The freezing transition in a classical three-dimensional system of rounded hard cubes with fixed, equal orientations is studied by computer simulation and fundamental-measure density functional theory. By switching the rounding parameter s from zero to one, one can smoothly interpolate between cubes with sharp edges and hard spheres. The equilibrium phase diagram of rounded parallel hard cubes is computed as a function of their volume fraction and the rounding parameter s. The second order freezing transition known for oriented cubes at s = 0 is found to be persistent up to s = 0.65. The fluid freezes into a simple-cubic crystal which exhibits a large vacancy concentration. Upon a further increase of s, the continuous freezing is replaced by a first-order transition into either a sheared simple cubic lattice or a deformed face-centered cubic lattice with two possible unit cells: body-centered orthorhombic or base-centered monoclinic. In principle, a system of parallel cubes could be realized in experiments on colloids using advanced synthesis techniques and a combination of external fields.

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Abstract. We review recent progress in the theoretical description of anisotropic hard colloidal particles. The shapes considered range from rods and dumbbells to rounded cubes, polyhedra to biaxial particles with arbitrary shape. Our focus is on both static and dynamical density functional theory and on computer simulations. We describe recent results for the structure, dynamics and phase behaviour in the bulk and in various confining geometries, e.g. established by two parallel walls which reduce the dimensionality of the system to two dimensions. We also include recent theoretical modelling for active particles, which are autonomously driven by some intrinsic motor, and highlight their fascinating nonequilibrium dynamics and collective behaviour.

Using both dynamical density functional theory and particle-resolved Brownian dynamics simulations, we explore the flow of two-dimensional colloidal solids and fluids driven through a linear channel with a constriction. The flow is generated by a constant external force acting on all colloids. The initial configuration is equilibrated in the absence of flow and then the external force is switched on instantaneously. Upon starting the flow, we observe four different scenarios: a complete blockade, a monotonic decay to a constant particle flux (typical for a fluid), a damped oscillatory behaviour in the particle flux, and a long-lived stop-and-go behaviour in the flow (typical for a solid). The dynamical density functional theory describes all four situations but predicts infinitely long undamped oscillations in the flow which are always damped in the simulations. We attribute the mechanisms of the underlying stop-and-go flow to symmetry conditions on the flowing solid. Our predictions are verifiable in real-space experiments on magnetic colloidal monolayers which are driven through structured microchannels and can be exploited to steer the flow throughput in microfluidics.

In this article we examine the dynamics of a colloidal particle driven by a modulated force over a sinusoidal optical potential energy landscape. Coupling between the competing frequencies of the modulated drive and that of particle motion over the periodic landscape leads to synchronisation of particle motion into discrete modes. This synchronisation manifests as steps in the average particle velocity, with mode locked steps covering a range of average driving velocities. The amplitude and frequency dependence of the steps are considered, and compared to results from analytic theory, Langevin dynamics simulations, and dynamic density functional theory. Furthermore, the critical driving velocity is studied, and simulation used to extend the range of conditions accessible in experiments alone. Finally, state diagrams from experiment, simulation, and theory are used to show the extent of the dynamically locked modes in two dimensions, as a function of both the amplitude and frequency of the modulated drive.