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Register a new userPolymer-Enforced Crystallization of a Eutectic Binary Hard Sphere Mixture
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We prepared a buoyancy matched binary mixture of polydisperse polystyrene microgel spheres of size ratio 0.785 and at a volume fraction of 0.567 just below the kinetic glass transition. In line with theoretical expectations, a eutectic phase behavior was observed, but only a minor fraction of the samples crystallized at all. By adding a short non-adsorbing polymer we enforce inter-species fractionation into coexisting pure component crystals, which in turn also shows signs of intra-species fractionation. We show that in formerly inaccessible regions of the phase diagram binary hard sphere physics is made observable using attractive hard spheres. Ancillary files: Correction to Soft Matter 2012, 8, 627
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Population annealing is a sequential Monte Carlo scheme well-suited to simulating equilibrium states of systems with rough free energy landscapes. Here we use population annealing to study a binary mixture of hard spheres. Population annealing is a parallel version of simulated annealing with an extra resampling step that ensures that a population of replicas of the system represents the equilibrium ensemble at every packing fraction in an annealing schedule. The algorithm and its equilibration properties are described and results are presented for a glass-forming fluid composed of a 50/50 mixture of hard spheres with diameter ratio of 1.4:1. For this system, we obtain precise results for the equation of state in the glassy regime up to packing fractions $varphi approx 0.60$ and study deviations from the BMCSL equation of state. For higher packing fractions, the algorithm falls out of equilibrium and a free volume fit predicts jamming at packing fraction $varphi approx 0.667$. We conclude that population annealing is an effective tool for studying equilibrium glassy fluids and the jamming transition.
We recently found that crystallization of monodisperse hard spheres from the bulk fluid faces a much higher free energy barrier in four than in three dimensions at equivalent supersaturation, due to the increased geometrical frustration between the simplex-based fluid order and the crystal [J.A. van Meel, D. Frenkel, and P. Charbonneau, Phys. Rev. E 79, 030201(R) (2009)]. Here, we analyze the microscopic contributions to the fluid-crystal interfacial free energy to understand how the barrier to crystallization changes with dimension. We find the barrier to grow with dimension and we identify the role of polydispersity in preventing crystal formation. The increased fluid stability allows us to study the jamming behavior in four, five, and six dimensions and compare our observations with two recent theories [C. Song, P. Wang, and H. A. Makse, Nature 453, 629 (2008); G. Parisi and F. Zamponi, Rev. Mod. Phys, in press (2009)].
An approach to obtain the structural properties of additive binary hard-sphere mixtures is presented. Such an approach, which is a nontrivial generalization of the one recently used for monocomponent hard-sphere fluids [S. Pieprzyk, A. C. Branka, and D. M. Heyes, Phys. Rev. E 95, 062104 (2017)], combines accurate molecular-dynamics simulation data, the pole structure representation of the total correlation functions, and the Ornstein-Zernike equation. A comparison of the direct correlation functions obtained with the present scheme with those derived from theoretical results stemming from the Percus-Yevick (PY) closure and the so-called rational-function approximation (RFA) is performed. The density dependence of the leading poles of the Fourier transforms of the total correlation functions and the decay of the pair correlation functions of the mixtures are also addressed and compared to the predictions of the two theoretical approximations. A very good overall agreement between the results of the present scheme and those of the RFA is found, thus suggesting that the latter (which is an improvement over the PY approximation) can safely be used to predict reasonably well the long-range behavior, including the structural crossover, of the correlation functions of additive binary hard-sphere mixtures.
The rheological properties of highly concentrated suspensions of hard-sphere particles are studied with particular reference to the rheological response of shear induced crystals. Using practically monodisperse hard spheres, we prepare shear induced crystals under oscillatory shear and examine their linear and non-linear mechanical response in comparison with their glassy counterparts at the same volume fraction. It is evident, that shear-induced crystallization causes a significant drop in the elastic and viscous moduli due to structural rearrangements that ease flow. For the same reason the critical (peak of G) and crossover (overlap of G and G) strain are smaller in the crystal compared to the glass at the same volume fraction. When, however the distance from the maximum packing in each state is taken into account the elastic modulus of the crystal is found to be larger than the glass at the same free volume suggesting a strengthened material due to long range order. Finally, shear induced crystals counter-intuitively exhibit similar rheological ageing to the glass (with a logarithmic increase of G), indicating that the shear induced structure is not at thermodynamic equilibrium.
We use numerical simulations to study the crystallization of monodisperse systems of hard aspherical particles. We find that particle shape and crystallizability can be easily related to each other when particles are characterized in terms of two simple and experimentally accessible order parameters: one based on the particle surface-to-volume ratio, and the other on the angular distribution of the perturbations away from the ideal spherical shape. We present a phase diagram obtained by exploring the crystallizability of 487 different particle shapes across the two-order-parameter spectrum. Finally, we consider the physical properties of the crystalline structures accessible to aspherical particles, and discuss limits and relevance of our results.
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