Two-dimensional lattice-fluid model with waterlike anomalies

Abstract

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.

Dynamic transitions in a three dimensional associating lattice gas model

“…The criticality of both lines is identified from the specific heat study as well as from the cumulant of energy. Our model has some resemblance with other lattice models in two [20][21][22][23] and three dimensions 16,24,25 that exhibit two liquid phases. We propose the characterization of the different liquid phases in terms of structural order through positional and orientational order parameters.…”

Diffusion anomaly and dynamic transitions in the Bell–Lavis water model

“…In analogy to other two length scale interaction lattice models, [18][19][20][21] this model is expected to exhibit a region of density anomalies in its phase diagram. The phase diagram of this model was investigated for different values of the bonding strength, with different approaches: under a mean-field approach, 17,22,23 with renormalization group techniques 24,25 and very recently, through detailed numerical simulations.…”

Thermodynamic anomalies in a lattice model of water: Solvation properties

“…In the previous paper 41 , we have introduced the approximation in the variational approach 44 , as a particular choice of the largest clusters left in the entropy expansion (basic clusters). Such a choice, sometimes denoted as cluster-site approximation 45 (the only clusters to be taken into account in the expansion are basic clusters and single sites), has not only the advantage of high simplicity, but also of relative accuracy, which has been recognized for different models 31,45 . The basic clusters are a number of irregular tetrahedra, namely, 4 out of 24 tetrahedra sharing a given site, as sketched in Fig.…”