玻璃化转变的分子串模型中分子串弛豫模式的计算机模拟

赵兴宇; 王丽娜; 樊小辉; 张丽丽; 卫来; 张晋鲁; 黄以能

doi:10.7498/aps.60.036403

摘要

基于玻璃化转变的分子串模型的哈密顿量(Hamiltonian),提出了模拟分子串第一和第二弛豫模式的蒙特卡罗(Monte Carlo)模拟方案.模拟得出的第一和第二弛豫模式的弛豫时间,与分子串模型中分子串弛豫方程所预言的结果完全一致,即理论预期和模拟结果相互印证.这不仅说明了分子串模型的分子串弛豫方程、至少是第一和第二弛豫模式的理论预言的正确性,同时也表明了本文所提出的模拟方法的有效性,并进一步明晰了分子串中分子的随机涨落和跃迁运动的图像,也为三态甚至是多态的分子串弛豫动力学研究,以及对进一步模拟分子串之

关键词:

Abstract

Monte Carlo protocols to simulate the string relaxation modes are proposed according to the Hamiltonian of the molecule-string model for glass transition. The simulated relaxation times of the 1st and 2nd modes are consistent with the predictions of the string relaxation equation of the model,thus matually verifying each other. The results show the reasonableness of not only the string relaxation equation, at least the theoretical predictions of the 1st and 2nd relaxation modes, but also the proposed simulation method, and further clarify the pictures of the molecule random energy fluctuations and jumps of the molceules in the strings, as well as provide gist and clews to the study of the multi-state molecule string relaxation dynamics and the further simulation of the complex interactions between the molecule strings.

Keywords:

作者及机构信息

1.
伊犁师范学院新疆凝聚态相变与微结构实验室,伊宁 835000

基金项目: 国家自然科学基金(批准号:10774064, 30860076),新疆自治区教育厅重点基金(批准号:XJEDU2007137)和新疆自治区科技厅自然基金(批准号:200821104,200821184)资助的课题.

Authors and contacts

1.
Xinjiang Laboratory of Phase Transitions and Microstructures of Condensed Matter Physics,Yili Normal University, Yining 835000, China

参考文献

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[5]	Zhao Z F, Wen P, Sheck C H, Wang W H 2007 Phys. Rev. B 75 174201
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[8]	Turnbull D 1949 Contem. Phys. 10 473
[9]	Cohen M H, Grest G S 1979 Phys. Rev. B 20 1077
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[12]	Das S P 2004 Rev. Mod. Phys. 76 785
[13]	Ritort F, Sollich P 2003 Adv. Phys. 52 219
[14]	Kivelson D, Zhao X, Nussinov Z, Tarjus G 1995 Physica A 219 27
[15]	Chamberlin R V 1995 Phys. Rev. Lett. 82 2520
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[20]	Brand R, Lunkenheimer P, Loidl A 2002 J. Chem. Phys. 116 10386
[21]	Lunkenheimer P, Loidl A 2006 J. Non-Crystal. Sol. 352 4556
[22]	Weeks E R, Crocker J C, Levitt A C, Schofield A 2000 Science 287 627
[23]	Pouligny B, Malzbender R, Ryan P, Clark N A 1990 Phys. Rev. B 42 988
[24]	Glotzer S C 2000 J. Non-Cryst. Solids 274 342
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[27]	Zhang J L, Zhou H W, Wu W H, Huang Y N Appl. Phys. Lett. 92 131906
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[29]	Jiang J G, Huang Y N 2009 Comp. Phys. Commun. 180 177
[30]	Jiang J G, Huang Y N, Wu J C 2009 J. Stat. Phys. 136 984
[31]	Guo X Z, Zhou H W, Zhang L L, Wu W H, Zhang J L, Huang Y N 2010 Acta Phys. Sin. 59 417 (in Chinese) [郭秀珍、周恒为、张丽丽、吴文慧、张晋鲁、黄以能 2010 59 417]
[32]	Zhang J L, Wang L N, Zhou H W, Zhang L L, Zhao X Y, Huang Y N 2010 Chin. Phys. B 19 056403
[33]	Chen Z H, Liu L J, Zhang B, Xi Y, Wang Q, Zu F Q 2004 Acta Phys. Sin. 53 3839 (in Chinese) [陈志浩、刘兰俊、张博、席赟、王强、祖方遒 2004 53 3839]
[34]	Dong Z G, Shen M R, Xu R, Gan Z Q, Ge S B 2002 Acta Phys. Sin. 51 2896 (in Chinese) [董正高、沈明荣、徐闰、甘肇强、葛水兵 2002 51 2896]
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[37]	Zhao M L, Zhong W L, Wang C L, Wang J F, Zhang P L 2002 Acta Phys. Sin. 51 1856 (in Chinese) [赵明磊、钟维烈、王春雷、王矜奉、张沛霖 2002 51 1856]
[38]	Li S T, Cheng P F, Zhao L, Li J Y 2009 Acta Phys. Sin. 58 523 (in Chinese) [李盛涛、成鹏飞、赵雷、李建英 2009 58 523]
[39]	Zhao S C, Li G R, Zhang L N, Wang T B, Ding A L 2006 Acta Phys. Sin. 55 3711 (in Chinese) [赵苏串、李国荣、张丽娜、王天宝、丁爱丽 2006 55 3711]
[40]	Jiang X P, Fang J W, Zeng H R, Pan X M, Chen D R, Yin Q R 2000 Acta Phys. Sin. 49 802 (in Chinese) [江向平、方健文、曾华荣、潘晓明、陈大任、殷庆瑞 2000 49 802]
[41]	Zhao M L, Wang C L, Zhong W L, Zhang P L, Wang J F 2002 Acta Phys. Sin. 51 420 (in Chinese) [赵明磊、王春雷、钟维烈、张沛霖、王矜奉 2002 51 420]
[42]	Zhao M L, Yi X J, Wang C L, Wang J F, Zhang J L 2006 Chin. Phys. 15 1611
[43]	Wen C 1995 Chin. Phys. 4 54
[44]	Zhao H P, Liu Z Y, Liu Y Y 2001 Chin. Phys. 10 35
[45]	Wang X J, Gong Z Q, Qian Y F, Zhu J, Chen X B 2007 Chin. Phys. 16 2131
[46]	Wang Q, Qiang J B, Wang Y M, Xia J H, Lin Z, Zhang X F, Dong C 2006 Acta Phys. Sin. 55 378 (in Chinese) [王清、羌建兵、王英敏、夏俊海、林哲、张新房、董闯 2006 55 378]
[47]	Zhang H T, Liu R S, Hou Z Y, Zhang A L, Chen X Y, Du S H 2006 Acta Phys. Sin. 55 2409 (in Chinese) [张海涛、刘让苏、侯兆阳、张爱龙、陈晓莹、杜生海 2006 55 2409]
[48]	Zhou H W, Zhang J L, Huang Y N, Ying X N, Zhang L, Wu W H, Shen Y F 2007 Acta Phys. Sin. 56 6547 (in Chinese) [周恒为、张晋鲁、黄以能、应学农、张亮、吴文惠、沈异凡 2007 56 6547]
[49]	Wang Z Y, Yang Y S, Tong W H, Li H Q, Hu Z L 2007 Acta Phys. Sin. 56 1543 (in Chinese) [王珍玉、杨院生、童文辉、李会强、胡壮麒 2007 56 1543]
[50]	Yi X H, Liu R S, Tian Z A, Hou Z Y, Wang X, Zhou Q Y 2006 Acta Phys. Sin. 55 5386 (in Chinese) [易学华、刘让苏、田泽安、侯兆阳、王鑫、周群益 2006 55 5386]
[51]	Xia M X, Meng Q G, Zhang S G, Ma C L, Li J G 2006 Acta Phys. Sin. 55 6543 (in Chinese) [夏明许、孟庆格、张曙光、马朝利、李建国 2006 55 6543]
[52]	Yu P, Bai H Y, Tang M B, Wang W L, Wang W H 2005 Acta Phys. Sin. 54 3284 (in Chinese) [余鹏、白海洋、汤美波、王万录、汪卫华 2005 54 3284]
[53]	Hou Z Y, Liu R S, Li C S, Zhou Q Y, Zheng C X 2005 Acta Phys. Sin. 54 5723 (in Chinese) [侯兆阳、刘让苏、李琛珊、周群益、郑采星 2005 54 5723]
[54]	Wei H Q, Long Z L, Zhang Z C, Li X A, Peng J, Zhang P 2009 Acta Phys. Sin. 58 2556 (in Chinese) [危洪清、龙志林、张志纯、李乡安、彭建、张平 2009 58 2556]
[55]	Hou Z Y, Liu R S, Wang X, Tian Z A, Zhou Q Y, Chen Z H 2007 Acta Phys. Sin. 56 376 (in Chinese) [侯兆阳、刘让苏、王鑫、田泽安、周群益、陈振华 2007 56 376]
[56]	Li J, Zhang Y, Zhang S C 1996 Acta Phys. Sin. 45 1359 (in Chinese) [李健、张烨、张声春 1996 45 1359]
[57]	Zhao J Z,Liu J,Zhao Y, Hu Z Q 2007 Acta Phys. Sin. 56 443 (in Chinese) [赵九洲、刘俊、赵毅、胡壮麒 2007 56 443]
[58]	Zhao Z F, Zhang Z, Li Z, Wei P, Zhao D Q, Pan M X, Wang W L, Wang W H 2004 Acta Phys. Sin. 53 850 (in Chinese) [赵作峰、张志、李正、闻平、赵德乾、潘明详、王万录、汪卫华 2004 53 850] [59] Vogel H 1921 Phys. Z. 22 645
[59]	Fulcher G S 1925 J. Am. Ceram. Soc. 8 339
[60]	Tammann G, Hesse W 1926 Z. Anorg. Allg. Chem. 156 245
[61]	Kohlrausch R 1874 Ann. Phys. Chem. (Leipzig) 91 179
[62]	Williams G, Watts D C 1970 Trans. Faraday Soc. 66 80
[63]	Davidson D W, Cole R H 1950 J. Chem. Phys. 18 1417
[64]	Bttcher C F J, Bordewijk P 1978 Theory of Electric Polarization (Amsterdam: Elsevier) vol. II
[65]	Yin Z W 2003 Dielectrics Physics (Beijing: Scientific Publication) 2nd edition
[66]	Combs A J, Yip S 1983 Phys. Rev. B 28 6873
[67]	Rouse P E 1953 J. Chem. Phys. 21 1273
[68]	Zimm B 1956 J. Chem. Phys. 24 269
[69]	Huang Y N unpublished

施引文献

[1]	Anderson P W 1995 Science 267 1615
[2]	Angell C A 1995 Science 267 1924
[3]	Stillinger F H 1995 Science 267 1935
[4]	Liu Y H, Wang G, Wang R J, Zhao D Q, Pan M X, Wang W H 2007 Science 315 1385
[5]	Zhao Z F, Wen P, Sheck C H, Wang W H 2007 Phys. Rev. B 75 174201
[6]	Ediger M D, Angell C A, Nagel S R 1996 J. Phys. Chem. 100 13200
[7]	Donth E 2001 The Glass Transition (Berlin: Spring)
[8]	Turnbull D 1949 Contem. Phys. 10 473
[9]	Cohen M H, Grest G S 1979 Phys. Rev. B 20 1077
[10]	Adam G, Gibbs J H 1965 J. Chem. Phys. 43 139
[11]	Ngai K L 1979 Comm. Sol. Stat. Phys. 9 127; 149
[12]	Das S P 2004 Rev. Mod. Phys. 76 785
[13]	Ritort F, Sollich P 2003 Adv. Phys. 52 219
[14]	Kivelson D, Zhao X, Nussinov Z, Tarjus G 1995 Physica A 219 27
[15]	Chamberlin R V 1995 Phys. Rev. Lett. 82 2520
[16]	Huang Y N, Wang C J, Riande E 2005 J. Chem. Phys. 122 144502
[17]	Huang Y N, Zhang J L, Ying X N 2006 Prog. Phys. 26 359 (in Chinese) [黄以能、张晋鲁、应学农2006 物理学进展 26 359]
[18]	Huang Y N 2006 J. Yili Normal University 3 39
[19]	Lunkenheimer P, Schneider U, Brand R, Loidl A 2000 Contemp. Phys. 41 15
[20]	Brand R, Lunkenheimer P, Loidl A 2002 J. Chem. Phys. 116 10386
[21]	Lunkenheimer P, Loidl A 2006 J. Non-Crystal. Sol. 352 4556
[22]	Weeks E R, Crocker J C, Levitt A C, Schofield A 2000 Science 287 627
[23]	Pouligny B, Malzbender R, Ryan P, Clark N A 1990 Phys. Rev. B 42 988
[24]	Glotzer S C 2000 J. Non-Cryst. Solids 274 342
[25]	The reasons we think that the basic structural and dynamical units of liquid state being the dynamical molecular string rather than the dynamical branched clusters are: 1) formally, supposing to first 'walk’ along a branch of a cluster, and if we meet the cross point of two or more branches, then we will randomly choose a branch to 'walk’, meanwhile 'cut’ the other branches. By doing such process repeatedly, the cluster will formally be divided into 'individual’ strings; 2) physically, the above processes are to re-express the cluster by some interacting strings, and the inter-string interacting points are the cross points of the branches; 3) mathematically, the above processes bring the corresponding mathematical problems become more easy to solve.
[26]	Wu W H, Zhang J L, Zhou H W, Huang Y N, Zhang L, Ying X N 2008 Appl. Phys. Lett. 92 011918
[27]	Zhang J L, Zhou H W, Wu W H, Huang Y N Appl. Phys. Lett. 92 131906
[28]	Zhang L L, Zhang J L, Jiang J G, Zhou H W, Huang Y N 2008 Acta Phys. Sin. 57 5817 (in Chinese) [张丽丽、张晋鲁、蒋建国、周恒为、黄以能 2008 57 5817]
[29]	Jiang J G, Huang Y N 2009 Comp. Phys. Commun. 180 177
[30]	Jiang J G, Huang Y N, Wu J C 2009 J. Stat. Phys. 136 984
[31]	Guo X Z, Zhou H W, Zhang L L, Wu W H, Zhang J L, Huang Y N 2010 Acta Phys. Sin. 59 417 (in Chinese) [郭秀珍、周恒为、张丽丽、吴文慧、张晋鲁、黄以能 2010 59 417]
[32]	Zhang J L, Wang L N, Zhou H W, Zhang L L, Zhao X Y, Huang Y N 2010 Chin. Phys. B 19 056403
[33]	Chen Z H, Liu L J, Zhang B, Xi Y, Wang Q, Zu F Q 2004 Acta Phys. Sin. 53 3839 (in Chinese) [陈志浩、刘兰俊、张博、席赟、王强、祖方遒 2004 53 3839]
[34]	Dong Z G, Shen M R, Xu R, Gan Z Q, Ge S B 2002 Acta Phys. Sin. 51 2896 (in Chinese) [董正高、沈明荣、徐闰、甘肇强、葛水兵 2002 51 2896]
[35]	Shao S F, Zheng P, Zhang J L, Niu X K, Wang C L, Zhong W L 2006 Acta Phys. Sin. 55 6661 (in Chinese) [邵守福、郑鹏、张家良、钮效鹍、王春雷、钟维烈 2006 55 6661]
[36]	Liu P, He Y, Li J, Zhu G Q, Bian X B 2007 Acta Phys. Sin. 56 5489 (in Chinese) [刘鹏、贺颖、李俊、朱刚强、边小兵 2007 56 5489]
[37]	Zhao M L, Zhong W L, Wang C L, Wang J F, Zhang P L 2002 Acta Phys. Sin. 51 1856 (in Chinese) [赵明磊、钟维烈、王春雷、王矜奉、张沛霖 2002 51 1856]
[38]	Li S T, Cheng P F, Zhao L, Li J Y 2009 Acta Phys. Sin. 58 523 (in Chinese) [李盛涛、成鹏飞、赵雷、李建英 2009 58 523]
[39]	Zhao S C, Li G R, Zhang L N, Wang T B, Ding A L 2006 Acta Phys. Sin. 55 3711 (in Chinese) [赵苏串、李国荣、张丽娜、王天宝、丁爱丽 2006 55 3711]
[40]	Jiang X P, Fang J W, Zeng H R, Pan X M, Chen D R, Yin Q R 2000 Acta Phys. Sin. 49 802 (in Chinese) [江向平、方健文、曾华荣、潘晓明、陈大任、殷庆瑞 2000 49 802]
[41]	Zhao M L, Wang C L, Zhong W L, Zhang P L, Wang J F 2002 Acta Phys. Sin. 51 420 (in Chinese) [赵明磊、王春雷、钟维烈、张沛霖、王矜奉 2002 51 420]
[42]	Zhao M L, Yi X J, Wang C L, Wang J F, Zhang J L 2006 Chin. Phys. 15 1611
[43]	Wen C 1995 Chin. Phys. 4 54
[44]	Zhao H P, Liu Z Y, Liu Y Y 2001 Chin. Phys. 10 35
[45]	Wang X J, Gong Z Q, Qian Y F, Zhu J, Chen X B 2007 Chin. Phys. 16 2131
[46]	Wang Q, Qiang J B, Wang Y M, Xia J H, Lin Z, Zhang X F, Dong C 2006 Acta Phys. Sin. 55 378 (in Chinese) [王清、羌建兵、王英敏、夏俊海、林哲、张新房、董闯 2006 55 378]
[47]	Zhang H T, Liu R S, Hou Z Y, Zhang A L, Chen X Y, Du S H 2006 Acta Phys. Sin. 55 2409 (in Chinese) [张海涛、刘让苏、侯兆阳、张爱龙、陈晓莹、杜生海 2006 55 2409]
[48]	Zhou H W, Zhang J L, Huang Y N, Ying X N, Zhang L, Wu W H, Shen Y F 2007 Acta Phys. Sin. 56 6547 (in Chinese) [周恒为、张晋鲁、黄以能、应学农、张亮、吴文惠、沈异凡 2007 56 6547]
[49]	Wang Z Y, Yang Y S, Tong W H, Li H Q, Hu Z L 2007 Acta Phys. Sin. 56 1543 (in Chinese) [王珍玉、杨院生、童文辉、李会强、胡壮麒 2007 56 1543]
[50]	Yi X H, Liu R S, Tian Z A, Hou Z Y, Wang X, Zhou Q Y 2006 Acta Phys. Sin. 55 5386 (in Chinese) [易学华、刘让苏、田泽安、侯兆阳、王鑫、周群益 2006 55 5386]
[51]	Xia M X, Meng Q G, Zhang S G, Ma C L, Li J G 2006 Acta Phys. Sin. 55 6543 (in Chinese) [夏明许、孟庆格、张曙光、马朝利、李建国 2006 55 6543]
[52]	Yu P, Bai H Y, Tang M B, Wang W L, Wang W H 2005 Acta Phys. Sin. 54 3284 (in Chinese) [余鹏、白海洋、汤美波、王万录、汪卫华 2005 54 3284]
[53]	Hou Z Y, Liu R S, Li C S, Zhou Q Y, Zheng C X 2005 Acta Phys. Sin. 54 5723 (in Chinese) [侯兆阳、刘让苏、李琛珊、周群益、郑采星 2005 54 5723]
[54]	Wei H Q, Long Z L, Zhang Z C, Li X A, Peng J, Zhang P 2009 Acta Phys. Sin. 58 2556 (in Chinese) [危洪清、龙志林、张志纯、李乡安、彭建、张平 2009 58 2556]
[55]	Hou Z Y, Liu R S, Wang X, Tian Z A, Zhou Q Y, Chen Z H 2007 Acta Phys. Sin. 56 376 (in Chinese) [侯兆阳、刘让苏、王鑫、田泽安、周群益、陈振华 2007 56 376]
[56]	Li J, Zhang Y, Zhang S C 1996 Acta Phys. Sin. 45 1359 (in Chinese) [李健、张烨、张声春 1996 45 1359]
[57]	Zhao J Z,Liu J,Zhao Y, Hu Z Q 2007 Acta Phys. Sin. 56 443 (in Chinese) [赵九洲、刘俊、赵毅、胡壮麒 2007 56 443]
[58]	Zhao Z F, Zhang Z, Li Z, Wei P, Zhao D Q, Pan M X, Wang W L, Wang W H 2004 Acta Phys. Sin. 53 850 (in Chinese) [赵作峰、张志、李正、闻平、赵德乾、潘明详、王万录、汪卫华 2004 53 850] [59] Vogel H 1921 Phys. Z. 22 645
[59]	Fulcher G S 1925 J. Am. Ceram. Soc. 8 339
[60]	Tammann G, Hesse W 1926 Z. Anorg. Allg. Chem. 156 245
[61]	Kohlrausch R 1874 Ann. Phys. Chem. (Leipzig) 91 179
[62]	Williams G, Watts D C 1970 Trans. Faraday Soc. 66 80
[63]	Davidson D W, Cole R H 1950 J. Chem. Phys. 18 1417
[64]	Bttcher C F J, Bordewijk P 1978 Theory of Electric Polarization (Amsterdam: Elsevier) vol. II
[65]	Yin Z W 2003 Dielectrics Physics (Beijing: Scientific Publication) 2nd edition
[66]	Combs A J, Yip S 1983 Phys. Rev. B 28 6873
[67]	Rouse P E 1953 J. Chem. Phys. 21 1273
[68]	Zimm B 1956 J. Chem. Phys. 24 269
[69]	Huang Y N unpublished

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