Multiple liquid-liquid critical points and density anomaly in core-softened potentials

Abstract

The relation between liquid-liquid phase transitions and waterlike density anomalies in coresoftened potentials of fluids was investigated in an exactly solvable one dimensional lattice model and a in a three dimensional fluid with fermi-like potential, the latter by molecular dynamics. Both systems were shown to present three liquid phases, two liquid-liquid phase transitions closely connected to two distinct regions of anomalous density increase. We propose that an oscillatory behavior observed on the thermal expansion coefficient as a function of pressure can be used as a signature of the connection between liquid-liquid phase and density.PACS numbers: 61.20. Gy, The phase behavior of single component systems as particles interacting via the o-called core-softened (CS) potentials has received attention since the pioneering work of Stell and Hemmer proposing the possibility of a second critical point in addition to the usual liquidgas critical point 1 . These potentials exhibit a repulsive core with a softening region with a shoulder or a ramp 1-3 which are analytically and computationally tractable while being capable of retaining the qualitative features of the real fluid systems. Furthermore, Debenedetti and collaborators 4 using thermodynamic arguments showed that the isobaric thermal expansion coefficient (α) of these potentials might have an anomalous negative value and consequently a region where density increases with temperature. Since for high temperatures density decreases with temperature these potentials can exhibit a temperature of maximum density (TMD) connecting the two regions.The thermodynamic anomalies predicted by these models occur in liquids such as Te 5 , Ga, Bi 6 , S 7,8 , liquid water 9 , and Ge 15 Te 85 10 , and were found in simulations for silica 11,12 , silicon 13 , and BeF 2 11 . In addition experiments in phosphorous indicate the presence of a liquidliquid phase transition 14 and similar transitions were observed by simulations in models of silica 15 , silicon 13 and liquid water 16 .In the particular case of water the hypothesis of the existence of two liquid phases has been indirectly supported by experimental results in confined systems 17 . In spite of the limit of 235 K below which water cannot be found in the liquid phase without crystallization, two amorphous phases, a low density amorphous phase and a high density amorphous phase, were observed at much lower temperatures and their relation to a metastable liquidliquid phase transition was argued 18 . More recently a third amorphous phase, the very high density amorphous phase, has been observed 19 what suggests the possibility of the existence of the very high density liquid phase.Therefore the issue of a liquid-liquid phase transition and its connection with the existence of a region in the pressure-temperature phase diagram where the density decreases with the decrease of temperature is itself an interesting topic. It is accepted that the presence of two accessible length scales in the potential allow for the system to ...

Residual entropy and waterlike anomalies in the repulsive one dimensional lattice gas

“…The model was studied through transfer matrix technique, the Takahashi method (within a two state approximation, as will be discussed latter), and Monte Carlo simulations. With the results obtained from these techniques a connection between temperature of maximum density and GSTP was found as in a previous work with more complex models [14]. In addition, it was also found that GSPT does present a residual entropy, due to phase mixing, and it is shown that this property is fundamental in determining waterlike anoma-lies for the model considered here.…”

“…Two ground state phase transitions are present at null temperature and were calculated by equating the enthalpy per particle at different phases: a G-SF at P = 0 and a SF-DF transition at P c , which will be called "second critical point" as in previous works [13,14,17].…”

“…[14]. In that work the Gibbs free energy per particle was approximated near the GSPT by realizing that on this region the probability of finding local states different from those of the coexisting structures was vanishing small.…”

“…To achieved this goal we previously investigate 1D lattice models with pair interaction between the first neighboring molecules, with interactions spanning two [13] and three lattice sites [14]. While in Ref.…”

“…[13] both van der Waals and hydrogen bond like interactions were used, resulting in a line of temperature of maximum density associated to a ground state phase transition (GSPT), in Ref. [14] it was proposed a core-softened fluid with pair interactions up to three sites, resulting in two temperature of maximum density lines associated to two GSPT. Besides obtaining exact results, in the latter work we used an analytical approximation in the neighborhood of the critical point to obtain a simple expression for Gibbs free energy, and used it to mathematically study the relation between anomalous density behavior and GSPT.…”