Spatial correlations in the dynamics of glassforming liquids: Experimental determination of their temperature dependence

Abstract : We use recently introduced three-point dynamic susceptibilities to obtain an experimental determination of the temperature evolution of the number of molecules N corr that are dynamically correlated during the structural relaxation of supercooled liquids. We first discuss in detail the physical content of three-point functions that relate the sensitivity of the averaged two-time dynamics to external control parameters such as temperature or density, as well as their connection to the more standard four-point dynamic susceptibility associated with dynamical heterogeneities. We then demonstrate that these functions can be experimentally determined with good precision. We gather available data to obtain the temperature dependence of N corr for a large number of supercooled liquids over a wide range of relaxation time scales from the glass transition up to the onset of slow dynamics. We find that N corr systematically grows when approaching the glass transition. It does so in a modest manner close to the glass transition, which is consistent with an activation-based picture of the dynamics in glassforming materials. For higher temperatures, there appears to be a regime where N corr behaves as a power-law of the relaxation time. Finally, we find that the dynamic response to density, while being smaller than the dynamic response to temperature, behaves similarly, in agreement with theoretical expectations.