Length scale for the onset of Fickian diffusion in supercooled liquidsL. Berthier1, 2, D. Chandler3 and J. P. Garrahan4
1 LDV UMR 5587, Université Montpellier II and CNRS - 34095 Montpellier, France
2 Rudolf Peierls Centre for Theoretical Physics, University of Oxford 1 Keble Road, Oxford, OX1 3NP, UK
3 Department of Chemistry, University of California - Berkeley, CA 94720-1460, USA
4 School of Physics and Astronomy, University of Nottingham Nottingham, NG7 2RD, UK
received 20 September 2004; accepted in final form 23 November 2004
published online 24 December 2004
The interplay between self-diffusion and excitation lines in space-time was recently studied in kinetically constrained models to explain the breakdown of the Stokes-Einstein law in supercooled liquids. Here, we further examine this interplay and its manifestation in incoherent scattering functions. In particular, we establish a dynamic length scale below which Fickian diffusion breaks down, as is observed in experiments and simulations. We describe the temperature dependence of this length scale in liquids of various fragilities, and provide analytical estimates for the van Hove and self-intermediate scattering functions.
05.20.Jj - Statistical mechanics of classical fluids.
05.70.Jk - Critical point phenomena.
64.70.Pf - Glass transitions.
© EDP Sciences 2005