By: Andrew Masters
From: School of Chemical Engineering and Analytical Science, University of Manchester, Manchester, M60 1QD.
At: Complexo Interdisciplinar, Anfiteatro
We present Monte Carlo simulation results and theoretical predictions for systems of truncated hard spheres (width L and thickness D) both in the bulk and in confined geometries. In the latter case we observe novel frustration effects. In the bulk, thin discs with L/D = 0.1, show isotropic – nematic – columnar transitions with increasing pressure. Thicker discs, with L/D = 0.2, instead show an isotropic – cubatic transition. In the cubatic phase, the discs are positionally disordered but exhibit a cubic orientational symmetry – i.e. the particles point preferentially along orthogonal x, y and z axes. This transition was first observed by Veerman and Frenkel  and we have now confirmed the stability of this cubatic phase with very extensive simulation studies. This transition is predicted theoretically by a high level virial expansion, but in order to capture the necessary inter-particle correlations, at least five virials must be calculated. The question arises as to what happens to these phases when they are confined. The nematic phase has been previously studied in planar geometry by Galindo et al. , but here we present results for the cubatic and columnar phases when they are confined both between planar walls and also within a cylinder. For the thicker discs with L/D = 0.2, we present profiles of the density and the nematic and cubatic order parameters and show that the effect of confinement is to lower the isotropic-cubatic transition pressure. Even in a planar geometry, however, the walls never stabilize the nematic phase sufficiently to allow it to be observed. For the thinner discs with L/D = 0.1, we examine the effects of confinement on the columnar phase. In circumstances where an integer number of columns do not fit neatly into the confining box, our simulations indicates the columns either tilt or, more dramatically, break up to form a cubatic-like structure that more effectively fills space.