A monatomic system with a liquid-liquid critical point and two distinct glassy states

We study the glass transition (GT) in a model system that exhibits the presence of more than one liquid or glassy state ("polyamorphism") using molecular dynamics simulations. We study the Jagla model [E. A. Jagla, J. Chem. Phys. 111, 8980 (1999)], a two-scale spherically symmetric ramp potential with both attractive and repulsive interactions. The Jagla model is particularly interesting since, depending on its parametrization, it predicts two phases ("polyamorphism") not only in the glassy state but also in equilibrium as a liquid-liquid phase transition (LLPT). The Jagla model may also be useful in understanding a recent observation of polyamorphism in metallic glasses containing cerium. We use a parametrization for which crystallization can be avoided and the GT and LLPT are clearly separated, providing a unique opportunity to study the effects of the LLPT on the GT. We follow the experimental protocol employed in the classical differential scanning calorimetry experiments used to characterize the GT, cooling and heating the system through the GT and calculating the constant-pressure specific heat C(P) and the thermal expansion coefficient alpha(P). At pressures below and well above the LLPT, the same basic GT phenomenology of metallic glasses is observed, i.e., a single peak in C(P) (typical of ergodicity restoration) occurs upon heating across the GT. At pressures above the LLPT, a second peak in C(P) develops at higher temperature above the GT. This second peak in C(P) arises from the presence of a Widom line T(W) defined as the locus of maximum correlation length in the one-phase region above the liquid-liquid critical point (LLCP). The behavior of alpha(P) is different across the GT and Widom line. Near the GT temperature T(g), alpha(P) displays a small peak upon heating, which makes a negligible contribution to the C(P) peak. On the other hand, near T(W), alpha(P) displays a much larger peak, which makes a substantial contribution to the C(P) peak at higher temperature. We find that T(g) is almost independent of pressure for each of the two coexisting liquids, but shows an apparent discontinuity upon crossing the LLPT line, to a lower value for the higher-entropy phase. We compare the entropies of both phases, and the corresponding temperature dependencies, with those of the crystal phase. We also study the dependence of the GT on heating rate and find that for pressures below the LLCP, slow heating results in crystallization, as occurs in laboratory experiments. Regarding the thermal expansion properties of the Jagla model, we study the interplay of the density minimum recently observed in confined water and the GT.