Diffusion in supercooled liquids via normal mode analysis

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Abstract
A theory is developed for diffusion in supercooled liquids. The viewpoint taken is that the dynamics of system, represented by a point in configuration space, consists of long sojourns in the vicinity of the local minima of the total potential, interrupted by relatively infrequent barrier crossings to adjacent minima. An equation due to Zwanzig, plus a new relation for the hopping rate among the local minima, are combined in a theory for the self-diffusion constant D. All the quantities entering the two equations are shown to be derivable from the configuration-averaged densities of vibrational states, 〈ρ(ω)〉, introduced by us previously; the contribution of unstable modes plays a crucial role. Solution of the coupled equations reveals the existence of a critical temperature below which D vanishes. The theory is in excellent agreement with molecular dynamics values for D, over a wide temperature range in which D displays activated behavior, in Lennard-Jones argon at a reduced density of unity.