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

Fractionation effects in phase equilibria of polydisperse hard sphere colloids

The equilibrium phase behaviour of hard spheres with size polydispersity is studied theoretically. We solve numerically the exact phase equilibrium equations that result from accurate free energy expressions for the fluid and solid phases, while accounting fully for size fractionation between coexisting phases. Fluids up to the largest polydispersities that we can study (around 14%) can phase separate by splitting off a solid with a much narrower size distribution. This shows that experimentally observed terminal polydispersities above which phase separation no longer occurs must be due to non-equilibrium effects. We find no evidence of re-entrant melting; instead, sufficiently compressed solids phase separate into two or more solid phases. Under appropriate conditions, coexistence of multiple solids with a fluid phase is also predicted. The solids have smaller polydispersities than the parent phase as expected, while the reverse is true for the fluid phase, which contains predominantly smaller particles but also residual amounts of the larger ones. The properties of the coexisting phases are studied in detail; mean diameter, polydispersity and volume fraction of the phases all reveal marked fractionation. We also propose a method for constructing quantities that optimally distinguish between the coexisting phases, using Principal Component Analysis in the space of density distributions. We conclude by comparing our predictions to perturbative theories for near-monodisperse systems and to Monte Carlo simulations at imposed chemical potential distribution, and find excellent agreement.Comment: 21 pages, 23 figures, 2 table

‘Unsticking’ a colloidal glass, and sticking it again

We study glass formation in hard spheres with short-range attraction. The system consists of nearly-hard-sphere polymethylmethacrylate particles and non-adsorbing random-coil polystyrene which induced a depletion attraction between the particles. The experiments reveal a re-entrant glass transition and two qualitatively distinct glassy states. Dynamic light scattering, covering eleven orders ofmagnitude in time, gives insight into the kinds of particle motion responsible for these observations. The possible relevance of our results to generic issues, such as the distinction between fragile and strong glass formers, the nature of the underlying ‘free energy landscape’, and the relative importance of temperature and pressure, is discussed

From compact to fractal crystalline clusters in concentrated systems of monodisperse hard spheres

We address the crystallization of monodisperse hard spheres in terms of the properties of finite- size crystalline clusters. By means of large scale event-driven Molecular Dynamics simulations, we study systems at different packing fractions {\phi} ranging from weakly supersaturated state points to glassy ones, covering different nucleation regimes. We find that such regimes also result in different properties of the crystalline clusters: compact clusters are formed in the classical-nucleation-theory regime ({\phi} \leq 0.54), while a crossover to fractal, ramified clusters is encountered upon increasing packing fraction ({\phi} \geq 0.56), where nucleation is more spinodal-like. We draw an analogy between macroscopic crystallization of our clusters and percolation of attractive systems to provide ideas on how the packing fraction influences the final structure of the macroscopic crystals. In our previous work (Phys. Rev. Lett., 106, 215701, 2011), we have demonstrated how crystallization from a glass (at {\phi} > 0.58) happens via a gradual (many-step) mechanism: in this paper we show how the mechanism of gradual growth seems to hold also in super-saturated systems just above freezing showing that static properties of clusters are not much affected by dynamics.Comment: Soft Matter, 201

Predicting phase equilibria in polydisperse systems

Many materials containing colloids or polymers are polydisperse: They comprise particles with properties (such as particle diameter, charge, or polymer chain length) that depend continuously on one or several parameters. This review focusses on the theoretical prediction of phase equilibria in polydisperse systems; the presence of an effectively infinite number of distinguishable particle species makes this a highly nontrivial task. I first describe qualitatively some of the novel features of polydisperse phase behaviour, and outline a theoretical framework within which they can be explored. Current techniques for predicting polydisperse phase equilibria are then reviewed. I also discuss applications to some simple model systems including homopolymers and random copolymers, spherical colloids and colloid-polymer mixtures, and liquid crystals formed from rod- and plate-like colloidal particles; the results surveyed give an idea of the rich phenomenology of polydisperse phase behaviour. Extensions to the study of polydispersity effects on interfacial behaviour and phase separation kinetics are outlined briefly.Comment: 48 pages, invited topical review for Journal of Physics: Condensed Matter; uses Institute of Physics style file iopart.cls (included

The Ultimate Fate of Supercooled Liquids

In recent years it has become widely accepted that a dynamical length scale {\xi}_{\alpha} plays an important role in supercooled liquids near the glass transition. We examine the implications of the interplay between the growing {\xi}_{\alpha} and the size of the crystal nucleus, {\xi}_M, which shrinks on cooling. We argue that at low temperatures where {\xi}_{\alpha} > {\xi}_M a new crystallization mechanism emerges enabling rapid development of a large scale web of sparsely connected crystallinity. Though we predict this web percolates the system at too low a temperature to be easily seen in the laboratory, there are noticeable residual effects near the glass transition that can account for several previously observed unexplained phenomena of deeply supercooled liquids including Fischer clusters, and anomalous crystal growth near T_g

Dispersal and reproductive careers of male mountain gorillas in Bwindi Impenetrable National Park, Uganda

Dispersal is a key event in the life of an animal and it influences individual reproductive success. Male mountain gorillas exhibit both philopatry and dispersal, resulting in a mixed one-male and multimale social organization. However, little is known about the relationship between male dispersal or philopatry and reproductive careers in Bwindi mountain gorillas. Here we analyze data spanning from 1993 to 2017 on social groups in Bwindi Impenetrable National Park, Uganda to examine the proportion of males that disperse, age of dispersal, pathways to attaining alpha status, fate of dispersing males and philopatric males, and male tenure length as well as make comparisons of these variables to the Virunga mountain gorilla population. We report previously undocumented cases of dispersal by immature males and old males and we also observed the only known case of a fully mature male immigrating into a breeding group. We used genetic tracking of known individuals to estimate that a minimum of 25% of males that disperse to become solitary males eventually form new groups. No differences were found between the Bwindi and Virunga population in the age of male dispersal, the proportion of males that disperse, the age of alpha male acquisition, and dominance tenure length. The lack of differences may be due to small sample sizes or because the observed ecological variability does not lead to life history differences between the populations. Males in both populations follow variable strategies to attain alpha status leading to the variable one-male and multimale social organization, including dispersal to become solitary and eventually form a group, via group fissioning, usurping another alpha male, or inheriting the alpha position when a previous group leader dies

The long lives of primates and the ‘invariant rate of ageing’ hypothesis

This work was supported by NIA P01AG031719 to J.W.V. and S.C.A., with additional support provided by the Max Planck Institute of Demographic Research and the Duke University Population Research Institute.Is it possible to slow the rate of ageing, or do biological constraints limit its plasticity? We test the ‘invariant rate of ageing’ hypothesis, which posits that the rate of ageing is relatively fixed within species, with a collection of 39 human and nonhuman primate datasets across seven genera. We first recapitulate, in nonhuman primates, the highly regular relationship between life expectancy and lifespan equality seen in humans. We next demonstrate that variation in the rate of ageing within genera is orders of magnitude smaller than variation in pre-adult and age-independent mortality. Finally, we demonstrate that changes in the rate of ageing, but not other mortality parameters, produce striking, species-atypical changes in mortality patterns. Our results support the invariant rate of ageing hypothesis, implying biological constraints on how much the human rate of ageing can be slowed.Publisher PDFPeer reviewe