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The mean-squared displacement of a molecule moving in a glassy system

S. -H. Chong·W. Gotze·M. R. Mayr
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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 $α$-process which cannot be described by the asymptotic formulas for the mode-coupling-theory-bifurcation dynamics. The $α$-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.

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S. -H. Chong, W. Gotze, M. R. Mayr. 2001-04-10. The mean-squared displacement of a molecule moving in a glassy system. https://doi.org/10.1103/physreve.64.011503

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