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Dynamic scaling approach to glass formation

Colby1

  • 1Materials Science and Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, USA.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|October 25, 2000
PubMed
Summary

Glass formation is explained by a phase transition model where free volume dynamics dictate relaxation times. This dynamic scaling approach, superior to the Vogel form, reveals universal exponents for glass-forming liquids.

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Area of Science:

  • Materials Science
  • Condensed Matter Physics
  • Physical Chemistry

Background:

  • The temperature dependence of relaxation times in glass-forming liquids is crucial for understanding their behavior.
  • Existing models like the Vogel form have limitations in explaining experimental data.
  • Dynamic scaling offers a potential framework for describing glass formation.

Purpose of the Study:

  • To propose a mean-field phase transition model for glass formation.
  • To investigate the validity and universality of dynamic scaling in glass-forming liquids.
  • To determine the critical exponents governing relaxation dynamics.

Main Methods:

  • Analysis of experimental data on temperature-dependent relaxation times and viscosity.
  • Application of dynamic scaling theory and mean-field approximations.
  • Comparison of theoretical predictions with experimental observations for various glass-formers.

Main Results:

  • Dynamic scaling, with relaxation time diverging as (T-T(c))(-nuz), is superior to the Vogel form.
  • The order parameter is the fraction of space with sufficient free volume, growing logarithmically above T(c).
  • A universal Fisher exponent tau=2 for cooperatively moving clusters is predicted.
  • Andrade creep suggests a dynamic critical exponent z=6.
  • The product nuz=9 appears universal for polymers and other glass-formers, with deviations attributed to energetic barriers in strong glasses.

Conclusions:

  • Glass formation can be modeled as a phase transition governed by free volume dynamics.
  • Dynamic scaling provides a robust framework for understanding relaxation in glass-forming liquids.
  • While free volume is necessary, energetic barriers are also critical for motion in strong glasses, leading to a universal nuz=9.

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