Diblock Copolymer Ordering Induced by Patterned Surfaces Above the Order-Disorder Transition

We investigate the morphology of diblock copolymers in the vicinity of flat, chemically patterned surfaces. Using a Ginzburg-Landau free energy, spatial variations of the order parameter are given in terms of a general two-dimensional surface pattern above the order-disorder transition. The propagation of several surface patterns into the bulk is investigated. The oscillation period and decay length of the surface $q$-modes are calculated in terms of system parameters. We observe lateral order parallel to the surface as a result of order perpendicular to the surface. Surfaces which has a finite size chemical pattern (e.g., a stripe of finite width) induces lamellar ordering extending into the bulk. Close to the surface pattern the lamellae are strongly perturbed adjusting to the pattern.Comment: 9 pages, 14 figures, to be published in Macromolecule

Attraction Between Like-Charge Surfaces in Polar Mixtures

We examine the force between two charged surfaces immersed in aqueous mixtures having a coexistence curve. For a homogeneous water-poor phase, as the distance between the surfaces is decreased, a water-rich phase condenses at a distance $D_t$ in the range 1-100nm. At this distance the osmotic pressure can become negative leading to a long-range attraction between the surfaces. The osmotic pressure vanishes at a distance $D_e<D_t$, representing a very deep metastable or globally stable energetic state. We give analytical and numerical results for $D_t$ and $D_e$ on the Poisson-Boltzmann level.Comment: 6 pages, 6 figure

Diblock copolymer thin films: Parallel and perpendicular lamellar phases in the weak segregation limit

We study morphologies of thin-film diblock copolymers between two flat and parallel walls. The study is restricted to the weak segregation regime below the order-disorder transition temperature. The deviation from perfect lamellar shape is calculated for phases which are perpendicular and parallel to the walls. We examine the undulations of the inter material dividing surface and its angle with the walls, and find that the deviation from its unperturbed position can be much larger than in the strong segregation case. Evaluating the weak segregation stability of the lamellar phases, it is shown that a surface interaction, which is quadratic in the monomer concentration, favors the perpendicular lamellar phase. In particular, the degeneracy between perpendicular and unfrustrated parallel lamellar phases for walls without a preferential adsorption is removed.Comment: 10 pages, 9 figures, submitted to European Physical Journal

Parallel and Perpendicular Lamellae on Corrugated Surfaces

We consider the relative stability of parallel and perpendicular lamellar layers on corrugated surfaces. The model can be applied to smectic phases of liquid crystals, to lamellar phases of short-chain amphiphiles and to lamellar phases of long-chain block copolymers. The corrugated surface is modelled by having a single $q$-mode lateral corrugation of a certain height. The lamellae deform close to the surface as a result of chemical interaction with it. The competition between the energetic cost of elastic deformations and the gain in surface energy determines whether parallel or perpendicular lamellar orientation (with respect to the surface) is preferred. Our main results are summarized in two phase diagrams, each exhibiting a transition line from the parallel to perpendicular orientations. The phase diagrams depend on the three system parameters: the lamellar natural periodicity, and the periodicity and amplitude of surface corrugations. For a fixed lamellar periodicity (or polymer chain length), the parallel orientation is preferred as the amplitude of surface corrugation decreases and/or its periodicity increases. Namely, for surfaces having small corrugations centered at long wavelengths. For a fixed corrugation periodicity, the parallel orientation is preferred for small corrugation amplitude and/or large lamellae periodicity. Our results are in agreement with recent experimental results carried out on thin block copolymer films of PS-PMMA (polystyrene-polymethylmethacrylate) in the lamellar phase, and in contact with several corrugated surfaces.Comment: 12 pages, 5 figure