Heterogeneous relaxation in supercooled liquids: A density functional theory analysis

Recent time domain experiments which allow selective study of the relaxation of slower subpopulations among the distributions of local, inhomogeneous regions, have shown the existence of a length scale (∼2–3 nm) beyond which the liquid behaves like a homogeneous liquid. Here we use the density functional theory to calculate the probability of creating a soft localized density fluctuation (density droplet). Theoretical calculation shows that the free energy penalty for creating a local inhomogeneity of small size is much less than that for a large size and that a dense supercooled system is unlikely to sustain inhomogeneity of a length, lf, which is larger than 5σ, where σ is the molecular diameter. We have calculated both the equilibrium and the nonequilibrium (subsequent to photobleaching) orientational correlation functions with the theoretically obtained inhomogeneous distributions. The nonequilibrium distribution relaxes at a slower rate. A simple two state exchange model has been used to mimic the re...