We present a theoretical framework based on a higher order density correlation
function, analogous to that used to investigate spin glasses, to describe dynamical
heterogeneities in simulated glass-forming liquids. These higher order correlation
functions are a four-point, time-dependent density correlation function
g4(r,t) and a corresponding
'structure factor' S4(q,t)
which measure the spatial correlations between the local liquid
density at two points in space, each at two different times.
g4(r,t) and
S4(q,t)
were extensively studied via molecular dynamics simulations of a binary
Lennard-Jones mixture approaching the mode coupling temperature from above in
Franz et al (1999 Phil. Mag. B 79 1827), Donati et al (2002 J. Non-Cryst. Solids 307
215), Glotzer et al (2000 J. Chem. Phys. 112 509), Lacević et al (2002 Phys. Rev. E 66
030101), Lacević et al (2003 J. Chem. Phys. submitted) and Lacević (2003 Dissertation
The Johns Hopkins University). Here, we examine the contribution to
g4(r,t),
S4(q,t) and
the corresponding dynamical correlation length, as well as the corresponding order parameter
Q(t) and generalized
susceptibility χ4(t),
from localized particles. We show that the dynamical correlation length ξ4SS(t)
of localized particles has a maximum as a function of time
t,
and the value of the maximum of ξ4SS(t)
increases steadily in the temperature range approaching the mode coupling
temperature from above.