Liquid theory for the instantaneous normal modes of a liquid. II. Solutions

Abstract

There are a number of different ways of thinking about the intermolecular vibrations present in liquids. The approach suggested by instantaneous normal modes is a particularly interesting one, not just because of its connections with short-time dynamics, but because these modes can be analyzed and computed using the statistical mechanical ideas of standard liquid theory—or at least they can for neat, atomic liquids. We show in this paper that the instantaneous normal modes of atomic mixtures can be handled in virtually an identical fashion. We construct a renormalized mean-field theory that allows us to predict not only the total density of states of the mixture’s instantaneous normal modes, but also its projections into species-specific parts. This projection then allows us to predict the separate dynamics of all the species present in the mixture. We illustrate these results by applying them first to mixtures of Ar and Kr and then to binary isotopic mixtures with far more extreme mass differences, comparing in both cases with simulation. For mixtures of atoms not much more disparate than Ar and Kr, we find that the solution densities of states can be described quantitatively, over the entire range of compositions, merely by regarding the system as an effective neat liquid in appropriately scaled units. When the masses of the components differ by an order of magnitude or more, this simple scaling no longer holds, but what is interesting is that the liquid’s behavior is also quite different from what one would have seen in substitutionally disordered crystals with this same mass ratio. The dynamics of a light solute in a liquid makes an especially sharp contrast with that of an analogous light impurity in a crystal lattice.