Wetting and capillary nematization of binary hard-platelet and hard-rod fluids

Density-functional theory is used to investigate the phase behavior of colloidal binary hard-platelet and hard-rod fluids near a single hard wall or confined in a slit pore. The Zwanzig model, in which the orientations of the particles of rectangular shape are restricted to three orthogonal orientations, is analyzed by numerical minimization of the grand potential functional. The density and orientational profiles as well as the surface contributions to the grand potential are determined. The calculations exhibit a wall-induced continuous surface transition from uniaxial to biaxial symmetry for the hard-rod fluid. Complete wetting of the wall -- isotropic liquid interface by a biaxial nematic film for rods and a uniaxial nematic film for platelets is found. For the fluids confined by two parallel hard walls we determine a first-order capillary nematization transition for large slit widths, which terminates in a capillary critical point upon decreasing the slit width.Comment: 11 pages, 11 figure

The structure of fluids with impurities

The influence of dilute impurities on the structure of a fluid solvent is investigated theoretically. General arguments, which do not rely on particular models, are used to derive an extension of the Ornstein-Zernike form for the solvent structure factor at small scattering vectors. It is shown that dilute impurities can influence the solvent structure only if they are composed of ions with significantly different sizes. Non-ionic impurities or ions of similar size are shown to not alter the solvent structure qualitatively. This picture is compatible with available experimental data. The derived form of the solvent structure factor is expected to be useful to infer information on the impurity-solvent interactions form measured scattering intensities

Phase behavior of a nematic liquid crystal in contact with a chemically and geometrically structured substrate

A nematic liquid crystal in contact with a grating surface possessing an alternating stripe pattern of locally homeotropic and planar anchoring is studied within the Frank--Oseen model. The combination of both chemical and geometrical surface pattern leads to rich phase diagrams, involving a homeotropic, a planar, and a tilted nematic texture. The effect of the groove depth and the anchoring strengths on the location and the order of phase transitions between different nematic textures is studied. A zenithally bistable nematic device is investigated by confining a nematic liquid crystal between the patterned grating surface and a flat substrate with strong homeotropic anchoring.Comment: 7 pages, 7 figure

Effective free energy method for nematic liquid crystals in contact with structured substrates

We study the phase behavior of a nematic liquid crystal confined between a flat substrate with strong anchoring and a patterned substrate whose structure and local anchoring strength we vary. By first evaluating an effective surface free energy function characterizing the patterned substrate we derive an expression for the effective free energy of the confined nematic liquid crystal. Then we determine phase diagrams involving a homogeneous state in which the nematic director is almost uniform and a hybrid aligned nematic state in which the orientation of the director varies through the cell. Direct minimization of the free energy functional were performed in order to test the predictions of the effective free energy method. We find remarkably good agreement between the phase boundaries calculated from the two approaches. In addition the effective energy method allows one to determine the energy barriers between two states in a bistable nematic device.Comment: 10 pages, 7 figures, submitte

Bulk and interfacial properties of binary hard-platelet fluids

Interfaces between demixed fluid phases of binary mixtures of hard platelets are investigated using density-functional theory. The corresponding excess free energy functional is calculated within a fundamental measure theory adapted to the Zwanzig model, in which the orientations of the particles of rectangular shape are restricted to three orthogonal orientations. Density and orientational order parameter profiles at interfaces between coexisting phases as well as the interfacial tension are determined. A density inversion, oscillatory density profiles, and a Fisher-Widom line have been found in a mixture of large thin and small thick platelets. The lowest interfacial tension corresponds to the mean bulk orientation of the platelets being parallel to the interface. For a mixture of large and small thin platelets, complete wetting of an isotropic-nematic interface by a second nematic phase is found.Comment: 7 pages, 6 figure

Phase behavior of ionic liquid crystals

Bulk properties of ionic liquid crystals are investigated using density functional theory. The liquid crystal molecules are represented by ellipsoidal particles with charges located in their center or at their tails. Attractive interactions are taken into account in terms of the Gay-Berne pair potential. Rich phase diagrams involving vapor, isotropic and nematic liquid, as well as smectic phases are found. The dependence of the phase behavior on various parameters such as the length of the particles and the location of charges on the particles is studied

Critical Casimir forces between planar and crenellated surfaces

We study critical Casimir forces between planar walls and geometrically structured substrates within mean-field theory. As substrate structures, crenellated surfaces consisting of periodic arrays of rectangular crenels and merlons are considered. Within the widely used proximity force approximation, both the top surfaces of the merlons and the bottom surfaces of the crenels contribute to the critical Casimir force. However, for such systems the full, numerically determined critical Casimir forces deviate significantly fromthe pairwise addition formalismunderlying the proximity force approximation. A first-order correction to the proximity force approximation is presented in terms of a step contribution arising from the critical Casimir interaction between a planar substrate and the right-angled steps of the merlons consisting of their upper and lower edges as well as their sidewalls.Comment: 9 pages, 6 figure

Thermodynamics and phase behavior of the lamellar Zwanzig model

Binary mixtures of lamellar colloids represented by hard platelets are studied within a generalization of the Zwanzig model for rods, whereby the square cuboids can take only three orientations along the $x$, $y$ or $z$ axes. The free energy is calculated within Rosenfeld's ''Fundamental Measure Theory'' (FMT) adapted to the present model. In the one-component limit, the model exhibits the expected isotropic to nematic phase transition, which narrows as the aspect ratio $\zeta=L/D$ ($D$ is the width and $L$ the thickness of the platelets) increases. In the binary case the competition between nematic ordering and depletion-induced segregation leads to rich phase behaviour.Comment: 9 pages, 6 figure

Alignment of cylindrical colloids near chemically patterned substrates induced by critical Casimir torques

Recent experiments have demonstrated a fluctuation-induced lateral trapping of spherical colloidal particles immersed in a binary liquid mixture near its critical demixing point and exposed to chemically patterned substrates. Inspired by these experiments, we study this kind of effective interaction, known as the critical Casimir effect, for elongated colloids of cylindrical shape. This adds orientational degrees of freedom. When the colloidal particles are close to a chemically structured substrate, a critical Casimir torque acting on the colloids emerges. We calculate this torque on the basis of the Derjaguin approximation. The range of validity of the latter is assessed via mean-field theory. This assessment shows that the Derjaguin approximation is reliable in experimentally relevant regimes, so that we extend it to Janus particles endowed with opposing adsorption preferences. Our analysis indicates that critical Casimir interactions are capable of achieving well-defined, reversible alignments both of chemically homogeneous and of Janus cylinders.Comment: 24 pages, 12 figures; v2: 22 pages, 12 figure

Bulk and wetting phenomena in a colloidal mixture of hard spheres and platelets

Density functional theory is used to study binary colloidal fluids consisting of hard spheres and thin platelets in their bulk and near a planar hard wall. This system exhibits liquid-liquid coexistence of a phase that is rich in spheres (poor in platelets) and a phase that is poor in spheres (rich in platelets). For the mixture near a planar hard wall, we find that the phase rich in spheres wets the wall completely upon approaching the liquid demixing binodal from the sphere-poor phase, provided the concentration of the platelets is smaller than a threshold value which marks a first-order wetting transition at coexistence. No layering transitions are found in contrast to recent studies on binary mixtures of spheres and non-adsorbing polymers or thin hard rods.Comment: 6 pages, 4 figure