Neighborship structure and dynamics in supercooled liquids

The neighbors of a central atom in the supercooled, unit-density Lennard-Jones liquid are sorted by “neighborship” (first neighbor, second neighbor, etc.), and an analysis of static and dynamical properties is presented. A preliminary model is that neighbors n=1–12 fall in the first shell S1, that n=13,14 are transitional neighbors, and that S2 begins at n=15. S1 is identified as the cage of the central atom, and S1 plus the central atom is considered as a possible cluster; diffusion is proposed to occur via S1→S2 transitions. The radial probability distribution functions, P(n,r), for the nth neighbor are calculated. With decreasing T the shells pull away from each other and from the transitional neighbors, and a mean-field theory of P(n,r) breaks down. It is suggested that such behavior correlates with a dynamical slowing down. Similarly, a diffusive model for the number of original S1 neighbors still in S1 at time t fails for (reduced) T⩽0.80, indicating the onset of collective slow cluster dynamics. Static and dynamic evidence points to T∼0.8 as a temperature below which the liquid becomes more complex. The need to separate fast vibrational dynamics from measures of diffusion is discussed; one atom makes a first passage S1→S2 very quickly. The two-atoms first passage time τ2 is therefore proposed as an approximate single-atom diffusive time. The rate τ2−1 is in excellent agreement with the barrier hopping rate ωh calculated from instantaneous normal mode theory.