Point-to-set dynamic length scale in binary Lennard-Jones glass-formers.

Abstract

Our recent molecular dynamics simulation results of binary particle glass-former systems demonstrated that the non-monotonic temperature T-dependence of the point-to-set dynamic length scale ξcdyn in harmonic (HM) systems is not an intrinsic property of bulk liquids but originates from wall effects. We would expect our results to apply equally to other simple models, such as Lennard-Jones (LJ) systems. However, Hocky et al. presented a monotonic T-dependent ξcdyn in a LJ system. Therefore, the present work employs molecular dynamics simulations to investigate the T-dependent behavior of ξcdyn in the LJ system employed by Hocky et al. to clarify our expectation. Results employing a geometry size d that is somewhat smaller than that employed by Hocky et al. reveal that a non-monotonic behavior exists in the LJ system. By varying the value of d, we demonstrate that the formation of a peak in ξcdyn with respect to T in the LJ system is the natural result of wall effects. More importantly, a new non-monotonic behavior is observed, where the temperature at which the ratio of the characteristic time required for the overlap profile of the system to decay to a given value for a point near the wall to the corresponding characteristic time at a point in the center attains a maximum is in good agreement with the temperature Tmax-c at which ξcdyn attains a maximum value, indicating that the non-monotonic behavior of ξcdyn with respect to T is a natural property of liquids in a sandwiched geometry. Furthermore, we find that, contrary to HM systems, where the values of Tmax-c obtained for all values of d considered were greater than the mode-coupling temperature Tc, the value of Tmax-c obtained for LJ systems can be either greater than, equal to, or less than Tc because an HM system has a stronger finite-size effect than that in a LJ system, indirectly implying that the conclusion derived from random first-order transition theory that a dramatic change occurs near Tc bears no necessary relationship with the non-monotonic evolution of ξcdyn with respect to T.