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

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 ξ 4 as the transition is approached. In need of easy-to-compute tools to measure ξ 4 , the dynamical susceptibility χ 4 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 χ 4 and the four-point correlation function G 4 . The spatial decrease of G 4 provides a direct access to ξ 4 , which is found to grow significantly with increasing volume fraction. However, this increase is not captured by χ 4 . We show that the assumptions that validate the connection between χ 4 and ξ 4 are not fulfilled in our experiments. We investigate dynamic heterogeneities with both a four-point correlation function G 4 and its associated dynamical susceptibility χ 4 , in dense suspensions of soft microgel particles.