Dynamical heterogeneity in simulated glass-forming liquids studied via a four-point spatiotemporal density correlation function

Relaxation in supercooled liquids at temperatures above their glass transition and below the onset temperature of “slow” dynamics involves the correlated motion of neighboring particles. This correlated motion results in the appearance of spatially heterogeneous dynamics or “dynamical heterogeneity”. Traditional, two-point, time-dependent density correlation functions, while providing information about the transient “caging” of particles on cooling, are unable to provide sufficiently detailed information about correlated motion and dynamical heterogeneity. Hence, we study a four-point, time-dependent density correlation function g₄( r, t) and corresponding “structure factor” S ₄(q, t) which measure the spatial correlations between the local liquid density at two points in space, each at two different times.; We study g₄(r, t) and S₄(q, t) via MD simulations of a binary Lennard-Jones mixture approaching the mode coupling temperature from above. We find that the correlations between particles measured by g ₄(r, t) and S₄( q; t) become increasingly pronounced on cooling. The corresponding dynamical correlation length ξ₄(t) has a maximum as a function of time t, and the value of the maximum of ξ ₄(t) increases steadily from less than one particle diameter to a value exceeding nine particle diameters in the temperature range approaching the mode coupling temperature from above. We examine the individual contributions to g₄(r, t), S₄(q, t), and ξ₄( t), well as the corresponding order parameter Q( t and generalized susceptibility χ₄(t). These contributions elucidate key differences between domains of localized, replaced and delocalized particles.; We examine particles' instantaneous pair forces belonging to domains of localized and replaced particles. We detect a relationship between high pair forces and replaced particles. We also construct “force chains” of particles interacting with low, average and high force and examine their distribution and relation to domains of localized and replaced particles. We find that “force chains” in glass-forming liquid do not appear to be related to dynamical heterogeneities as has been suggested. We demonstrate that spatially heterogeneous dynamics is directly related to spatially heterogeneous transport and mechanical properties of supercooled liquids by calculating stress-stress correlation functions and elastic constants. These studies contribute to a deeper general understanding of the physics of supercooled liquids and more specifically the similarities between supercooled liquids and granular materials.