Liquid crystals of hard rectangles on flat and cylindrical manifolds.

Using the classical density functional theory of freezing and Monte Carlo computer simulations, we explore the liquid-crystalline phase behavior of hard rectangles on flat and cylindrical manifolds. Moreover, we study the effect of a static external field which couples to the rectangles' orientations, aligning them towards a preferred direction. In the flat and field-free case, the bulk phase diagram involves stable isotropic, nematic, tetratic, and smectic phases depending on the aspect ratio and number density of the particles. The external field shifts the transition curves significantly and generates a binematic phase at the expense of the tetratic phase. On a cylindrical manifold, we observe tilted smectic-like order, as obtained by wrapping a smectic layer around a cylinder. We find in general good agreement between our density functional calculations and particle-resolved computer simulations and mention possible setups to verify our predictions in experiments.

Phase diagram of two-dimensional hard rods from fundamental mixed measure density functional theory.

A density functional theory for the bulk phase diagram of two-dimensional orientable hard rods is proposed and tested against Monte Carlo computer simulation data. In detail, an explicit density functional is derived from fundamental mixed measure theory and freely minimized numerically for hard discorectangles. The phase diagram, which involves stable isotropic, nematic, smectic, and crystalline phases, is obtained and shows good agreement with the simulation data. Our functional is valid for a multicomponent mixture of hard particles with arbitrary convex shapes and provides a reliable starting point to explore various inhomogeneous situations of two-dimensional hard rods and their Brownian dynamics.

Hard rectangles near curved hard walls: Tuning the sign of the Tolman length.

Combining analytic calculations, computer simulations, and classical density functional theory we determine the interfacial tension of orientable two-dimensional hard rectangles near a curved hard wall. Both a circular cavity holding the particles and a hard circular obstacle surrounded by particles are considered. We focus on moderate bulk densities (corresponding to area fractions up to 50%) where the bulk phase is isotropic and vary the aspect ratio of the rectangles and the curvature of the wall. The Tolman length, which gives the leading curvature correction of the interfacial tension, is found to change sign at a finite density, which can be tuned via the aspect ratio of the rectangles.

Kinks in experimental diffusion profiles of a dissolving semi-crystalline polymer explained by a concentration-dependent diffusion coefficient.

The dissolution of polyethylene oxide (PEO) tablets in water has been followed in situ by neutron radiography. When in contact with water, the crystalline phase of semi-crystalline PEO melts once a certain water content is attained. Polymer concentration profiles obtained from the neutron transmission images exhibited a pronounced kink which corresponds to a sharp front in the images and which is related to the melting transition. Sharp diffusion fronts and phase transitions are often linked to non-Fickian behaviour. However, by considering the time evolution of the complete concentration profiles in detail it is shown that the dissolution process can be explained using Fickian diffusion equations with a concentration-dependent diffusion coefficient.