Bulk inhomogeneous phases of anisotropic particles: A fundamental measure functional study of the restricted orientations model

The phase diagram of prolate and oblate particles in the restricted orientations approximation (Zwanzig model) is calculated. Transitions to different inhomogeneous phases (smectic, columnar, oriented, or plastic solid) are studied through minimization of the fundamental measure functional (FMF) of hard parallelepipeds. The study of parallel hard cubes (PHC's) as a particular case is also included motivated by recent simulations of this system. As a result a rich phase behavior is obtained which include, apart from the usual liquid crystal phases, a very peculiar phase (called here discotic smectic) which was already found in the only existing simulation of the model, and which turns out to be stable because of the restrictions imposed on the orientations. The phase diagram is compared at a qualitative level with simulation results of other anisotropic particle systems.Comment: 11 pages, 10 figure

Biaxial nematic phases in fluids of hard board-like particles

We use density-functional theory, of the fundamental-measure type, to study the relative stability of the biaxial nematic phase, with respect to non-uniform phases such as smectic and columnar, in fluids made of hard board-like particles with sizes $\sigma_1>\sigma_2>\sigma_3$. A restricted-orientation (Zwanzig) approximation is adopted. Varying the ratio $\kappa_1=\sigma_1/\sigma_2$ while keeping $\kappa_2=\sigma_2/\sigma_3$, we predict phase diagrams for various values of $\kappa_2$ which include all the uniform phases: isotropic, uniaxial rod- and plate-like nematics, and biaxial nematic. In addition, spinodal instabilities of the uniform phases with respect to fluctuations of the smectic, columnar and plastic-solid type, are obtained. In agreement with recent experiments, we find that the biaxial nematic phase begins to be stable for $\kappa_2\simeq 2.5$. Also, as predicted by previous theories and simulations on biaxial hard particles, we obtain a region of biaxility centred on $\kappa_1\approx\kappa_2$ which widens as $\kappa_2$ increases. For \kappa_2\agt 5 the region $\kappa_2\approx\kappa_1$ of the packing-fraction vs. $\kappa_1$ phase diagrams exhibits interesting topologies which change qualitatively with $\kappa_2$. We have found that an increasing biaxial shape anisotropy favours the formation of the biaxial nematic phase. Our study is the first to apply FMT theory to biaxial particles and, therefore, it goes beyond the second-order virial approximation. Our prediction that the phase diagram must be asymmetric is a genuine result of the present approach, which is not accounted for by previous studies based on second-order theories.Comment: Preprint format. 18 pages, 5 figure

Enhancement by polydispersity of the biaxial nematic phase in a mixture of hard rods and plates

The phase diagram of a polydisperse mixture of uniaxial rod-like and plate-like hard parallelepipeds is determined for aspect ratios $\kappa=5$ and 15. All particles have equal volume and polydispersity is introduced in a highly symmetric way. The corresponding binary mixture is known to have a biaxial phase for $\kappa=15$, but to be unstable against demixing into two uniaxial nematics for $\kappa=5$. We find that the phase diagram for $\kappa=15$ is qualitatively similar to that of the binary mixture, regardless the amount of polydispersity, while for $\kappa=5$ a sufficient amount of polydispersity stabilizes the biaxial phase. This provides some clues for the design of an experiment in which this long searched biaxial phase could be observed.Comment: 4 pages, 5 eps figure files, uses RevTeX 4 styl

Dimensional crossover of the fundamental-measure functional for parallel hard cubes

We present a regularization of the recently proposed fundamental-measure functional for a mixture of parallel hard cubes. The regularized functional is shown to have right dimensional crossovers to any smaller dimension, thus allowing to use it to study highly inhomogeneous phases (such as the solid phase). Furthermore, it is shown how the functional of the slightly more general model of parallel hard parallelepipeds can be obtained using the zero-dimensional functional as a generating functional. The multicomponent version of the latter system is also given, and it is suggested how to reformulate it as a restricted-orientation model for liquid crystals. Finally, the method is further extended to build a functional for a mixture of parallel hard cylinders.Comment: 4 pages, no figures, uses revtex style files and multicol.sty, for a PostScript version see http://dulcinea.uc3m.es/users/cuesta/cross.p

Fundamental measure theory for lattice fluids with hard core interactions

We present the extension of Rosenfeld's fundamental measure theory to lattice models by constructing a density functional for d-dimensional mixtures of parallel hard hypercubes on a simple hypercubic lattice. The one-dimensional case is exactly solvable and two cases must be distinguished: all the species with the same lebgth parity (additive mixture), and arbitrary length parity (nonadditive mixture). At the best of our knowledge, this is the first time that the latter case is considered. Based on the one-dimensional exact functional form, we propose the extension to higher dimensions by generalizing the zero-dimensional cavities method to lattice models. This assures the functional to have correct dimensional crossovers to any lower dimension, including the exact zero-dimensional limit. Some applications of the functional to particular systems are also shown.Comment: 22 pages, 7 figures, needs IOPP LaTeX styles file

Phase behaviour of additive binary mixtures in the limit of infinite asymmetry

We provide an exact mapping between the density functional of a binary mixture and that of the effective one-component fluid in the limit of infinite asymmetry. The fluid of parallel hard cubes is thus mapped onto that of parallel adhesive hard cubes. Its phase behaviour reveals that demixing of a very asymmetric mixture can only occur between a solvent-rich fluid and a permeated large particle solid or between two large particle solids with different packing fractions. Comparing with hard spheres mixtures we conclude that the phase behaviour of very asymmetric hard-particle mixtures can be determined from that of the large component interacting via an adhesive-like potential.Comment: Full rewriting of the paper (also new title). 4 pages, LaTeX, uses revtex, multicol, epsfig, and amstex style files, to appear in Phys. Rev. E (Rapid Comm.

Two-dimensional nematics in bulk and confined geometries

El pdf del artículo es la versión pre-print: arXiv:1207.3256Two-dimensional nematics possess peculiar properties that have been studied recently using computer simulation and various theoretical models. Here we review our own contribution to the field using density-functional theory, and present some preliminary simulation results on confined two-dimensional nematics. First we discuss the possible stable bulk phases and phase diagrams and the relation between phases and particle geometry. We then explore the adsorption properties on a single substrate and the confinement effects that arise when the fluid is confined between parallel walls. Next, confinement in circular cavities is presented; this geometry allows us to measure some properties of the simplest defects that arise in two-dimensional nematics. Finally, preliminary Monte Carlo simulation results of confined nematics in circular geometry are shown. © 2012 Elsevier B.V.We acknowledge financial support from Comunidad Autónoma de Madrid under the R& D Program of Activities MODELICO-CM/S2009ESP-1691, and from MINECO (Spain) under grants MOSAICO, FIS2010-22047-C01, FIS2010-22047-C04 and FIS2010-22047-C05.Peer Reviewe

Two-dimensional nematics in bulk and confined geometries

El pdf del artículo es la versión pre-print: arXiv:1207.3256Two-dimensional nematics possess peculiar properties that have been studied recently using computer simulation and various theoretical models. Here we review our own contribution to the field using density-functional theory, and present some preliminary simulation results on confined two-dimensional nematics. First we discuss the possible stable bulk phases and phase diagrams and the relation between phases and particle geometry. We then explore the adsorption properties on a single substrate and the confinement effects that arise when the fluid is confined between parallel walls. Next, confinement in circular cavities is presented; this geometry allows us to measure some properties of the simplest defects that arise in two-dimensional nematics. Finally, preliminary Monte Carlo simulation results of confined nematics in circular geometry are shown. © 2012 Elsevier B.V.We acknowledge financial support from Comunidad Autónoma de Madrid under the R& D Program of Activities MODELICO-CM/S2009ESP-1691, and from MINECO (Spain) under grants MOSAICO, FIS2010-22047-C01, FIS2010-22047-C04 and FIS2010-22047-C05.Peer Reviewe