Analysis of a growing dynamic length scale in a glass-forming binary hard-sphere mixture
Abstract
We examine a length scale that characterizes the spatial extent of heterogeneous dynamics in a glass-forming binary hard-sphere mixture up to the mode-coupling volume fraction ϕc. First, we characterize the system’s dynamics. Then, we utilize a method [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.105.217801 105, 217801 (2010)] to extract and analyze the ensemble-independent dynamic susceptibility χ4(t) and the dynamic correlation length ξ(t) for a range of times between the β and α relaxation times. We find that in this time range the dynamic correlation length follows a volume fraction-independent master curve ξ(t)~ln(t). For longer times, ξ(t) departs from this master curve and remains constant up to the largest time at which we can determine the length accurately. In addition to the previously established correlation τα~exp[ξ(τα)] between the α relaxation time, τα, and the dynamic correlation length at this time, ξ(τα), we also find a similar correlation for the diffusion coefficient D~exp[ξ(τα)θ] with θ≈0.6. We discuss the relevance of these findings for different theories of the glass transition.
- Publication:
-
Physical Review E
- Pub Date:
- May 2011
- DOI:
- 10.1103/PhysRevE.83.051501
- arXiv:
- arXiv:1101.2655
- Bibcode:
- 2011PhRvE..83e1501F
- Keywords:
-
- 64.70.P-;
- 61.20.Lc;
- 61.20.Ja;
- Glass transitions of specific systems;
- Time-dependent properties;
- relaxation;
- Computer simulation of liquid structure;
- Condensed Matter - Soft Condensed Matter;
- Condensed Matter - Statistical Mechanics
- E-Print:
- doi:10.1103/PhysRevE.83.051501