Neighborship structure and dynamics in supercooled liquids

The neighbors of a central atom in the supercooled, unit-density Lennard-Jo nes liquid are sorted by "neighborship" (first neighbor, second neighbor, e tc.), and an analysis of static and dynamical properties is presented. A pr eliminary 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 i dentified 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-->S 2 transitions. The radial probability distribution functions, P(n,r), for t he 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 d ynamical slowing down.. Similarly, a diffusive model for the number of orig inal S1 neighbors still in S1 at time r fails fbr (reduced) T less than or equal to 0.80, indicating the onset of collective slow cluster dynamics. St atic and dynamic evidence points to T similar to 0.8 as a temperature below which the liquid becomes more complex. The need to separate fast vibration al dynamics from measures of diffusion is discussed; one atom makes a first passage S1-->S2 very quickly. The two-atoms first passage time tau(2) is t herefore proposed as an approximate single-atom diffusive time. The rate ta u(2)(-1) is in excellent agreement with the barrier hopping rate omega(h) c alculated from instantaneous normal mode theory. (C) 1999 American Institut e of Physics. [S0021-9606(99)52302-7].