Inclusions in Thin Smectic Filns

We study theoretically the behaviour of inclusions in thin films of smectic-A liquid crystal consisting of a stack of regularly spaced membranes. Such membranes are frequently formed in thin diblock copolymer films or in solutions of amphiphilic surfactants. Inclusions, such as colloidal particles or large proteins, couple locally to the smectic and may deform the membranes over a large length scale. Using the Landau-de Gennes description of smectic liquid crystals we obtain the deformation field of the membranes for the two cases of a freely suspended film and a film on a rigid substrate. In the first case we compare and contrast with earlier work on inclusions confined between two membranes and in a lamellar phase of infinite thickness. We show that the existence of an overshoot in the deformation of the layers is intrinsically related to the finite size of the sample. This leads to qualitative differences in the interaction potential between two inclusions for finite and infinite systems. The interaction, monotonically attractive for infinite systems, becomes repulsive at large distance is the sample is finite. We show that the equilibrium position of the particle depends on the surface tension at the film boundary and give quantitative predictions for the particle-induced deformation of the membranes.