The relationship between unstable localized vibrational modes and dynamical heterogeneity in glass formers

The heterogenous dynamics of glass-forming materials is commonly characterized by the spatially correlated particles (clusters) with high and low mobilities, and are helpful for explaining the temperature dependence of the non-Arrhenius behavior of relaxation time. Due to the inherent difficulty to experimentally observe heterogeneous dynamical clusters, we consider the possibility that the localized unstable modes of the vibrational spectrum may be related to dynamical clusters. Specifically, we analyze the instantaneous normal modes (INMs) associated with the Hessian matrix of glass-forming liquids. We find that the particles that contribute most to the unstable, localized modes form spatially correlated clusters. We quantify the degree to which these clusters correlate to string-like cooperative motions and mobile clusters, and how polymer topology affects these clusters.