Assembly of trivalent particles under confinement: from an exotic solid phase to a liquid phase at low temperature.

Using computer simulations, we study the phase diagram of a two-dimensional system of disk particles with three patches distributed symmetrically along the particle equator. The geometry of the particles is compatible with a honey-comb lattice at moderately low temperature and pressure, whereas it is expected that the system forms a close-packed triangular lattice at high temperature and pressure. The effect of patch size within the single bond per patch regime was investigated, and it was found that the topology of the phase diagram changes drastically with patch size. Interestingly, in particles with small patches (with a half opening angle of 10°), the fluid transforms upon increasing the pressure into a rather exotic phase that can be understood as a honey-comb lattice whose voids are filled continuously with additional particles that remain, on average, unbound. Eventually, all the voids are occupied so that particles are located at the positions of a triangular lattice, but only two thirds of the particles are orientationally ordered whereas the remaining one third can rotate almost freely as in a plastic crystal. At moderately low temperature, the fluid transforms into a nearly empty honey-comb lattice, whereas at high temperature it transforms directly into the almost filled lattice. Interestingly, for particles with big patches (with a half opening angle of 20°), the honey-comb and triangular lattices are separated by a liquid phase that remains stable down to fairly low temperatures. Less surprisingly, only particles with big patches exhibit an equilibrium gas-liquid separation.

Pattern formation in binary fluid mixtures induced by short-range competing interactions.

Molecular dynamics simulations and integral equation calculations of a simple equimolar mixture of diatomic molecules and monomers interacting via attractive and repulsive short-range potentials show the existence of pattern formation (microheterogeneity), mostly due to depletion forces away from the demixing region. Effective site-site potentials extracted from the pair correlation functions using an inverse Monte Carlo approach and an integral equation inversion procedure exhibit the features characteristic of a short-range attractive and a long-range repulsive potential. When charges are incorporated into the model, this becomes a coarse grained representation of a room temperature ionic liquid, and as expected, intermediate range order becomes more pronounced and stable.

Nematic phase in the J(1)-J(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 κ=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.

Inclusions of a two dimensional fluid with competing interactions in a disordered, porous matrix.

The behavior of a fluid with competing interaction ranges adsorbed in a controlled pore size disordered matrix is studied by means of grand canonical Monte Carlo simulations in order to analyze the effects of confinement. The disordered matrix model is constructed from a two-dimensional non-additive hard-sphere fluid (which shows close to its demixing critical point large fluctuations in the concentration), after a subsequent quenching of the particle positions and removal of one of the components. The topology of the porous network is analyzed by means of a Delaunay tessellation procedure. The porous cavities are large enough to allow for cluster formation, which is however somewhat hindered as a result of the confinement, as seen from the comparison of cluster size distributions calculated for the fluid under confinement and in the bulk. The occurrence of lamellar phases is impeded by the disordered nature of the porous network. Analysis of two-dimensional density maps of the adsorbed fluid for given matrix configurations shows that clusters tend to build up in specific locations of the porous matrix, so as to minimize inter-cluster repulsion.

Theory of repulsive charged colloids in slit-pores.

Using classical density functional theory (DFT) we analyze the structure of the density profiles and solvation pressures of negatively charged colloids confined in slit pores. The considered model, which was already successfully employed to study a real colloidal (silica) suspension [S. H. L. Klapp et al., Phys. Rev. Lett. 100, 118303 (2008)], involves only the macroions which interact via the effective Derjaguin-Landau-Verwey-Overbeek (DLVO) potential supplemented by a hard core interaction. The solvent enters implicitly via the screening length of the DLVO interaction. The free energy functional describing the colloidal suspension consists of a hard sphere contribution obtained from fundamental measure theory and a long range contribution which is treated using two types of approximations. One of them is the mean field approximation (MFA) and the remaining is based on Rosenfeld's perturbative method for constructing the Helmholtz energy functional. These theoretical calculations are carried out at different bulk densities and wall separations to compare finally to grand canonical Monte Carlo simulations. We also consider the impact of charged walls. Our results show that the perturbative DFT method yields generally qualitatively consistent and, for some systems, also quantitatively reliable results. In MFA, on the other hand, the neglect of charge-induced correlations leads to a breakdown of this approach in a broad range of densities.

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.