Relationship between vibrations and dynamical heterogeneity in a model glass former: Extended soft modes but local relaxation

  • D. J. AshtonEmail author
  • J. P. Garrahan
Regular Article


We study the relation between short-time vibrational modes and long-time relaxational dynamics in a kinetically constrained lattice gas with harmonic interactions between neighbouring particles. We find a correlation between the location of the low- (high-) frequency vibrational modes and regions of high (low) propensity for motion. This is similar to what was observed in continuous force systems, but our interpretation is different: in our case relaxation is due to localised excitations which propagate through the system; these localised excitations act as background disorder for the elastic network, giving rise to anomalous vibrational modes. Our results provide an example whereby a correlation between spatially extended low-frequency modes and high-propensity regions does not imply that relaxational dynamics originates in extended soft modes but rather belies their common origin. We consider other measures of elastic heterogeneity, such as non-affine displacement fields and mode localisation lengths, and discuss implications of our results to interpretations of dynamic heterogeneity more generally.


64.70.Q- Theory and modelling of the glass transition 63.50.Lm Glasses and amorphous solids 83.80.Ab Rheology: solids: e.g., composites, glasses, semicrystalline polymers 


  1. 1.
    For reviews on dynamic heterogeneity see: H. Sillescu, J. Non-Cryst. Solids 243, 81 (1999); M.D. Ediger, Annu. Rev. Phys. Chem. 51, 99 (2000); S.C. Glotzer, J. Non-Cryst. Solids 274, 342 (2000); R. Richert, J. Phys. Condens. Matter 14, R703 (2002); H.C. Andersen, Proc. Natl. Acad. Sci. U.S.A. 102, 6686 (2005).CrossRefADSGoogle Scholar
  2. 2.
    For reviews on the glass transition see, M.D. Ediger, C.A. Angell, S.R. Nagel, J. Phys. Chem. 100, 13200 (1996); C.A. Angell, Science 267, 1924 (1995); P.G. Debenedetti, F.H. Stillinger, Nature 410, 259 (2001).CrossRefGoogle Scholar
  3. 3.
    W.A. Phillips (Editor), Amorphous solids, Low temperature properties (Springer, Berlin) 1981; C.A. Angell et al., J. Appl. Phys. 88, 3113 (2000); K. Binder, W. Kob, in Glassy Materials and Disordered Solids: An Introduction to their Statistical Mechanics (World Scientific, Singapore, 2005).Google Scholar
  4. 4.
    See also, L.E. Silbert, A.J. Liu, S.R. Nagel, Phys. Rev. Lett. 95, 098301 (2005); M. Wyart, S.R. Nagel, T.A. Witten, Europhys. Lett. 72, 486 (2005).CrossRefADSGoogle Scholar
  5. 5.
    C. Brito, M. Wyart, J. Stat. Mech. L08003 (2007).Google Scholar
  6. 6.
    C. Brito, M. Wyart, arXiv:0804.2439.Google Scholar
  7. 7.
    A. Widmer-Cooper et al., Nature Phys. 4, 711 (2008).CrossRefADSGoogle Scholar
  8. 8.
    F. Ritort, P. Sollich, Adv. Phys. 52, 219 (2003).CrossRefADSGoogle Scholar
  9. 9.
    A. Widmer-Cooper, P. Harrowell, H. Fynewever, Phys. Rev. Lett. 93, 135701 (2004).CrossRefADSGoogle Scholar
  10. 10.
    L.O. Hedges, J.P. Garrahan, J. Phys.: Condens. Matter 19, 205124 (2007).CrossRefADSGoogle Scholar
  11. 11.
    J. Jäckle, A. Krönig, J. Phys.: Condens. Matter 6, 7633 (1994).CrossRefGoogle Scholar
  12. 12.
    C. Toninelli, G. Biroli, D.S. Fisher, Phys. Rev. Lett. 92, 185504 (2004).CrossRefADSGoogle Scholar
  13. 13.
    A.C. Pan, J.P. Garrahan, D. Chandler, Phys. Rev. E. 72, 041106 (2005).CrossRefADSGoogle Scholar
  14. 14.
    W. Kob, H.C. Andersen, Phys. Rev. E 48, 4364 (1993).CrossRefADSGoogle Scholar
  15. 15.
    J. Kurchan, L. Peliti, M. Sellito, Europhys. Lett. 39, 365 (1997).CrossRefADSGoogle Scholar
  16. 16.
    D.J. Ashton, PhD Thesis, University of Nottingham, (2008)
  17. 17.
    M.F. Thorpe, J. Non-Cryst. Solids 57, 355 (1983); S. Feng, P.N. Sen, Phys. Rev. Lett. 52, 216 (1984); A. Feng, M.F. Thorpe, E. Garboczi, Phys. Rev. B 31, 276 (1985).CrossRefADSGoogle Scholar
  18. 18.
    M.F. Thorpe, E.J. Garboczi, Phys. Rev. B 35, 8579 (1987).CrossRefADSGoogle Scholar
  19. 19.
    Z. Zeravcic, W. van Saarloos, D.R. Nelson, EPL 83, 44001 (2008).CrossRefADSGoogle Scholar
  20. 20.
    N. Hatano, D.R. Nelson, Phys. Rev. Lett. 77, 570 (1996).CrossRefADSGoogle Scholar
  21. 21.
    B.A. DiDonna, T.C. Lubensky, Phys. Rev. E 72, 066619 (2005).CrossRefADSGoogle Scholar
  22. 22.
    F. Leonforte, A. Tanguy, J.P. Wittmer, J.L. Barrat, Phys. Rev. Lett. 97, 055501 (2006).CrossRefADSGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  1. 1.School of Physics and AstronomyUniversity of NottinghamNottinghamUK
  2. 2.Department of PhysicsUniversity of BathBathUK

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