Affiliation:
1. Department of Physics and Astronomy, University of Pennsylvania, 209 South 33rd St., Philadelphia, PA 19104, USA
Abstract
My model, it has three layers,
Three layers is nematic.
And had it just two layers,
it would be a smectic.
We study a reduced model of smectic formation in two dimensions where the particles occupy three equally spaced layers. The role of particle geometry comes in through the interactions between particles on the central layer and those above and below. The system is understood to be a perfect smectic when the central layer is empty, and nematic when all three are equally occupied. It is possible to compute the free energies of these states exactly. We find that the free energy of the nematic can only exceed that of the perfect smectic if the particle tips are sufficiently wide. While not an indication of a true smectic transition, this mirrors the fact that ellipsoids do not make a smectic but sphero-cylinders do.