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Dynamic glass transition in two dimensions.

M Bayer1, J M Brader, F Ebert

  • 1Fachbereich Physik, Universität Konstanz, 78457 Konstanz, Germany.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 7, 2007
PubMed
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Mode coupling theory reveals a dynamic glass transition in two-dimensional hard disks at a critical packing fraction. This finding is consistent with simulations and experimental data for quasi-two-dimensional systems.

Area of Science:

  • Condensed matter physics
  • Statistical mechanics
  • Computational physics

Background:

  • The existence of a structural glass transition in two dimensions remains an open question.
  • Mode coupling theory (MCT) provides a theoretical framework for understanding glass transitions.

Purpose of the Study:

  • To investigate the dynamic glass transition in two-dimensional systems using MCT.
  • To determine the dimensionality dependence of the MCT memory functional.
  • To compare theoretical predictions with simulation and experimental results.

Main Methods:

  • Numerical solution of MCT equations for monodisperse hard disks in two dimensions.
  • Determination of the explicit d-dependence of the memory functional.
  • Analysis of critical packing fractions and cage motion characteristics.

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Main Results:

  • A dynamic glass transition is predicted at a critical packing fraction (phi(c)d=2) of approximately 0.697.
  • This critical packing fraction is significantly higher than in three dimensions (phi(c)d=3 ≈ 0.516).
  • Results show qualitative agreement with Monte Carlo and molecular dynamics simulations, and experimental data for quasi-two-dimensional systems.

Conclusions:

  • MCT supports the existence of a dynamic glass transition in two dimensions.
  • The critical packing fraction scales with the random close packing value.
  • The theory successfully describes experimental measurements of mean-squared displacements in quasi-two-dimensional systems.