INCLUSIONS IN THIN SMECTIC FILMS

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