Relationship between the liquid-liquid phase transition and dynamic behaviour in the Jagla model

Using molecular dynamics simulations, we study a spherically symmetric 'two-scale' Jagla potential with both repulsive and attractive ramps. This potential displays a liquid-liquid phase transition with a positively sloped coexistence line ending at a critical point well above the equilibrium melting line. We study the dynamic behaviour in the vicinity of this liquid-liquid critical point. Below the critical point, we find that the dynamics in the more ordered high density liquid (HDL) are much slower then the dynamics in the less ordered low density liquid (LDL). Moreover, the behaviour of the diffusion constant and relaxation time in the HDL phase follows approximately an Arrhenius law, while in the LDL phase the slope of the Arrhenius fit increases upon cooling. Above the critical pressure, as we cool the system at constant pressure, the behaviour of the dynamics smoothly changes with temperature. It resembles the behaviour of the LDL at high temperatures and resembles the behaviour of the HDL at low temperatures. This dynamic crossover happens in the vicinity of the Widom line ( the extension of the coexistence line into the one-phase region) which also has a positive slope. Our work suggests a possible general relation between a liquid-liquid phase transition and the change in dynamics.