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

Abstract

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 critical point well above the equilibrium melting line. We study the dynamic behavior in the vicinity of this liquid-liquid critical point. We find that the dynamics in the more ordered high density phase (HDL) are much slower then the dynamics in the less ordered low density phase (LDL). Moreover, the behavior 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. On the other hand, if we cool the system at constant pressure above the critical pressure behavior of the dynamics smoothly changes with temperature. It resembles the behavior of the LDL at high temperatures and resembles the behavior 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.

The puzzling unsolved mysteries of liquid water: Some recent progress

“…Two of the models (the TIP5P [45] and the ST2 [46]) treat water as a multiple site rigid body, interacting via electrostatic site-site interactions complemented by a Lennard-Jones potential. The third model is the spherical ''two-scale'' Jagla potential with attractive and repulsive ramps which has been studied in the context of liquid-liquid phase transitions and liquid anomalies [21,[30][31][32]47,48]. For all three models, Xu et al evaluated the loci of maxima of the relevant response functions, compressibility and specific heat, which coincide close to the critical point and give rise to the Widom line.…”

Dynamic transitions in a two dimensional associating lattice gas model

“…Beyond this point, at which the response functions diverge, one finds lines of maxima of these functions which asymptotically approach the critical point. This extension of the first-order phase boundary into the one-phase region has been called Widom line 7 at T L ͑P͒. Even though this line does not exhibit any thermodynamic transition, experiments on water show that the specific heat, shear viscosity and thermal diffusivity 8 exhibit a peak when crossing the Widom line.…”

“…4,5 The dynamic crossover has also been associated with liquid-liquid transitions in silicon 6 and in nontetrahedral liquids. 7 The basic surmise behind the link between the dynamic crossover and the presence of a second critical point goes as follows. The liquid-liquid coexistence line that separates two liquid phases terminates at a critical point.…”

Joule Inversion Temperatures for Some Simple Real Gases

“…kT u A (6) where u(r) is the intermolecular potential, k the Boltzmann's constant, N A the Avogadro's number, and r is the distance between a pair of molecules. In the present article we use the Lennard-Jones (LJ) potential, that is, ( ) = 6 12 4 r r r u (7) being the well depth and the point where u(r) = 0.…”

“…Instituto Politécnico Nacional, U. P. Adolfo López Mateos, C. P. 07738, México D. F.; Tel: +52 (55) 57296000 ext 55034; E-mail: caesar_erik@yahoo.com modify hard-core potentials to predict real fluid properties at low densities, including the inversion temperature. In the present article we discuss the problem of the Joule inversion temperature by means of a Lennard-Jones potential slightly modified in its repulsive and positive part according to the so-called Jagla potential [6]. This potential allows to obtain analytical expressions for the second virial coefficient and for its first derivative dB/dT, necessary to calculate the Joule inversion temperature.…”