Questioning the relationship between the $\chi$4 susceptibility and the dynamical correlation length in a glass former

TL;DR

This study examines the relationship between the dynamical susceptibility $oldsymbol{}$ and the correlation length $oldsymbol{\xi}$4 in glass formers, revealing that $oldsymbol{}$ does not reliably indicate $oldsymbol{\xi}$4 growth in dense microgel suspensions.

Contribution

The paper challenges the assumed direct link between $oldsymbol{}$ and $oldsymbol{\xi}$4, demonstrating their decoupling in experimental glassy systems using image correlation analysis.

Findings

$oldsymbol{\xi}$4 increases with volume fraction.

$oldsymbol{}$ does not reflect the growth of $oldsymbol{\xi}$4.

Assumptions linking $oldsymbol{}$ and $oldsymbol{\xi}$4 are invalid in these experiments.

Abstract

Clusters of fast and slow correlated particles, identified as dynamical heterogeneities (DHs), con-stitute a central aspect of glassy dynamics. A key ingredient of the glass transition scenario is asignificant increase of the cluster size $\xi$4 as the transition is approached. In need of easy-to-computetools to measure $\xi$4 , the dynamical susceptibility $\chi$4 was introduced recently, and used in various ex-perimental works to probe DHs. Here, we investigate DHs in dense microgel suspensions using imagecorrelation analysis, and compute both $\chi$4 and the four-point correlation function G4 . The spatialdecrease of G4 provides a direct access to $\xi$4 , which is found to grow significantly with increasingvolume fraction. However, this increase is not captured by $\chi$4 . We show that the assumptions thatvalidate the connection between $\chi$4 and $\xi$4 are not fulfilled in our experiments.