Growing point-to-set length scales in Lennard-Jones glass-forming liquids

We study the point-to-set length scales and dynamics in three-dimensional Kob-Andersen glass-forming liquids with amorphous boundary conditions by using molecular dynamics simulation, where a set of particles in an equilibrium configuration are pinned while other particles move as before. We consider three different geometries, i.e., spherical cavity, cubic cavity, and walls, for the pinning set of particles. We present the growing static and dynamic point-to-set correlation length scales in the temperature range higher than the ideal mode-coupling theory transition temperature of the bulk. Our results reveal that the two-point static spatial correlations are almost the same for these three geometries at the same temperature, which implies weak geometry dependence on the structure of such glass-forming liquids. By analyzing z (the distance from the wall) dependent point-to-set overlaps, we find that the particles in the layers near the pinning wall relax slower than those far away from the wall. Associated with the dynamical slowdown, the static length scale increases modestly while the dynamic length scale increases dramatically as the temperature is lowered. Compared with the two cavities, the "Walls" system relaxes faster at the same temperature and the same distance from the wall and has smaller length scales. Moreover, the relation between time scale and static length scales depends on the degree of supercooling and the type of geometries. We did not see any clear evidence for the one-to-one correspondence between static and dynamic point-to-set length scales, and also for the one-to-one correspondence between static length scales and relaxation time in the deep supercooled regime. Our results provide clues for the existence of multi-relaxation modes in the supercooled regime in three-dimensional Kob-Andersen glass-forming liquids.