Monte Carlo simulations of the relaxation dynamics of the spatial relaxation modes in the molecule-string model

Fan Xiao-Hui; Zhao Xing-Yu; Wang Li-Na; Zhang Li-Li; Zhou Heng-Wei; Zhang Jin-Lu; Huang Yi-Neng

doi:10.7498/aps.60.126401

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:

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

References

[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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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

Cited By

[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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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

[1]	Wang Li-Na, Zhao Xing-Yu, Shang Jie-Ying, Zhou Heng-Wei. Measurement and analysis of Debye relaxation dynamics of n-propanol, n-butanol and n-octanol. Acta Physica Sinica, 2023, 72(3): 037701. doi: 10.7498/aps.72.20221856
[2]	Xun Zhi-Peng, Hao Da-Peng. Monte Carlo simulation of bond percolation on square lattice with complex neighborhoods. Acta Physica Sinica, 2022, 71(6): 066401. doi: 10.7498/aps.71.20211757
[3]	Wang Li-Min, Duan Bing-Huang, Xu Xian-Guo, Li Hao, Chen Zhi-Jun, Yang Kun-Jie, Zhang Shuo. Simulation of neutron irradiation damage in lead lanthanum zirconate titanate by Monte Carlo method. Acta Physica Sinica, 2022, 71(7): 076101. doi: 10.7498/aps.71.20212041
[4]	Huang Jian-Bang, Nan Hu, Zhang Feng, Zhang Jia-Le, Liu Lai-Jun, Wang Da-Wei. Diffuse phase transition and thermal hysteresis in relaxor ferroelectrics from modified Ising model. Acta Physica Sinica, 2021, 70(11): 110501. doi: 10.7498/aps.70.20202019
[5]	Jiang Wen-Long. Mechanism and quantitative study of specific heat change during glass transition of amorphous polystyrene and Pd₄₀Ni₁₀Cu₃₀P₂₀. Acta Physica Sinica, 2020, 69(12): 126401. doi: 10.7498/aps.69.20200331
[6]	Wu Zhen-Wei, Wang Wei-Hua. Linking local connectivity to atomic-scale relaxation dynamics in metallic glass-forming systems. Acta Physica Sinica, 2020, 69(6): 066101. doi: 10.7498/aps.69.20191870
[7]	Lin Sheng-Jun, Huang Yin, Xie Dong-Ri, Min Dao-Min, Wang Wei-Wang, Yang Liu-Qing, Li Sheng-Tao. Molecular relaxation and glass transition properties of epoxy resin at high temperature. Acta Physica Sinica, 2016, 65(7): 077701. doi: 10.7498/aps.65.077701
[8]	Li Wen-Fang, Du Jin-Jin, Wen Rui-Juan, Yang Peng-Fei, Li Gang, Zhang Tian-Cai. Single-atom transfer in a strongly coupled cavity quantum electrodynamics: experiment and Monte Carlo simulation. Acta Physica Sinica, 2014, 63(24): 244205. doi: 10.7498/aps.63.244205
[9]	Hua Yu-Chao, Dong Yuan, Cao Bing-Yang. Monte Carlo simulation of phonon ballistic diffusive heat conduction in silicon nanofilm. Acta Physica Sinica, 2013, 62(24): 244401. doi: 10.7498/aps.62.244401
[10]	Lan Mu, Xiang Gang, Gu Gang-Xu, Zhang Xi. A Monte Carlo simulation study on growth mechanism of horizontal nanowires on crystal surface. Acta Physica Sinica, 2012, 61(22): 228101. doi: 10.7498/aps.61.228101
[11]	Wei Lai, Zhou Lan-Lan, Lu Gui-Hua, Zhang Wen, Zhang Wu-Zhi, Zhang Shang, Feng Yong-Hong, Zhou Heng-Wei, Zhang Jin-Lu, Huang Yi-Neng. Measuring and analyzing the cooling dielectric spectra of the -relaxation in dimethyl phthalate series materials. Acta Physica Sinica, 2012, 61(1): 017701. doi: 10.7498/aps.61.017701
[12]	Xu Chun-Long, Hou Zhao-Yang, Liu Rang-Su. Simulation study on thermodynamic, dynamic and structural transition mechanisms during the formation of Ca70Mg30 metallic glass. Acta Physica Sinica, 2012, 61(13): 136401. doi: 10.7498/aps.61.136401
[13]	Zhou Xue-Mao, Chen Xiao-Meng, Wu Xue-Bang, Shui Jia-Peng, Zhu Zhen-Gang. Dynamic relaxation behaviors of poly(methyl methacrylate)/Ga nanocomposites. Acta Physica Sinica, 2011, 60(3): 036102. doi: 10.7498/aps.60.036102
[14]	Zhao Xing-Yu, Wang Li-Na, Fan Xiao-Hui, Zhang Li-Li, Wei Lai, Zhang Jin-Lu, Huang Yi-Neng. Computer simulation of the string relaxation modes of the molecule-string model for glass transition. Acta Physica Sinica, 2011, 60(3): 036403. doi: 10.7498/aps.60.036403
[15]	Xiong Kai-Guo, Feng Guo-Lin, Hu Jing-Guo, Wan Shi-Quan, Yang Jie. Monte Carlo simulation of the record-breaking high temperature events of climate changes. Acta Physica Sinica, 2009, 58(4): 2843-2852. doi: 10.7498/aps.58.2843
[16]	Gao Fei, Ryoko Yamada, Mitsuo Watanabe, Liu Hua-Feng. Use of Monte Carlo simulations for the scatter events analysis of PET scanners. Acta Physica Sinica, 2009, 58(5): 3584-3591. doi: 10.7498/aps.58.3584
[17]	Xu Lan-Qing, Li Hui, Xiao Zheng-Ying. Discussion on backscattered photon numbers and their scattering events in a turbid media. Acta Physica Sinica, 2008, 57(9): 6030-6035. doi: 10.7498/aps.57.6030
[18]	Zhang Li-Li, Zhang Jin-Lu, Jiang Jian-Guo, Zhou Heng-Wei, Huang Yi-Neng. Modeling the inter-molecular orientational correlation in orientational glassformers and the simulation analysis. Acta Physica Sinica, 2008, 57(9): 5817-5822. doi: 10.7498/aps.57.5817
[19]	Zhou Heng-Wei, Zhang Jin-Lu, Huang Yi-Neng, Ying Xue-Nong, Zhang Liang, Wu Wen-Hui, Shen Yi-Fan. Measurements of dimethyl phthalate series by the reed-vibration mechanical spectroscopy for liquids. Acta Physica Sinica, 2007, 56(11): 6547-6551. doi: 10.7498/aps.56.6547
[20]	He Qing-Fang, Xu Zheng, Liu De-Ang, Xu Xu-Rong. Monte Carlo simulation of the effect of impact ionization in thin-film electroluminescent devices. Acta Physica Sinica, 2006, 55(4): 1997-2002. doi: 10.7498/aps.55.1997

Catalog

Vol. 60, Issue 12 - 2011-06-20

Metrics

Abstract views: 7862
PDF Downloads: 559
Cited By: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

Search

Article

留言板