Length scale for the onset of Fickian diffusion in supercooled liquids

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: 23 November 2004

Abstract

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.