Phase behavior of hard colloidal platelets using free energy calculations

Abstract

We investigate the phase behavior of a model for colloidal hard platelets and rigid discotic molecules: oblate hard spherocylinders (OHSC). We perform free energy calculations using Monte Carlo simulations to map out the phase diagram as a function of the aspect ratio L/D of the particles. The phase diagram displays a stable isotropic phase, a nematic liquid crystal phase for L/D ≤ 0.12, a columnar phase for L/D 0.3, a tilted crystal phase for L 0.45, and an aligned crystal phase for L/D 0.45. We compare the results to the known phase diagram of hard cut spheres. Thin cut spheres are almost cylinder-shaped, while the interactions between real discotic mesogens and colloidal platelets are more consistent with the toroidal rims of the OHSC. Since the shapes of the OHSC and the cut spheres are otherwise similar, the phase diagrams of the two types of particles are quite akin. However, the tilted crystal phase for OHSC, which is of a crystal type that is frequently found in experiments on disklike molecules, has not been found for hard cut spheres. Furthermore, although we have found a cubatic phase, it was shown to be definitely unstable, whereas the stability of the cubatic phase of cut spheres is still disputed. Finally, we also show that the phase boundaries differ significantly from those for cut spheres. These are remarkable consequences of a subtle change in particle shape, which show that for a detailed comparison with the phase behavior of experimental particles, the OHSC should be used as a model particle.

Interplay of anisotropy in shape and interactions in charged platelet suspensions

“…Our phase diagram highlights the importance of intrinsic anisotropy of the electrostatic potential between charged platelets and shows that the phase diagram of charged disks can not be obtained by a simple rescaling of particles dimensions from the phase diagram of hard spherocylinders [50] or uniaxial ellipsoidal particles [52]. Nevertheless in the limit of very low ionic strengths where the potential is isotropic, we observe the same trend as ellipsoidal particles with aspect ratios close to unity where the system goes from an isotropic fluid to a plastic crystal and finally an orientationally ordered crystal with FCC structure upon increase of density albeit with a different symmetry than the one observed for charged disks (BCC symmetry).…”

“…In the typical example, ρ * = 8 and κσ = 10, shown in Fig. 12, a = 0.73σ which is smaller than one particle diameter, indicating that the disks are interdigitated, similar to the observed columnar structures for hard spherocylinders [50]. The hexagonal nature of the lattice is also inspected by computing the hexagonal bond-orientational order parameter q 6 , (see Appendix B for its definition).…”

Phase diagram of two-dimensional hard ellipses

“…One should note that the overall appearance obtained for the 2D phase diagram (Fig. 7) markedly resembles that of 3D systems of prolate and oblate ellipsoids, spherocylinders, and cut-spheres with variable aspect ratio (see references 32,[45][46][47] ). In particular, the isotropic-nematic transition line goes up in occupied area (volume) fraction upon decreasing the particle aspect ratio to eventually meet up with a strongly first-order and almost anisometric-independent fluid-solid transition.…”

Predicting patchy particle crystals: Variable box shape simulations and evolutionary algorithms

“…10,16,17,42 As the two methods covered here have both advantages as well as shortcomings, we list potential improvements in the following. A possibility to overcome kinetic trapping in gel-like states for variable box-shape simulations is to combine this method with moves that correspond to larger leaps in configuration space, comparable to mating and mutation operations of an evolutionary algorithm; this would move the method further away from being a thermodynamic approach into the direction of an optimization technique.…”

“…9,10,16,17 The present paper is dedicated to the prediction of crystal structures of patchy particle systems. To be more specific, we study a variety of patchy models that have been proposed in literature 18 and search for their crystal structures, using both the variable box shape simulation method as well as an optimization approach based on ideas of evolutionary algorithms.…”