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Logarithmic relaxation in glass-forming systems.

W Götze1, M Sperl

  • 1Physik Department, Technische Universität München, D-85747 Garching, Germany.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 21, 2002
PubMed
Summary

Mode-coupling theory reveals new insights into ideal glass transitions. Logarithmic time laws and polynomial corrections describe structural relaxation dynamics near singularities, impacting beta and alpha processes.

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Area of Science:

  • Condensed Matter Physics
  • Theoretical Physics

Background:

  • Mode-coupling theory (MCT) is a key framework for understanding ideal glass transitions.
  • Glass-forming systems exhibit complex dynamics near transition singularities.

Purpose of the Study:

  • Analyze correlation functions near higher-order glass-transition singularities within MCT.
  • Investigate asymptotic solutions of equations of motion for these systems.

Main Methods:

  • Asymptotic expansion of solutions in polynomials of the logarithm of time (t).
  • Analysis of correlation functions and their interpolation between different dynamic scenarios.

Main Results:

  • A leading-order logarithmic decay law (ln(t)) is identified.
  • Leading corrections are described by a fourth-order polynomial.
  • Three distinct scenarios for structural relaxation dynamics are elucidated, including vanishing corrections, reduced von Schweidler's law validity, and replacement of beta-process decay.

Conclusions:

  • The study provides a detailed theoretical description of dynamics near glass transition singularities.
  • Findings offer explanations for phenomena like strong alpha relaxation stretching and two-peak susceptibility spectra.
  • The results advance the understanding of structural relaxation in glass-forming materials.

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