Dynamical susceptibility of glass formers: Contrasting the predictions of theoretical scenarios
- 14 April 2005
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review E
- Vol. 71 (4), 041505
- https://doi.org/10.1103/physreve.71.041505
Abstract
We compute analytically and numerically the four-point correlation function that characterizes nontrivial cooperative dynamics in glassy systems within several models of glasses: elastoplastic deformations, mode-coupling theory (MCT), collectively rearranging regions (CRR’s), diffusing defects, and kinetically constrained models (KCM’s). Some features of the four-point susceptibility are expected to be universal: at short times we expect a power-law increase in time as due to ballistic motion ( if the dynamics is Brownian) followed by an elastic regime (most relevant deep in the glass phase) characterized by a or growth, depending on whether phonons are propagative or diffusive. We find in both the and early regime that , where is directly related to the mechanism responsible for relaxation. This regime ends when a maximum of is reached at a time of the order of the relaxation time of the system. This maximum is followed by a fast decay to zero at large times. The height of the maximum also follows a power law . The value of the exponents and allows one to distinguish between different mechanisms. For example, freely diffusing defects in lead to and , whereas the CRR scenario rather predicts either or a logarithmic behavior depending on the nature of the nucleation events and a logarithmic behavior of . MCT leads to and , where and are the standard MCT exponents. We compare our theoretical results with numerical simulations on a Lennard-Jones and a soft-sphere system. Within the limited time scales accessible to numerical simulations, we find that the exponent is rather small, , with a value in reasonable agreement with the MCT predictions, but not with the prediction of simple diffusive defect models, KCM’s with noncooperative defects, and CRR’s. Experimental and numerical determination of for longer time scales and lower temperatures would yield highly valuable information on the glass formation mechanism.
Keywords
This publication has 63 references indexed in Scilit:
- On the Adam-Gibbs-Kirkpatrick-Thirumalai-Wolynes scenario for the viscosity increase in glassesThe Journal of Chemical Physics, 2004
- Diverging length scale and upper critical dimension in the Mode-Coupling Theory of the glass transitionEurophysics Letters, 2004
- Time and length scales in supercooled liquidsPhysical Review E, 2004
- Spatially heterogeneous dynamics investigated via a time-dependent four-point density correlation functionThe Journal of Chemical Physics, 2003
- Growing correlation length on cooling below the onset of caging in a simulated glass-forming liquidPhysical Review E, 2002
- Geometric Approach to the Dynamic Glass TransitionPhysical Review Letters, 2002
- Three-Dimensional Direct Imaging of Structural Relaxation Near the Colloidal Glass TransitionScience, 2000
- Heterogeneous Diffusion in Highly Supercooled LiquidsPhysical Review Letters, 1998
- Nonequilibrium dynamics of spin glassesPhysical Review B, 1988
- Kinetic Ising Model of the Glass TransitionPhysical Review Letters, 1984