Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
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).
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).
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).
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).
C. Brito, M. Wyart, J. Stat. Mech. L08003 (2007).
C. Brito, M. Wyart, arXiv:0804.2439.
A. Widmer-Cooper et al., Nature Phys. 4, 711 (2008).
F. Ritort, P. Sollich, Adv. Phys. 52, 219 (2003).
A. Widmer-Cooper, P. Harrowell, H. Fynewever, Phys. Rev. Lett. 93, 135701 (2004).
L.O. Hedges, J.P. Garrahan, J. Phys.: Condens. Matter 19, 205124 (2007).
J. Jäckle, A. Krönig, J. Phys.: Condens. Matter 6, 7633 (1994).
C. Toninelli, G. Biroli, D.S. Fisher, Phys. Rev. Lett. 92, 185504 (2004).
A.C. Pan, J.P. Garrahan, D. Chandler, Phys. Rev. E. 72, 041106 (2005).
W. Kob, H.C. Andersen, Phys. Rev. E 48, 4364 (1993).
J. Kurchan, L. Peliti, M. Sellito, Europhys. Lett. 39, 365 (1997).
D.J. Ashton, PhD Thesis, University of Nottingham, (2008) http://etheses.nottingham.ac.uk/623/.
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).
M.F. Thorpe, E.J. Garboczi, Phys. Rev. B 35, 8579 (1987).
Z. Zeravcic, W. van Saarloos, D.R. Nelson, EPL 83, 44001 (2008).
N. Hatano, D.R. Nelson, Phys. Rev. Lett. 77, 570 (1996).
B.A. DiDonna, T.C. Lubensky, Phys. Rev. E 72, 066619 (2005).
F. Leonforte, A. Tanguy, J.P. Wittmer, J.L. Barrat, Phys. Rev. Lett. 97, 055501 (2006).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Ashton, D.J., Garrahan, J.P. Relationship between vibrations and dynamical heterogeneity in a model glass former: Extended soft modes but local relaxation. Eur. Phys. J. E 30, 303 (2009). https://doi.org/10.1140/epje/i2009-10531-6
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1140/epje/i2009-10531-6