The emergence of cooperativity accompanying vitrification: Insights from density fluctuation dynamics

We discuss the emergence and growth of the cooperativity accompanying vitrification based on the density fluctuation dynamics for fragile glass-forming liquids. (i) The relaxation of density fluctuations proceeds by the particle (density) exchange process, and is diffusive; that is, the allowable kinetic paths are strongly restricted by the local conservation law. (ii) In normal liquid states, this exchange process is less cooperative, and the diffusion coefficient of density fluctuations $D_c$ is given as $D_c\sim \lambda^2/\tau_\alpha$, where $\lambda$ is the particle size and $\tau_\alpha$ is the structural relaxation time. On the other hand, in supercooled states the restriction on the kinetic path is more severe with increasing the degree of supercooling, which makes the exchange process more cooperative, resulting in $D_c \sim \xi_{\rm d}^2/\tau_\alpha$ with $\xi_{\rm d}$ being the cooperative length scale. (iii) The molecular dynamics simulation results show that the self-diffusion coefficient of the tagged particle, $D_s$, almost coincides with $D_c$, suggesting that the collective density diffusion and the particle diffusion closely share the same mechanism: in normal states $D_s$ determines $D_c$, but vice versa in supercooled states. This immediately leads to the idea that the breakdown of the Stokes-Einstein relation is not the anomaly in the single-particle dynamics but reflects the increase in the cooperativity in the density diffusion at the length scale of $\xi_{\rm d}$.