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Seminário de Mecânica Estatística

Apresentador: Dora Izzo, IF UFRJ

We study the orientational profile of a system of small cylinders inside a container of curved surface. We are interested in situations in which the ratio between size of the cylinders and the surface radius of curvature is large enough so that rods have to accomodate to fill the space, producing a very interesting orientation profile. In order to study this problem, we map it onto a three-state Potts model on a semi infinite two dimensional lattice and use a mean-field approach; boundary conditions on the surface and in the bulk are fixed. Towards the bulk the alignment of the rods is enhanced due to the curvature: there is an increase in the effective volume interactions. This effect is obtained by introducing increasing intralayer nearest neighbor interactions. The mean field equations are iterated numerically and we obtain various interesting results that show how the profile accommodates under different anchoring and bulk boundary conditions. There is always a first order transition; when the surface is disordered and the bulk ordered, the profile may be smooth or present a step with a width that depends on the degree of disorder on the surface and on the rate of increase of the interactions. We make connections with other theoretical predictions and experimental results.