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Sticky hard spheres, i.e., hard particles decorated with a short-ranged attractive interaction potential, constitute a relatively simple model with highly non-trivial glassy dynamics. The mode-coupling theory of the glass transition (MCT) offers a qualitative account of the complex reentrant dynamics of sticky hard spheres, but the predicted glass transition point is notoriously underestimated. Here we apply an improved first-principles-based theory, referred to as generalized mode-coupling theory (GMCT), to sticky hard spheres. This theoretical framework seeks to go beyond MCT by hierarchically expanding the dynamics in higher-order density correlation functions -- an approach that may become exact if sufficiently many correlations are taken into account. We predict the phase diagrams from the first few levels of the GMCT hierarchy and the dynamics-related critical exponents, all of which are much closer to the empirical observations than MCT. Notably, the prominent reentrant glassy dynamics, the glass-glass transition, and the higher-order bifurcation singularity classes ($A_3$ and $A_4$) of sticky hard spheres are found to be preserved within GMCT at arbitrary order. Moreover, we demonstrate that when the hierarchical order of GMCT increases, the effect of the short-ranged attractive interactions becomes more evident in the dynamics. This implies that GMCT is more sensitive to subtle microstructural differences than MCT, and that the framework provides a promising first-principles approach to systematically go beyond the MCT regime.
We use the swap Monte Carlo algorithm to analyse the glassy behaviour of sticky spheres in equilibrium conditions at densities where conventional simulations and experiments fail to reach equilibrium, beyond predicted phase transitions and dynamic si
G. Brambilla et al. Reply to a Comment by J. Reinhardt et al. questioning the existence of equilibrium dynamics above the critical volume fraction of colloidal hard spheres predicted by mode coupling theory.
A colloidal system of spheres interacting with both a deep and narrow attractive potential and a shallow long-ranged barrier exhibits a prepeak in the static structure factor. This peak can be related to an additional mesoscopic length scale of clust
The coupling-parameter method, whereby an extra particle is progressively coupled to the rest of the particles, is applied to the sticky-hard-sphere fluid to obtain its equation of state in the so-called chemical-potential route ($mu$ route). As a co
The smallest maximum kissing-number Voronoi polyhedron of 3d spheres is the icosahedron and the tetrahedron is the smallest volume that can show up in Delaunay tessalation. No periodic lattice is consistent with either and hence these dense packings