Principal component analysis of the excluded area of two-dimensional hard particles.

The excluded area between a pair of two-dimensional hard particles with given relative orientation is the region in which one particle cannot be located due to the presence of the other particle. The magnitude of the excluded area as a function of the relative particle orientation plays a major role in the determination of the bulk phase behavior of hard particles. We use principal component analysis (PCA) to identify the different types of excluded areas corresponding to randomly generated two-dimensional hard particles modeled as non-self-intersecting polygons and star lines (line segments radiating from a common origin).

The role of sample height in the stacking diagram of colloidal mixtures under gravity.

Bulk phase separation is responsible for the occurrence of stacks of different layers in sedimentation of colloidal mixtures. A recently proposed theory (de las Heras and Schmidt 2013 Soft Matter 9 8636) establishes a unique connection between the bulk phase behaviour and sedimentation-diffusion-equilibrium. The theory constructs a stacking diagram of all possible sequences of stacks under gravity in the limit of very high (infinite) sample heights.

Confinement of two-dimensional rods in slit pores and square cavities.

Using Monte Carlo simulation, we analyse the behaviour of two-dimensional hard rods in four different types of geometric confinement: (i) a slit pore where the particles are confined between two parallel walls with homeotropic anchoring; (ii) a hybrid slit pore formed by a planar and a homeotropic wall; square cavities that frustrate the orientational order by imposing either (iii) homeotropic or (iv) planar wall anchoring. We present results for the state diagram as a function of the packing fraction and the degree of confinement. Under extreme confinement, unexpected states appear with lower symmetries than those of the corresponding stable states in bulk, such as the formation of states that break the anchoring constraints or the symmetry imposed by the surfaces.