Properties of cage rearrangements observed near the colloidal glass transition

We use confocal microscopy to study the motions of particles in concentrated colloidal systems. Near the glass transition, diffusive motion is inhibited, as particles spend time trapped in transient ``cages'' formed by neighboring particles. We measure the cage sizes and lifetimes, which respectively shrink and grow as the glass transition approaches. Cage rearrangements are more prevalent in regions with lower local concentrations and higher disorder. Neighboring rearranging particles typically move in parallel directions, although a nontrivial fraction move in anti-parallel directions, usually from pairs of particles with initial separations corresponding to the local maxima and minima of the pair correlation function $g(r)$, respectively.Comment: 5 pages, 4 figures; text & figures revised in v

Crystallization of hard-sphere glasses

We study by molecular dynamics the interplay between arrest and crystallization in hard spheres. For state points in the plane of volume fraction ($0.54 \leq phi \leq 0.63$) and polydispersity ($0 \leq s \leq 0.085$), we delineate states that spontaneously crystallize from those that do not. For noncrystallizing (or precrystallization) samples we find isodiffusivity lines consistent with an ideal glass transition at $\phi_g \approx 0.585$, independent of $s$. Despite this, for $s<0.05$, crystallization occurs at $\phi > \phi_g$. This happens on time scales for which the system is aging, and a diffusive regime in the mean square displacement is not reached; by those criteria, the system is a glass. Hence, contrary to a widespread assumption in the colloid literature, the occurrence of spontaneous crystallization within a bulk amorphous state does not prove that this state was an ergodic fluid rather than a glass.Comment: 4 pages, 3 figure

Equilibrium phase behavior of polydisperse hard spheres

We calculate the phase behavior of hard spheres with size polydispersity, using accurate free energy expressions for the fluid and solid phases. Cloud and shadow curves, which determine the onset of phase coexistence, are found exactly by the moment free energy method, but we also compute the complete phase diagram, taking full account of fractionation effects. In contrast to earlier, simplified treatments we find no point of equal concentration between fluid and solid or re-entrant melting at higher densities. Rather, the fluid cloud curve continues to the largest polydispersity that we study (14%); from the equilibrium phase behavior a terminal polydispersity can thus only be defined for the solid, where we find it to be around 7%. At sufficiently large polydispersity, fractionation into several solid phases can occur, consistent with previous approximate calculations; we find in addition that coexistence of several solids with a fluid phase is also possible

Hard Spheres: Crystallization and Glass Formation

Motivated by old experiments on colloidal suspensions, we report molecular dynamics simulations of assemblies of hard spheres, addressing crystallization and glass formation. The simulations cover wide ranges of polydispersity s (standard deviation of the particle size distribution divided by its mean) and particle concentration. No crystallization is observed for s > 0.07. For 0.02 < s < 0.07, we find that increasing the polydispersity at a given concentration slows down crystal nucleation. The main effect here is that polydispersity reduces the supersaturation since it tends to stabilise the fluid but to destabilise the crystal. At a given polydispersity (< 0.07) we find three regimes of nucleation: standard nucleation and growth at concentrations in and slightly above the coexistence region; "spinodal nucleation", where the free energy barrier to nucleation appears to be negligible, at intermediate concentrations; and, at the highest concentrations, a new mechanism, still to be fully understood, which only requires small re-arrangement of the particle positions. The cross-over between the second and third regimes occurs at a concentration, around 58% by volume, where the colloid experiments show a marked change in the nature of the crystals formed and the particle dynamics indicate an "ideal" glass transition

From random walk to single-file diffusion

We report an experimental study of diffusion in a quasi-one-dimensional (q1D) colloid suspension which behaves like a Tonks gas. The mean squared displacement as a function of time is described well with an ansatz encompassing a time regime that is both shorter and longer than the mean time between collisions. This ansatz asserts that the inverse mean squared displacement is the sum of the inverse mean squared displacement for short time normal diffusion (random walk) and the inverse mean squared displacement for asymptotic single-file diffusion (SFD). The dependence of the single-file 1D mobility on the concentration of the colloids agrees quantitatively with that derived for a hard rod model, which confirms for the first time the validity of the hard rod SFD theory. We also show that a recent SFD theory by Kollmann leads to the hard rod SFD theory for a Tonks gas.Comment: 4 pages, 4 figure

Towards a Comparative Measure for Legged Agility

We introduce an agility measure enabling the comparison of two very different leaping-from-rest transitions by two comparably powered but morphologically different legged robots. We use the measure to show that a flexible spine outperforms a rigid back in the leaping- from-rest task. The agility measure also sheds light on the source of this benefit: core actuation through a sufficiently powerful parallel elastic actuated spine outperforms a similar power budget applied either only to preload the spine or only to actuate the spine during the leap, as well as a rigid backed configuration of the identical machine

Dynamic regimes of hydrodynamically coupled self-propelling particles

We analyze the collective dynamics of self-propelling particles (spps) which move at small Reynolds numbers including the hydrodynamic coupling to the suspending solvent through numerical simulations. The velocity distribution functions show marked deviations from Gaussian behavior at short times, and the mean-square displacement at long times shows a transition from diffusive to ballistic motion for appropriate driving mechanism at low concentrations. We discuss the structures the spps form at long times and how they correlate to their dynamic behavior.Comment: 7 pages, 4 figure

Mixtures of Charged Colloid and Neutral Polymer: Influence of Electrostatic Interactions on Demixing and Interfacial Tension

The equilibrium phase behavior of a binary mixture of charged colloids and neutral, non-adsorbing polymers is studied within free-volume theory. A model mixture of charged hard-sphere macroions and ideal, coarse-grained, effective-sphere polymers is mapped first onto a binary hard-sphere mixture with non-additive diameters and then onto an effective Asakura-Oosawa model [S. Asakura and F. Oosawa, J. Chem. Phys. 22, 1255 (1954)]. The effective model is defined by a single dimensionless parameter -- the ratio of the polymer diameter to the effective colloid diameter. For high salt-to-counterion concentration ratios, a free-volume approximation for the free energy is used to compute the fluid phase diagram, which describes demixing into colloid-rich (liquid) and colloid-poor (vapor) phases. Increasing the range of electrostatic interactions shifts the demixing binodal toward higher polymer concentration, stabilizing the mixture. The enhanced stability is attributed to a weakening of polymer depletion-induced attraction between electrostatically repelling macroions. Comparison with predictions of density-functional theory reveals a corresponding increase in the liquid-vapor interfacial tension. The predicted trends in phase stability are consistent with observed behavior of protein-polysaccharide mixtures in food colloids.Comment: 16 pages, 5 figure

Public Library Teen Space Design: An Evaluation of Theory in Practice

While a review of the literature reveals a set of accepted standards for quality teen space design, this paper seeks to determine if public library teen spaces currently succeed in meeting these standards. Teen space design is significant not only for its aesthetic value, but for its impact on teens, who face many developmental challenges as well as a lack of safe and welcoming environments in which to experience them. Library teen spaces were examined both in theory and in practice, comparing the standards portrayed through available literature to reality. An extensive literature review was conducted, and a compendium of recommendations was used to establish a set of accepted standards. A selection of public library teen spaces was then evaluated to determine their adherence to these standards. Gaps in service were analyzed, and, finally, changes to improve service to the teen population were recommended

The short-time self-diffusion coefficient of a sphere in a suspension of rigid rods

The short--time self diffusion coefficient of a sphere in a suspension of rigid rods is calculated in first order in the rod volume fraction. For low rod concentrations the correction to the Einstein diffusion constant of the sphere is a linear function of the rod volume fraction with the slope proportional to the equilibrium averaged mobility diminution trace of the sphere interacting with a single freely translating and rotating rod. The two--body hydrodynamic interactions are calculated using the so--called bead model in which the rod is replaced by a stiff linear chain of touching spheres. The interactions between spheres are calculated numerically using the multipole method. Also an analytical expression for the diffusion coefficient as a function of the rod aspect ratio is derived in the limit of very long rods. We show that in this limit the correction to the Einstein diffusion constant does not depend on the size of the tracer sphere. The higher order corrections depending on the applied model are computed numerically. An approximate expression is provided, valid for a wide range of aspect ratios.Comment: 11 pages, 6 figure