Nematic phase in the J1_1-J2_2 square lattice Ising model in an external field

The J$_1$-J$_2$ Ising model in the square lattice in the presence of an external field is studied by two approaches: the Cluster Variation Method (CVM) and Monte Carlo simulations. The use of the CVM in the square approximation leads to the presence of a new equilibrium phase, not previously reported for this model: an Ising-nematic phase, which shows orientational order but not positional order, between the known stripes and disordered phases. Suitable order parameters are defined and the phase diagram of the model is obtained. Monte Carlo simulations are in qualitative agreement with the CVM results, giving support to the presence of the new Ising-nematic phase. Phase diagrams in the temperature-external field plane are obtained for selected values of the parameter $\kappa=J_2/|J_1|$ which measures the relative strength of the competing interactions. From the CVM in the square approximation we obtain a line of second order transitions between the disordered and nematic phases, while the nematic-stripes phase transitions are found to be of first order. The Monte Carlo results suggest a line of second order nematic-disordered phase transitions in agreement with the CVM results. Regarding the stripes-nematic transitions, the present Monte Carlo results are not precise enough to reach definite conclusions about the nature of the transitions.Comment: 13 pages, 10 figure

Demixing in a single-peak distributed polydisperse mixture of hard spheres

An analytic derivation of the spinodal of a polydisperse mixture is presented. It holds for fluids whose excess free energy can be accurately described by a function of a few moments of the size distribution. It is shown that one such mixture of hard spheres in the Percus-Yevick approximation never demixes, despite its size distribution. In the Boublik-Mansoori-Carnahan-Starling-Leland approximation, though, it demixes for a sufficiently wide log-normal size distribution. The importance of this result is twofold: first, this distribution is unimodal, and yet it phase separates; and second, log-normal size distributions appear in many experimental contexts. The same phenomenon is shown to occur for the fluid of parallel hard cubes.Comment: 4 pages, 2 figures, needs revtex, multicol, epsfig and amstex style file

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 L 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 L. This structural order is lost at T = T(L) depending on L according to a Kelvin-like equation. Above the Kelvin temperature T(L) 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 L optimal for the stripe pattern the heat capacity as a function of temperature takes the maximum at T = T(L).Peer Reviewe

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 neighbors 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.Comment: 14 pages, 8 figures, uses RevTex

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 solute/solvent is controlled by tuning the energy interactions between the patches of ALG model. We have studied three set of parameters, resulting on, 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 last case (hydrophobic), the excess properties reproduce the behavior of ionic liquids in aqueous solution.Comment: 28 pages, 13 figure

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

© 2015 AIP Publishing LLC. 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. Pękalski 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.Peer Reviewe

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.Comment: Submitted to Physical Review

Multiscale, patient-specific computational fluid dynamics models predict formation of neointimal hyperplasia in saphenous vein grafts

Stenosis due to neointimal hyperplasia (NIH) is among the major causes of peripheral graft failure. Its link to abnormal hemodynamics in the graft is complex, and isolated use of hemodynamic markers is insufficient to fully capture its progression. Here, a computational model of NIH growth is presented, establishing a link between computational fluid dynamics simulations of flow in the lumen and a biochemical model representing NIH growth mechanisms inside the vessel wall. For all three patients analyzed, NIH at proximal and distal anastomoses was simulated by the model, with values of stenosis comparable to the computed tomography scans