Particulate inclusions in a lamellar phase

Abstract

We study theoretically the effect of colloidal inclusions in a smectic liquid crystal. Our treatment is appropriate for any type of particle that exerts a small force perpendicular to the nearest layers. This force may either be outward, forming a local 'bulge,' or inwards, pinching the neighboring membranes together. We calculate both the distortion field and associated energy due to one such inclusion, as well as the membrane mediated two body interaction potential. Aggregation of particles to form polydisperse disklike assemblies is treated using a simple Flory-Huggins theory. In this case there exists a characteristic aggregate radius $\sqrt{\ensuremath{\lambda}d}$, where \ensuremath{\lambda} is the usual characteristic smectic penetration length and d is the layer spacing. A novel feature of this system is that 'large' disklike aggregates of this size may be formed. There is no such length for disklike aggregation in solution, where it is difficult to obtain aggregates much bigger than the particle size. Our treatment of aggregation neglects interaggregate interactions studied in more detail elsewhere. In this approximation, we find that for certain systems, such as strongly segregated copolymer melts and stacks of surfactant bilayers stabilized by electrostatic interactions, some significant aggregation is occurring. On the other hand we predict only weak aggregation in a stack of flexible surfactants bilayers governed by the Helfrich interaction. We use our results, combined with a simplistic mean field theory, to study an inclusion driven binding transition.