Shapes of dynamically heterogeneous regions in glassy fluids with attractive and repulsive interactions as revealed through anisotropic four-point correlation functions

We investigate the size and anisotropy of dynamically heterogeneous regions in glassy fluids with attractive and repulsive interactions. To this end we simulate a binary Lennard-Jones mixture and its Weeks-Chandler-Andersen truncation. We use a four-point correlation function $G_4(\vec{k},\vec{r};t)$, which depends on the angle between $\vec{k}$ and $\vec{r}$, and its associated structure factor $S_4(\vec{k},\vec{q};t)$, which depends on the angle $\theta$ between $\vec{k}$ and $\vec{q}$, to characterize the size and anisotropy of the dynamically correlated regions. In particular, $G_4(\vec{k},\vec{r};t)$ allows us to explore dynamic heterogeneities at shorter distances. In contrast, to investigate dynamic heterogeneities at longer distances we analyze the small $q$ behavior of $S_4(\vec{k},\vec{q};t)$ and obtain an anisotropic dynamic correlation length $\xi(\theta)$. We explore the dependence of dynamic heterogeneities at shorter and longer distances on the presence of attractive interactions.