Solving the initial condition of the string relaxation equation of the string model for glass transition: part-I

doi:10.1088/1674-1056/19/5/056403

中国物理B ›› 2010, Vol. 19 ›› Issue (5): 56403-056403.doi: 10.1088/1674-1056/19/5/056403

Solving the initial condition of the string relaxation equation of the string model for glass transition: part-I

王丽娜¹, 周恒为¹, 张丽丽¹, 赵兴宇¹, 张晋鲁², 黄以能²

(1)Department of Physics and National Lab of Solid State Microstructures, Nanjing University, Nanjing 210093, China; (2)Department of Physics and National Lab of Solid State Microstructures, Nanjing University, Nanjing 210093, China;Xinjiang Lab of Phase-transitions and Microstructures of Condensed Matters, Yili Normal University, Yining 835000, China

收稿日期:2009-06-01 修回日期:2009-11-02 出版日期:2010-05-15 发布日期:2010-05-15
基金资助:
Project supported by the National Natural Science Foundations of China (Grant Nos.~10774064 and 30860076), the Key Foundation of Xinjiang Education Department (Grant No.~XJEDU2007137), and the Natural Science Foundations of Xinjiang Science and Technology Department of China (Grant Nos.~2008211042 and 200821184).

Solving the initial condition of the string relaxation equation of the string model for glass transition: part-I

Zhang Jin-Lu(张晋鲁)^a)b), Wang Li-Na(王丽娜)^a), Zhou Heng-Wei(周恒为)^a), Zhang Li-Li(张丽丽)^a), Zhao Xing-Yu(赵兴宇)^a), and Huang Yi-Neng(黄以能)^a)b)†

^a Department of Physics and National Lab of Solid State Microstructures, Nanjing University, Nanjing 210093, China; ^bXinjiang Lab of Phase-transitions and Microstructures of Condensed Matters, Yili Normal University, Yining 835000, China

Received:2009-06-01 Revised:2009-11-02 Online:2010-05-15 Published:2010-05-15
Supported by:
Project supported by the National Natural Science Foundations of China (Grant Nos.~10774064 and 30860076), the Key Foundation of Xinjiang Education Department (Grant No.~XJEDU2007137), and the Natural Science Foundations of Xinjiang Science and Technology Department of China (Grant Nos.~2008211042 and 200821184).

摘要/Abstract

摘要： The string model for the glass transition can quantitatively describe the universal $\alpha $-relaxation in glassformers, including the average relaxation time, the distribution function of the relaxation time, and the relaxation strength as functions of temperature. The string relaxation equation (SRE) of the model, at high enough temperatures, simplifies to the well-known single particle mean-field Debye relaxation equation, and at low enough temperatures to the well-known Rouse--Zimm relaxation equation that describes the relaxation dynamics of linear macromolecules. However, its initial condition, necessary to the further model predictions of glassy dynamics, has not been solved. In this paper, the special initial condition (SIC) of the SRE, i.e. for straight strings and the dielectric spectrum technique that is one of the most common methods to measure the glassy dynamics, was solved exactly. It should be expected that the obtained SIC would benefit the solution of the general initial condition of the SRE of the string model, i.e. for stochastically spatially configurating strings, as will be described in separate publications.

Abstract: The string model for the glass transition can quantitatively describe the universal $\alpha $-relaxation in glassformers, including the average relaxation time, the distribution function of the relaxation time, and the relaxation strength as functions of temperature. The string relaxation equation (SRE) of the model, at high enough temperatures, simplifies to the well-known single particle mean-field Debye relaxation equation, and at low enough temperatures to the well-known Rouse--Zimm relaxation equation that describes the relaxation dynamics of linear macromolecules. However, its initial condition, necessary to the further model predictions of glassy dynamics, has not been solved. In this paper, the special initial condition (SIC) of the SRE, i.e. for straight strings and the dielectric spectrum technique that is one of the most common methods to measure the glassy dynamics, was solved exactly. It should be expected that the obtained SIC would benefit the solution of the general initial condition of the SRE of the string model, i.e. for stochastically spatially configurating strings, as will be described in separate publications.

Key words: glass transition, relaxation phenomenon, dielectric relaxation

中图分类号: (Glass transitions of specific systems)

64.70.P-

77.22.Gm (Dielectric loss and relaxation) 63.70.+h (Statistical mechanics of lattice vibrations and displacive phase transitions) 61.43.Fs (Glasses)

张晋鲁, 王丽娜, 周恒为, 张丽丽, 赵兴宇, 黄以能. Solving the initial condition of the string relaxation equation of the string model for glass transition: part-I[J]. 中国物理B, 2010, 19(5): 56403-056403.

Zhang Jin-Lu(张晋鲁), Wang Li-Na(王丽娜), Zhou Heng-Wei(周恒为), Zhang Li-Li(张丽丽), Zhao Xing-Yu(赵兴宇), and Huang Yi-Neng(黄以能). Solving the initial condition of the string relaxation equation of the string model for glass transition: part-I[J]. Chin. Phys. B, 2010, 19(5): 56403-056403.

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Solving the initial condition of the string relaxation equation of the string model for glass transition: part-I

Solving the initial condition of the string relaxation equation of the string model for glass transition: part-I

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