Effect of polydispersity on the crystallization kinetics of suspensions of colloidal hard spheres when approaching the glass transition

We present a comprehensive study of the solidification scenario in suspensions of colloidal hard spheres for three polydispersities between 4.8% and 5.8%, over a range of volume fractions from near freezing to near the glass transition. From these results, we identify four stages in the crystallization process: (i) an induction stage where large numbers of precursor structures are observed, (ii) a conversion stage as precursors are converted to close packed structures, (iii) a nucleation stage, and (iv) a ripening stage. It is found that the behavior is qualitatively different for volume fractions below or above the melting volume fraction. The main effect of increasing polydispersity is to increase the duration of the induction stage, due to the requirement for local fractionation of particles of larger or smaller than average size. Near the glass transition, the nucleation process is entirely frustrated, and the sample is locked into a compressed crystal precursor structure. Interestingly, neither polydispersity nor volume fraction significantly influences the precursor stage, suggesting that the crystal precursors are present in all solidifying samples. We speculate that these precursors are related to the dynamical heterogeneities observed in a number of dynamical studies.     

Polydisperse hard spheres at a hard wall

The structural properties of polydisperse hard spheres in the presence of a hard wall are investigated via Monte Carlo simulation and density functional theory (DFT). Attention is focused on the local density distribution rho(sigma,z), measuring the number density of particles of diameter sigma at a distance z from the wall. Estimates of rho(sigma,z) are obtained for bulk volume fractions eta(b)=0.2 and eta(b)=0.4, and for two choices of the bulk parent distribution: a top-hat form, which we study for degrees of polydispersity delta=11.5% and delta=40.4%, and a truncated Schulz form having delta=40.7%. Excellent overall agreement is found between the DFT and simulation results, particularly at eta(b)=0.2. A detailed analysis of rho(sigma,z) confirms the presence of oscillatory size segregation effects, as observed in a previous DFT study [I. Pagonabarraga, M. E. Cates, and G. J. Ackland, Phys. Rev. Lett. 84, 911 (2000)]. For large delta, the character of these oscillation is observed to depend strongly on the shape of the parent distribution. In the vicinity of the wall, attractive sigma-dependent depletion interactions are found to greatly enhance the density of the largest particles. The local degree of polydispersity delta(z) is suppressed in this region, while further from the wall it exhibits oscillations.     

Polymer induced changes of the crystallization scenario in suspensions of hard sphere like microgel particles

We investigated the crystallization scenario of highly cross linked polystyrene particles dispersed in the good solvent 2-ethylnaphtalene and their mixtures with non-adsorbing low molecular weight polysterene polymer using time resolved static light scattering. The samples were prepared slightly below the melting volume fraction of the polymer free system. For the polymer free samples, we obtained polycrystalline solids via crystallization scenario known from hard sphere suspensions with little competition of wall crystal formation. Addition of non-adsorbing low molecular weight polystyrene polymer leads to a considerably slowing down of the bulk crystallization kinetics. We observed a delay of the precursor to crystal conversion for the bulk crystallization while the induction times for the wall nucleation are reduced. The increased polymer concentration thus shifts the balance between the two competing crystallization pathways giving the possibility to tune the relative amount of wall based crystals.     

On the caging number of two- and three-dimensional hard spheres

Local structural arrest in random packings of colloidal or granular spheres is quantified by a caging number, defined as the average minimum number of randomly placed spheres on a single sphere that immobilize all its translations. We present an analytic solution for the caging number for two-dimensional hard disks immobilized by neighbor disks which are placed at random positions under the constraint of a nonoverlap condition. Immobilization of a disk with radius r = 1 by arbitrary larger neighbor disks with radius r > or = 1 is solved analytically, whereas for contacting neighbors with radius 0 < r < 1, the caging number can be evaluated accurately with an approximate excluded volume model that also applies to spheres in higher Euclidean dimension. Comparison of our exact two-dimensional caging number with studies on random disk packing indicates that it relates to the average coordination number of random loose packing, whereas the parking number is more indicative for coordination in random dense packing of disks.     

On the relation between virial coefficients and the close-packing of hard disks and hard spheres

The question of whether the known virial coefficients are enough to determine the packing fraction η(∞) at which the fluid equation of state of a hard-sphere fluid diverges is addressed. It is found that the information derived from the direct Pade? approximants to the compressibility factor constructed with the virial coefficients is inconclusive. An alternative approach is proposed which makes use of the same virial coefficients and of the equation of state in a form where the packing fraction is explicitly given as a function of the pressure. The results of this approach both for hard-disk and hard-sphere fluids, which can straightforwardly accommodate higher virial coefficients when available, lends support to the conjecture that η(∞) is equal to the maximum packing fraction corresponding to an ordered crystalline structure.     

Templated crystallization of octadecanol on patterned nanoassemblies

A serial templating methodology using linked aminosilane/stannane units and simple beaker chemistry yields thin film nanoassemblies on semiconductor surfaces that provide nucleating sites for crystallization of octadecanol, the morphologies of which could be tailored using subtle variations in the backbone structure of bridged aminosilane/stannanes.     

Inclusion-mediated lipid organization in supported membranes on a patterned substrate

We theoretically investigate the effects of inclusions on the domain formation in mixed lipid bilayers supported on a geometrically patterned substrate. It is found that the inclusions may distribute quite differently with varying volume fraction and size of inclusions. The distribution of inclusions will effectively change the spontaneous curvature of the inclusion-rich lipid domains, and consequently can sort the lipid domains in the supported bilayers. By varying the volume fraction and size of inclusions, we obtain a rich variety of laterally organized lipid bilayers and reveal some interesting transitions between these structures. The present model provides a possible strategy to control the domain formation in the supported membranes, and may yield some theoretical insight into the design of biosensors by the reorganization of lipids and inclusions.     

On the impossibility of defining adhesive hard spheres as sticky limit of a hard-sphere-Yukawa potential

For fluids of molecules with short-ranged hard-sphere-Yukawa (HSY) interactions, it is proven that the Noro-Frenkel "extended law of corresponding states" cannot be applied down to the vanishing attraction range, since the exact HSY second virial coefficient diverges in such a limit. It is also shown that, besides Baxter's original approach, a fully correct alternative definition of "adhesive hard spheres" can be obtained by taking the vanishing-range-limit (sticky limit) not of a Yukawa tail, as is commonly done, but of a slightly different potential with a logarithmic-Yukawa attraction.     

Metastable states in the system of hard spheres

Approximate equations of the theory of liquids were applied to analyze the special features of the structural behavior of the system of hard spheres in the region of densities at which crystals are stable. Correlation functions for the liquid metastable state were obtained. The correlation functions of crystal-like metastable states that can exist under the same conditions as liquid metastable states are also considered. The reliability of the results is substantiated by a thermodynamic comparison with the data obtained using analytic equations of state.     

Viscosity of hard sphere suspensions

A simple functional representation of the concentration dependence of the low-shear viscosity eta of hard sphere suspensions is proposed. The representation, which agrees with published literature at all volume fractions phi, has a hitherto-unremarked transition in its functional form at phi approximately 0.42 identical with phi(t). phi(t) is definitely less than the volume fraction 0.49 of the hard sphere melting transition.     

Diffusion of spheres in crowded suspensions of rods

Translational tracer diffusion of spherical macromolecules in crowded suspensions of rodlike colloids is investigated. Experiments are done using several kinds of spherical tracers in fd-virus suspensions. A wide range of size ratios L/2a of the length L of the rods and the diameter 2a of the tracer sphere is covered by combining several experimental methods: fluorescence correlation spectroscopy for small tracer spheres, dynamic light scattering for intermediate sized spheres, and video microscopy for large spheres. Fluorescence correlation spectroscopy is shown to measure long-time diffusion only for relatively small tracer spheres. Scaling of diffusion coefficients with a/xi, predicted for static networks, is not found for our dynamical network of rods (with xi the mesh size of the network). Self-diffusion of tracer spheres in the dynamical network of freely suspended rods is thus fundamentally different as compared to cross-linked networks. A theory is developed for the rod-concentration dependence of the translational diffusion coefficient at low rod concentrations for freely suspended rods. The proposed theory is based on a variational solution of the appropriate Smoluchowski equation without hydrodynamic interactions. The theory can, in principle, be further developed to describe diffusion through dynamical networks at higher rod concentrations with the inclusion of hydrodynamic interactions. Quantitative agreement with the experiments is found for large tracer spheres, and qualitative agreement for smaller spheres. This is probably due to the increasing importance of hydrodynamic interactions as compared to direct interactions as the size of the tracer sphere decreases.     

Phase separation of polymer-dispersed liquid crystals on a chemically patterned substrate

The surface-induced structure formation of polymer-dispersed liquid crystals (PDLCs) on a chemically patterned substrate was studied for the first time. The patterns on the substrate were successfully transferred to the PDLC film, resulting in alternating LC-rich and polymer-rich phases. This simple approach offers a new means of organizing micrometer-sized LC domains into well-ordered structures in a polymer matrix of PDLCs.     

Self-diffusion in two-dimensional hard ellipsoid suspensions

We studied the self-diffusion of colloidal ellipsoids in a monolayer near a flat wall by video microscopy. The image processing algorithm can track the positions and orientations of ellipsoids with subpixel resolution. The translational and rotational diffusions were measured in both the laboratory frame and the body frame along the long and short axes. The long-time and short-time diffusion coefficients of translational and rotational motions were measured as functions of the particle concentration. We observed the nondiffusive crossover region in the intermediate time regime due to the caging of neighboring particles. Both the beginning and the ending times of the intermediate regime exhibit power-law dependence on concentration. The long-time and short-time diffusion anisotropies change nonmonotonically with concentration and reach minima in the semidilute regime because the motions along long axes are caged at lower concentrations than the motions along short axes. The time derivatives of mean-square displacements change linearly with the inverse of time in the intermediate time regimes at various particle densities. This indicates that their relaxation functions decay as 1/t which provides new challenges in theory. The effects of coupling between rotational and translational Brownian motions were demonstrated and the two time scales corresponding to anisotropic particle shape and anisotropic neighboring environment were measured.     

Stacking in sediments of colloidal hard spheres

We use computer simulations to investigate the crystallization dynamics of sedimenting hard spheres in large systems (hundreds of thousands of particles). We show that slow sedimentation results primarily in face-centered cubic (fcc) stacked crystals, instead of random hexagonal close packed or hexagonal close packed (hcp) crystals. We also find slanted stacking faults, in the fcc regions. However, we attribute the formation of fcc to the free energy difference between fcc and hcp and not to the presence of these slanted stacking faults. Although the free energy difference between hcp and fcc per particle is small (only 10(-3) times the thermal energy), it can become considerable, when multiplied by the number of particles in each domain. The ratio of fcc to hcp obtained from dynamic simulations is in excellent agreement with well-equilibrated Monte Carlo simulations, in which no slanted stacking faults were found. Our results explain a range of experiments on colloids, in which the amount of fcc increases upon lowering the sedimentation rate or decreasing the initial volume fraction.     

Dielectric properties of a liquid of dipole hard spheres

The Kirkwood factor g _K of a model polar liquid of dipolar hard spheres (DHSs) was approximated by analytical equations using the approximation of the interaction of the second neighbors within the hindered rotation model. The derived equations describe the temperature and density dependences of the dielectric functions of the DHS liquid.     

Phase ordering of hard needles on a quasicrystalline substrate

Quasicrystals possess long-range positional and orientational order. However, they cannot be periodic in space due to their non-crystallographic symmetries such as a 10-fold rotational axis. We perform Monte Carlo simulations of two-dimensional hard-needle systems subject to a quasiperiodic substrate potential. We determine phase diagrams as a function of density and potential strength for two needle lengths. With increasing potential strength short needles tend to form isolated clusters that display directional order along the decagonal directions. Long needles create interacting clusters that stabilize the nematic phase. At large potential strengths the clusters position themselves on two interwoven Fibonacci sequences perpendicular to the cluster orientation. Alternatively, one obtains extended domains of needle clusters which are aligned along all decagonal symmetry directions.     

The influence of bond rigidity and cluster diffusion on the self-diffusion of hard spheres with square well interaction

Hard spheres interacting through a square well potential were simulated by using two different methods: Brownian cluster dynamics (BCD) and event driven Brownian dynamics (EDBD). The structure of the equilibrium states obtained by both methods was compared and found to be almost identical. Self-diffusion coefficients (D) were determined as a function of the interaction strength. The same values were found by using BCD or EDBD. Contrary to EDBD, BCD allows one to study the effect of bond rigidity and hydrodynamic interaction within the clusters. When the bonds are flexible, the effect of attraction on D is relatively weak compared to systems with rigid bonds. D increases first with increasing attraction strength, and then decreases for stronger interaction. Introducing intracluster hydrodynamic interaction weakly increases D for a given interaction strength. Introducing bond rigidity causes a strong decrease in D which no longer shows a maximum as function of the attraction strength.     

The ferroelectric transition of dipolar hard spheres

We investigate by Monte Carlo simulation the size dependence of the variation of the polarization and the dielectric constant with temperature for dipolar hard spheres at the two densities rho sigma3=0.80 and 0.88. From the crossing of the fourth-order cumulant for different system sizes first more precise estimates of the ferroelectric transition temperatures are obtained. Theoretical approaches, when predicting an ordering transition, are shown to generally overestimate the critical temperature.     

The ideal glass transition of hard spheres

We use the replica method to study the ideal glass transition of a liquid of identical hard spheres. We obtain estimates of the configurational entropy in the liquid phase, of the Kauzmann packing fraction phi(K), in the range of 0.58-0.62, and of the random close packing density phi(c), in the range of 0.64-0.67, depending on the approximation we use for the equation of state of the liquid. We also compute the pair-correlation function in the glassy states (i.e., dense amorphous packings) and we find that the mean coordination number at phi(c) is equal to 6. All these results compare well with numerical simulations and with other existing theories.     

Diffusion of spheres in isotropic and nematic suspensions of rods

Diffusion of a small tracer sphere (apoferritin) in isotropic and nematic networks [of fd virus] is discussed. For a tracer sphere that is smaller than the mesh size of the network, screened hydrodynamic interactions between the sphere and the network determine its diffusion coefficient. A theory is developed for such interactions as well as their relation to the long-time self-diffusion coefficient. Fluorescence correlation spectroscopy measurements on mixtures of apoferritin and fd virus are presented. The long-time self-diffusion coefficient of apoferritin is measured as a function of the fd-virus concentration, both in the isotropic and nematic state, in directions parallel and perpendicular to the nematic director. The hydrodynamic screening length of the fd-virus network as a function of fd concentration is obtained by combining these experimental data with the theory. Surprisingly, the screening length increases with increasing concentration in nematic networks. This is due to the increase in the degree of alignment, which apparently leads to a strong increase of the screening length. Hydrodynamic screening is thus strongly diminished by alignment. A self-consistent calculation of the screening length does not work at higher concentrations, probably due to the strong variation of the typical incident flow fields over the contour of a rod.