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Research Article

Equilibrium phase diagram of a randomly pinned glass-former

Misaki Ozawa, View ORCID ProfileWalter Kob, Atsushi Ikeda, and Kunimasa Miyazaki
PNAS June 2, 2015 112 (22) 6914-6919; first published May 14, 2015; https://doi.org/10.1073/pnas.1500730112
Misaki Ozawa
aInstitute of Physics, University of Tsukuba, Tsukuba 305-8571, Japan;
bDepartment of Physics, Nagoya University, Nagoya 464-8602, Japan;
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Walter Kob
cLaboratoire Charles Coulomb, UMR 5221, University of Montpellier and CNRS, 34095 Montpellier, France; and
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  • ORCID record for Walter Kob
  • For correspondence: walter.kob@univ-montp2.fr
Atsushi Ikeda
dFukui Institute for Fundamental Chemistry, Kyoto University, Kyoto 606-8103, Japan
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Kunimasa Miyazaki
bDepartment of Physics, Nagoya University, Nagoya 464-8602, Japan;
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  1. Edited by Pablo G. Debenedetti, Princeton University, Princeton, NJ, and approved April 16, 2015 (received for review January 13, 2015)

This article has a Letter. Please see:

  • Vanishing of configurational entropy may not imply an ideal glass transition in randomly pinned liquids - August 17, 2015

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  • Reply to Chakrabarty et al.
    - Aug 17, 2015
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Significance

Confirming by experiments or simulations whether or not an ideal glass transition really exists is a daunting task, because at this point the equilibration time becomes astronomically large. Recently it has been proposed that this difficulty can be bypassed by pinning a fraction of the particles in the glass-forming system. Here we study numerically a liquid with such random pinned particles and identify the ideal glass transition point TK at which the configurational entropy vanishes, thus realizing for the first time, to our knowledge, a glass with zero entropy. We find that as the fraction of pinned particles increases, the TK line crosses the dynamical transition line, implying the existence of an end point at which theory predicts a new type of criticality.

Abstract

We use computer simulations to study the thermodynamic properties of a glass-former in which a fraction c of the particles has been permanently frozen. By thermodynamic integration, we determine the Kauzmann, or ideal glass transition, temperature TK(c) at which the configurational entropy vanishes. This is done without resorting to any kind of extrapolation, i.e., TK(c) is indeed an equilibrium property of the system. We also measure the distribution function of the overlap, i.e., the order parameter that signals the glass state. We find that the transition line obtained from the overlap coincides with that obtained from the thermodynamic integration, thus showing that the two approaches give the same transition line. Finally, we determine the geometrical properties of the potential energy landscape, notably the T- and c dependence of the saddle index, and use these properties to obtain the dynamic transition temperature Td(c). The two temperatures TK(c) and Td(c) cross at a finite value of c and indicate the point at which the glass transition line ends. These findings are qualitatively consistent with the scenario proposed by the random first-order transition theory.

  • ideal glass transition
  • computer simulations
  • random first-order transition theory
  • Kauzmann temperature
  • configurational entropy

Footnotes

  • ↵1To whom correspondence should be addressed. Email: walter.kob{at}univ-montp2.fr.
  • Author contributions: M.O., W.K., A.I., and K.M. designed research, performed research, analyzed data, and wrote the paper.

  • The authors declare no conflict of interest.

  • This article is a PNAS Direct Submission.

  • This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1500730112/-/DCSupplemental.

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Equilibrium pinned glass-former
Misaki Ozawa, Walter Kob, Atsushi Ikeda, Kunimasa Miyazaki
Proceedings of the National Academy of Sciences Jun 2015, 112 (22) 6914-6919; DOI: 10.1073/pnas.1500730112

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Equilibrium pinned glass-former
Misaki Ozawa, Walter Kob, Atsushi Ikeda, Kunimasa Miyazaki
Proceedings of the National Academy of Sciences Jun 2015, 112 (22) 6914-6919; DOI: 10.1073/pnas.1500730112
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Proceedings of the National Academy of Sciences: 112 (22)
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