Stability of LS and LS2 crystal structures in binary mixtures of hard and charged spheres.

We study by computer simulations the stability of various crystal structures in a binary mixture of large and small spheres interacting either with a hard sphere or a screened-Coulomb potential. In the case of hard-core systems, we consider structures that have atomic prototypes CrB, gammaCuTi, alphaIrV, HgBr2, AuTe2, Ag2Se and the Laves phases (MgCu2, MgNi2, and MgZn2) as well as a structure with space group symmetry 74. By utilizing Monte Carlo simulations to calculate Gibbs free energies, we determine composition versus pressure and constant volume phase diagrams for diameter ratios of q=0.74, 0.76, 0.8, 0.82, 0.84, and 0.85 for the small and large spheres. For diameter ratios 0.76 < or = q < or = 0.84, we find the Laves phases to be stable with respect to the other crystal structures that we considered and the fluid mixture. By extrapolating to the thermodynamic limit, we show that the MgZn2 structure is the most stable one of the Laves structures. We also calculate phase diagrams for equally and oppositely charged spheres for size ratio of 0.73 taking into consideration the Laves phases and CsCl. In the case of equally charged spheres, we find a pocket of stable Laves phases, while in the case of oppositely charged spheres, Laves phases are found to be metastable with respect to the CsCl and fluid phases.

Phase diagrams of charged colloids from thermodynamic integration.

We present full phase diagrams (including solid phases) of spherical charged colloids, using Monte Carlo sampling and thermodynamic integration of the Helmholtz free energy. Colloids and their co- and counterions are described by the primitive model for ionic systems that consists of hard-spheres with central point charges, while the solvent is taken into account solely through its dielectric constant. Two systems are considered: (i) a size-asymmetric system of oppositely charged spheres with size ratios q = 0.3 and 0.5 and (ii) a charge- and size-asymmetric system with colloid charge Q = 10 and counterions of charge -1 in the presence of monovalent added salt. In system (i), for both size ratios, the stable solid phase is equivalent to the NaCl crystal where the oppositely charged spheres take the lattice positions of Na and Cl ions. In system (ii), the phase diagram consists of gas-liquid and fluid-solid coexistence regions. We show that added salt stabilizes the fluid phase and shrinks the fluid-solid coexistence region, in agreement with experimental and theoretical results.

Disappearance of the gas-liquid phase transition for highly charged colloids.

We calculate the full phase diagram of spherical charged colloidal particles using Monte Carlo free energy calculations. The system is described using the primitive model, consisting of explicit hard-sphere colloids and point counterions in a uniform dielectric continuum. We show that the gas-liquid critical point becomes metastable with respect to a gas-solid phase separation at colloid charges Q > or =20 times the counterion charge. Approximate free energy calculations with only one and four particles in the fluid and solid phases, respectively, are used to determine the critical line for highly charged colloids up to Q=2000. We propose the scaling law T*(c) approximately Q(1/2) for this critical temperature.

Layering in sedimentation of suspensions of charged colloids: simulation and theory.

We study the equilibrium sediment of a multicomponent system of charged colloids using primitive model Monte Carlo simulations, which include counterions explicitly. We find separation of the different colloidal components into almost pure layers, where colloids with large charge-to-mass ratio sediment higher in the sample. This effect appears due to a competition between ionic entropy, gravitational energy, and electrostatic energy. Our simulations provide a direct confirmation of recent theoretical predictions on the sedimentation of multicomponent mixtures of charged colloids in regimes with relatively low total densities and low colloidal charges. To explore the limitations of the theory we perform simulations at higher total densities for monodisperse and multicomponent systems and at stronger electrostatic couplings by increasing the colloidal charge for monodisperse suspensions. We find good agreement between theory and simulation when the colloidal charge is increased in the monodisperse case. However, we find deviations between simulations and theory upon increasing the total densities in the monodisperse and multicomponent systems. The density profiles obtained from simulations are more homogeneous than those predicted by theory. The spontaneous formation of layered structures predicted by the theory and found by simulation can serve as a useful tool to separate different components from a mixture of charged colloids.

Prediction and observation of crystal structures of oppositely charged colloids.

We studied crystal structures in mixtures of large and small oppositely charged spherical colloids with size ratio 0.31 using Monte Carlo simulations and confocal microscopy. We developed an interactive method based on simulated annealing to predict new binary crystal structures with stoichiometries from 1 to 8. Employing these structures in Madelung energy calculations using a screened Coulomb potential, we constructed a ground-state phase diagram, which shows a remarkably rich variety of crystals. Our phase diagram displays colloidal analogs of simple-salt structures and of the doped fullerene C60 structures, but also novel structures that do not have an atomic or molecular analog. We found three of the predicted structures experimentally, which provides confidence that our method yields reliable results.

CuAu structure in the restricted primitive model and oppositely charged colloids.

We study the phase behavior of oppositely charged equal-size hard spheres both theoretically and experimentally, using Monte Carlo simulations and confocal microscopy. In the simulations, two systems are considered: the restricted primitive model (RPM) and a system of screened Coulomb particles. We construct the phase diagrams of both systems by computer simulations and predict a novel solid phase that has the CuAu structure. In addition, the CuAu structure is observed experimentally in a system of oppositely charged colloids. The qualitative agreement between the RPM, the screened Coulomb system, and the experiments shows that colloids form a suitable model system to study phase behavior in ionic systems.

Effect of three-body interactions on the phase behavior of charge-stabilized colloidal suspensions.

We study numerically the effect of attractive triplet interactions on the phase behavior of suspensions of highly charged colloidal particles at low salinity. In our computer simulations, we employ the pair and triplet potentials that were obtained from a numerical Poisson-Boltzmann study [Phys. Rev. E 66, 011402 (2002)]]. On the basis of free energy calculations, we determine the phase diagram of an aqueous suspension of identical spheres of diameter sigma=32 nm and charge Z=80 as a function of colloid concentration and salinity, both for the purely pairwise additive system and for the system with pair and triplet interactions. The main effect of including the triplet interactions is a destabilization of the body-centered-cubic (bcc) crystal phase in favor of the face-centered-cubic (fcc) crystal phase. As a consequence the phase diagram features the coexistence of a rather dilute fluid with an almost-close-packed fcc phase at low salinity and bcc-fcc coexistence with a big density jump at intermediate salinity. The triplet attractions do not affect the phase behavior at sufficiently high salinity; under these conditions the system is well described by the pairwise potential.