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Complex Dynamics of Glass-Forming LiquidsA Mode-Coupling Theory$
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Wolfgang Götze

Print publication date: 2008

Print ISBN-13: 9780199235346

Published to Oxford Scholarship Online: May 2009

DOI: 10.1093/acprof:oso/9780199235346.001.0001

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Extensions of the Mode-Coupling Theory for the Evolution of Glassy Dynamics of Liquids

Extensions of the Mode-Coupling Theory for the Evolution of Glassy Dynamics of Liquids

Chapter:
(p.304) 5 Extensions of the Mode-Coupling Theory for the Evolution of Glassy Dynamics of Liquids
Source:
Complex Dynamics of Glass-Forming Liquids
Author(s):

Wolfgang Götze

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199235346.003.0005

It is demonstrated in this chapter that states of simple systems with density-fluctuation arrest exhibit positive static shear moduli and perfect particle localization. Approaching a generic glass-transition point, there evolve plateaus for the frequency-dependent storage moduli and negative long-time tails for the velocity correlations. Equations are derived for a statistical description of the dynamics of mixtures and of molecular liquids by generalizing the mode-coupling-theory formulas for simple systems to ones for matrices of correlation functions. It is shown that the slowest relaxation processes in binary mixtures of hard spheres are accelerated due to an increase of the mixing percentage for large size disparity of the particles while it is delayed for small ones. It is explained that the glassy reorientation dynamics of liquids of symmetric linear molecules exhibits different features for strong, weak, and very weak rotation–translation coupling.

Keywords:   static shear moduli, localization, storage moduli, long-time tails, binary mixtures, molecular liquids, symmetric linear molecules, rotation–translation coupling

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