Giancarlo Franzese

Generic mechanism for generating a liquid–liquid phase transition

Recent experimental results indicate that phosphorus—a single-component system—can have a high-density liquid (HDL) and a low-density liquid (LDL) phase. A first-order transition between two liquids of different densities is consistent with experimental data for a variety of materials, including single-component systems such as water, silica and carbon. Molecular dynamics simulations of very specific models for supercooled water, liquid carbon and supercooled silica predict a LDL–HDL critical point, but a coherent and general interpretation of the LDL–HDL transition is lacking. Here we show that the presence of a LDL and a HDL can be directly related to an interaction potential with an attractive part and two characteristic short-range repulsive distances. This kind of interaction is common to other single-component materials in the liquid state (in particular, liquid metals), and such potentials are often used to describe systems that exhibit a density anomaly. However, our results show that the LDL and HDL phases can occur in systems with no density anomaly. Our results therefore present an experimental challenge to uncover a liquid–liquid transition in systems like liquid metals, regardless of the presence of a density anomaly.

Effect of hydrogen bond cooperativity on the behavior of water

Four scenarios have been proposed for the low-temperature phase behavior of liquid water, each predicting different thermodynamics. The physical mechanism that leads to each is debated. Moreover, it is still unclear which of the scenarios best describes water, because there is no definitive experimental test. Here we address both open issues within the framework of a microscopic cell model by performing a study combining mean-field calculations and Monte Carlo simulations. We show that a common physical mechanism underlies each of the four scenarios, and that two key physical quantities determine which of the four scenarios describes water: (i) the strength of the directional component of the hydrogen bond and (ii) the strength of the cooperative component of the hydrogen bond. The four scenarios may be mapped in the space of these two quantities. We argue that our conclusions are model independent. Using estimates from experimental data for H-bond properties the model predicts that the low-temperature phase diagram of water exhibits a liquid–liquid critical point at positive pressure.

The Widom line of supercooled water

Water can be supercooled to temperatures as low as −92 ◦ C, the experimental crystal homogeneous nucleation temperature TH at 2 kbar. Within the supercooled liquid phase its response functions show an anomalous increase consistent with the presence of a liquid–liquid critical point located in a region inaccessible to experiments on bulk water. Recent experiments on the dynamics of confined water show that a possible way to understand the properties of water is to investigate the supercooled phase diagram in the vicinity of the Widom line (locus of maximum correlation length) that emanates from the hypothesized liquid–liquid critical point. Here we explore the Widom line for a Hamiltonian model of water using an analytic approach, and discuss the plausibility of the hypothesized liquid–liquid critical point, as well as its possible consequences, on the basis of the assumptions of the model. The present analysis allows us (i) to find an analytic expression for the spinodal line of the high-density liquid phase, with respect to the low-density liquid phase, showing that this line becomes flat in the P–T phase diagram in the physical limit of a large number of available orientations for the hydrogen bonds, as recently seen in simulations and experiments (Xu et al 2005 Proc. Natl Acad. Sci. 102 16558); (ii) to find an estimate of the values for the hypothesized liquid–liquid critical point coordinates that compare very well with Monte Carlo results; and (iii) to show how the Widom line can be located by studying the derivative of the probability of forming hydrogen bonds with local tetrahedral orientation which can be calculated analytically within this approach. (Some figures in this article are in colour only in the electronic version)

Waterlike hierarchy of anomalies in a continuous spherical shouldered potential

We investigate by molecular dynamics simulations a continuous isotropic core-softened potential with attractive well in three dimensions, introduced by Franzese [J. Mol. Liq. 136, 267 (2007)], that displays liquid-liquid coexistence with a critical point and waterlike density anomaly. Besides the thermodynamic anomalies, here we find diffusion and structural anomalies. The anomalies, not observed in the discrete version of this model, occur with the same hierarchy that characterizes water. We discuss the differences in the anomalous behavior of the continuous and the discrete model in the framework of the excess entropy, calculated within the pair correlation approximation.

Liquid-liquid phase transitions for soft-core attractive potentials.

Using event-driven molecular dynamics simulations, we study a three-dimensional one-component system of spherical particles interacting via a discontinuous potential combining a repulsive square soft core and an attractive square well. In the case of a narrow attractive well, it has been shown that this potential has two metastable gas-liquid critical points. Here we systematically investigate how the changes of the parameters of this potential affect the phase diagram of the system. We find a broad range of potential parameters for which the system has both a gas-liquid critical point C1 and a liquid-liquid critical point C2. For the liquid-gas critical point we find that the derivatives of the critical temperature and pressure, with respect to the parameters of the potential, have the same signs: they are positive for increasing width of the attractive well and negative for increasing width and repulsive energy of the soft core. This result resembles the behavior of the liquid-gas critical point for standard liquids. In contrast, for the liquid-liquid critical point the critical pressure decreases as the critical temperature increases. As a consequence, the liquid-liquid critical point exists at positive pressures only in a finite range of parameters. We present a modified van der Waals equation which qualitatively reproduces the behavior of both critical points within some range of parameters, and gives us insight on the mechanisms ruling the dependence of the two critical points on the potentials parameters. The soft-core potential studied here resembles model potentials used for colloids, proteins, and potentials that have been related to liquid metals, raising an interesting possibility that a liquid-liquid phase transition may be present in some systems where it has not yet been observed.

Nanoscale Dynamics of Phase Flipping in Water near its Hypothesized Liquid-Liquid Critical Point

One hypothesized explanation for waters anomalies imagines the existence of a liquid-liquid (LL) phase transition line separating two liquid phases and terminating at a LL critical point. We simulate the classic ST2 model of water for times up to 1000 ns and system size up to N = 729. We find that for state points near the LL transition line, the entire system flips rapidly between liquid states of high and low density. Our finite-size scaling analysis accurately locates both the LL transition line and its associated LL critical point. We test the stability of the two liquids with respect to the crystal and find that of the 350 systems simulated, only 3 of them crystallize and these 3 for the relatively small system size N = 343 while for all other simulations the incipient crystallites vanish on a time scales smaller than ≈ 100 ns.

Metastable liquid-liquid phase transition in a single-component system with only one crystal phase and no density anomaly

We investigate the phase behavior of a single-component system in three dimensions with spherically-symmetric, pairwise-additive, soft-core interactions with an attractive well at a long distance, a repulsive soft-core shoulder at an intermediate distance, and a hard-core repulsion at a short distance, similar to potentials used to describe liquid systems such as colloids, protein solutions, or liquid metals. We showed [Nature (London) 409, 692 (2001)] that, even with no evidence of the density anomaly, the phase diagram has two first-order fluid-fluid phase transitions, one ending in a gas-low-density-liquid (LDL) critical point, and the other in a gas-high-density-liquid (HDL) critical point, with a LDL-HDL phase transition at low temperatures. Here we use integral equation calculations to explore the three-parameter space of the soft-core potential and perform molecular dynamics simulations in the interesting region of parameters. For the equilibrium phase diagram, we analyze the structure of the crystal phase and find that, within the considered range of densities, the structure is independent of the density. Then, we analyze in detail the fluid metastable phases and, by explicit thermodynamic calculation in the supercooled phase, we show the absence of the density anomaly. We suggest that this absence is related to the presence of only one stable crystal structure.

Intramolecular coupling as a mechanism for a liquid-liquid phase transition

We study a model for water with a tunable intramolecular interaction J(sigma), using mean-field theory and off-lattice Monte Carlo simulations. For all J(sigma)> or =0, the model displays a temperature of maximum density. For a finite intramolecular interaction J(sigma)>0, our calculations support the presence of a liquid-liquid phase transition with a possible liquid-liquid critical point for water, likely preempted by inevitable freezing. For J=0, the liquid-liquid critical point disappears at T=0.

Models for a liquid–liquid phase transition

We use molecular dynamics simulations to study two- and three-dimensional models with the isotropic double-step potential which in addition to the hard core has a repulsive soft core of larger radius. Our results indicate that the presence of two characteristic repulsive distances (hard core and soft core) is sufficient to explain liquid anomalies and a liquid–liquid phase transition, but these two phenomena may occur independently. Thus liquid–liquid transitions may exist in systems like liquid metals, regardless of the presence of the density anomaly. For 2D, we propose a model with a specific set of hard core and soft core parameters, that qualitatively reproduces the phase diagram and anomalies of liquid water. We identify two solid phases: a square crystal (high density phase), and a triangular crystal (low density phase) and discuss the relation between the anomalies of liquid and the polymorphism of the solid. Similarly to real water, our 2D system may have the second critical point in the metastable liquid phase beyond the freezing line. In 3D, we find several sets of parameters for which two fluid–fluid phase transition lines exist: the first line between gas and liquid and the second line between high-density liquid (HDL) and low-density liquid (LDL). In all cases, the LDL phase shows no density anomaly in 3D. We relate the absence of the density anomaly with the positive slope of the LDL–HDL phase transition line.

Liquid-Liquid Phase Transition for an Attractive Isotropic Potential with Wide Repulsive Range

We investigate how the phase diagram of a repulsive soft-core attractive potential, with a liquid-liquid phase transition in addition to the standard gas-liquid phase transition, changes by varying the parameters of the potential. We extend our previous work on short soft-core ranges to the case of large soft-core ranges, by using an integral equation approach in the hypernetted-chain approximation. We show, using a modified van der Waals equation we recently introduced, that if there is a balance between the attractive and repulsive part of the potential this potential has two fluid-fluid critical points well separated in temperature and in density. This implies that for the repulsive (attractive) energy U(R)(U(A)) and the repulsive (attractive) range w(R)(w(A)) the relation U(R)/U(A) proportional to w(R)/w(A) holds for short soft-core ranges, while U(R)/U(A) proportional to 3w(R)/w(A) holds for large soft-core ranges.