Simple three-state lattice model for liquid water

Abstract

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.

An unconstrained DFT approach to microphase formation and application to binary Gaussian mixtures

“…Here, we will not try to elucidate the reason of such an interesting behavior, aside of the obvious remark that this system differs from block copolymers in three respects: First, there is no connectivity; second, its compressibility is non-vanishing; and third, particles of different species are more compatible (or less incompatible) with each other than those of the same species. The above observation that the same sequence of phases displayed by block copolymers has been reported also in fluids of unconnected particles with competing interactions 8,10 indicates that lack of connectivity alone is not sufficient to explain the behavior found here. We leave this point to future investigation.…”

“…As one moves out of this region by either decreasing or increasing the concentration, one meets first a gyroid phase, then a triangular phase of cylindrical rods, then a cubic bcc phase, and finally the homogeneous fluid. 25,26 It should also be remarked that recently effective DFT and SCFT approaches have predicted essentially the same sequence of phases in fluids with competing short-range attractive and longer-range repulsive interactions, [8][9][10] in which the inverse temperature and the density play the roles of the variables χN and c in block copolymer melts (in Ref. 9, a Fddd phase was found instead of the gyroid, but that was traced back in the same paper to the approximations inherent to the effective DFT).…”

“…The phase diagram of this model fluid has already been thoroughly studied in two dimensions. 6,7 In three dimensions, some general features of the phase diagram were obtained by combining numerical simulation and integral-equation theories, 70 and a detailed investigation of the structure of microphases was subsequently carried out by means of effective free-energy functionals, [8][9][10] which uncovered essentially the same sequence of microphases (bcc-triangular-gyroidlamellae) previously found in block copolymer models. 25,26,38 It would be interesting to see whether application of the present DFT will also predict the same scenario.…”

“…When the competition between attraction and repulsion is strong enough, the gas-liquid phase transition is suppressed, and the phase diagram of the fluid has been shown to present microphases in both two [5][6][7] and three dimensions. [8][9][10] Irrespective of its specific nature, the attitude of a onecomponent system to form microphases ultimately rests upon a property of the effective interaction between its constituents: if the Fourier transform of the interaction has a negative minimum at some non-vanishing wave vector k, then density modulations with characteristic length d ∼ 2π/k will be strongly favored over the other Fourier components of the density profile and can lead to inhomogeneous phases under suitable thermodynamic conditions. 1 Another instance of this rather general scenario which has gained considerable attention in recent times is cluster formation in particles interacting via isotropic, bounded repulsive potentials of ultrasoft type such that not only are the overlaps between particles allowed but also the resulting energy penalty is very low.…”

Theoretical description of cluster formation in two-Yukawa competing fluids

“…This evidence (together with the fact that the second virial coefficient is always positive, see Figure 2b), further corroborates At low enough temperatures, a universal sequence of cluster phases (comprising ordered, periodic bcc, hexagonal and lamellar phases), and the existence of a gyroid phase (possibly related to a network-forming cluster of colloids in colloid/polymer mixtures) were predicted in Refs. [24,25] by means of a mesoscopic, coarse-grain theory for soft materials combining density functional and statistical field theory; more recently, the same formalism was used to investigate the general features of microscopic interaction potentials leading to inhomogeneous structures [26]. For the clarity sake, we have also slightly rearranged the rest of the same paragraph.…”