The mean-squared displacement of a molecule moving in a glassy system
Abstract
The mean-squared displacement (MSD) of a hard sphere and of a dumbbell molecule consisting of two fused hard spheres immersed in a dense hard-sphere system is calculated within the mode-coupling theory for ideal liquid-glass transitions. It is proven that the velocity correlator, which is the second time derivative of the MSD, is the negative of a completely monotone function for times within the structural-relaxation regime. The MSD is found to exhibit a large time interval for structural relaxation prior to the onset of the -process which cannot be described by the asymptotic formulas for the mode-coupling-theory-bifurcation dynamics. The -process for molecules with a large elongation is shown to exhibit an anomalously wide cross-over interval between the end of the von-Schweidler decay and the beginning of normal diffusion. The diffusivity of the molecule is predicted to vary non-monotonically as function of its elongation.
Keywords
Cite
@article{arxiv.cond-mat/0104159,
title = {The mean-squared displacement of a molecule moving in a glassy system},
author = {S. -H. Chong and W. Gotze and M. R. Mayr},
journal= {arXiv preprint arXiv:cond-mat/0104159},
year = {2009}
}
Comments
18 pages, 12 figures, Phys. Rev. E, in print