Solving the initial condition of the string relaxation equation of the string model for glass transition: part-I |
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Authors: | Zhang Jin-Lu Wang Li-N Zhou Heng-Wei Zhang Li-Li Zhao Xing-Yu and Huang Yi-Neng |
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Institution: | 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 |
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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. |
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Keywords: | glass transition relaxation phenomenon dielectric
relaxation |
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