Gravity-induced aging in glasses of colloidal hard spheres

The influence of gravity on the long-time behavior of the mean squared displacement in glasses of polydisperse colloidal hard spheres was studied by means of real-space fluorescent recovery after photobleaching. We present, for the first time, a significant influence of gravity on the mean squared displacements of the particles. In particular, we observe that systems which are glasses under gravity (with a gravitational length on the order of tens of micrometers) show anomalous diffusion over several decades in time if the gravitational length is increased by an order of magnitude. No influence of gravity was observed in systems below the glass transition density. We show that this behavior is caused by gravity dramatically accelerating aging in colloidal hard sphere glasses. This behavior explains the observation that colloidal hard sphere systems which are a glass on Earth rapidly crystallize in space.     

Dynamic broadening of the crystal-fluid interface of colloidal hard spheres

We investigate the structure and dynamics of the crystal-fluid interface of colloidal hard spheres in real space by confocal microscopy. Tuning the buoyancy of the particles allows us to study the interface close to and away from equilibrium. We find that the interface broadens from 8-9 particle diameters close to equilibrium to 15 particle diameters away from equilibrium. Furthermore, the interfacial velocity, i.e., the velocity by which the interface moves upwards, increases significantly. The increasing gravitational drive leads to supersaturation of the fluid above the crystal surface. This dramatically affects crystal nucleation and growth, resulting in the observed dynamic broadening of the crystal-fluid interface.     

Experimental observation of structural crossover in binary mixtures of colloidal hard spheres

Using confocal microscopy, we investigate the structure of binary mixtures of colloidal hard spheres with size ratio q=0.61. As a function of the packing fraction of the two particle species, we observe a marked change of the dominant wavelength in the pair-correlation function. This behavior is in excellent agreement with a recently predicted structural crossover in such mixtures. In addition, the repercussions of structural crossover on the real-space structure of a binary fluid are analyzed. We suggest a relation between crossover and the lateral extension of networks containing only equally-sized particles that are connected by nearest-neighbor bonds. This is supported by Monte Carlo simulations which are performed at different packing fractions and size ratios.     

Brownian dynamics simulations of colloidal hard spheres. Effects of sample dimensionality on self-diffusion

The self-diffusion coefficients of colloidal hard spheres were determined by Brownian dynamics (BD) computer simulations using a new efficient algorithm for treatment of the hard-sphere interactions. Calculations were done on an Apple PC type MacIIcx and on a Micro VAX 3000, considering samples in two and three dimensions at varying particle concentrations. Our results in three dimensions are compared with experimental results from our own group which were obtained by forced Rayleigh scattering (FRS), and with numerical results from a dynamical Monte Carlo simulation by Cichocki and Hinsen. Good agreement with the latter was found for particle volume fractions up to 0.40. Differences in the dynamical behavior of our numerically treated 2D and 3D samples are discussed using a simple geometrical model to enable comparison of particle concentrations in samples with different dimensionality.     

Brownian dynamics of polydisperse colloidal hard spheres: Equilibrium structures and random close packings

Recently we presented a new technique for numerical simulations of colloidal hard-sphere systems and showed its high efficiency. Here, we extend our calculations to the treatment of both 2- and 3-dimensional monodisperse and 3-dimensional polydisperse systems (with sampled finite Gaussian size distribution of particle radii), focusing on equilibrium pair distribution functions and structure factors as well as volume fractions of random close packing (RCP). The latter were determined using in principle the same technique as Woodcock or Stillinger had used. Results for the monodisperse 3-dimensional system show very good agreement compared to both pair distribution and structure factor predicted by the Percus-Yevick approximation for the fluid state (volume fractions up to 0.50). We were not able to find crystalline 3d systems at volume fractions 0.50–0.58 as shown by former simulations of Reeet al. or experiments of Pusey and van Megen, due to the fact that we used random start configurations and no constraints of particle positions as in the cell model of Hoover and Ree, and effects of the overall entropy of the system, responsible for the melting and freezing phase transitions, are neglected in our calculations. Nevertheless, we obtained reasonable results concerning concentration-dependent long-time selfdiffusion coefficients (as shown before) and equilibrium structure of samples in the fluid state, and the determination of the volume fraction of random close packing (RCP, glassy state). As expected, polydispersity increases the respective volume fraction of RCP due to the decrease in free volume by the fraction of the smaller spheres which fill gaps between the larger particles.     

Mixtures of hard spherocylinders and hard spheres

Monte Carlo simulations have been performed for equimolar mixtures of hard prolate spherocylinders of length: breadth ratio 2:1 and hard spheres, in the fluid region. Two systems have been studied. In the first the breadth of the spherocylinder was equal to the hard sphere diameter, and in the second system both components were of equal molecular volume.

The compressibility factor, PV/NkT, has been obtained for both mixtures at four reduced densities (packing fractions) from 0·20 to 0·45. The results have been compared with the predictions of several analytical equations appropriate to mixtures of hard convex molecules, and an equation due to Pavlicek et al. was found to be very accurate. The results have been used to calculate the excess volumes of mixing at constant pressure, in an attempt to establish the relative importance of the effects of differences in molecular volume and shape on the thermodynamic properties.

The structural properties of the mixtures have also been investigated by calculating pair distribution functions for the three types of pair interactions present in these mixtures.     

Brownian dynamics of colloidal hard spheres. 3. Extended investigations at the phase transition regime

The phase behavior of hard-sphere colloidal systems in the volume fraction regime 0.46<<0.64 has been studied in detail using a new and efficient algorithm to treat the nonanalytic interaction pair potential. In particular the influence of various initial configurations such as purely random and facecentered cubic (FCC) has been investigated, and former simulations have been extended toward much longer time scales. Thus, in the case of randomly initiated systems, crystallization could be suppressed for a comparably long time (500 _R , where _R is the structural relaxation time) where the system remained in a metastable glassy state. The concentration dependence of the long-time self-diffusion coefficients of these systems has been analyzed according to free volume theory (Doolittle equation). Numerical data fit excellently to the theoretical predictions, and the volume fraction of zero particle mobility was found close to the expected value of random close packing. In case of the FCC initiated systems, samples remained crystalline within the simulated evolution time of 500 _R if their volume fraction was above the predicted freezing transition _F = 0.494, whereas at lower concentrations rapid melting into a fluidlike disordered state is observed. It should be noted that this algorithm, which neglects higher-order correlations, considering only direct pair interactions, nevertheless yields the correct hard-sphere crystallization phase behavior as predicted in the literature.     

Kinetic theory of hard spheres

Kinetic equations for the hard-sphere system are derived by diagrammatic techniques. A linear equation is obtained for the one-particle-one particle equilibrium time correlation function and a nonlinear equation for the one-particle distribution function in nonequilibrium. Both equations are nonlocal, noninstantaneous, and extremely complicated. They are valid for general density, since statistical correlations are taken into account systematically. This method derives several known and new results from a unified point of view. Simple approximations lead to the Boltzmann equation for low densities and to a modified form of the Enskog equation for higher densities.     

Colour conductivity of hard spheres

We present an analytic solution for the d-dimensional (d > 1) hard-sphere free flight trajectories in a thermostatted colour field. The solution shows that particles can only reach a finite distance in the direction perpendicular to the field in the absence of collisions. Using a numerical algorithm we designed to simulate many-body hard-sphere systems with curved trajectories, we study the onset of the instability leading to phase separation in the two-dimensional case for a range of field strengths and three densities. For the two fluid densities we find that phase separation occurs for sufficiently strong fields regardless of the initial configuration, and that the phase-separated state eventually becomes a collisionless, non-ergodic steady state. For solid densities the phase-separated configuration is stable and conducting, but is not an attractor for other charge distributions because of the impossibility of particle rearrangement.     

Reentrant transitions in colloidal or dusty plasma bilayers

The phase diagram of crystalline bilayers of particles interacting via a Yukawa potential is calculated for arbitrary screening lengths and particle densities. Staggered rectangular, square, rhombic, and triangular structures are found to be stable including a first-order transition between two different rhombic structures. For varied screening length at fixed density, one of these rhombic phases exhibits both a single and even a double reentrant transition. Our predictions can be verified experimentally in strongly confined charged colloidal suspensions or dusty plasma bilayers.     

Dissipative dynamics for hard spheres

The dynamics for a system of hard spheres with dissipative collisions is described at the levels of statistical mechanics, kinetic theory, and simulation. The Liouville operator(s) and associated binary scattering operators are defined as the generators for time evolution in phase space. The BBGKY hierarchy for reduced distribution functions is given, and an approximate kinetic equation is obtained that extends the revised Enskog theory to dissipative dynamics. A Monte Carlo simulation method to solve this equation is described, extending the Bird method to the dense, dissipative hard-sphere system. A practical kinetic model for theoretical analysis of this equation also is proposed. As an illustration of these results, the kinetic theory and the Monte Carlo simulations are applied to the homogeneous cooling state of rapid granular flow.     

Phase diagram of dipolar hard and soft spheres: manipulation of colloidal crystal structures by an external field

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.     

Equilibrium fluid-solid coexistence of hard spheres

We present a tethered Monte Carlo simulation of the crystallization of hard spheres. Our method boosts the traditional umbrella sampling to the point of making practical the study of constrained Gibbs' free energies depending on several crystalline order parameters. We obtain high-accuracy estimates of the fluid-crystal coexistence pressure for up to 2916 particles (enough to accommodate fluid-solid interfaces). We are able to extrapolate to infinite volume the coexistence pressure [p(co)=11.5727(10)k(B)T/σ(3)] and the interfacial free energy [γ({100})=0.636(11)k(B)T/σ(2)].