Potential energy landscape and mechanisms of diffusion in liquids

The mechanism of diffusion in supercooled liquids is investigated from the potential energy landscape point of view, with emphasis on the crossover from high- to low-T dynamics over the range T(A) > or =T > or =T(c). Molecular dynamics simulations with a time dependent mapping to the associated local minimum or inherent structure (IS) are performed on unit-density Lennard-Jones. Dynamical quantities introduced include r2(is)(t), the mean-square displacement (MSD) within a basin of attraction of an IS, R2(t), the MSD of the IS itself, and g(t), the distribution of IS waiting times. The configuration space is treated as a composite of the contributions of cooperative local regions, and a method is given to obtain the physically meaningful g(loc)(t) and mean waiting time tau(loc) from g(t). An understanding of the crossover is obtained in terms of r2(is)(t) and tau(loc). At intermediate T, r2(is)(t) possesses an interval of linear t dependence allowing calculation of an intrabasin diffusion constant D(is). Near T(c), where intrabasin diffusion is well established for t<tau(loc), diffusion is intrabasin dominated with D=D(is); D may be calculated within a basin. Below T(c), tau(loc) exceeds the time tau(pl) needed for the system to explore the basin, indicating the action of barriers at the border; tau(loc)=tau(pl) is a criterion for transition to activated hopping. Intrabasin diffusion provides a means of confinement not involving barriers and plays a key role in the dynamics above T(c). The distinction is discussed between motion among the IS (IS dynamics) below T(c) and saddle or border dynamics above T(c), where the system is always close to one of the saddle barriers connecting the basins and IS boundaries are closely spaced and easily crossed. A border index is introduced based upon the relation of R2(t) to the conventional MSD, and shown to vanish at T approximately T(c). It is proposed that intrabasin diffusion is a manifestation of saddle dynamics.