Noé G. Almarza

Phase behavior of attractive and repulsive ramp fluids : Integral equation and computer simulation studies

Using computer simulations and a thermodynamically self-consistent integral equation we investigate the phase behavior and thermodynamic anomalies of a fluid composed of spherical particles interacting via a two-scale ramp potential (a hard core plus a repulsive and an attractive ramp) and the corresponding purely repulsive model. Both simulation and integral equation results predict a liquid-liquid demixing when attractive forces are present, in addition to a gas-liquid transition. Furthermore, a fluid-solid transition emerges in the neighborhood of the liquid-liquid transition region, leading to a phase diagram with a somewhat complicated topology. This solidification at moderate densities is also present in the repulsive ramp fluid, but in this case inhibits the fluid-fluid separation.

Demixing in binary mixtures of apolar and dipolar hard spheres

We study the demixing transition of mixtures of equal size hard spheres and dipolar hard spheres using computer simulation and integral equation theories. Calculations are carried out at constant pressure, and it is found that there is a strong correlation between the total density and the composition. The critical temperature and the critical total density are found to increase with pressure. The critical mole fraction of the dipolar component on the contrary decreases as pressure is augmented. These qualitative trends are reproduced by the theoretical approaches that on the other hand overestimate by far the value of the critical temperature. Interestingly, the critical parameters for the liquid-vapor equilibrium extrapolated from the mixture results in the limit of vanishing neutral hard sphere concentration agree rather well with recent estimates based on the extrapolation of charged hard dumbbell phase equilibria when dumbbell elongation shrinks to zero [G. Ganzenmuller and P. J. Camp, J. Chem. Phys. 126, 191104 (2007)].

Periodic ordering of clusters and stripes in a two-dimensional lattice model. II. Results of Monte Carlo simulation

The triangular lattice model with nearest-neighbor attraction and third-neighbor repulsion, introduced by Pȩkalski, Ciach, and Almarza [J. Chem. Phys. 140, 114701 (2014)] is studied by Monte Carlo simulation. Introduction of appropriate order parameters allowed us to construct a phase diagram, where different phases with patterns made of clusters, bubbles or stripes are thermodynamically stable. We observe, in particular, two distinct lamellar phases-the less ordered one with global orientational order and the more ordered one with both orientational and translational order. Our results concern spontaneous pattern formation on solid surfaces, fluid interfaces or membranes that is driven by competing interactions between adsorbing particles or molecules.

Phase diagram of a two-dimensional lattice gas model of a ramp system

Using Monte Carlo simulation and fundamental measure theory we study the phase diagram of a two-dimensional lattice gas model with a nearest neighbor hard core exclusion and a next-to-nearest neighbor finite repulsive interaction. The model presents two competing ranges of interaction and, in common with many experimental systems, exhibits a low density solid phase, which melts back to the fluid phase upon compression. The theoretical approach is found to provide a qualitatively correct picture of the phase diagram of our model system.

Periodic ordering of clusters and stripes in a two-dimensional lattice model. I. Ground state, mean-field phase diagram and structure of the disordered phases

The short-range attraction and long-range repulsion between nanoparticles or macromolecules can lead to spontaneous pattern formation on solid surfaces, fluid interfaces, or membranes. In order to study the self-assembly in such systems we consider a triangular lattice model with nearest-neighbor attraction and third-neighbor repulsion. At the ground state of the model (T = 0) the lattice is empty for small values of the chemical potential μ, and fully occupied for large μ. For intermediate values of μ periodically distributed clusters, bubbles, or stripes appear if the repulsion is sufficiently strong. At the phase coexistences between the vacuum and the ordered cluster phases and between the cluster and the lamellar (stripe) phases the entropy per site does not vanish. As a consequence of this ground state degeneracy, disordered fluid phases consisting of clusters or stripes are stable, and the surface tension vanishes. For T > 0 we construct the phase diagram in the mean-field approximation and calculate the correlation function in the self-consistent Brazovskii-type field theory.

Surface tension of the Widom-Rowlinson model

We consider the computation of the surface tension of the fluid-fluid interface for the Widom-Rowlinson [J. Chem. Phys. 52, 1670 (1970)] binary mixture from direct simulation of the inhomogeneous system. We make use of the standard mechanical route, in which the surface tension follows from the computation of the normal and tangential components of the pressure tensor of the system. In addition to the usual approach, which involves simulations of the inhomogeneous system in the canonical ensemble, we also consider the computation of the surface tension in an ensemble where the pressure perpendicular (normal) to the planar interface is kept fixed. Both approaches are seen to provide consistent values of the interfacial tension. The issue of the system-size dependence of the surface tension is addressed. In addition, simulations of the fluid-fluid coexistence properties of the mixture are performed in the semigrand canonical ensemble. Our results are compared with existing data of the Widom-Rowlinson mixture and are also examined in the light of the vapor-liquid equilibrium of the thermodynamically equivalent one-component penetrable sphere model.

Three-dimensional patchy lattice model: Ring formation and phase separation

We investigate the structural and thermodynamic properties of a model of particles with 2 patches of type A and 10 patches of type B. Particles are placed on the sites of a face centered cubic lattice with the patches oriented along the nearest neighbor directions. The competition between the self-assembly of chains, rings, and networks on the phase diagram is investigated by carrying out a systematic investigation of this class of models, using an extension of Wertheims theory for associating fluids and Monte Carlo numerical simulations. We varied the ratio r ≡ εAB/εAA of the interaction between patches A and B, εAB, and between A patches, εAA (εBB is set to 0) as well as the relative position of the A patches, i.e., the angle θ between the (lattice) directions of the A patches. We found that both r and θ (60°, 90°, or 120°) have a profound effect on the phase diagram. In the empty fluid regime (r < 1/2) the phase diagram is reentrant with a closed miscibility loop. The region around the lower critical point exhibits unusual structural and thermodynamic behavior determined by the presence of relatively short rings. The agreement between the results of theory and simulation is excellent for θ = 120° but deteriorates as θ decreases, revealing the need for new theoretical approaches to describe the structure and thermodynamics of systems dominated by small rings.

Periodic ordering of clusters in a one-dimensional lattice model

A generic lattice model for systems containing particles interacting with short-range attraction long-range repulsion (SALR) potential that can be solved exactly in one dimension is introduced. We assume attraction J1 between the first neighbors and repulsion J2 between the third neighbors. The ground state of the model shows existence of two homogeneous phases (gas and liquid) for J2/J1 <1/3. In addition to the homogeneous phases, the third phase with periodically distributed clusters appears for J2/J1 > 1/3. Phase diagrams obtained in the self-consistent mean-field approximation for a range of values of J2/J1 show very rich behavior, including reentrant melting, and coexistence of two periodic phases (one with strong and the other one with weak order) terminated at a critical point. We present exact solutions for the equation of state as well as for the correlation function for characteristic values of J2/J1. Based on the exact results, for J2/J1 > 1/3 we predict pseudo-phase transitions to the ordered cluster phase indicated by a rapid change of density for a very narrow range of pressure, and by a very large correlation length for thermodynamic states where the periodic phase is stable in mean field. For 1/9 < J2/J1 < 1/3 the correlation function decays monotonically below certain temperature, whereas above this temperature exponentially damped oscillatory behavior is obtained. Thus, even though macroscopic phase separation is energetically favored and appears for weak repulsion at T = 0, local spatial inhomogeneities appear for finite T. Monte Carlo simulations in canonical ensemble show that specific heat has a maximum for low density ρ that we associate with formation of living clusters, and if the repulsion is strong, another maximum for ρ = 1/2.

Closed-loop liquid-vapor equilibrium in a one-component system.

We report Monte Carlo simulations that show a closed-loop liquid-vapor equilibrium in a pure substance. This finding has been achieved on a two-dimensional lattice model for patchy particles that can form network fluids. We have considered related models with a slightly different patch distribution in order to understand the features of the distribution of patches on the surface of the particles that make possible the presence of the closed-loop liquid-vapor equilibrium, and its relation to the phase diagram containing so-called empty liquids. Finally we discuss the likelihood of finding the closed-loop liquid-vapor equilibria on related models for three-dimensional models of patchy particles in the continuum, and speculate on the possible relationship between the mechanism behind the closed-loop liquid-vapor equilibrium of our simple lattice model and the salt-induced reentrant condensation found in complex systems.

Three-dimensional patchy lattice model for empty fluids

The phase diagram of a simple model with two patches of type A and ten patches of type B (2A10B) on the face centred cubic lattice has been calculated by simulations and theory. Assuming that there is no interaction between the B patches the behavior of the system can be described in terms of the ratio of the AB and AA interactions, r. Our results show that, similarly to what happens for related off-lattice and two-dimensional lattice models, the liquid-vapor phase equilibria exhibit reentrant behavior for some values of the interaction parameters. However, for the model studied here the liquid-vapor phase equilibria occur for values of r lower than 1/3, a threshold value which was previously thought to be universal for 2AnB models. In addition, the theory predicts that below r=1/3 (and above a new condensation threshold which is <1/3) the reentrant liquid-vapor equilibria are so extreme that it exhibits a closed loop with a lower critical point, a very unusual behavior in single-component systems. An order-disorder transition is also observed at higher densities than the liquid-vapor equilibria, which shows that the liquid-vapor reentrancy occurs in an equilibrium region of the phase diagram. These findings may have implications in the understanding of the condensation of dipolar hard spheres given the analogy between that system and the 2AnB models considered here.