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

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.

Keywords: glass transition relaxation phenomenon dielectric relaxation

Received: 01 June 2009
Revised: 02 November 2009
Accepted manuscript online:

PACS:	64.70.P-	(Glass transitions of specific systems)
	77.22.Gm	(Dielectric loss and relaxation)
	63.70.+h	(Statistical mechanics of lattice vibrations and displacive phase transitions)
	61.43.Fs	(Glasses)

Fund: 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).

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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 2010 Chin. Phys. B 19 056403

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

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