Dynamics of highly supercooled liquids: Heterogeneity, rheology, and diffusion

Abstract

Highly supercooled liquids with soft-core potentials are studied via molecular-dynamics simulations in two and three dimensions in quiescent and sheared conditions. We may define bonds between neighboring particle pairs unambiguously owing to the sharpness of the first peak of the pair correlation functions. Upon structural rearrangements, they break collectively in the form of clusters whose sizes grow with lowering the temperature T. The bond lifetime ${\ensuremath{\tau}}_{b},$ which depends on $T$ and the shear rate $\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{\ensuremath{\gamma}}$, is on the order of the usual structural or $\ensuremath{\alpha}$ relaxation time ${\ensuremath{\tau}}_{\ensuremath{\alpha}}$ in weak shear $\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{\ensuremath{\gamma}}{\ensuremath{\tau}}_{\ensuremath{\alpha}}\ensuremath{\ll}1,$ while it decreases as $1/\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{\ensuremath{\gamma}}$ in strong shear $\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{\ensuremath{\gamma}}{\ensuremath{\tau}}_{\ensuremath{\alpha}}\ensuremath{\gg}1$ due to shear-induced cage breakage. Accumulated broken bonds in a time interval $(\ensuremath{\sim}0.05{\ensuremath{\tau}}_{b})$ closely resemble the critical fluctuations of Ising spin systems. For example, their structure factor is well fitted to the Ornstein-Zernike form, which yields the correlation length $\ensuremath{\xi}$ representing the maximum size of the clusters composed of broken bonds. We also find a dynamical scaling relation, ${\ensuremath{\tau}}_{b}\ensuremath{\sim}{\ensuremath{\xi}}^{z},$ valid for any T and $\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{\ensuremath{\gamma}}$ with $z=4$ in two dimensions and $z=2$ in three dimensions. The viscosity is of order ${\ensuremath{\tau}}_{b}$ for any T and $\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{\ensuremath{\gamma}},$ so marked shear-thinning behavior emerges. The shear stress is close to a limiting stress in a wide shear region. We also examine motion of tagged particles in shear in three dimensions. The diffusion constant is found to be of order ${\ensuremath{\tau}}_{b}^{\ensuremath{-}\ensuremath{\nu}}$ with $\ensuremath{\nu}=0.75\ensuremath{\sim}0.8$ for any T and $\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{\ensuremath{\gamma}},$ so it is much enhanced in strong shear compared with its value at zero shear. This indicates a breakdown of the Einstein-Stokes relation in accord with experiments. Some possible experiments are also proposed.