Two simple examples of spontaneous chiral symmetry breaking are presented. The first is close-packed cylindrically confined spheres. As the cylinder diameter is varied, one obtains a variety of chiral phases. The second example involves unconfined dipolar particles with an isotropic attraction, which also exhibits chiral ground states. We speculate that a dilute magnetorheological fluid film, with the addition of smaller particles to provide an attractive entropic interaction, will exhibit a chiral columnar ground state.

An analysis of the morphological behavior of substrate-supported diblock copolymer films for thicknesses t below the equilibrium period L 0 of the copolymer is presented. Substrate-supported films generally exhibit dissimilar interactions between the copolymer block components and the free and substrate surfaces. Accordingly, in this study, self-consistent-field calculations that incorporate asymmetric surface energetics were used to assess equilibrium film morphologies. Phase diagrams were constructed as a function of film thickness, surface interaction energies, the segmental interaction, and the chain length. In conjunction, experiments were conducted on a series of polystyrene-b-poly(n-alkyl methacrylate) copolymer films supported by silicon substrates. These employed a novel atomic force microscopy technique that allowed for the precise tracking of morphology as a function of film thickness. Comparison of the experimental results and calculations revealed several common trends. In particular, hybrid morphologies, incorporating both surface-parallel and surface-perpendicular elements, were observed both experimentally and through the calculations for the thickness regime, t ∼ 0.5L 0. The stability of such structures was found to be closely linked to the symmetry of the surface energetics.

Using a two-dimensional Scheutjens and Fleer self-consistent field calculation, we determine the equilibrium morphology of thin films of symmetric AB diblock copolymers confined between hard, smooth plates. A lamellar phase is established with the stripes either perpendicular or parallel to the walls. With neutral walls, the perpendicular orientation is stabilized by the nematic ordering of the monomers, which arises from the orientational constraint imposed by the walls. When the substrates are composed of pure A monomer (thus repulsive to B), there are transitions from strained parallel conformations, which wet the substrates with A polymer, to distorted perpendicular configurations as the film thickness is varied. It is possible that the removal of one of the walls (the usual experimental scenario of thin films spun cast onto a substrate) can still lead to spontaneous and robust pattern formation on the scale of tens of nanometers.

We theoretically investigate the equilibrium orientation of lamellae arising from symmetric diblock copolymers in the presence of a hard wall. Firstly, the wall may preferentially wet with one of the species of the copolymer, thus favoring lamellar planes parallel to the wall. Secondly, chains are more easily stretched along the wall than they are in bulk; this favors the lamellar planes being perpendicular to the wall.Finally, the enhanced chain end density near the wall in the parallel orientation favors the planes flat along the wall. As molecular weight M approaches infinity, the most important effect is the wetting ~Af°, followed by the nematic effect ~M-2/3, and lastly followed by the end effect ~ ~®/9. In experimentally available copolymer domains, we find that the nematic and end effects have comparable magnitude. This magnitude appears more than adequate to influence the orientation of the lamellae. Lastly, we discuss effects of substrate roughness.

I consider a brush consisting of dendritic polymer end-grafted by its initial segment to a flat, impenetrable surface, in both the molten and solvated cases. The parabolic profile of linear grafted brushes is maintained, but the distribution of the free tips is quite different from the linear brush case. In particular, free ends are comparatively buried in the brush or "forest" layer compared to linear chains, an effect which is magnified by going to higher and higher generations. There is no appreciable tendency for dendritic arms to fold backward into the layer, however. The results of the classical path analysis compare favorably to lattice self-consistent-field calculations on the same systems.