Phase behavior of attractive and repulsive ramp fluids: Integral equation and computer simulation studies

Stability of the high-density Jagla liquid in 2D: sensitivity to parameterisation

We computed the pressure-temperature phase diagram of the hard-core two-scale ramp potential in two-dimensions, with the parameterisation originally suggested by Jagla [E. A. Jagla, Phys. Rev. E, 63, 061501 (2001)], as well as with a series of systematically modified variants of the model to reveal the sensitivity of the stability of phases. The nested sampling method was used to explore the potential energy landscape, allowing the identification of thermodynamically relevant phases, such as low- and high-density liquids and various crystalline forms, some of which have not been reported before. We also proposed a smooth version of the potential, which is differentiable beyond the hard-core. This potential reproduces the density anomaly, but forms a dodecahedral quasi-crystal structure at high pressure. Our results allow to hypothesise on the necessary modifications of the original model in order to improve the stability of the metastable high-density liquid phase in 3D.

Thermodynamic mechanism of the density and compressibility anomalies of water in the range - 30 < T (°C) < 100

Compared to normal liquids, water exhibits a variety of anomalous thermal behaviors. This fact has been known for centuries. However, the thermodynamic mechanisms behind them have not been elucidated despite the efforts of many researchers. Under such circumstances, the author theoretically reproduced the measured values of the density-temperature curve at 1 atm for water above 0 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^\circ $$\end{document}∘C. Then, the mystery of negative thermal expansion was clarified in relation to the shapes of the intermolecular interactions. In this paper, the author develops this line of work further and presents the interactions between water molecules to simultaneously reproduce the measured values of both the density-temperature curve and the isothermal compressibility-temperature curve in the range \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$-30<T(^\circ {\mathrm{C}})<100$$\end{document}-30<T(∘C)<100 at 1 atm. Then, the thermodynamic mechanism that produces these thermal behaviors is clarified in relation to the shapes of the interactions between molecules. Unraveling the mystery of related phenomena in relation to the shapes of the interaction between molecules has been a traditional and fundamental method in physics since the days of Newton.

Insight into Liquid Polymorphism from the Complex Phase Behavior of a Simple Model

We systematically explored the phase behavior of the hard-core two-scale ramp model suggested by Jagla [Phys. Rev. E 63, 061501 (2001)PRESCM1539-375510.1103/PhysRevE.63.061501] using a combination of the nested sampling and free energy methods. The sampling revealed that the phase diagram of the Jagla potential is significantly richer than previously anticipated, and we identified a family of new crystalline structures, which is stable over vast regions in the phase diagram. We showed that the new melting line is located at considerably higher temperature than the boundary between the low- and high-density liquid phases, which was previously suggested to lie in a thermodynamically stable region. The newly identified crystalline phases show unexpectedly complex structural features, some of which are shared with the high-pressure ice VI phase.

Liquid-liquid phase separation in an inhomogeneous ternary colloid-polymer mixture

Suspended colloids are often considered as models for molecules, which are sufficiently big so that they can be observed directly in (light) microscopes and for which the effective interaction among each other can be tailored. The Asakura-Oosawa model of ideal colloid-polymer mixtures captures the idea of tuning the interaction between the colloids via a potential, which possesses a range set by the size of the polymers and an attractive strength characterized by the (reservoir) number density of the polymers, which plays the role of an inverse temperature. The celebrated Asakura-Oosawa depletion potential allows one to recreate the bulk phase diagram of a simple fluid by employing a colloid-polymer mixture. This has been verified in theory, by computer simulations, and via experiments. Here, we study the phase behavior of a confined colloid-polymer mixture with two polymer species. The sizes and densities are chosen such that the resulting bulk phase diagram exhibits a second stable critical point within the framework of the classical density functional theory. Our results suggest that a suitably tuned colloid-polymer mixture can be an interesting model system to study fluids with two critical points.

Toward a density-functional theory for the Jagla fluid

The so-called Jagla fluid is well known to exhibit, in addition to the usual gas-liquid critical point, also a liquid-liquid critical point, as well as a density anomaly. This makes it an interesting toy model for water, for which a liquid-liquid critical point is considered to exist but so far eludes experimental verification due to crystallization occurring in the corresponding metastable, deeply supercooled state. With the Jagla fluid being understood quite well in bulk-mostly via simulation studies-the focus of the present study is to describe the spatially inhomogeneous fluid in terms of classical density-functional theory (DFT) with the aim to be able to control its phase behavior on changing the shape or the nature of the confinement of the fluid. This information might contribute to guide potential experimental tests of the liquid-liquid critical point of actual water. We first determine the bulk phase diagram for the Jagla fluid by using thermodynamical perturbation theory. In doing so we explain why the perturbation theories of Barker and Henderson as well as of Weeks, Chandler, and Anderson fail to describe the Jagla fluid. We then continue to construct a perturbative DFT based on our bulk model, which shows significant improvement over the standard mean-field DFT valid at high temperatures. But ultimately the perturbative DFT breaks down at state points close to the binodal line and at low temperatures. This prevents us from achieving the original aim to study a highly confined, inhomogeneous Jagla fluid close to its liquid-liquid binodal.

Structural properties of the Jagla fluid

The structural properties of the Jagla fluid are studied by Monte Carlo (MC) simulations, numerical solutions of integral equation theories, and the (semi-analytical) rational-function approximation (RFA) method. In the latter case, the results are obtained from the assumption (supported by our MC simulations) that the Jagla potential and a potential with a hard core plus an appropriate piecewise constant function lead to practically the same cavity function. The predictions obtained for the radial distribution function, g(r), from this approach are compared against MC simulations and integral equations for the Jagla model, and also for the limiting cases of the triangle-well potential and the ramp potential, with a general good agreement. The analytical form of the RFA in Laplace space allows us to describe the asymptotic behavior of g(r) in a clean way and compare it with MC simulations for representative states with oscillatory or monotonic decay. The RFA predictions for the Fisher-Widom and Widom lines of the Jagla fluid are obtained.

Temperature of maximum density and excess properties of short-chain alcohol aqueous solutions: A simplified model simulation study

We perform an extensive computational study of binary mixtures of water and short-chain alcohols resorting to two-scale potential models to account for the singularities of hydrogen bonded liquids. Water molecules are represented by a well studied core softened potential which is known to qualitatively account for a large number of water's characteristic anomalies. Along the same lines, alcohol molecules are idealized by dimers in which the hydroxyl groups interact with each other and with water with a core softened potential as well. Interactions involving non-polar groups are all deemed purely repulsive. We find that the qualitative behavior of excess properties (excess volume, enthalpy, and constant pressure heat capacity) agrees with that found experimentally for alcohols such as t-butanol in water. Moreover, we observe that our simple solute under certain conditions acts as a "structure-maker," in the sense that the temperature of maximum density of the bulk water model increases as the solute is added, i.e., the anomalous behavior of the solvent is enhanced by the solute.

Exactly solvable model for self-assembly of hard core-soft shell particles at interfaces

A generic model for self-assembly of a monolayer of hybrid core-shell particles at an interface is developed. We assume that for distances larger than the size of the incompressible core a soft repulsion appears, and the repulsion is followed by an attraction at larger separations. The model is solved exactly in a one-dimensional lattice version. One, two or three periodic structures and variety of shapes of the pressure-density isotherms may occur in different versions of the model. For strong interactions the isotherm consists of nearly vertical segments at densities optimal for the periodic structures that are connected by segments with a small slope. The range of order depends very strongly on the strength of attraction and on the density. Our results agree with experimental observations.

Integral equation study of soft-repulsive dimeric fluids

We study fluid structure and water-like anomalies of a system constituted by dimeric particles interacting via a purely repulsive core-softened potential by means of integral equation theories. In our model, dimers interact through a repulsive pair potential of inverse-power form with a softened repulsion strength. By employing the Ornstein-Zernike approach and the reference interaction site model (RISM) theory, we study the behavior of water-like anomalies upon progressively increasing the elongation λ of the dimers from the monomeric case ([Formula: see text]) to the tangent configuration ([Formula: see text]). For each value of the elongation we consider two different values of the interaction potential, corresponding to one and two length scales, with the aim to provide a comprehensive description of the possible fluid scenarios of this model. Our theoretical results are systematically compared with already existing or newly generated Monte Carlo data: we find that theories and simulations agree in providing the picture of a fluid exhibiting density and structural anomalies for low values of λ and for both the two values of the interaction potential. Integral equation theories give accurate predictions for pressure and radial distribution functions, whereas the temperatures where anomalies occur are underestimated. Upon increasing the elongation, the RISM theory still predicts the existence of anomalies; the latter are no longer observed in simulations, since their development is likely precluded by the onset of crystallization. We discuss our results in terms of the reliability of integral equation theories in predicting the existence of water-like anomalies in core-softened fluids.

Reentrant disorder-disorder transitions in generalized multicomponent Widom-Rowlinson models

In the lattice version of the multicomponent Widom-Rowlinson (WR) model, each site can be either empty or singly occupied by one of M different particles, all species having the same fugacity z. The only nonzero interaction potential is a nearest-neighbor hard-core exclusion between unlike particles. For M<M(0) with some minimum M(0) dependent on the lattice structure, as z increases from 0 to ∞ there is a direct transition from the disordered (gas) phase to a demixed (liquid) phase with one majority component at z>z(d) (M). If M≥M(0), there is an intermediate ordered "crystal phase" (composed of two nonequivalent even and odd sublattices) for z lying between z(c)(M) and z(d)(M) which is driven by entropy. We generalize the multicomponent WR model by replacing the hard-core exclusion between unlike particles by more realistic large (but finite) repulsion. The model is solved exactly on the Bethe lattice with an arbitrary coordination number. The numerical calculations, based on the corner transfer matrix renormalization group, are performed for the two-dimensional square lattice. The results for M=4 indicate that the second-order phase transitions from the disordered gas to the demixed phase become of first order, for an arbitrarily large finite repulsion. The results for M≥M(0) show that, as the repulsion weakens, the region of the crystal phase diminishes itself. For weak enough repulsions, the direct transition between the crystal and demixed phases changes into a separate pair of crystal-gas and gas-demixed transitions; this is an example of a disorder-disorder reentrant transition via an ordered crystal phase. If the repulsion between unlike species is too weak, the crystal phase disappears from the phase diagram. It is shown that the generalized WR model belongs to the Ising universality class.

Properties of a soft-core model of methanol: an integral equation theory and computer simulation study

Thermodynamic and structural properties of a coarse-grained model of methanol are examined by Monte Carlo simulations and reference interaction site model (RISM) integral equation theory. Methanol particles are described as dimers formed from an apolar Lennard-Jones sphere, mimicking the methyl group, and a sphere with a core-softened potential as the hydroxyl group. Different closure approximations of the RISM theory are compared and discussed. The liquid structure of methanol is investigated by calculating site-site radial distribution functions and static structure factors for a wide range of temperatures and densities. Results obtained show a good agreement between RISM and Monte Carlo simulations. The phase behavior of methanol is investigated by employing different thermodynamic routes for the calculation of the RISM free energy, drawing gas-liquid coexistence curves that match the simulation data. Preliminary indications for a putative second critical point between two different liquid phases of methanol are also discussed.

Model of waterlike fluid under confinement for hydrophobic and hydrophilic particle-plate interaction potentials

Molecular dynamic simulations were employed to study a waterlike model confined between hydrophobic and hydrophilic plates. The phase behavior of this system is obtained for different distances between the plates and particle-plate potentials. For both hydrophobic and hydrophilic walls, there are the formation of layers. Crystallization occurs at lower temperature at the contact layer than at the middle layer. In addition, the melting temperature decreases as the plates become more hydrophobic. Similarly, the temperatures of maximum density and extremum diffusivity decrease with hydrophobicity.

NVU perspective on simple liquids' quasiuniversality

The last half-century of research into the structure, dynamics, and thermodynamics of simple liquids has revealed a number of approximate universalities. This paper argues that simple liquids' reduced-coordinate constant-potential-energy hypersurfaces constitute a quasiuniversal family of compact Riemannian manifolds parametrized by a single number; from this follows the quasiuniversalities.

Ising universality class for the liquid-liquid critical point of a one component fluid: a finite-size scaling test

We present a finite-size scaling study of the liquid-liquid critical point in the Jagla model, a prototype model for liquids that present the same thermodynamic anomalies which characterize liquid water. Performing successive umbrella sampling grand canonical Monte Carlo simulations, we evaluate an accurate density of states for different system sizes and determine the size-dependent critical parameters. Extrapolation to infinite size provides estimates of the bulk critical values for this model. The finite-size study allows us to establish that critical fluctuations are consistent with the Ising universality class and to provide definitive evidence for the existence of a liquid-liquid critical point in the Jagla potential. This finding supports the possibility of the existence of a genuine liquid-liquid critical point in anomalous one-component liquids like water.

Hydration and anomalous solubility of the Bell-Lavis model as solvent

We address the investigation of the solvation properties of the minimal orientational model for water originally proposed by [Bell and Lavis, J. Phys. A 3, 568 (1970)]. The model presents two liquid phases separated by a critical line. The difference between the two phases is the presence of structure in the liquid of lower density, described through the orientational order of particles. We have considered the effect of a small concentration of inert solute on the solvent thermodynamic phases. Solute stabilizes the structure of solvent by the organization of solvent particles around solute particles at low temperatures. Thus, even at very high densities, the solution presents clusters of structured water particles surrounding solute inert particles, in a region in which pure solvent would be free of structure. Solute intercalates with solvent, a feature which has been suggested by experimental and atomistic simulation data. Examination of solute solubility has yielded a minimum in that property, which may be associated with the minimum found for noble gases. We have obtained a line of minimum solubility (TmS) across the phase diagram, accompanying the line of maximum density. This coincidence is easily explained for noninteracting solute and it is in agreement with earlier results in the literature. We give a simple argument which suggests that interacting solute would dislocate TmS to higher temperatures.

Effect of hydrophobic environments on the hypothesized liquid-liquid critical point of water

The complex behavior of liquid water, along with its anomalies and their crucial role in the existence of life, continue to attract the attention of researchers. The anomalous behavior of water is more pronounced at subfreezing temperatures and numerous theoretical and experimental studies are directed towards developing a coherent thermodynamic and dynamic framework for understanding supercooled water. The existence of a liquid-liquid critical point in the deep supercooled region has been related to the anomalous behavior of water. However, the experimental study of supercooled water at very low temperatures is hampered by the homogeneous nucleation of the crystal. Recently, water confined in nanoscopic structures or in solutions has attracted interest because nucleation can be delayed. These systems have a tremendous relevance also for current biological advances; e.g., supercooled water is often confined in cell membranes and acts as a solvent for biological molecules. In particular, considerable attention has been recently devoted to understanding hydrophobic interactions or the behavior of water in the presence of apolar interfaces due to their fundamental role in self-assembly of micelles, membrane formation and protein folding. This article reviews and compares two very recent computational works aimed at elucidating the changes in the thermodynamic behavior in the supercooled region and the liquid-liquid critical point phenomenon for water in contact with hydrophobic environments. The results are also compared to previous reports for water in hydrophobic environments.

Widom line and the liquid-liquid critical point for the TIP4P/2005 water model

The Widom line and the liquid-liquid critical point of water in the deeply supercooled region are investigated via computer simulation of the TIP4P/2005 model. The Widom line has been calculated as the locus of compressibility maxima. It is quite close to the experimental homogeneous nucleation line and, in the region studied, it is almost parallel to the curve of temperatures of maximum density at fixed pressure. The critical temperature is determined by examining which isotherm has a region with flat slope. An interpolation in the Widom line gives the rest of the critical parameters. The computed critical parameters are T(c)=193 K, p(c)=1350 bar, and ρ(c)=1.012 g/cm(3). Given the performance of the model for the anomalous properties of water and for the properties of ice phases, the calculated critical parameters are probably close to those of real water.

Effect of polydispersity on the ordering transition of adsorbed self-assembled rigid rods

Extensive Monte Carlo simulations were carried out to investigate the nature of the ordering transition of a model of adsorbed self-assembled rigid rods on the bonds of a square lattice [Tavares, Phys. Rev. E 79, 021505 (2009)]. The polydisperse rods undergo a continuous ordering transition that is found to be in the two-dimensional Ising universality class, as in models where the rods are monodisperse. This finding is in sharp contrast with the recent claim that equilibrium polydispersity changes the nature of the phase transition in this class of models [López, Phys. Rev. E 80, 040105(R) (2009)].

Effect of hydrophobic solutes on the liquid-liquid critical point

Jagla ramp particles, interacting through a ramp potential with two characteristic length scales, are known to show in their bulk phase thermodynamic and dynamic anomalies, similar to what is found in water. Jagla particles also exhibit a line of phase transitions separating a low density liquid phase and a high density liquid phase, terminating in a liquid-liquid critical point in a region of the phase diagram that can be studied by simulations. Employing molecular dynamics computer simulations, we study the thermodynamics and the dynamics of solutions of hard spheres (HS) in a solvent formed by Jagla ramp particles. We consider the cases of HS mole fraction xHS=0.10, 0.15, and 0.20, and also the case xHS=0.50 (a 1:1 mixture of HS and Jagla particles). We find a liquid-liquid critical point, up to the highest HS mole fraction; its position shifts to higher pressures and lower temperatures upon increasing xHS. We also find that the diffusion coefficient anomalies appear to be preserved for all the mole fractions studied.

Liquid-liquid phase transition and glass transition in a monoatomic model system

We review our recent study on the polyamorphism of the liquid and glass states in a monatomic system, a two-scale spherical-symmetric Jagla model with both attractive and repulsive interactions. This potential with a parametrization for which crystallization can be avoided and both the glass transition and the liquid-liquid phase transition are clearly separated, displays water-like anomalies as well as polyamorphism in both liquid and glassy states, providing a unique opportunity to study the interplay between the liquid-liquid phase transition and the glass transition. Our study on a simple model may be useful in understanding recent studies of polyamorphism in metallic glasses.

Unusual phase behavior of one-component systems with two-scale isotropic interactions

We study the phase behavior of systems of particles interacting through pair potentials with a hard core plus a soft repulsive component. We consider several different forms of soft repulsion, including a square shoulder, a linear ramp and a quasi-exponential tail. The common feature of these potentials is the presence of two repulsive length scales, which may be the origin of unusual phase behaviors such as polyamorphism both in the equilibrium liquid phase and in the glassy state, water-like anomalies in the liquid state and anomalous melting at very high pressures.

Phase behavior of the hard-sphere Maier-Saupe fluid under spatial confinement

The Maier-Saupe hard-sphere fluid is one of the simplest models that accounts for the isotropic-nematic transition characteristic of liquid crystal phases. At low temperatures the model is known to present a gas-liquid-like transition with a large difference between the densities of the coexistence phases, whereas at higher temperature the transition becomes a weak first-order transition resembling the typical order-disorder (nematic-isotropic) phase change of liquid crystals. Spatial dimensionality directly conditions the character of the orientational phase change (i.e., the high temperature transition), that goes from a first-order transition in the purely three-dimensional case, to a Berezinskii-Kosterlitz-Thouless-like continuous transition which occurs when the three dimensional Maier-Saupe spins are constrained to lie on a plane. In the latter instance, the ordered phase is not endowed with true long-range order. In this work we investigate how the continuous transition transforms into a true first-order phase change, by analyzing the phase behavior of a system of three dimensional Maier-Saupe hard spheres confined between two parallel plates, with separations ranging from the quasi-two-dimensional regime to the bulk three-dimensional limit. Our results indicate that spatial confinement in one direction induces the change from first order to a continuous transition with a corresponding decrease of the transition temperatures. As to the gas-liquid transition, the estimated "critical" temperatures and densities also decrease as the fluid is confined, in agreement with previous results for other simple systems.

Anomalous phase behavior of a soft-repulsive potential with a strictly monotonic force

We study the phase behavior of a classical system of particles interacting through a strictly convex soft-repulsive potential which, at variance with the pairwise softened repulsions considered so far in the literature, lacks a region of downward or zero curvature. Nonetheless, such interaction is characterized by two length scales, owing to the presence of a range of interparticle distances where the repulsive force increases, for decreasing distance, much more slowly than in the adjacent regions. We investigate, using extensive Monte Carlo simulations combined with accurate free-energy calculations, the phase diagram of the system under consideration. We find that the model exhibits a fluid-solid coexistence line with multiple re-entrant regions, an extremely rich solid polymorphism with solid-solid transitions, and waterlike anomalies. In spite of the isotropic nature of the interparticle potential, we find that among the crystal structures in which the system can exist, there are also a number of non-Bravais lattices, such as cI16 and diamond.

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.

Local structures of fluid with discrete spherical potential: Theory and grand canonical ensemble Monte Carlo simulation

Grand canonical Monte Carlo simulation and theoretical calculations based on Ornstein-Zernike (OZ) integral equation and third order+second order perturbation density functional theory (DFT) are performed to study a system of spherical particles interacting through a core-softened (CS) potential combining a repulsive square soft core and an attractive square well. Both theoretical predictions and simulation results reveal peculiar homogeneous and inhomogeneous local structures originating from the discontinuous nature of the CS potential. The bulk radial distribution function displays discontinuities at the distances coinciding with the ranges of the successive repulsive and attractive parts in the CS potential function. The density profiles of confined CS fluid show the shapes arising from the complex interplay among the steric effects and the competition between the repulsive and attractive parts of the CS potential. Satisfactory agreement between the theoretical results and simulation data leads to the following conclusions: (i) a modified hypernetted chain approximation combined with a hard sphere bridge function, which has been recently proposed by one of the authors of this study, is sufficiently reliable for the structural studies of CS fluid, and (ii) the third order+second order perturbation DFT, which has proven successful for the study of inhomogeneous structure of model fluids with continuous intermolecular potential function, posses a high adaptability to be applied for various types of interaction potentials and performs well also in the case of discontinuous CS model.

Simple three-state lattice model for liquid water

A simple three-state lattice model that incorporates two states for locally ordered and disordered forms of liquid water in addition to empty cells is introduced. The model is isomorphic to the Blume-Emery-Griffith model. The locally ordered (O) and disordered (D) forms of water are treated as two components, and we assume that the density of the D component is larger. The density of the sample is determined by the fraction of cells occupied by the O and D forms of water. Due to the larger density of the D state, the strength of the van der Waals (vdW) interactions increases in the direction O-O<O-D<D-D. On the other hand, the H-bond interactions are assumed only for the O-O pairs. For the vdW and H-bond interaction parameters and the density ratio of the close-packed and ice forms of water compatible with experimentally known values, we find liquid-vapor and liquid-liquid transitions and the corresponding critical points in good agreement with other approaches. Water anomalies are correctly predicted within the mean-field approximation on a qualitative level.

Phase behavior of a simple lattice model with a two-scale repulsive interaction

The properties of a simple one-dimensional lattice model with two repulsive ranges are studied in terms of its analytic solution. Its phase behavior is characterized by the presence of a disorder-order-disorder transition (or a fluid-solid-fluid transition in lattice gas language). A similar situation was discussed by Hemmer and Stell [Phys. Rev. Lett. 24, 1284 (1970)] when considering the purely repulsive version of their ramp potential. The melting of the solid phase, when pressure is increased along an isotherm, is a feature common to both models and one of the characteristic features of water.

Frustration and anomalous behavior in the Bell-Lavis model of liquid water

We have reconsidered the Bell-Lavis model of liquid water and investigated its relation to its isotropic version, the antiferromagnetic Blume-Emery-Griffiths model on the triangular lattice. Our study was carried out by means of an exact solution on the sequential Husimi cactus. We show that the ground states of both models share the same topology and that fluid phases (gas and low- and high-density liquids) can be mapped onto magnetic phases (paramagnetic, antiferromagnetic, and dense paramagnetic, respectively). Both models present liquid-liquid coexistence and several thermodynamic anomalies. This result suggests that anisotropy introduced through orientational variables play no specific role in producing the density anomaly, in agreement with a similar conclusion discussed previously following results for continuous soft core models. We propose that the presence of liquid anomalies may be related to energetic frustration, a feature common to both models.