Inhomogeneous Mode-Coupling Theory and Growing Dynamic Length in Supercooled Liquids

TL;DR

This paper extends Mode-Coupling Theory to inhomogeneous conditions in supercooled liquids, revealing a diverging length scale and extended cage structures, with implications for understanding dynamic heterogeneity near the glass transition.

Contribution

It introduces inhomogeneous MCT equations and demonstrates a diverging dynamic length scale, providing new insights into the structure and dynamics of supercooled liquids.

Findings

Dynamic length scale diverges as |T-T_c|^-1/4 near transition

Cages are extended objects with fractal dimensions larger in alpha regime

Inhomogeneous MCT equations derived to second order in gradients

Abstract

We extend Mode-Coupling Theory (MCT) to inhomogeneous situations, relevant for supercooled liquid in pores, close to a surface, or in an external field. We compute the response of the dynamical structure factor to a static inhomogeneous external potential and provide the first direct evidence that the standard formulation of MCT is associated with a diverging length scale. We find in particular that the so called ``cages'' are in fact extended objects. Although close to the transition the dynamic length grows as |T-T_c|^-1/4 in _both_ the beta and alpha regimes, our results suggest that the fractal dimension of correlated clusters is larger in the alpha regime. We also derive inhomogeneous MCT equations valid to second order in gradients.