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

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

Critical adsorption on non-spherical colloidal particles

We consider a non-spherical colloidal particle immersed in a fluid close to its critical point. The temperature dependence of the corresponding order parameter profile is calculated explicitly. We perform a systematic expansion of the order parameter profile in powers of the local curvatures of the surface of the colloidal particle. This curvature expansion reduces to the short distance expansion of the order parameter profile in the case that the solvent is at the critical composition.Comment: 9 pages, 7 figure

Interaction of cylindrical polymer brushes in dilute and semi-dilute solution

We present a systematic study of flexible cylindrical brush-shaped macromolecules in a good solvent by small-angle neutron scattering (SANS), static light scattering (SLS), and by dynamic light scattering (DLS) in dilute and semi-dilute solution. The SLS and SANS data extrapolated to infinite dilution lead to the shape of the polymer that can be modeled in terms of a worm-like chain with a contour length of 380 nm and a persistence length of 17.5 nm. SANS data taken at higher polymer concentration were evaluated by using the polymer reference interaction site model (PRISM). We find that the persistence length reduce from 17.5 nm at infinite dilution to 5.3 nm at the highest concentration (volume fraction 0.038). This is comparable with the decrease of the persistence length in semi-dilute concentration predicted theoretically for polyelectrolytes. This finding reveals a softening of stiffness of the polymer brushes caused by their mutual interaction

Softening of the stiffness of bottlebrush polymers by mutual interaction

We study bottlebrush macromolecules in a good solvent by small-angle neutron scattering (SANS), static light scattering (SLS), and dynamic light scattering (DLS). These polymers consist of a linear backbone to which long side chains are chemically grafted. The backbone contains about 1600 monomer units (weight average) and every second monomer unit carries side-chains with ca. 60 monomer units. The SLS- and SANS data extrapolated to infinite dilution lead to the form factor of the polymer that can be described in terms of a worm-like chain with a contour length of 380 nm and a persistence length of 17.5 nm. An analysis of the DLS data confirm these model parameters. The scattering intensities taken at finite concentration can be modeled using the polymer reference interaction site model. It reveals a softening of the bottlebrush polymers caused by their mutual interaction. We demonstrate that the persistence decreases from 17.5 nm down to 5 nm upon increasing the concentration from dilute solution to the highest concentration 40.59 g/l under consideration. The observed softening of the chains is comparable to the theoretically predicted decrease of the electrostatic persistence length of linear polyelectrolyte chains at finite concentrations.Comment: 4 pages, 4 figure

Structure and equation of state of interaction site models for disc-shaped lamellar colloids

We apply RISM (Reference Interaction Site Model) and PRISM (polymer-RISM) theories to calculate the site-site pair structure and the osmotic equation of state of suspensions of circular or hexagonal platelets (lamellar colloids) over a range of ratios of the particle diameter over thickness. Despite the neglect of edge effects, the simpler PRISM theory yields results in good agreement with the more elaborate RISM calculations, provided the correct form factor, characterizing the intramolecular structure of the platelets, is used. The RISM equation of state is sensitive to the number of sites used to model the platelets, but saturates when the hard spheres, associated with the interaction sites, nearly touch; the limiting equation of state agrees reasonably well with available simulation data for all densities up to the isotropic-nematic transition. When properly scaled with the second virial coefficient, the equations of state of platelets with different aspect ratios nearly collapse on a single master curve.Comment: 10 Pages, 11 Figures, Typesetted using RevTeX

Fluids of platelike particles near a hard wall

Fluids consisting of hard platelike particles near a hard wall are investigated using density functional theory. The density and orientational profiles as well as the surface tension and the excess coverage are determined and compared with those of a fluid of rodlike particles. Even for low densities slight orientational packing effects are found for the platelet fluid due to larger intermolecular interactions between platelets as compared with those between rods. A net depletion of platelets near the wall is exhibited by the excess coverage, whereas a change of sign of the excess coverage of hard-rod fluids is found upon increasing the bulk density.Comment: 6 pages, 9 figure

A fundamental-measure density functional for mixtures of parallel hard cylinders

We obtain a fundamental measure density functional for mixtures of parallel hard cylinders. To this purpose we first generalize to multicomponent mixtures the fundamental measure functional proposed by Tarazona and Rosenfeld for a one-component hard disk fluid, through a method alternative to the cavity formalism of these authors. We show the equivalence of both methods when applied to two-dimensional fluids. The density functional so obtained reduces to the exact density functional for one-dimensional mixtures of hard rods when applied to one-dimensional profiles. In a second step we apply an idea put forward some time ago by two of us, based again on a dimensional reduction of the system, and derive a density functional for mixtures of parallel hard cylinders. We explore some features of this functional by determining the fluid-fluid demixing spinodals for a binary mixture of cylinders with the same volume, and by calculating the direct correlation functions.Comment: 19 pages, 4 figure

Characterization of local dynamics and mobilities in polymer melts - a simulation study

The local dynamical features of a PEO melt studied by MD simulations are compared to two model chain systems, namely the well-known Rouse model as well as the semiflexible chain model (SFCM) that additionally incorporates chain stiffness. Apart from the analysis of rather general quantities such as the mean square displacement (MSD), we present a new statistical method to extract the local bead mobility from the simulation data on the basis of the Langevin equation, thus providing a complementary approach to the classical Rouse-mode analysis. This allows us to check the validity of the Langevin equation and, as a consequence, the Rouse model. Moreover, the new method has a broad range of applications for the analysis of the dynamics of more complex polymeric systems like comb-branched polymers or polymer blends.Comment: 6 pages, 5 figure