LAUSR

We study the orientational profile of a semi-infinite system of cylinders bounded in two different ways: by a flat and by a curved wall. The latter corresponds to the interior of a spherical shell, where the dimensions of the rods are comparable to the radius of curvature of the container: they have to accomodate to fill the available space, leading to a rich orientation profile. In order to study these problems, we make a mapping onto a three-state Potts model on a semi-infinite lattice, which is solved using a mean-field approach; we fix the boundary conditions on the surface and in the bulk. In the case of a curved surface, the increase in the effective volume interactions towards the bulk, due to compression, is obtained by increasing the nearest neighbor interactions. The mean-field equations are iterated numerically and we obtain various interesting results concerning the free energy and the orientation profile. We show that there is always a first order transition and the stability of the coexistin...