Questioning the relationship between the χ4 susceptibility and the dynamical correlation length in a glass former

Abstract

Clusters of fast and slow correlated particles, identified as dynamical heterogeneities (DHs), constitute a central aspect of glassy dynamics. A key factor of the glass transition scenario is a significant increase of the cluster size ξ₄ as the transition is approached. In need of easy-to-compute tools to measure ξ₄, the dynamical susceptibility χ₄ was introduced recently, and used in various experimental studies to probe DHs. Here, we investigate DHs in dense microgel suspensions using image correlation analysis, and compute both χ₄ and the four-point correlation function G₄. The spatial decrease of G₄ provides a direct access to ξ₄, which is found to grow significantly with increasing volume fraction. However, this increase is not captured by χ₄. We show that the assumptions that validate the connection between χ₄ and ξ₄ are not fulfilled in our experiments.