Differential capacitance of the electric double layer: The interplay between ion finite size and dielectric decrement

We study the electric double layer by combining the effects of ion finite size and dielectric decrement. At high surface potential, both mechanisms can cause saturation of the counter-ion concentration near a charged surface. The modified Grahame equation and differential capacitance are derived analytically for a general expression of a permittivity epsilon(n) that depends on the local ion concentration, n, and under the assumption that the co-ions are fully depleted from the surface. The concentration at counter-ion saturation is found for any epsilon(n), and a criterion predicting which of the two mechanisms (steric vs. dielectric decrement) is the dominant one is obtained. At low salinity, the differential capacitance as function of surface potential has two peaks (so-called camel-shape). Each of these two peaks is connected to a saturation of counter-ion concentration caused either by dielectric decrement or by their finite size. Because these effects depend mainly on the counter-ion concentration at the surface proximity, for opposite surface-potential polarity either the cations or anions play the role of counter-ions, resulting in an asymmetric camel-shape. At high salinity, we obtain and analyze the crossover in the differential capacitance from a double-peak shape to a uni-modal one. Finally, several nonlinear models of the permittivity decrement are considered, and we predict that the concentration at dielectrophoretic saturation shifts to higher concentration than those obtained by the linear decrement model

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

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

Self-Assembly in Mixtures of Polymers and Small Associating Molecules

The interaction between a flexible polymer in good solvent and smaller associating solute molecules such as amphiphiles (surfactants) is considered theoretically. Attractive correlations, induced in the polymer because of the interaction, compete with intra-chain repulsion and eventually drive a joint self-assembly of the two species, accompanied by partial collapse of the chain. Results of the analysis are found to be in good agreement with experiments on the onset of self-assembly in diverse polymer-surfactant systems. The threshold concentration for self-assembly in the mixed system (critical aggregation concentration, cac) is always lower than the one in the polymer-free solution (critical micelle concentration, cmc). Several self-assembly regimes are distinguished, depending on the effective interaction between the two species. For strong interaction, corresponding experimentally to oppositely charged species, the cac is much lower than the cmc. It increases with ionic strength and depends only weakly on polymer charge. For weak interaction, the cac is lower but comparable to the cmc, and the two are roughly proportional over a wide range of cmc values. Association of small molecules with amphiphilic polymers exhibiting intra-chain aggregation (polysoaps) is gradual, having no sharp onset.Comment: 21 pages, 5 figures, RevTex, the published version, see also cond-mat/990305

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

Adhesion-Induced Lateral Phase Separation in Membranes

Adhesion between membranes is studied using a phenomenological model, where the inter-membrane distance is coupled to the concentration of sticker molecules on the membranes. The model applies to both for adhesion of two flexible membranes and to adhesion of one flexible membrane onto a second membrane supported on a solid substrate. We mainly consider the case where the sticker molecules form bridges and adhere directly to both membranes. The calculated mean-field phase diagrams show an upward shift of the transition temperature indicating that the lateral phase separation in the membrane is enhanced due to the coupling effect. Hence the possibility of adhesion-induced lateral phase separation is predicted. For a particular choice of the parameters, the model exhibits a tricritical behavior. We also discuss the non-monotonous shape of the inter-membrane distance occurring when the lateral phase separation takes place. The inter-membrane distance relaxes to the bulk values with two symmetric overshoots. Adhesion mediated by other types of stickers is also considered.Comment: 13 pages, 9 PostScript figures included. To be published in Euro. Phys. J - E. Minor revision