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

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

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

Colloidal hard-rod fluids near geometrically structured substrates

Density functional theory is used to study colloidal hard-rod fluids near an individual right-angled wedge or edge as well as near a hard wall which is periodically patterned with rectangular barriers. The Zwanzig model, in which the orientations of the rods are restricted to three orthogonal orientations but their positions can vary continuously, is analyzed by numerical minimization of the grand potential. Density and orientational order profiles, excess adsorptions, as well as surface and line tensions are determined. The calculations exhibit an enrichment [depletion] of rods lying parallel and close to the corner of the wedge [edge]. For the fluid near the geometrically patterned wall, complete wetting of the wall -- isotropic liquid interface by a nematic film occurs as a two-stage process in which first the nematic phase fills the space between the barriers until an almost planar isotropic -- nematic liquid interface has formed separating the higher-density nematic fluid in the space between the barriers from the lower-density isotropic bulk fluid. In the second stage a nematic film of diverging film thickness develops upon approaching bulk isotropic -- nematic coexistence.Comment: 9 pages, 9 figure

Critical Casimir effect for colloids close to chemically patterned substrates

Colloids immersed in a critical or near-critical binary liquid mixture and close to a chemically patterned substrate are subject to normal and lateral critical Casimir forces of dominating strength. For a single colloid we calculate these attractive or repulsive forces and the corresponding critical Casimir potentials within mean-field theory. Within this approach we also discuss the quality of the Derjaguin approximation and apply it to Monte Carlo simulation data available for the system under study. We find that the range of validity of the Derjaguin approximation is rather large and that it fails only for surface structures which are very small compared to the geometric mean of the size of the colloid and its distance from the substrate. For certain chemical structures of the substrate the critical Casimir force acting on the colloid can change sign as a function of the distance between the particle and the substrate; this provides a mechanism for stable levitation at a certain distance which can be strongly tuned by temperature, i.e., with a sensitivity of more than 200nm/K.Comment: 27 pages, 14 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

Tunability of Critical Casimir Interactions by Boundary Conditions

We experimentally demonstrate that critical Casimir forces in colloidal systems can be continuously tuned by the choice of boundary conditions. The interaction potential of a colloidal particle in a mixture of water and 2,6-lutidine has been measured above a substrate with a gradient in its preferential adsorption properties for the mixture's components. We find that the interaction potentials at constant temperature but different positions relative to the gradient continuously change from attraction to repulsion. This demonstrates that critical Casimir forces respond not only to minute temperature changes but also to small changes in the surface properties.Comment: 4 figures; http://www.iop.org/EJ/article/0295-5075/88/2/26001/epl_88_2_26001.htm

Contact line stability of ridges and drops

Within the framework of a semi-microscopic interface displacement model we analyze the linear stability of sessile ridges and drops of a non-volatile liquid on a homogeneous, partially wet substrate, for both signs and arbitrary amplitudes of the three-phase contact line tension. Focusing on perturbations which correspond to deformations of the three-phase contact line, we find that drops are generally stable while ridges are subject only to the long-wavelength Rayleigh-Plateau instability leading to a breakup into droplets, in contrast to the predictions of capillary models which take line tension into account. We argue that the short-wavelength instabilities predicted within the framework of the latter macroscopic capillary theory occur outside its range of validity and thus are spurious.Comment: 6 pages, 1 figur

Critical adsorption and critical Casimir forces for geometrically structured confinements

We study the behavior of fluids, confined by geometrically structured substrates, upon approaching a critical point at T = Tc in their bulk phase diagram. As generic substrate structures periodic arrays of wedges and ridges are considered. Based on general renormalization group arguments we calculate, within mean field approximation, the universal scaling functions for order parameter profiles of a fluid close to a single structured substrate and discuss the decay of its spatial variation into the bulk. We compare the excess adsorption at corrugated substrates with the one at planar walls. The confinement of a critical fluid by two walls generates effective critical Casimir forces between them. We calculate corresponding universal scaling functions for the normal critical Casimir force between a flat and a geometrically structured substrate as well as the lateral critical Casimir force between two identically patterned substrates.Comment: 25 pages, 21 figure