Liquid polymorphism, order-disorder transitions and anomalous behavior: A Monte Carlo study of the Bell–Lavis model for 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.

Order-disorder transition in a two-dimensional associating lattice gas

We study an associating lattice gas (ALG) using Monte Carlo simulation on the triangular lattice and semianalytical solutions on Husimi lattices. In this model, the molecules have an orientational degree of freedom and the interactions depend on the relative orientations of nearest-neighbor molecules, mimicking the formation of hydrogen bonds. We focus on the transition between the high-density liquid (HDL) phase and the isotropic phase in the limit of full occupancy, corresponding to chemical potential μ→∞, which has not yet been studied systematically. Simulations yield a continuous phase transition at τ_{c}=k_{B}T_{c}/γ=0.4763(1) (where -γ is the bond energy) between the low-temperature HDL phase, with a nonvanishing mean orientation of the molecules, and the high-temperature isotropic phase. Results for critical exponents and the Binder cumulant indicate that the transition belongs to the three-state Potts model universality class, even though the ALG Hamiltonian does not have the full permutation symmetry of the Potts model. In contrast with simulation, the Husimi lattice analyses furnish a discontinuous phase transition, characterized by a discontinuity of the nematic order parameter. The transition temperatures (τ_{c}=0.51403 and 0.51207 for trees built with triangles and hexagons, respectively) are slightly higher than that found via simulation. Since the Husimi lattice studies show that the ALG phase diagram features a discontinuous isotropic-HDL line for finite μ, three possible scenarios arise for the triangular lattice. The first is that in the limit μ→∞ the first-order line ends in a critical point; the second is a change in the nature of the transition at some finite chemical potential; the third is that the entire line is one of continuous phase transitions. Results from other ALG models and the fact that mean-field approximations show a discontinuous phase transition for the three-state Potts model (known to possess a continuous transition) lends some weight to the third alternative.

Assembly of trivalent particles under confinement: from an exotic solid phase to a liquid phase at low temperature

Using computer simulations, we study the phase diagram of a two-dimensional system of disk particles with three patches distributed symmetrically along the particle equator. The geometry of the particles is compatible with a honey-comb lattice at moderately low temperature and pressure, whereas it is expected that the system forms a close-packed triangular lattice at high temperature and pressure. The effect of patch size within the single bond per patch regime was investigated, and it was found that the topology of the phase diagram changes drastically with patch size. Interestingly, in particles with small patches (with a half opening angle of 10°), the fluid transforms upon increasing the pressure into a rather exotic phase that can be understood as a honey-comb lattice whose voids are filled continuously with additional particles that remain, on average, unbound. Eventually, all the voids are occupied so that particles are located at the positions of a triangular lattice, but only two thirds of the particles are orientationally ordered whereas the remaining one third can rotate almost freely as in a plastic crystal. At moderately low temperature, the fluid transforms into a nearly empty honey-comb lattice, whereas at high temperature it transforms directly into the almost filled lattice. Interestingly, for particles with big patches (with a half opening angle of 20°), the honey-comb and triangular lattices are separated by a liquid phase that remains stable down to fairly low temperatures. Less surprisingly, only particles with big patches exhibit an equilibrium gas-liquid separation.

Cross-impact of surface and interaction anisotropy in the self-assembly of organic adsorption monolayers: a Monte Carlo and transfer-matrix study

We have theoretically studied the features of self-assembly in organic adsorption layers where both “molecule–surface” and “molecule–molecule” interactions are anisotropic.

Phase transition properties of the Bell-Lavis model

Using Monte Carlo calculations we analyze the order and the universality class of phase transitions into a low-density (honeycomb) phase of a triangular antiferromagnetic three-state Bell-Lavis model. The results are obtained in a whole interval of chemical potential μ corresponding to the honeycomb phase. Our results demonstrate that the phase transitions might be attributed to the three-state Potts universality class for all μ values except for the edges of the honeycomb phase existence. At the honeycomb phase and the low-density gas phase boundary the transitions become of the first order. At another, honeycomb-to-frustrated phase boundary, we observe the approach to the crossover from the three-state Potts to the Ising model universality class. We also obtain the Schottky anomaly in the specific heat close to this edge. We show that the intermediate planar phase, found in a very similar antiferromagnetic triangular Blume-Capel model, does not occur in the Bell-Lavis model.

Antiferromagnetic triangular Blume-Capel model with hard-core exclusions

Using Monte Carlo simulation, we analyze phase transitions of two antiferromagnetic (AFM) triangular Blume-Capel (BC) models with AFM interactions between third-nearest neighbors. One model has hard-core exclusions between the nearest-neighbor (1NN) particles (3NN1 model) and the other has them between the nearest-neighbor and next-nearest-neighbor particles (3NN12 model). Finite-size scaling analysis reveals that in these models, the transition from the paramagnetic to long-range order (LRO) AFM phase is either of the first order or goes through an intermediate phase which might be attributed to the Berezinskii-Kosterlitz-Thouless (BKT) type. The properties of the low-temperature phase transition to the AFM phase of the 1NN, 3NN1, and 3NN12 models are found to be very similar for almost all values of a normalized single-ion anisotropy parameter, 0 < δ < 1.5. Higher temperature behavior of the 3NN12 and 3NN1 models is rather different from that of the 1NN model. Three phase transitions are observed for the 3NN12 model: from the paramagnetic phase to the phase with domains of the LRO AFM phase at T(c), from this structure to the diluted frustrated BKT-type phase at T(2), and from the frustrated phase to the AFM LRO phase at T(1). For the 3NN12 model, T(c) > T(2) > T(1) at 0 < δ < 1.15 (range I), T(c) ≈ T(2) > T(1) at 1.15 < δ < 1.3 (range II), and T(c) = T(2) = T(1) at 1.3 < δ < 1.5 (range III). For the 3NN1 model, T(c) ≈ T(2) > T(1) at 0 < δ < 1.2 (range II) and T(c) = T(2) = T(1) at 1.2 < δ < 1.5 (range III). There is only one first-order phase transition in range III. The transition at T(c) is of the first order in range II and either of a weak first order or a second order in range I.

Unified description of solvent effects in the helix-coil transition

We analyze the problem of the helix-coil transition in explicit solvents analytically by using spin-based models incorporating two different mechanisms of solvent action: explicit solvent action through the formation of solvent-polymer hydrogen bonds that can compete with the intrinsic intra-polymer hydrogen bonded configurations (competing interactions) and implicit solvent action, where the solvent-polymer interactions tune biopolymer configurations by changing the activity of the solvent (non-competing interactions). The overall spin Hamiltonian is comprised of three terms: the background in vacuo Hamiltonian of the "Generalized Model of Polypeptide Chain" type and two additive terms that account for the two above mechanisms of solvent action. We show that on this level the solvent degrees of freedom can be explicitly and exactly traced over, the ensuing effective partition function combining all the solvent effects in a unified framework. In this way we are able to address helix-coil transitions for polypeptides, proteins, and DNA, with different buffers and different external constraints. Our spin-based effective Hamiltonian is applicable for treatment of such diverse phenomena as cold denaturation, effects of osmotic pressure on the cold and warm denaturation, complicated temperature dependence of the hydrophobic effect as well as providing a conceptual base for understanding the behavior of intrinsically disordered proteins and their analogues.

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.

General approach for studying first-order phase transitions at low temperatures

By combining different ideas, a general and efficient protocol to deal with discontinuous phase transitions at low temperatures is proposed. For small T's, it is possible to derive a generic analytic expression for appropriate order parameters, whose coefficients are obtained from simple simulations. Once in such regimes simulations by standard algorithms are not reliable; an enhanced tempering method, the parallel tempering-accurate for small and intermediate system sizes with rather low computational cost-is used. Finally, from finite size analysis, one can obtain the thermodynamic limit. The procedure is illustrated for four distinct models, demonstrating its power, e.g., to locate coexistence lines and the phase density at the coexistence.

Competition for hydrogen-bond formation in the helix-coil transition and protein folding

The problem of the helix-coil transition of biopolymers in explicit solvents, such as water, with the ability for hydrogen bonding with a solvent is addressed analytically using a suitably modified version of the Generalized Model of Polypeptide Chains. Besides the regular helix-coil transition, an additional coil-helix or reentrant transition is also found at lower temperatures. The reentrant transition arises due to competition between polymer-polymer and polymer-water hydrogen bonds. The balance between the two types of hydrogen bonding can be shifted to either direction through changes not only in temperature, but also by pressure, mechanical force, osmotic stress, or other external influences. Both polypeptides and polynucleotides are considered within a unified formalism. Our approach provides an explanation of the experimental difficulty of observing the reentrant transition with pressure and underscores the advantage of pulling experiments for studies of DNA. Results are discussed and compared with those reported in a number of recent publications with which a significant level of agreement is obtained.

A simple protocol for the probability weights of the simulated tempering algorithm: applications to first-order phase transitions

The simulated tempering (ST) is an important method to deal with systems whose phase spaces are hard to sample ergodically. However, it uses accepting probabilities weights, which often demand involving and time consuming calculations. Here it is shown that such weights are quite accurately obtained from the largest eigenvalue of the transfer matrix--a quantity straightforward to compute from direct Monte Carlo simulations--thus simplifying the algorithm implementation. As tests, different systems are considered, namely, Ising, Blume-Capel, Blume-Emery-Griffiths, and Bell-Lavis liquid water models. In particular, we address first-order phase transition at low temperatures, a regime notoriously difficulty to simulate because the large free-energy barriers. The good results found (when compared with other well established approaches) suggest that the ST can be a valuable tool to address strong first-order phase transitions, a possibility still not well explored in the literature.

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.