Spatially modulated phases in monolayers of mixed surfactants

We present a theoretical study of spatially modulated phases in self-assembled monolayers of mixed surfactants. We propose two models which are appropriate, respectively, for monolayers at a fluid-fluid interface and monolayers on a solid substrate. We show that in both cases, the molecular shape asymmetry, coupled with the local composition variation, can lead to spontaneous formation of periodic structures. In the case of liquid-supported monolayers, the molecular shape asymmetry is manifested as a spontaneous curvature of each component of the f?lm, which induces periodic variations both in the composition of the amphiphiles and in the height profile of the interface (ripples). In the case of solid-supported monolayers, the shape asymmetry is reflected in the spontaneous splay of the orientation of the amphiphiles, and the spatial modulation involves the composition as well as the orientation of the amphiphilic molecules. We analyze these models in some detail near the critical region, where we highlight the roles played by various length scales in determining the critical wavelength. We show that gravity has some very subtle and nontrivial effects for a liquid-supported, tension-free monolayer. We also present some preliminary results for the low temperature cases.