分子串模型中空间弛豫模式的弛豫动力学的蒙特卡罗模拟

樊小辉; 赵兴宇; 王丽娜; 张丽丽; 周恒为; 张晋鲁; 黄以能

doi:10.7498/aps.60.126401

摘要

基于玻璃化转变的分子串模型的分子串弛豫方程,提出了更为精确的模拟分子串中所有空间弛豫模式(SRM)的蒙特卡罗模拟方案. 模拟得出各个SRM的弛豫时间随温度和分子串长度的变化结果与分子串模型中分子串弛豫方程的预言完全一致,即理论预期和模拟结果相互印证. 应当指出,分子串能否作为液态中集体单元的必要条件是在考虑到分子串之间的不均匀随机相互作用后,分子串的所有SRM的定性特征是不能改变的,这就需要对不同分子串的SRM之间的耦合进行研究. 但是迄今为止,仍未发现相关的严格解,仅有近似的自洽弛豫平均场方法. 由此可知,所提出的模拟方案为研究不同分子串的SRM之间的耦合(包括上述自洽场的可行性)提供了必要的基础.

关键词:

Abstract

According to the molecule-string model for glass transition, a more exact Monte Carlo protocol to simulate all the spatial relaxation modes (SRMs) of the string are proposed. The variations of the simulated relaxation times of the SRMs with temperature and string length are consistent with the predictions of the string relaxation equation of the model, i.e. the theretical predictions and the simulation results verify each other. It should be pointed out that the necessary condition of molecule string used as a collective unit in liquid is that the qualitative characteristics of the SRMs cannot be changed when the inter-string interactions are taken into account. This needs to study the coupling between the SRMs, but till now, the corresponding exact solutions have not been achieved, and only the self-consistent relaxation mean-field method is vailable. Therefore, the present simulation protocol will provide a necessary basis to study the coupling between the SRMs of neighboring strings, including the feasibility of the mean-field method.

Keywords:

作者及机构信息

1.
伊犁师范学院物理科学与技术学院,新疆凝聚态相变与微结构实验室,伊宁 835000;

2.
南京大学物理学院,固体微结构物理国家重点实验室,南京 210093;

3.
新疆教育学院科研处,乌鲁木齐 830043

基金项目: 国家自然科学基金(批准号:10774064, 30860076)、新疆维吾尔自治区科技计划(批准号:200916126)和新疆维吾尔自治区自然科学基金(批准号:200821104,200821184)资助的课题.

Authors and contacts

1.
Laboratory of Phase Transitions and Microstructures in Condensed Matter Physics of Xinjiang, College of Physical Science and Technology, Yili Normal University, Yining 835000, China;

2.
National Laboratory of Solid State Microstructures, College of Physics, Nanjing University, Nanjing 210093, China;

3.
Research Department, Xinjiang Educational University, Urumqi 830043, China

参考文献

[1]	Anderson P W 1995 Science 267 1615
[2]
[3]	Angell C A 1995 Science 267 1924
[4]
[5]	Stillinger F H 1995 Science 267 1935
[6]	Liu Y H, Wang G, Wang R J, Zhao D Q, Pan M X, Wang W H 2007 Science 315 1385
[7]
[8]
[9]	Zhao Z F, Wen P, Sheck C H, Wang W H 2007 Phys. Rev. B 75 174201
[10]
[11]	Ediger M D, Angell C A, Nagel S R 1996 J. Phys. Chem. 100 13200
[12]	Donth E 2001 The Glass Transition (Berlin: Springer)
[13]
[14]
[15]	Turnbull D 1949 Contemp. Phys. 10 473
[16]
[17]	Cohen M H, Grest G S 1979 Phys. Rev. B 20 1077
[18]	Adam G, Gibbs J H 1965 J. Chem. Phys. 43 139
[19]
[20]
[21]	Ngai K L 1979 Commun. Sol. Stat. Phys. 9 127
[22]
[23]	Das S P 2004 Rev. Mod. Phys. 76 785
[24]
[25]	Ritort F, Sollich P 2003 Adv. Phys. 52 219
[26]	Kivelson D, Zhao X, Nussinov Z, Tarjus G 1995 Physica A 219 27
[27]
[28]
[29]	Chamberlin R V 1995 Phys. Rev. Lett. 82 2520
[30]	Huang Y N, Wang C J, Riande E 2005 J. Chem. Phys. 122 144502
[31]
[32]	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]
[33]
[34]	Huang Y N 2006 J. Yili Normal Univ. 3 39 (in Chinese) [黄以能 2006 伊犁师范学院学报 3 39]
[35]
[36]
[37]	Zhang J L, Wang L N, Zhou H W, Zhang L L, Zhao X Y, Huang Y N 2010 Chin. Phys. B 19 056403
[38]
[39]	Zhao X Y, Wang L N, Fan X H, Zhang L L, Wei L, Zhang J L, Huang Y N 2011 Acta Phys. Sin. 60 036403 (in Chinese) [赵兴宇、王丽娜、樊小辉、张丽丽、卫来、张晋鲁、黄以能 2011 物理学报 60 036403]
[40]
[41]	Bttcher C F J, Bordewijk P 1978 Theory of Electric Polarization (Amsterdam: Elsevier) Vol Ⅱ
[42]	Fang J X, Yin Z W 2003 Dielectrics Physics (2nd ed) (Beijing: Science Press) p50 (in Chinese) [方俊鑫、殷之文 2003 电介质物理学 (第二版) (北京: 科学出版社) 第50页]
[43]
[44]	Combs A J, Yip S 1983 Phys. Rev. B 28 6873
[45]
[46]	Glauber R G 1963 J. Math. Phys. 4 294
[47]
[48]	Weeks E R, Crocker J C, Levitt A C, Schofield A, Weitz D A 2000 Science 287 627
[49]
[50]	Pouligny B, Malzbender R, Ryan P, Clark N A 1990 Phys. Rev. B 42 988
[51]
[52]	Glotzer S C 2000 J. Non-Cryst. Solids 274 342
[53]
[54]
[55]	Wu W H, Zhang J L, Zhou H W, Huang Y N, Zhang L, Ying X N 2008 Appl. Phys. Lett. 92 011918
[56]
[57]	Zhang J L, Zhou H W, Wu W H, Huang Y N 2008 Appl. Phys. Lett. 92 131906
[58]	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 物理学报 57 5817]
[59]
[60]
[61]	Jiang J G, Huang Y N 2009 Comput. Phys. Commun. 180 177
[62]
[63]	Jiang J G, Huang Y N, Wu J C 2009 J. Stat. Phys. 136 984
[64]	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 物理学报 59 417]
[65]
[66]
[67]	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 物理学报 53 3839]
[68]	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 物理学报 51 2896]
[69]
[70]
[71]	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 物理学报 55 6661]
[72]
[73]	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 物理学报 56 5489]
[74]
[75]	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 物理学报 51 1856]
[76]
[77]	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 物理学报 58 523]
[78]	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 物理学报 55 3711]
[79]
[80]	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 物理学报 49 802]
[81]
[82]
[83]	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 物理学报 51 420]
[84]
[85]	Zhao M L, Yi X J, Wang C L, Wang J F, Zhang J L 2006 Chin. Phys. B 15 1611
[86]	Wen C 1995 Chin. Phys. B 4 54
[87]
[88]	Zhao H P, Liu Z Y, Liu Y Y 2001 Chin. Phys. B 10 35
[89]
[90]	Wang X J, Gong Z Q, Qian Y F, Zhu J, Chen X B 2007 Chin. Phys. 16 2131
[91]
[92]	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 物理学报 55 378]
[93]
[94]	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 物理学报 55 2409]
[95]
[96]
[97]	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 物理学报 56 6547]
[98]	Lunkenheimer P, Schneider U, Brand R, Loidl A 2000 Contemp. Phys. 41 15
[99]
[100]	Brand R, Lunkenheimer P, Loidl A 2002 J. Chem. Phys. 116 10386
[101]
[102]
[103]	Lunkenheimer P, Loidl A 2006 J. Non-Cryst. Sol. 352 4556

施引文献

[1]	Anderson P W 1995 Science 267 1615
[2]
[3]	Angell C A 1995 Science 267 1924
[4]
[5]	Stillinger F H 1995 Science 267 1935
[6]	Liu Y H, Wang G, Wang R J, Zhao D Q, Pan M X, Wang W H 2007 Science 315 1385
[7]
[8]
[9]	Zhao Z F, Wen P, Sheck C H, Wang W H 2007 Phys. Rev. B 75 174201
[10]
[11]	Ediger M D, Angell C A, Nagel S R 1996 J. Phys. Chem. 100 13200
[12]	Donth E 2001 The Glass Transition (Berlin: Springer)
[13]
[14]
[15]	Turnbull D 1949 Contemp. Phys. 10 473
[16]
[17]	Cohen M H, Grest G S 1979 Phys. Rev. B 20 1077
[18]	Adam G, Gibbs J H 1965 J. Chem. Phys. 43 139
[19]
[20]
[21]	Ngai K L 1979 Commun. Sol. Stat. Phys. 9 127
[22]
[23]	Das S P 2004 Rev. Mod. Phys. 76 785
[24]
[25]	Ritort F, Sollich P 2003 Adv. Phys. 52 219
[26]	Kivelson D, Zhao X, Nussinov Z, Tarjus G 1995 Physica A 219 27
[27]
[28]
[29]	Chamberlin R V 1995 Phys. Rev. Lett. 82 2520
[30]	Huang Y N, Wang C J, Riande E 2005 J. Chem. Phys. 122 144502
[31]
[32]	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]
[33]
[34]	Huang Y N 2006 J. Yili Normal Univ. 3 39 (in Chinese) [黄以能 2006 伊犁师范学院学报 3 39]
[35]
[36]
[37]	Zhang J L, Wang L N, Zhou H W, Zhang L L, Zhao X Y, Huang Y N 2010 Chin. Phys. B 19 056403
[38]
[39]	Zhao X Y, Wang L N, Fan X H, Zhang L L, Wei L, Zhang J L, Huang Y N 2011 Acta Phys. Sin. 60 036403 (in Chinese) [赵兴宇、王丽娜、樊小辉、张丽丽、卫来、张晋鲁、黄以能 2011 物理学报 60 036403]
[40]
[41]	Bttcher C F J, Bordewijk P 1978 Theory of Electric Polarization (Amsterdam: Elsevier) Vol Ⅱ
[42]	Fang J X, Yin Z W 2003 Dielectrics Physics (2nd ed) (Beijing: Science Press) p50 (in Chinese) [方俊鑫、殷之文 2003 电介质物理学 (第二版) (北京: 科学出版社) 第50页]
[43]
[44]	Combs A J, Yip S 1983 Phys. Rev. B 28 6873
[45]
[46]	Glauber R G 1963 J. Math. Phys. 4 294
[47]
[48]	Weeks E R, Crocker J C, Levitt A C, Schofield A, Weitz D A 2000 Science 287 627
[49]
[50]	Pouligny B, Malzbender R, Ryan P, Clark N A 1990 Phys. Rev. B 42 988
[51]
[52]	Glotzer S C 2000 J. Non-Cryst. Solids 274 342
[53]
[54]
[55]	Wu W H, Zhang J L, Zhou H W, Huang Y N, Zhang L, Ying X N 2008 Appl. Phys. Lett. 92 011918
[56]
[57]	Zhang J L, Zhou H W, Wu W H, Huang Y N 2008 Appl. Phys. Lett. 92 131906
[58]	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 物理学报 57 5817]
[59]
[60]
[61]	Jiang J G, Huang Y N 2009 Comput. Phys. Commun. 180 177
[62]
[63]	Jiang J G, Huang Y N, Wu J C 2009 J. Stat. Phys. 136 984
[64]	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 物理学报 59 417]
[65]
[66]
[67]	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 物理学报 53 3839]
[68]	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 物理学报 51 2896]
[69]
[70]
[71]	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 物理学报 55 6661]
[72]
[73]	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 物理学报 56 5489]
[74]
[75]	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 物理学报 51 1856]
[76]
[77]	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 物理学报 58 523]
[78]	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 物理学报 55 3711]
[79]
[80]	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 物理学报 49 802]
[81]
[82]
[83]	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 物理学报 51 420]
[84]
[85]	Zhao M L, Yi X J, Wang C L, Wang J F, Zhang J L 2006 Chin. Phys. B 15 1611
[86]	Wen C 1995 Chin. Phys. B 4 54
[87]
[88]	Zhao H P, Liu Z Y, Liu Y Y 2001 Chin. Phys. B 10 35
[89]
[90]	Wang X J, Gong Z Q, Qian Y F, Zhu J, Chen X B 2007 Chin. Phys. 16 2131
[91]
[92]	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 物理学报 55 378]
[93]
[94]	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 物理学报 55 2409]
[95]
[96]
[97]	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 物理学报 56 6547]
[98]	Lunkenheimer P, Schneider U, Brand R, Loidl A 2000 Contemp. Phys. 41 15
[99]
[100]	Brand R, Lunkenheimer P, Loidl A 2002 J. Chem. Phys. 116 10386
[101]
[102]
[103]	Lunkenheimer P, Loidl A 2006 J. Non-Cryst. Sol. 352 4556

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