狀態下的非均質動力行為亦被觀測。更進一步，平移跟旋轉自由度的擴散運動隨溫度變化發生了分離，但位移跟指向變化間的關聯性卻隨之上升。此一看似矛盾的結果可藉由此系統的典型集體運動描述。在低溫時旋轉方向的躍遷會破壞區域整齊性並導致周遭結構平移方向的躍遷，此一現象意味著指向方向的躍遷無法獨立的發生。反之，平移方向的躍遷可獨立發生不牽涉到指向方向的改變。此單方向的連結可提供一關於過冷液體中平移及旋轉運動關聯性之解釋。縮短柱狀液體分子之長度可壓抑tetratic結構的產生並仍可防止結晶化的發生。此結果意味著非均向性幾何形狀對結晶化程序有極為重要的影響。

摘要(英)

Rapid cooling below the melting temperature can prevent liquids from crystallization. The dynamics of the quenched liquid is slow and heterogeneous. In the past decade, the origin of the slow and heterogeneous motion of the quenched liquid was studied by the molecular dynamics (MD) simulation or colloidal experiments. However, to prevent crystallization, some size inhomogeneity are commonly introduced into the system. Considering that the interaction of real liquid molecules are usually anisotropic, can the anisotropic interaction replace the size inhomogeneity to prevent crystallization is still an open and important issue. In this work, we study the phase behavior and the dynamics of 2D rodlike liquids in different transient and steady states through the Langevin dynamics simulation. An intermediate tetratic phase is identified between the isotropic liquid state and the crystal state under cooling. Although the potential energy of the phase is higher than that of the crystal, the stable local tetratic orders provide a high barrier to prevent crystallization. Similar to the typical supercooled liquid, the heterogeneous dynamics in the tetratic state is observed. Moreover, the translational and orientational diffusions in the system are decoupled but the correlation between displacement and orientation change shows the increased coupling. The conflict can be explained by the typical cooperative excitations of the system. At low temperature, the occurrence of the orientational hopping deteriorates the local structure and induces the surrounding translational hopping. It means that the orientational hopping cannot independently occur. On the contrary, the translational hopping can independently occur without inducing any orientation change. The unilateral coupling may be a building block to explain the similar behavior about the coupling and decoupling between translational and rotational dynamics in a supercooled liquid. Although the presence of the tetratic order of make the system different from the standard supercooled liquid, it is observed that shorten the rod length can suppress the formation of the tetratic order and still sufficiently prevent crystallization. The result suggests the importance of the anisotropic shape of particles to prevent crystallization.

關鍵字(中)

★ 液晶
★ 過冷液體
★ 慢動態
★ 玻璃化

關鍵字(英)

★ liquid crystal
★ supercooled liquid
★ slow dynamics
★ glassy behavior

論文目次

1 Introduction 1
2 Background and Theory 7
2.1 General Behaviors of a Liquid . . . . . . . . . . . . . . . . . . 7
2.1.1 Structure of a Liquid . . . . . . . . . . . . . . . . . . 7
2.1.2 Dynamics of a Liquid . . . . . . . . . . . . . . . . . . . 9
2.1.3 Simple Liquid and Some Modeling Systems . . . . . . . 11
2.1.4 Stokes-Einstein Relation and the Stokes-Einstein-Debye
Relation . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2 Two-dimensional Melting Transition . . . . . . . . . . . . . . . 15
2.2.1 Topological Defect . . . . . . . . . . . . . . . . . . . . 15
2.2.2 KTHNY Theory . . . . . . . . . . . . . . . . . . . . . 16
2.3 Supercooled Liquid and Glass Transition . . . . . . . . . . . . 18
2.3.1 General Behaviors of a Supercooled Liquid . . . . . . 18
2.3.2 Dynamic Heterogeneity of a Supercooled Liquid . . . . 20
2.4 Liquid Crystal Behavior . . . . . . . . . . . . . . . . . . . . . 21
2.4.1 Nematic and Smectic Mesophase and Associated Mi-
crodynamics . . . . . . . . . . . . . . . . . . . . . . . . 22
2.4.2 Phase Transition in a 2d Rodlike Liquid . . . . . . . . 23
3 Simulation 25
3.1 Simulation Model . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.1.1 Model of Rodlike Particles . . . . . . . . . . . . . . . . 25
3.1.2 Equation of Motion . . . . . . . . . . . . . . . . . . . . 27
3.1.3 Anisotropic friction coecient . . . . . . . . . . . . . . 29
3.1.4 Parameter Setting and Numerical Method . . . . . . . 30
3.2 Computation Methods . . . . . . . . . . . . . . . . . . . . . . 31
3.2.1 Periodic Boundary Condition . . . . . . . . . . . . . . 31
3.2.2 Subbox Calculations . . . . . . . . . . . . . . . . . . . 33
3.2.3 Neighboring List Generator . . . . . . . . . . . . . . . 33
4 Result and Discussion 35
4.1 Transient evolution of the rodlike liquid . . . . . . . . . . . . . 35
4.1.1 Quenching a rodlike liquid . . . . . . . . . . . . . . . . 35
4.1.2 Hysteresis and the formation of the tetratic phase . . . 43
4.2 The dynamics in the tetratic phase . . . . . . . . . . . . . . . 50
4.2.1 Ordering in the tetratic phase . . . . . . . . . . . . . . 50
4.2.2 Heterogeneous dynamics in the tetratic phase . . . . . 51
4.2.3 Collective excitation and the coupled dynamics . . . . 63
4.3 Suppressing the tetratic order . . . . . . . . . . . . . . . . . . 67
4.3.1 Supercooled liquid behavior of the short rodlike liquid 67
5 Conclusion 71

參考文獻

[1] J. P. Hansen and I. R. McDonald, Theory of Simple Liquids (ACA-
DEMIC PRESS LIMITED 1986).
[2] J.L. Yarnell, M.J. Katz, R.G. Wenzel, Phys. Rev. A 7, 2130 (1974).
[3] P. M. Chaikin and T. C. Lubensky, Principles of Condensed Matter
Physics (Cambridge University Press 1995).
[4] P. N. Pusey, W. van Megen, P. Bartlett, B. J. Ackerson, J. G. Rarity,
and S. M. Underwood, Phys. Rev. Lett. 63, 2753 (1989).
[5] E. R. Weeks, J. C. Crocker, A. C. Levitt. A. Schoeld, and D. A. Weitz,
Science 287, 627 (2000).
[6] U. Gasser, Eric R. Weeks, A. Schoeld, P.N. Pusey, and D. A. Weitz,
Science 292, 258 (2001).
[7] L. Assoud, F. Ebert, P. Keim, R. Messina, G. Maret, and H. Lowen,
Phys. Rev. Lett. 102,238301 (2009).
[8] Y. Peng, Z. Wang, A. M. Alsayed, A. G. Yodh, and Y. Han, Phys. Rev.
Lett. 104, 205703 (2010).
[9] H. M. Jaeger, S. R. Nagel, and R. P. Behringer, Rev. Mod. Phys. 68,
1259 (1996).
[10] P. M. Reis, R. A. Ingale, and M. D. Shattuck, Phys. Rev. Lett. 98,188301
(2007)
[11] K. Watanabe and H. Tanaka, Phys. Rev. Lett. 100, 158002 (2008).
[12] L. I, W. T. Juan, C. H. Chiang, J. H. Chu, Science 272, 1626 (1996).
[13] Y.J. Lai and L. I, Phys. Rev. Lett. 89, 155002 (2002).
[14] C. Yang, C. W. Io, and L. I, Phys. Rev. Lett. 109, 225003 (2012).
[15] J. Q. Broughton, G. H. Gilmer, and J. D. Weeks, Phys. Rev. B 25, 4651
(1982).
[16] K. J. Naidoo and J. Schnitker, J. Chem. Phys. 100, 3114 (1994).
[17] L. A. Cameron, M. J. Footer, A. van Oudenaarden, and J. A. Theriot,
Proc. Natl. Acad. Sci. USA 96, 4909 (1999).
[18] H. P. Zhang , A. Be′er, E. L. Florin, and H. L. Swinney, Proc. Natl.
Acad. Sci. USA 107, 13626 (2010).
[19] T. C. Halsey and W. Toor, Phys. Rev. Lett. 65, 2820 (1990).
[20] T. C. Halsey, J. E. Martin, and D. Adolf, Phys. Rev. Lett. 68, 1519
(1992).
[21] V. N. Manoharan, M. T. Elsesser, and D. J. Pine, Science 301, 483
(2003).
[22] K. Zhao and T. G. Mason, Phys. Rev. Lett. 103,208302 (2009)
[23] M. D. Ediger, C. A. Angell and S. R. Nagel, J. Phys. Chem. 100, 13200
(1996).
[24] S. A. Kivelson, X. Zhao, D. Kivelson, T. M. Fischer, C. M. Knobler, J.
Chem. Phys. 101, 2391 (1994).
[25] Y. Han, N. Y. Ha, A. M. Alsayed, and A. G. Yodh, Phys. Rev. E 77,
041406 (2008).
[26] M. A. Bates and D. Frenkel, J. Chem. Phys. 112, 10034 (2000).
[27] R. Huang, I. Chavez, K. M. Taute, B. Lukic’, S. Jeney , M. G. Raizen
and E.-L. Florin, Nature Physics 7, 576 (2011).
[28] Aleksandar Donev, Joshua Burton, Frank H. Stillinger, and Salvatore
Torquato, Phys. Rev. B 73, 054109 (2006).
[29] Tanja Schilling and Daan Frenkel, Phys. Rev. Lett. 92, 085505 (2004).
[30] P. G. Debenedetti and F. H. Stillinger, Nature. 410, 259 (2001).
[31] Andrea Cavagna, Physics Reports 476 (2009).
[32] Ludovic Berthier and Giulio Biroli, Rev. Mod. Phys. 83, 587 (2011).
[33] Hajime Tanaka, Takeshi Kawasaki, Hiroshi Shintani and Keiji Watan-
abe, Nature Materials 9, 324 (2010).
[34] Peter Yunker, Zexin Zhang, Kevin B. Aptowicz, and A. G. Yodh, Phys.
Rev. Lett. 103, 115701 (2009).
[35] Zhongyu Zheng, Feng Wang, and Yilong Han, Phys. Rev. Lett. 107,
065702 (2011).
[36] Hiroshi Shintani and Hajime Tanaka, Nature Phys. 2, 200 (2006).
[37] Yen-Shuo Su, Yu-Hsuan Liu, and Lin I, Phys. Rev. Lett. 109, 195002
(2012).
[38] K. J. Strandburg, Bond-Orientational Order in Condensed Matter Sys-
tems (Springer, New York, 1992).
[39] Song-Ho Chong, and Walter Kob, Phys. Rev. Lett. 102, 025702 (2009).
[40] Kazem V. Edmond , Mark T. Elsesser , Gary L. Hunter , David J. Pine
, and Eric R. Weeks, Proc. Natl. Acad. Sci. USA 109, 17891 (2012).
[41] J. Jonas and J. A. Akai, J. Phys. Chem. 66, 4946 (1977).
[42] Alessandro Patti, and Alejandro Cuetos, Phys. Rev. E 86, 011403
(2009).
[43] Alessandro Patti, Djamel El Masri, Rene’van Roij, and Marjolein Dijk-
stra, Phys. Rev. Lett. 103, 248304 (2009).
[44] Vijay Narayan, Narayanan Menon, and Sriram Ramaswamy, J. Stat.
Mech. P01005 (2006).
[45] Taro Kihara, Rev. Mod. Phys. 25, 831 (1953)
[46] Muataz S. Al-Barwani and Michael P. Allen, Phys. Rev. E 62, 6706
(2000).
[47] A. Cuetos, B. Mart’nez-Haya, L. F. Rull, and S. Lago, J. Chem. Phys.
117, 2934 (2002).
[48] S. Tavaddod, M.A. Charsooghi, F.Abdi, H.R. Khalesifard,
andR.Golestanian, Eur. Phys. J. E 34, 16 (2011).

指導教授

伊林(Lin I)

審核日期

2014-5-16

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