Thermodynamic anomalies in a lattice model of water

Phase diagram and critical properties of a two-dimensional associating lattice gas

We revisit the associating lattice gas (ALG) introduced by Henriques et al. [Phys. Rev. E 71, 031504 (2005)PLEEE81539-375510.1103/PhysRevE.71.031504] in its symmetric version. In this model, defined on the triangular lattice, interaction between molecules occupying nearest-neighbor sites depends on their relative orientation, mimicking the formation of hydrogen bonds in network-forming fluids. Although all previous studies of this model agree that it has a disordered fluid (DF), a low-density liquid (LDL), and a high-density liquid (HDL) phase, quite different forms have been reported for its phase diagram. Here, we present a thorough investigation of its phase behavior using both transfer matrix calculations and Monte Carlo (MC) simulations, along with finite-size scaling extrapolations. Results in striking agreement are found using these methods. The critical point associated with the DF-HDL transition at full occupancy, identified by Furlan et al. [Phys. Rev. E 100, 022109 (2019)2470-004510.1103/PhysRevE.100.022109] is shown to be one terminus of a critical line separating these phases. In opposition to previous simulation studies, we find that the transition between the DF and LDL phases is always discontinuous, similar to the LDL-HDL transition. The associated coexistence lines meet at the point where the DF-HDL critical line ends, making it a critical-end-point. Overall, the form of the phase diagram observed in our simulations is very similar to that found in the exact solution of the model on a Husimi lattice. Our results confirm that, despite the existence of some waterlike anomalies in this model, it is unable to reproduce key features of the phase behavior of liquid water.

A hydro-kinetic scheme for the dynamics of hydrogen bonds in water-like fluids

A hydro-kinetic scheme for water-like fluids, based on a lattice version of the Boltzmann equation, is presented and applied to the popular TIP3P model of liquid water. By proceeding in much larger steps than molecular dynamics, the scheme proves to be very effective in attaining global minima of classical pair potentials with directional and radial interactions, as confirmed by further simulations using the three-dimensional Ben-Naim water potential. The scheme is shown to reproduce the propensity of water to form nearly four hydrogen bonds per molecule, as well as their statistical distribution in the presence of thermal fluctuations, at a linear cost of computational time with the system size.

Role of anisotropic interactions for proteins and patchy nanoparticles

Protein–protein interactions are inherently anisotropic to some degree, with orientation-dependent interactions between repulsive and attractive or complementary regions or “patches” on adjacent proteins. In some cases it has been suggested that such patch–patch interactions dominate the thermodynamics of dilute protein solutions, as captured by the osmotic second virial coefficient (B₂₂), but delineating when this will or will not be the case remains an open question. A series of simplified but exactly solvable models are first used to illustrate that a delicate balance exists between the strength of attractive patch–patch interactions and the patch size, and that repulsive patch–patch interactions contribute significantly to B₂₂ for only those conditions where the repulsions are long-ranged. Finally, B₂₂ is reformulated, without approximations, in terms of the density of states for a given interaction energy and particle–particle distance. Doing so illustrates the inherent balance of entropic and energetic contributions to B₂₂. It highlights that simply having strong patch–patch interactions will only cause anisotropic interactions to dominate B₂₂ solution properties if the unavoidable entropic penalties are overcome, which cannot occur if patches are too small. The results also indicate that the temperature dependence of B₂₂ may be a simple experimental means to assess whether a small number of strongly attractive configurations dominate the dilute solution behavior.

Ice polyamorphism in the minimal Mercedes-Benz model of water

We investigate ice polyamorphism in the context of the two-dimensional Mercedes-Benz model of water. We find a first-order phase transition between a crystalline phase and a high-density amorphous phase. Furthermore, we find a reversible transformation between two amorphous structures of high and low density; however, we find this to be a continuous and not an abrupt transition, as the low-density amorphous phase does not show structural stability. We discuss the origin of this behavior and its implications with regard to the minimal generic modeling of polyamorphism.

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.

Solution of an associating lattice-gas model with density anomaly on a Husimi lattice

We study a model of a lattice gas with orientational degrees of freedom which resemble the formation of hydrogen bonds between the molecules. In this model, which is the simplified version of the Henriques-Barbosa model, no distinction is made between donors and acceptors in the bonding arms. We solve the model in the grand-canonical ensemble on a Husimi lattice built with hexagonal plaquettes with a central site. The ground state of the model, which was originally defined on the triangular lattice, is exactly reproduced by the solution on this Husimi lattice. In the phase diagram, one gas and two liquid [high density liquid (HDL) and low density liquid (LDL)] phases are present. All phase transitions (GAS-LDL, GAS-HDL, and LDL-HDL) are discontinuous, and the three phases coexist at a triple point. A line of temperatures of maximum density in the isobars is found in the metastable GAS phase, as well as another line of temperatures of minimum density appears in the LDL phase, part of it in the stable region and another in the metastable region of this phase. These findings are at variance with simulational results for the same model on the triangular lattice, which suggested a phase diagram with two critical points. However, our results show very good quantitative agreement with the simulations, both for the coexistence loci and the densities of particles and of hydrogen bonds. We discuss the comparison of the simulations with our results.

Revisiting waterlike network-forming lattice models

We revisit different three-dimensional network-forming lattice models proposed in the literature to investigate water anomalies. We perform a semianalytical calculation based on a cluster-variation technique, showing a quite good agreement with independent Monte Carlo results. The method allows us to clarify the structure of the phase diagrams, which turn out to exhibit different kinds of orientationally ordered phases. We point out 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 in terms of "equivalent" models defined on random lattices.

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.

Liquid polymorphism and density anomaly in a three-dimensional associating lattice gas

The authors investigate the phase diagram of a three-dimensional associating lattice gas (ALG) model. This model combines orientational icelike interactions and "van der Waals" that might be repulsive, representing, in this case, a penalty for distortion of hydrogen bonds. These interactions can be interpreted as two competing distances, making the connection between this model and continuous isotropic soft-core potentials. The authors present Monte Carlo studies of the ALG model showing the presence of two liquid phases, two critical points, and density anomaly.

Hydrophobic Hydration in an Orientational Lattice Model

To shed light on the microscopic mechanism of hydrophobic hydration, we study a simplified lattice model for water solutions in which the orientational nature of hydrogen bonding as well as the degeneracy related to proton distribution are taken into account. Miscibility properties of the model are looked at for both polar (hydrogen bonding) and nonpolar (non-hydrogen bonding) solutes. A quasichemical solution for the pure system is reviewed and extended to include the different kinds of solute. A Monte Carlo study of our model yields a novel feature for the local structure of the hydration layer: energy correlation relaxation times for solvation water are larger than the corresponding relaxation times for bulk water. This result suggests the presence of ordering of water particles in the first hydration shell. A nonassociating model solvent, represented by a lattice gas, presents opposite behavior, indicating that this effect is a result of the directionality of the interaction. In presence of polar solutes, we find an ordered mixed pseudophase at low temperatures, indicating the possibility of closed loops of immiscibility.

Thermodynamic anomalies in a lattice model of water: Solvation properties

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. 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 the 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.

Properties of the H-bond network for two-dimensional lattice water model

A microscopic Hamiltonian of the hydrogen-bond network in two-dimensional lattice water is proposed, which describes the formation and disruption of the H bonds, their bending, and which satisfies the Bernal-Fowler rules [J. D. Bernal and R. H. Fowler, J. Chem. Phys. 1, 515 (1933)]. The thermodynamic properties of the H-bond network are studied using the method of many-particle irreducible distribution functions, which is a generalization of the Kikuchi cluster approach [R. Kikuchi, Phys. Rev. 81, 988 (1951)] and the Bethe-Peierls quasiactivities method [H. A. Bethe, Prog. R. Soc. A 150, 552 (1935)]. The temperature dependencies of the average number of H bonds per molecules, the contribution of the H bonds into the heat capacity of the system, and the parameters describing the correlations between the states of molecules on the neighboring sites are investigated. It is shown that depending on the magnitude of the interaction between the H bonds in the H-bond subsystem either smooth or sharp first-order phase transition can occur. The role of different factors in the formation of the properties of the H-bond network is discussed.