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

We report Monte Carlo simulations that show closed-loop liquid-vapor equilibrium in a pure substance. As far as we know, this is the first time that such a topology of the phase diagram has been found for one-component systems. 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 the 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 with the phase diagram containing the 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.Comment: 5 pages (two columns); 7 Figures (Submitted to Physical Review

Phase behaviour of the confined lattice gas Lebwohl-Lasher model

The phase behaviour of the Lebwohl-Lasher lattice gas model (one of the simplest representations of a nematogenic fluid) confined in a slab is investigated by means of extensive Monte Carlo simulations. The model is known to yield a first order gas-liquid transition in both the 2D and 3D limits, that is coupled with an orientational order-disorder transition. This latter transition happens to be first order in the 3D limit and it shares some characteristic features with the continuous defect mediated Berezinskii-Kosterlitz-Thouless transition in 2D. In this work we will analyze in detail the behaviour of this system taking full advantage of the lattice nature of the model and the particular symmetry of the interaction potential, which allows for the use of efficient cluster algorithms.Comment: 6 pages, 5 figure

Phase behaviour 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 behaviour 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 de-mixing when attractive forces are present, in addition to a gas-liquid transition. Furthermore, a fluid-solid transition emerges in the neighbourhood 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, thus preventing fluid-fluid separation.Comment: 29 pages, 10 figure

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

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 $\epsilon_s$. We consider the cases where the favoured alignments at the two walls are the same (symmetric cell) or different (asymmetric or hybrid cell). In the latter case, we demonstrate the existence of a {\it 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.Comment: 40 pages 19 figures (preprint format). Part of the text and some figures were modified. New figure was include

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 Wertheim's theory for associating fluids and Monte Carlo numerical simulations. We varied the ratio $r\equiv\epsilon_{AB}/\epsilon_{AA}$ of the interaction between patches $A$ and $B$, $\epsilon_{AB}$, and between $A$ patches, $\epsilon_{AA}$ ($\epsilon_{BB}$ is set to $0$) as well as the relative position of the $A$ patches, i.e., the angle $\theta$ between the (lattice) directions of the $A$ patches. We found that both $r$ and $\theta$ ($60^\circ,90^\circ,$ or $120^\circ$) have a profound effect on the phase diagram. In the empty fluid regime ($r < 1/2$) the phase diagram is re-entrant 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 $\theta=120^\circ$ but deteriorates as $\theta$ decreases, revealing the need for new theoretical approaches to describe the structure and thermodynamics of systems dominated by small rings.Comment: 26 pages, 10 figure

Surface tension of the Widom-Rowlinson model

11 pags., 5 figs., 3 tabs.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. © 2007 American Institute of Physics.Financial support is due to the Spanish Dirección General de Investigación Project Nos. FIS2004-06627-C02-01 E.d.M. and FIS2004-02954-C03-01 N.G.A. and from Universidad de Huelva and Junta de Andalucía. Additional funding from the Dirección General de Universidades e Investigación Comunidad de Madrid, Spain under the MOSSNOHO-CM program Grant No. S0505/ESP/0299 and from the Engineering and Physical Sciences EPSRC of the UK Grant Nos. GR/N20317, GR/N03358, GR/N35991, GR/R09497, and EP/E016340, the Joint Research Equipment Initiative JREI GR/M94427, and the Royal Society Wolfson Foundation refurbishment grant is also acknowledged. Finally we are grateful to the Royal Society for the award of a International Short Visit grant which has facilitated the collaborative work

Nematic phase in the J1-J2 square-lattice Ising model in an external field

© 2015 American Physical Society. The J1-J2 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 κ=J2/|J1| 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.Peer Reviewe