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Relationship between bond-breakage correlations and four-point correlations in heterogeneous glassy dynamics: Configuration changes and vibration modes

Hayato Shiba1,*, Takeshi Kawasaki2,*, and Akira Onuki2

  • 1Institute for Solid State Physics, University of Tokyo, Chiba 277-8581, Japan
  • 2Department of Physics, Kyoto University, Kyoto 606-8502, Japan

  • *These two authors contributed equally to this work.
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Phys. Rev. E 86, 041504 – Published 10 October, 2012Errata Phys. Rev. E 86, 049907 (2012); Phys. Rev. E 95, 069901 (2017)

DOI: https://doi.org/10.1103/PhysRevE.86.041504

Abstract

We investigate the dynamic heterogeneities of glassy particle systems in the theoretical schemes of bond breakage and four-point correlation functions. In the bond-breakage scheme, we introduce the structure factor Sb(q,t) and the susceptibility χb(t) to detect the spatial correlations of configuration changes. Here χb(t) attains a maximum at t=tbmax as a function of time t, where the fraction of the particles with broken bonds φb(t) is about 1/2. In the four-point scheme, treating the structure factor S4(q,t) and the susceptibility χ4(t), we detect superpositions of the heterogeneity of bond breakage and that of thermal low-frequency vibration modes. While the former grows slowly, the latter emerges quickly to exhibit complex space-time behavior. In two dimensions, the vibration modes extending over the system yield significant contributions to the four-point correlations, which depend on the system size logarithmically. A maximum of χ4(t) is attained at t=t4max, where these two contributions become of the same order. As a result, t4max is considerably shorter than tbmax.

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Corrections

24 October, 2012

Errata

Publisher's Note: Relationship between bond-breakage correlations and four-point correlations in heterogeneous glassy dynamics: Configuration changes and vibration modes [Phys. Rev. E 86, 041504 (2012)]

Hayato Shiba, Takeshi Kawasaki, and Akira Onuki
Phys. Rev. E 86, 049907 (2012)

Erratum: Relationship between bond-breakage correlations and four-point correlations in heterogeneous glassy dynamics: Configuration changes and vibration modes [Phys. Rev. E 86, 041504 (2012)]

Hayato Shiba, Takeshi Kawasaki, and Akira Onuki
Phys. Rev. E 95, 069901 (2017)

Article Text

References (59)

  1. K. Binder and W. Kob, Glassy Materials and Disordered Solids (World Scientific, Singapore, 2005).
  2. G. Adam and J. H. Gibbs, J. Chem. Phys. 43, 139 (1965).
  3. H. Sillescu, J. Non-Cryst. Solids 243, 81 (1999).
  4. M. D. Ediger, Annu. Rev. Phys. Chem. 51, 99 (2000).
  5. L. Berthier, G. Biroli, J.-P. Bouchaud, L. Cipelletti, and W. van Saarloos, Dynamical Heterogeneities in Glasses, Colloids, and Granular Media (Oxford University Press, Oxford, 2011).
  6. K. Maeda and S. Takeuchi, Phys. Status Solidi A 44, 685 (1978); Philos. Mag. A 44, 643 (1981).
  7. D. Srolovitz, V. Vitek, and T. Egami, Acta. Metall. 31, 335 (1983).
  8. D. Deng, A. S. Argon, and S. Yip, Philos. Trans. R. Soc. London, Ser. A 329, 595 (1989); 329, 613 (1989).
  9. M. M. Hurley and P. Harrowell, Phys. Rev. E 52, 1694 (1995).
  10. D. N. Perera and P. Harrowell, Phys. Rev. Lett. 81, 120 (1998); J. Chem. Phys. 111, 5441 (1999).
  11. T. Muranaka and Y. Hiwatari, Phys. Rev. E 51, R2735 (1995).
  12. Y. Hiwatari and T. Muranaka, J. Non-Cryst. Solids 235–237, 19 (1998). Figure 6 of their paper is similar to Fig. 7(a) in the present paper.
  13. R. Yamamoto and A. Onuki, J. Phys. Soc. Jpn. 66, 2545 (1997).
  14. R. Yamamoto and A. Onuki, Phys. Rev. E 58, 3515 (1998). See Fig. 16 of this paper for the relation between τb and τα; J. Phys.: Condens. Matter 29, 6323 (2000).
  15. W. Kob, C. Donati, S. J. Plimpton, P. H. Poole, and S. C. Glotzer, Phys. Rev. Lett. 79, 2827 (1997); C. Donati, J. F. Douglas, W. Kob, S. J. Plimpton, P. H. Poole, and S. C. Glotzer, ibid. 80, 2338 (1998); C. Donati, S. C. Glotzer, P. H. Poole, W. Kob, and S. J. Plimpton, Phys. Rev. E 60, 3107 (1999).
  16. D. N. Perera, J. Phys.: Condens. Matter 10, 10115 (1998).
  17. B. Doliwa and A. Heuer, Phys. Rev. E 61, 6898 (2000); J. Non-Cryst. Solids 307–310, 32 (2002).
  18. D. Chandler, J. P. Garrahan, R. L. Jack, L. Maibaum, and A. C. Pan, Phys. Rev. E 74, 051501 (2006).
  19. G. Biroli, J.-P. Bouchaud, K. Miyazaki, and D. R. Reichman, Phys. Rev. Lett. 97, 195701 (2006).
  20. R. Candelier, A. Widmer-Cooper, J. K. Kummerfeld, O. Dauchot, G. Biroli, P. Harrowell, and D. R. Reichman, Phys. Rev. Lett. 105, 135702 (2010).
  21. T. Kawasaki, T. Araki, and H. Tanaka, Phys. Rev. Lett. 99, 215701 (2007).
  22. R. Yamamoto and A. Onuki, Phys. Rev. Lett. 81, 4915 (1998).
  23. N. Lačević, F. W. Starr, T. B. Schroder, and S. C. Glotzer, J. Chem. Phys. 119, 7372 (2003).
  24. L. Berthier, G. Biroli, J.-P. Bouchaud, L. Cipelletti, D. E. Masri, D. L'Hôte, F. Ladieu, and M. Pierno, Science 310, 1797 (2005).
  25. L. Berthier, G. Biroli, J.-P. Bouchaud, W. Kob, K. Miyazaki, and D. R. Reichman, J. Chem. Phys. 126, 184503 (2007); 126, 184504 (2007).
  26. D. Chandler, J. P. Garrahan, R. L. Jack, L. Maibaum, and A. C. Pan, Phys. Rev. E 74, 051501 (2006).
  27. S. Karmakar, C. Dasgupta, and S. Sastry, Phys. Rev. Lett. 105, 015701 (2010); 105, 019801 (2010).
  28. E. Flenner, M. Zhang, and G. Szamel, Phys. Rev. E 83, 051501 (2011).
  29. H. Mizuno and R. Yamamoto, Phys. Rev. E 84, 011506 (2011).
  30. A. Furukawa and H. Tanaka, Phys. Rev. E 84, 061503 (2011).
  31. H. R. Schober and B. B. Laird, Phys. Rev. B 44, 6746 (1991).
  32. W. Schirmacher, G. Diezemann, and C. Ganter, Phys. Rev. Lett. 81, 136 (1998).
  33. H. R. Schober, C. Oligschleger, and B. B. Laird, J. Non-Cryst. Solids 156–158, 965 (1993); C. Oligschleger and H. R. Schober, Phys. Rev. B 59, 811 (1999).
  34. L. Angelani, M. Montagna, G. Ruocco, and G. Viliani, Phys. Rev. Lett. 84, 4874 (2000).
  35. A. Tanguy, J. P. Wittmer, F. Leonforte, and J.-L. Barrat, Phys. Rev. B 66, 174205 (2002); F. Leonforte, R. Boissiere, A. Tanguy, J. P. Wittmer, and J.-L. Barrat, ibid. 72, 224206 (2005); F. Leonforte, A. Tanguy, J. P. Wittmer, and J.-L. Barrat, Phys. Rev. Lett. 97, 055501 (2006).
  36. H. R. Schober and G. Ruocco, Philos. Mag. 84, 1361 (2004).
  37. H. Shintani and H. Tanaka, Nature Mater. 7, 870 (2008).
  38. C. Brito and M. Wyart, J. Chem. Phys. 131, 024504 (2009).
  39. A. Widmer-Cooper, H. Perry, P. Harrowell, and D. R. Reichman, Nature Phys. 4, 711 (2008); J. Chem. Phys. 131, 194508 (2009).
  40. A. Ghosh, V. K. Chikkadi, P. Schall, J. Kurchan, and D. Bonn, Phys. Rev. Lett. 104, 248305 (2010).
  41. K. Chen, W. G. Ellenbroek, Z. Zhang, D. T. N. Chen, P. J. Yunker, S. Henkes, C. Brito, O. Dauchot, W. van Saarloos, A. J. Liu, and A. G. Yodh, Phys. Rev. Lett. 105, 025501 (2010).
  42. K. Chen, M. L. Manning, P. J. Yunker, W. G. Ellenbroek, Z. Zhang, A. J. Liu, and A. G. Yodh, Phys. Rev. Lett. 107, 108301 (2011).
  43. K. Vollmayr-Lee, W. Kob, K. Binder, and A. Zippelius, J. Chem. Phys. 116, 5158 (2002).
  44. A. Widmer-Cooper and P. Harrowell, Phys. Rev. Lett. 96, 185701 (2006).
  45. T. Hamanaka and A. Onuki, Phys. Rev. E 74, 011506 (2006); 75, 041503 (2007).
  46. H. Zhang, D. J. Srolovitz, J. F. Douglas, and J. A. Warren, Phys. Rev. B 74, 115404 (2006); Proc. Natl. Acad. Sci. USA 106, 7735 (2009).
  47. H. Shiba and A. Onuki, Phys. Rev. E 81, 051501 (2010).
  48. M. Tsamados, A. Tanguy, C. Goldenberg, and J.-L. Barrat, Phys. Rev. E 80, 026112 (2009).
  49. K. Yoshimoto, T. S. Jain, K. Van Workum, P. F. Nealey, and J. J. de Pablo, Phys. Rev. Lett. 93, 175501 (2004).
  50. Y. Shi, M. B. Katz, H. Li, and M. L. Falk, Phys. Rev. Lett. 98, 185505 (2007); A. Lemaitre and C. Caroli, Phys. Rev. E 76, 036104 (2007); A. Furukawa, K. Kim, S. Saito, and H. Tanaka, Phys. Rev. Lett. 102, 016001 (2009).
  51. M. L. Manning and A. J. Liu, Phys. Rev. Lett. 107, 108302 (2011).
  52. E. Rabani, J. D. Gezelter, and B. J. Berne, J. Chem. Phys. 107, 6867 (1997); Phys. Rev. Lett. 82, 3649 (1999).
  53. A. R. Abate and D. J. Durian, Phys. Rev. E 74, 031308 (2006).
  54. B. Jancovici, Phys. Rev. Lett. 19, 20 (1967); Y. Imry and L. Gunther, Phys. Rev. B 3, 3939 (1971); D. R. Nelson and B. I. Halperin, ibid. 19, 2457 (1979).
  55. In our simulation, the transverse and longitudinal sound velocities are given by c⊥=(μ/ρ)1/2≅4.1 and c∥=[(K+μ)/ρ]1/2≅8.9 in units of σ1/τ0 at T=0.56 in 2D, where ρ=1.06m1σ1−2 is the average mass density.
  56. T. Muranaka and Y. Hiwatari, Mol. Simul. 16, 387 (1996); J. Horbach, W. Kob, K. Binder, and C. A. Angell, Phys. Rev. E 54, R5897 (1996).
  57. K. Kim and R. Yamamoto, Phys. Rev. E 61, R41 (2000).
  58. O. Dauchot, G. Marty, and G. Biroli, Phys. Rev. Lett. 95, 265701 (2005).
  59. G. Pastore, B. Bernu, J. P. Hansen, and Y. Hiwatari, Phys. Rev. A 38, 454 (1988).

Outline

Information

Phys. Rev. E 86, 041504– Published 10 October, 2012
  • Received 28 May 2012
  • Corrected 24 October 2012

©2012 American Physical Society

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