Lattice model for water-solute mixtures

A lattice model for the study of mixtures of associating liquids is proposed. Solvent and solute are modeled by adapting the associating lattice gas (ALG) model. The nature of interaction of solute/solvent is controlled by tuning the energy interactions between the patches of ALG model. We have studied three set of parameters, resulting in, hydrophilic, inert, and hydrophobic interactions. Extensive Monte Carlo simulations were carried out, and the behavior of pure components and the excess properties of the mixtures have been studied. The pure components, water (solvent) and solute, have quite similar phase diagrams, presenting gas, low density liquid, and high density liquid phases. In the case of solute, the regions of coexistence are substantially reduced when compared with both the water and the standard ALG models. A numerical procedure has been developed in order to attain series of results at constant pressure from simulations of the lattice gas model in the grand canonical ensemble. The excess properties of the mixtures, volume and enthalpy as the function of the solute fraction, have been studied for different interaction parameters of the model. Our model is able to reproduce qualitatively well the excess volume and enthalpy for different aqueous solutions. For the hydrophilic case, we show that the model is able to reproduce the excess volume and enthalpy of mixtures of small alcohols and amines. The inert case reproduces the behavior of large alcohols such as propanol, butanol, and pentanol. For the last case (hydrophobic), the excess properties reproduce the behavior of ionic liquids in aqueous solution.

Effects of confinement on pattern formation in two dimensional systems with competing interactions

Template-assisted pattern formation in monolayers of particles with competing short-range attraction and long-range repulsion interactions (SALR) is studied by Monte Carlo simulations in a simple generic model [N. G. Almarza et al., J. Chem. Phys., 2014, 140, 164708]. We focus on densities corresponding to formation of parallel stripes of particles and on monolayers laterally confined between straight parallel walls. We analyze both the morphology of the developed structures and the thermodynamic functions for broad ranges of temperature T and the separation L2 between the walls. At low temperature stripes parallel to the boundaries appear, with some corrugation when the distance between the walls does not match the bulk periodicity of the striped structure. The stripes integrity, however, is rarely broken for any L2. This structural order is lost at T = TK(L2) depending on L2 according to a Kelvin-like equation. Above the Kelvin temperature TK(L2) many topological defects such as breaking or branching of the stripes appear, but a certain anisotropy in the orientation of the stripes persists. Finally, at high temperature and away from the walls, the system behaves as an isotropic fluid of elongated clusters of various lengths and with various numbers of branches. For L2 optimal for the stripe pattern the heat capacity as a function of temperature takes the maximum at T = TK(L2).

Generalization of Wertheim's theory for the assembly of various types of rings

We generalize Wertheim's first order perturbation theory to account for the effect in the thermodynamics of the self-assembly of rings characterized by two energy scales. The theory is applied to a lattice model of patchy particles and tested against Monte Carlo simulations on a fcc lattice. These particles have 2 patches of type A and 10 patches of type B, which may form bonds AA or AB that decrease the energy by εAA and by εAB ≡ rεAA, respectively. The angle θ between the 2 A-patches on each particle is fixed at 60°, 90° or 120°. For values of r below 1/2 and above a threshold rth(θ) the models exhibit a phase diagram with two critical points. Both theory and simulation predict that rth increases when θ decreases. We show that the mechanism that prevents phase separation for models with decreasing values of θ is related to the formation of loops containing AB bonds. Moreover, we show that by including the free energy of B-rings (loops containing one AB bond), the theory describes the trends observed in the simulation results, but that for the lowest values of θ, the theoretical description deteriorates due to the increasing number of loops containing more than one AB bond.

Effects of rigid or adaptive confinement on colloidal self-assembly. Fixed vs. fluctuating number of confined particles

The effects of confinement on colloidal self-assembly in the case of fixed number of confined particles are studied in the one dimensional lattice model solved exactly in the grand canonical ensemble (GCE) in Pȩkalski et al. [J. Chem. Phys. 142, 014903 (2015)]. The model considers a pair interaction defined by a short-range attraction plus a longer-range repulsion. We consider thermodynamic states corresponding to self-assembly into clusters. Both fixed and adaptive boundaries are studied. For fixed boundaries, there are particular states in which, for equal average densities, the number of clusters in the GCE is larger than in the canonical ensemble. The dependence of pressure on density has a different form when the system size changes with fixed number of particles and when the number of particles changes with fixed size of the system. In the former case, the pressure has a nonmonotonic dependence on the system size. The anomalous increase of pressure for expanding system is accompanied by formation of a larger number of smaller clusters. In the case of elastic confining surfaces, we observe a bistability, i.e., two significantly different system sizes occur with almost the same probability. The mechanism of the bistability in the closed system is different to that of the case of permeable walls, where the two equilibrium system sizes correspond to a different number of particles.

Bistability in a self-assembling system confined by elastic walls: exact results in a one-dimensional lattice model

The impact of confinement on self-assembly of particles interacting with short-range attraction and long-range repulsion potential is studied for thermodynamic states corresponding to local ordering of clusters or layers in the bulk. Exact and asymptotic expressions for the local density and for the effective potential between the confining surfaces are obtained for a one-dimensional lattice model introduced by J. Pȩkalski et al. [J. Chem. Phys. 138, 144903 (2013)]. The simple asymptotic formulas are shown to be in good quantitative agreement with exact results for slits containing at least 5 layers. We observe that the incommensurability of the system size and the average distance between the clusters or layers in the bulk leads to structural deformations that are different for different values of the chemical potential μ. The change of the type of defects is reflected in the dependence of density on μ that has a shape characteristic for phase transitions. Our results may help to avoid misinterpretation of the change of the type of defects as a phase transition in simulations of inhomogeneous systems. Finally, we show that a system confined by soft elastic walls may exhibit bistability such that two system sizes that differ approximately by the average distance between the clusters or layers are almost equally probable. This may happen when the equilibrium separation between the soft boundaries of an empty slit corresponds to the largest stress in the confined self-assembling system.

Adsorption of probe molecules in pillared interlayered clays: experiment and computer simulation

In this paper we investigate the adsorption of various probe molecules in order to characterize the porous structure of a series of pillared interlayered clays (PILC). To that aim, volumetric and microcalorimetric adsorption experiments were performed on various Zr PILC samples using nitrogen, toluene, and mesitylene as probe molecules. For one of the samples, neutron scattering experiments were also performed using toluene as adsorbate. Various structural models are proposed and tested by means of a comprehensive computer simulation study, using both geometric and percolation analysis in combination with Grand Canonical Monte Carlo simulations in order to model the volumetric and microcalorimetric isotherms. On the basis of this analysis, we propose a series of structural models that aim at accounting for the adsorption experimental behavior, and make possible a microscopic interpretation of the role played by the different interactions and steric effects in the adsorption processes in these rather complex disordered microporous systems.

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.

Theory and simulation of the confined Lebwohl-Lasher model

We discuss the Lebwohl-Lasher model of nematic liquid crystals in a confined geometry, using Monte Carlo simulation and mean-field theory. A film of material is sandwiched between two planar, parallel plates that couple to the adjacent spins via a surface strength ε(s). We consider the cases where the favored alignments at the two walls are the same (symmetric cell) or different (asymmetric cell). In the latter case, we demonstrate the existence of a single phase transition in the slab for all values of the cell thickness. This transition has been observed before in the regime of narrow cells, where the two structures involved correspond to different arrangements of the nematic director. By studying wider cells, we show that the transition is in fact the usual isotropic-to-nematic (capillary) transition under confinement in the case of antagonistic surface forces. We show results for a wide range of values of film thickness and discuss the phenomenology using a mean-field model.

Effect of polydispersity on the ordering transition of adsorbed self-assembled rigid rods

Extensive Monte Carlo simulations were carried out to investigate the nature of the ordering transition of a model of adsorbed self-assembled rigid rods on the bonds of a square lattice [Tavares, Phys. Rev. E 79, 021505 (2009)]. The polydisperse rods undergo a continuous ordering transition that is found to be in the two-dimensional Ising universality class, as in models where the rods are monodisperse. This finding is in sharp contrast with the recent claim that equilibrium polydispersity changes the nature of the phase transition in this class of models [López, Phys. Rev. E 80, 040105(R) (2009)].

Phase behavior of the confined Lebwohl-Lasher model

The phase behavior of confined nematogens is studied using the Lebwohl-Lasher model. For three-dimensional systems the model is known to exhibit a discontinuous nematic-isotropic phase transition, whereas the corresponding two-dimensional systems apparently show a continuous Berezinskii-Kosterlitz-Thouless-like transition. In this paper, we study the phase transitions of the Lebwohl-Lasher model when confined between planar slits of different widths in order to establish the behavior of intermediate situations between the pure planar model and the three-dimensional system, and compare with previous estimates for the critical thickness, i.e., the slit width at which the transition switches from continuous to discontinuous.

Topological considerations on microporous adsorption processes in simple models for pillared interlayered clays

The microporous structure of pillared interlayered clays is determined by their interlayer separation and the distribution of the pillars that separate their layers. The pillars provide stability to these quasi-two-dimensional high surface area materials. In this work we present a topological analysis of available and accessible volumes within various simple models of pillared interlayered clays. Each model is characterized by a distribution of pillars. Both fully ordered structures and disordered pillar distributions with either attractive or repulsive interpillar correlations are considered. Particular attention is paid to the problem of accessibility. In systems with similar degrees of porosity, even when cavities within each model might be able to host the same adsorbate molecules, their accessibility will strongly depend on the pillar distribution. The theoretical analysis presented in this work may facilitate the interpretation of experimental results, pointing out those quantities that are key to describe the texture of the porous material.

Phase behavior of the hard-sphere Maier-Saupe fluid under spatial confinement

The Maier-Saupe hard-sphere fluid is one of the simplest models that accounts for the isotropic-nematic transition characteristic of liquid crystal phases. At low temperatures the model is known to present a gas-liquid-like transition with a large difference between the densities of the coexistence phases, whereas at higher temperature the transition becomes a weak first-order transition resembling the typical order-disorder (nematic-isotropic) phase change of liquid crystals. Spatial dimensionality directly conditions the character of the orientational phase change (i.e., the high temperature transition), that goes from a first-order transition in the purely three-dimensional case, to a Berezinskii-Kosterlitz-Thouless-like continuous transition which occurs when the three dimensional Maier-Saupe spins are constrained to lie on a plane. In the latter instance, the ordered phase is not endowed with true long-range order. In this work we investigate how the continuous transition transforms into a true first-order phase change, by analyzing the phase behavior of a system of three dimensional Maier-Saupe hard spheres confined between two parallel plates, with separations ranging from the quasi-two-dimensional regime to the bulk three-dimensional limit. Our results indicate that spatial confinement in one direction induces the change from first order to a continuous transition with a corresponding decrease of the transition temperatures. As to the gas-liquid transition, the estimated "critical" temperatures and densities also decrease as the fluid is confined, in agreement with previous results for other simple systems.

A cluster algorithm for Monte Carlo simulation at constant pressure

We propose an efficient algorithm to sample the volume in Monte Carlo simulations in the isobaric-isothermal ensemble. The method is designed to be applied in the simulation of hard-core models at high density. The algorithm is based in the generation of clusters of particles. At the volume change step, the distances between pairs of particles belonging to the same cluster do not change. This is done by rescaling the positions of the center of mass of each cluster instead of the position of each individual particle. We have tested the performance of the algorithm by simulating fluid and solid phases of hard spheres, finding that in both cases the algorithm is much more efficient than the standard procedure. Moreover, the efficiency of the method measured in terms of correlation "time" does not depend on the system size in contrast with the standard method, in which the sampling becomes rapidly inefficient as the system size increases. We have used the procedure to compute with high precision the equation of state of the face-centered-cubic phase of the hard sphere system for different system sizes. Using these results we have estimated the equation of state at the thermodynamic limit. The results are compared to different equations of state proposed in literature.

Phase behavior of a family of continuous two-dimensional n -vector models with n=2, 3, and 4

In this work we investigate the phase behavior of a family of continuous bidimensional n -vector models (with n=2, 3, and 4) using Monte Carlo simulation. In all cases we detect the presence of a defect mediated order-disorder transition of the Berezinskii-Kosterlitz-Thouless type with critical temperatures that decrease with the spin dimensionality. Coupled with the order-disorder transition a gas-liquid equilibrium is found at low temperatures. Here one observes that the stability region of the liquid phase shrinks with the growing spin dimensionality, in parallel with a decrease in magnitude of the angular averaged spin-spin interaction.

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.

Cluster algorithm to perform parallel Monte Carlo simulation of atomistic systems

We propose an efficient algorithm to perform Monte Carlo simulations of dense systems using multiple particle moves. The method is intended to be used in the atomistic simulation of complex systems, where the computing requirements for a single simulation run make advisable the use of parallel computing. The algorithm is based on the use of steps in which all the particle positions of the system are perturbed simultaneously. A division of the system in clusters of particles is performed, using a bonding criterion which makes feasible that the acceptance or rejection of the new particle coordinates can be carried out independently for each cluster.

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.

Computation of the free energy of solids

We present a procedure to compute the absolute free energy of solid phases by Monte Carlo simulation. The method is based on the so-called "Einstein-crystal" method of Frenkel and Ladd [J. Chem. Phys. 81, 3188 (1984)]. The new technique is more general and simplifies the calculation for systems with hard core interactions. In addition, the reference Einstein crystal is built up to fulfill translational invariance, which seems to reduce the system size dependence of the results.

Phase behavior of a hard sphere Maier-Saupe nematogenic system in three dimensions

We present a detailed computer simulation and integral equation study of the phase behavior of a nematogenic system composed of hard spheres with embedded three-dimensional Maier-Saupe spins. For this well-known system, we map the gas-liquid equilibrium, which is coupled to a first-order isotropic-nematic transition. The anisotropic integral equation theory is found to yield excellent agreement with the simulation data within the fluid regime. Additionally, we determine the fluid-solid equilibrium transition by means of computer simulation.

Simulation study of the phase behavior of a planar Maier-Saupe nematogenic liquid

Using extensive Monte Carlo simulations and a simple approximation in density functional theory, we study the phase behavior of a fluid of nematogenic molecules with centers of mass constrained to lie in a plane but with axes free to rotate in any direction, both with and without an external disorienting field perpendicular to the plane. We find that simulation predicts the existence of an order-disorder phase transition belonging to the Berezinskii-Kosterlitz-Thouless type, along with a low temperature gas-liquid transition. In contrast to the simulation results, density functional theory predicts a first-order orientational phase transition coupled continuously with a first-order gas-liquid transition. The approximate theoretical approach qualitatively reproduces the field dependence of the order-disorder and gas-liquid transitions but is far from quantitative.

Determination of effective pair interactions from the structure factor

In this work we present an efficient procedure to evaluate effective pair potentials, compatible with "experimental" structure factors, using a Monte Carlo simulation scheme. The procedure does not require the use of inverse Fourier transforms and is robust and rapidly convergent. As a test case the structure factor of liquid Selenium obtained from a Tight-Binding Molecular Dynamics simulation is inverted to obtain an effective pair potential and, as a by-product, the pair distribution function. The inversion procedure yields a pair structure in perfect agreement with the original molecular dynamics calculations and the analysis of the triplet structure and the dynamics also illustrates the limitations of the use of pair potentials in the description of liquids with strongly directional bonding, such as the covalent liquid Selenium.

Determination of the interaction potential from the pair distribution function: an inverse Monte Carlo technique

In this work we present an efficient procedure to evaluate effective pair potentials compatible with "experimental" distribution functions using a Monte Carlo simulation scheme. Using computer simulation results for the pair distribution functions, we have applied the method to a Lennard-Jones fluid and to a model of liquid aluminum. In both cases the procedure was able to recover with high accuracy the actual interaction potential of the systems. Moreover, the procedure can easily incorporate additional information, for instance, thermodynamic properties, in order to improve the reliability of the results.

Local density approach for modeling fluids with density-dependent interactions

In a recent paper [Phys. Rev. Lett. 86, 2038 (2001)] a simple fluid with a particular density-dependent pair potential was shown to exhibit, together with the vapor-liquid transition, a liquid-liquid phase separation and it was evidenced that, in order to adequately define the correct boundaries of stability, a simulation procedure based on the use of local densities had to be devised. It was found that for certain thermodynamic states the potential drives the system toward a phase separation that is otherwise frustrated by the change in the interactions induced by density fluctuations. Therefore, when integral equations or global density simulations are used, the critical points estimated from the thermodynamics are not associated with divergent correlations and vice versa. Here, we will explore in depth this fluid and introduce a detailed account of the proposed local density simulation technique. The results presented bear general significance for density-dependent potentials, like those of liquid metals or charge-stabilized colloids.

Critical behavior of ionic solids

Phase transitions of lattice models of ionic crystals are studied by computer simulation. The nature of order-disorder transitions on different crystal structures is established and compared with the behavior of related Ising models. It is found that for both, continuous and first order transitions the basic features seem to be similar to those of Ising systems.

Reentrant miscibility in fluids with spherical interactions

We have obtained the closed-loop fluid-fluid immiscibility in the phase diagram of a binary mixture with interactions with spherical symmetry. That topology appears when a short-range attractive interaction is considered between unlike pair molecules. We present "exact" results obtained from Monte Carlo simulation on different ensembles and results from the application of a first-order perturbation theory.

Evidence of double criticality in a fluid model with density-dependent interactions

Evidence of a liquid-liquid equilibrium in simple fluids has recently been exposed for a density-dependent pair potential in the framework of a van der Waals theory. Here this double criticality is investigated by means of computer simulation, a perturbation theory, and integral equation theory. It is found that the critical point estimated from the integral equation thermodynamics is not associated with divergent correlations. To cope with these features, a special simulation procedure, based on the definition of local densities, is devised. Monte Carlo calculations confirm the existence of two critical points, in agreement with the predictions of perturbation theory.