Detailed Quantification of String-Like Cooperative Motion Provides Insight into the Dynamic Crossover in Glass-Forming Liquids

Using atomistic simulations, we conduct a detailed investigation of string-like cooperative motion, and in particular the formation of strings of various lengths in model glass-formers. We show that the maximum values of the average string length and the fraction of atoms that are participating in string-like motion exhibit non-Arrhenius behavior, in which a transition is seen to occur at the dynamic crossover temperature $T_X$. Interestingly, we observe that the population of atoms participating in cooperatively-rearranging pairs (strings composed of two atoms) exhibits a non-monotonic variation in temperature. The population variance with temperature of longer strings is monotonic and becomes increasingly Arrhenius with increasing string length. As a consequence of our analysis, we propose a mechanism for string formation by which single, mobile atoms "latch on" to existing shorter strings to form longer strings. Our findings lend support to the hypothesis that the temperature $T_X$ corresponds to increased presence of activated dynamics in glass-forming liquids at lower temperatures.