Thermodynamic anomalies in a lattice model of water

We investigate a lattice-fluid model of water, defined on a three-dimensional body centered cubic lattice. Model molecules possess a tetrahedral symmetry, with four equivalent bonding arms, aiming to mimic the formation of hydrogen bonds. The model is similar to the one proposed by Roberts and Debenedetti [J. Chem. Phys. 105, 658 (1996)], simplified in that no distinction between bond "donors" and "acceptors" is imposed. Bond formation depends both on orientation and local density. In the ground state, we show that two different ordered (ice) phases are allowed. At finite temperature, we analyze homogeneous phases only, working out phase diagram, response functions, the temperature of maximum density locus, and the Kauzmann line. We make use of a generalized first order approximation on a tetrahedral cluster. In the liquid phase, the model exhibits several anomalous properties observed in real water. In the low temperature region (supercooled liquid), there are evidences of a second critical point and, for some range of parameter values, this scenario is compatible with the existence of a reentrant spinodal.Comment: 12 pages, 9 figures, 1 tabl

Cluster-variation approximation for a network-forming lattice-fluid model

We consider a 3-dimensional lattice model of a network-forming fluid, which has been recently investigated by Girardi and coworkers by means of Monte Carlo simulations [J. Chem. Phys. \textbf{126}, 064503 (2007)], with the aim of describing water anomalies. We develop an approximate semi-analytical calculation, based on a cluster-variation technique, which turns out to reproduce almost quantitatively different thermodynamic properties and phase transitions determined by the Monte Carlo method. Nevertheless, our calculation points out the existence of two different phases characterized by long-range orientational order, and of critical transitions between them and to a high-temperature orientationally-disordered phase. Also, the existence of such critical lines allows us to explain certain ``kinks'' in the isotherms and isobars determined by the Monte Carlo analysis. The picture of the phase diagram becomes much more complex and richer, though unfortunately less suitable to describe real water.Comment: 10 pages, 9 figures, submitted to J. Chem. Phy

Thermodynamic anomalies in a lattice model of water: Solvation properties

We investigate a lattice-fluid model of water, defined on a 3-dimensional body-centered cubic lattice. Model molecules possess a tetrahedral symmetry, with four equivalent bonding arms. The model is similar to the one proposed by Roberts and Debenedetti [J. Chem. Phys. 105, 658 (1996)], simplified by removing distinction between "donors" and "acceptors". We focus on solvation properties, mainly as far as an ideally inert (hydrophobic) solute is concerned. As in our previous analysis, devoted to neat water [J. Chem. Phys. 121, 11856 (2004)], we make use of a generalized first order approximation on a tetrahedral cluster. We show that the model exhibits quite a coherent picture of water thermodynamics, reproducing qualitatively several anomalous properties observed both in pure water and in solutions of hydrophobic solutes. As far as supercooled liquid water is concerned, the model is consistent with the second critical point scenario.Comment: 12 pages, 9 figures, 1 tabl

Hydration of an apolar solute in a two-dimensional waterlike lattice fluid

In a previous work, we investigated a two-dimensional lattice-fluid model, displaying some waterlike thermodynamic anomalies. The model, defined on a triangular lattice, is now extended to aqueous solutions with apolar species. Water molecules are of the "Mercedes Benz" type, i.e., they possess a D3 (equilateral triangle) symmetry, with three equivalent bonding arms. Bond formation depends both on orientation and local density. The insertion of inert molecules displays typical signatures of hydrophobic hydration: large positive transfer free energy, large negative transfer entropy (at low temperature), strong temperature dependence of the transfer enthalpy and entropy, i.e., large (positive) transfer heat capacity. Model properties are derived by a generalized first order approximation on a triangle cluster.Comment: 9 pages, 5 figures, 1 table; submitted to Phys. Rev.

Revisiting waterlike network-forming lattice models

In a previous paper [J. Chem. Phys. 129, 024506 (2008)] we studied a 3 dimensional lattice model of a network-forming fluid, recently proposed in order to investigate water anomalies. Our semi-analytical calculation, based on a cluster-variation technique, turned out to reproduce almost quantitatively several Monte Carlo results and allowed us to clarify the structure of the phase diagram, including different kinds of orientationally ordered phases. Here, we extend the calculation to different parameter values and to other similar models, known in the literature. We observe that analogous ordered phases occur in all these models. Moreover, we show that certain "waterlike" thermodynamic anomalies, claimed by previous studies, are indeed artifacts of a homogeneity assumption made in the analytical treatment. We argue that such a difficulty is common to a whole class of lattice models for water, and suggest a possible way to overcome the problem.Comment: 13 pages, 12 figure

Diffusion Anomaly in a three dimensional lattice gas

We investigate the relation between thermodynamic and dynamic properties of an associating lattice gas (ALG) model. The ALG combines a three dimensional lattice gas with particles interacting through a soft core potential and orientational degrees of freedom. From the competition between the directional attractive forces and the soft core potential results two liquid phases, double criticality and density anomaly. We study the mobility of the molecules in this model by calculating the diffusion constant at a constant temperature, $D$. We show that $D$ has a maximum at a density $\rho_{max}$ and a minimum at a density $\rho_{min}<\rho_{max}$. Between these densities the diffusivity differs from the one expected for normal liquids. We also show that in the pressure-temperature phase-diagram the line of extrema in diffusivity is close to the liquid-liquid critical point and it is partially inside the temperature of maximum density (TMD) line

Two-dimensional lattice-fluid model with water-like anomalies

We investigate a lattice-fluid model defined on a two-dimensional triangular lattice, with the aim of reproducing qualitatively some anomalous properties of water. Model molecules are of the "Mercedes Benz" type, i.e., they possess a D3 (equilateral triangle) symmetry, with three bonding arms. Bond formation depends both on orientation and local density. We work out phase diagrams, response functions, and stability limits for the liquid phase, making use of a generalized first order approximation on a triangle cluster, whose accuracy is verified, in some cases, by Monte Carlo simulations. The phase diagram displays one ordered (solid) phase which is less dense than the liquid one. At fixed pressure the liquid phase response functions show the typical anomalous behavior observed in liquid water, while, in the supercooled region, a reentrant spinodal is observed.Comment: 9 pages, 1 table, 7 figure

Zinc and other metals deficiencies and risk of type 1 diabetes: an ecological study in the high risk Sardinia island

Type 1 diabetes incidence presents a decreasing gradient in Europe from the Nordic countries to the Mediterranean ones. Exception to this gradient is represented by Sardinia, the second largest Mediterranean island whose population shows the highest incidence in Europe, after Finland. The genetic features of this population have created a fertile ground for the epidemic of the disease, however, as well as being strikingly high, the incidence rate has suddenly presented a continuous increase from the '50s, not explainable by accumulation of new genetic variants. Several environmental factors have been taken into account, possibly interacting with the genetic/epigenetic scenario, but there are no strong evidences to date

Cooperative Behavior of Kinetically Constrained Lattice Gas Models of Glassy Dynamics

Kinetically constrained lattice models of glasses introduced by Kob and Andersen (KA) are analyzed. It is proved that only two behaviors are possible on hypercubic lattices: either ergodicity at all densities or trivial non-ergodicity, depending on the constraint parameter and the dimensionality. But in the ergodic cases, the dynamics is shown to be intrinsically cooperative at high densities giving rise to glassy dynamics as observed in simulations. The cooperativity is characterized by two length scales whose behavior controls finite-size effects: these are essential for interpreting simulations. In contrast to hypercubic lattices, on Bethe lattices KA models undergo a dynamical (jamming) phase transition at a critical density: this is characterized by diverging time and length scales and a discontinuous jump in the long-time limit of the density autocorrelation function. By analyzing generalized Bethe lattices (with loops) that interpolate between hypercubic lattices and standard Bethe lattices, the crossover between the dynamical transition that exists on these lattices and its absence in the hypercubic lattice limit is explored. Contact with earlier results are made via analysis of the related Fredrickson-Andersen models, followed by brief discussions of universality, of other approaches to glass transitions, and of some issues relevant for experiments.Comment: 59 page

On the cavity method for decimated random constraint satisfaction problems and the analysis of belief propagation guided decimation algorithms

We introduce a version of the cavity method for diluted mean-field spin models that allows the computation of thermodynamic quantities similar to the Franz-Parisi quenched potential in sparse random graph models. This method is developed in the particular case of partially decimated random constraint satisfaction problems. This allows to develop a theoretical understanding of a class of algorithms for solving constraint satisfaction problems, in which elementary degrees of freedom are sequentially assigned according to the results of a message passing procedure (belief-propagation). We confront this theoretical analysis to the results of extensive numerical simulations.Comment: 32 pages, 24 figure