Re. Larsen et al., LIQUID THEORY FOR THE INSTANTANEOUS NORMAL-MODES OF A LIQUID .2. SOLUTIONS, The Journal of chemical physics, 104(8), 1996, pp. 2987-3002
There are a number of different ways of thinking about the intermolecu
lar vibrations present in liquids. The approach suggested by instantan
eous normal modes is a particularly interesting one, not just because
of its connections with short-time dynamics, but because these modes c
an 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 mi
xtures can be handled in virtually an identical fashion. We construct
a renormalized mean-field theory that allows us to predict not only th
e 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 pr
esent in the mixture. We illustrate these results by applying them fir
st to mixtures of Ar and Kr and then to binary isotopic mixtures with
far more extreme mass differences, comparing in both cases with simula
tion. For;mixtures of atoms not much more disparate than Ar and Kr, we
find that the solution densities of states can be described quantitat
ively, 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 rati
o. The dynamics of a light solute in a liquid makes an especially shar
p contrast with that of an analogous light impurity in a crystal latti
ce. (C) 1996 American Institute of Physics.