0 Switch of lamellae orientation in slits

Effect of hydrophilicity of the confining walls on lamellar phases in oil-water-surfactant mixtures is studied in a slit geometry. In contrast to strongly hydrophilic or hydrophobic walls, which induce parallel orientation of lamel-lae, the lamellae can be oriented perpendicularly to the neutral walls when the material properties and the termodynamical state of the sample are suitably chosen. When the elastic energy associated with compression or decompres-sion of the lamellae parallel to very weakly hydrophilic walls is sufficiently large, then changes of the film thickness lead to a switch from the parallel to the perpendicular orientation of the lamellae. Our general arguments are confirmed by explicit mean-field calculations in a lattice vector model. In self-assembling systems such as diblock copolymer melts, binary or ternary surfactant mixtures, lipids etc., various ordered structures occur spontaneously on a nanometer length scale [1–3]. The most common is the lamellar phase [4]. In ternary surfactant mixtures the lamellar phase consists of oil-and water-rich layers separated by monolayers of surfactant. It is natural to expect that the layers are parallel to the confining walls and the parallel orientation of lamellae is commonly assumed. Indeed, near a strongly hydrophilic or hy-drophobic wall a water-rich or an oil-rich layer is adsorbed at the surface respectively, by which the orientation of the subsequent layers is fixed [5–8]. However, when the surface is neutral, i.e. it is neither hydrophilic nor hydrophobic, then neither component is favored and no orientation of amphiphiles is preferred near the wall. Therefore perpendicular rather than parallel orientation of the lamellar phase may be stable between two parallel surfaces that are neither hydrophilic nor hydrophobic (see Fig.1). In the case of very weakly hy-drophilic walls perpendicular orientation was indeed observed in Monte Carlo simulations [8] of the phenomenological Landau-Ginzburg model [3]. Perpendicular orientation should be favoured when the distance between the walls and the period of the lamellar phase do not match. On the other hand, when the distance between the lamellae fits the distance between the weakly hydrophilic walls, parallel orientation can be stable. Films with the lamellae oriented parallelly or perpendicularly to the walls have different mechanical, electrical, optical etc. properties. Therefore the possibility of inducing a switch between the two orientations by changing a control parameter such as the distance between the walls L is potentially very important for various applications. For example, when some electrolyte is added, the electrical conductivity between the confining …