Frustration and anomalous behavior in the Bell-Lavis model 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.

Multicritical behavior of the ferromagnetic Blume-Emery-Griffiths model with repulsive biquadratic couplings

The ferromagnetic (J>0) version of the Blume-Emery-Griffiths model in the region of repulsive biquadratic couplings (K<0) is considered on a Cayley tree of coordination z, reducing the statistical problem to the analysis of a two-dimensional nonlinear discrete map. In order to investigate the effect of the coordination z on the system multicritical behavior, we study the particular case K/J=-3.5 with the inclusion of crystal fields (D≠0), but vanishing external magnetic fields (H=0), for two distinct lattice coordinations (z=4 and z=6). The thermodynamic solutions on the Bethe lattice (the central region of a large Cayley tree) are associated with the attractors of the two-dimensional map. The phase diagrams display several thermodynamic phases (paramagnetic, ferromagnetic, ferrimagnetic, and staggered quadrupolar). In some cases, there are regions of numerical costability of two different attractors of the map, associated with discontinuous phase transitions between the corresponding phases. To verify the thermodynamic stability of the phases and to locate the first-order boundaries, the analytical expression of the Gibbs free energy was obtained by the method proposed by Gujrati [Phys. Rev. Lett. 74, 809 (1995)PRLTAO0031-900710.1103/PhysRevLett.74.809]. For lower coordinations (z=4) the transition between the ferrimagnetic and the staggered quadrupolar phases is always continuous, while the transition between the ferromagnetic and the ferrimagnetic phases is discontinuous at low temperatures, turning into continuous for temperatures above a tricritical point. On the other hand, for higher coordinations (z=6), the transition between the ferromagnetic and the ferrimagnetic phases is always continuous. However, the transition between the ferrimagnetic and the staggered quadrupolar phases is continuous for higher temperatures and discontinuous for temperatures below a tricritical point, in agreement with previous results obtained in the mean-field approximation (infinity-coordination limit). In both cases, the occurrence and the thermodynamic stability of the ferrimagnetic phase is confirmed.

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.

Residual entropy and waterlike anomalies in the repulsive one dimensional lattice gas

The thermodynamics and kinetics of the one dimensional lattice gas with repulsive interaction are investigated using transfer matrix technique and Monte Carlo simulations. This simple model is shown to exhibit waterlike anomalies in density, thermal expansion coefficient, and self-diffusion. An unified description for the thermodynamic anomalies in this model is achieved based on the ground state residual entropy which appears in the model due to mixing entropy in a ground state phase transition.

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.

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.

Molecular correlations and solvation in simple fluids

We study the molecular correlations in a lattice model of a solution of a low-solubility solute, with emphasis on how the thermodynamics is reflected in the correlation functions. The model is treated in the Bethe-Guggenheim approximation, which is exact on a Bethe lattice (Cayley tree). The solution properties are obtained in the limit of infinite dilution of the solute. With h(11)(r), h(12)(r), and h(22)(r) the three pair correlation functions as functions of the separation r (subscripts 1 and 2 referring to solvent and solute, respectively), we find for r > or = 2 lattice steps that h(22)(r)/h(12)(r) is identical with h(12)(r)/h(11)(r). This illustrates a general theorem that holds in the asymptotic limit of infinite r. The three correlation functions share a common exponential decay length (correlation length), but when the solubility of the solute is low the amplitude of the decay of h(22)(r) is much greater than that of h(12)(r), which in turn is much greater than that of h(11)(r). As a consequence the amplitude of the decay of h(22)(r) is enormously greater than that of h(11)(r). The effective solute-solute attraction then remains discernible at distances at which the solvent molecules are essentially no longer correlated, as found in similar circumstances in an earlier model. The second osmotic virial coefficient is large and negative, as expected. We find that the solvent-mediated part W(r) of the potential of mean force between solutes, evaluated at contact, r = 1, is related in this model to the Gibbs free energy of solvation at fixed pressure, DeltaG(p)(*), by (Z/2)W(1) + DeltaG(p)(*) is identical with pv(0), where Z is the coordination number of the lattice, p is the pressure, and v(0) is the volume of the cell associated with each lattice site. A large, positive DeltaG(p)(*) associated with the low solubility is thus reflected in a strong attraction (large negative W at contact), which is the major contributor to the second osmotic virial coefficient. In this model, the low solubility (large positive DeltaG(p)(*)) is due partly to an unfavorable enthalpy of solvation and partly to an unfavorable solvation entropy, unlike in the hydrophobic effect, where the enthalpy of solvation itself favors high solubility, but is overweighed by the unfavorable solvation entropy.