Colloidal suspensions are widely used to study processes such as melting, freezing and glass transitions. This is because they display the same phase behaviour as atoms or molecules, with the nano- to micrometre size of the colloidal particles making it possible to observe them directly in real space. Another attractive feature is that different types of colloidal interactions, such as long-range repulsive, short-range attractive, hard-sphere-like and dipolar, can be realized and give rise to equilibrium phases. However, spherically symmetric, long-range attractions (that is, ionic interactions) have so far always resulted in irreversible colloidal aggregation. Here we show that the electrostatic interaction between oppositely charged particles can be tuned such that large ionic colloidal crystals form readily, with our theory and simulations confirming the stability of these structures. We find that in contrast to atomic systems, the stoichiometry of our colloidal crystals is not dictated by charge neutrality; this allows us to obtain a remarkable diversity of new binary structures. An external electric field melts the crystals, confirming that the constituent particles are indeed oppositely charged. Colloidal model systems can thus be used to study the phase behaviour of ionic species. We also expect that our approach to controlling opposite-charge interactions will facilitate the production of binary crystals of micrometre-sized particles, which could find use as advanced materials for photonic applications.

Three-dimensional photonic crystals, or periodic materials, that do not allow the propagation of photons in all directions with a wavelength in the visible region have not been experimentally fabricated, despite there being several potential structures and the interesting applications and physics that this would lead to. We show using computer simulations that two structures that would enable a bandgap in the visible region, diamond and pyrochlore, can be self-assembled in one crystal structure from a binary colloidal dispersion. In our approach, these two structures are obtained as the large (Mg) and small (Cu) sphere components of the colloidal analogue of the MgCu(2) Laves phase, whose growth can be selected and directed using appropriate wall patterning. The method requires that the particles consist of different materials, so that one of them can be removed selectively after drying (for example, by burning or dissolution). Photonic calculations show that gaps appear at relatively low frequencies indicating that they are robust and open for modest contrast, enabling fabrication from more materials.

Using computer simulations we study the phase behaviour of hard spheres with repulsive Yukawa interactions and with the repulsion set to zero at distances larger than a density-dependent cut-off distance. Earlier studies based on experiments and computer simulations in colloidal suspensions have shown that the effective colloid-colloid pair interaction that takes into account many-body effects resembles closely this truncated Yukawa potential. We present a phase diagram for the truncated Yukawa system by combining Helmholtz free energy calculations and the Kofke integration method. Compared to the non-truncated Yukawa system we observe (i) a radical reduction of the stability of the body centred cubic (BCC) phase, (ii) a wider fluid region due to instability of the face centred cubic (FCC) phase and due to a re-entrant fluid phase and (iii) hardly any shift of the (FCC) melting line when compared with the (BCC) melting line for the full Yukawa potential for sufficiently high salt concentrations, i.e. truncation of the potential does not affect the location of the solid-fluid line but replaces only the BCC phase with the FCC at the melting line. We compare our results with earlier results on the truncated Yukawa potential and with results from simulations where the full many-body Poisson-Boltzmann problem is solved.

Phase diagrams of hard and soft spheres with a fixed dipole moment are determined by calculating the Helmholtz free energy using simulations. The pair potential is given by a dipole-dipole interaction plus a hard-core and a repulsive Yukawa potential for soft spheres. Our system models colloids in an external electric or magnetic field, with hard spheres corresponding to uncharged and soft spheres to charged colloids. The phase diagram of dipolar hard spheres shows fluid, face-centered-cubic (fcc), hexagonal-close-packed (hcp), and body-centered-tetragonal (bct) phases. The phase diagram of dipolar soft spheres exhibits, in addition to the above mentioned phases, a body-centered-orthorhombic (bco) phase, and it agrees well with the experimental phase diagram [Nature (London) 421, 513 (2003)]. Our results show that bulk hcp, bct, and bco crystals can be realized experimentally by applying an external field.