Dynamic Heterogeneity in a Glass Forming Fluid: Susceptibility, Structure Factor, and Correlation Length

We investigate the growth of dynamic heterogeneity in a glassy hard-sphere mixture for volume fractions up to and including the mode-coupling transition. We use an 80 000 particle system to test a new procedure to evaluate a dynamic correlation length xi(t): we determine the ensemble independent dynamic susceptibility chi(4)(t) and use it to facilitate evaluation of xi(t) from the small wave vector behavior of the four-point structure factor. We analyze relations between the alpha relaxation time tau(alpha),chi(4)(tau(alpha)), and xi(tau(alpha)). We find that mode-coupling-like power laws provide a reasonable description of the data over a restricted range of volume fractions, but the power laws' exponents differ from those predicted by the inhomogeneous mode-coupling theory. We find xi(tau(alpha)) similar to ln(tau(alpha)) over the full range of volume fractions studied, which is consistent with an Adam-Gibbs-type relation.