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Register a new userDirect Observation in 3d of Structural Crossover in Binary Hard Sphere Mixtures
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For binary fluid mixtures of spherical particles in which the two species are sufficiently different in size, the dominant wavelength of oscillations of the pair correlation functions is predicted to change from roughly the diameter of the large species to that of the small species along a sharp crossover line in the phase diagram [C. Grodon, M. Dijkstra, R. Evans & R. Roth, J.Chem.Phys. 121, 7869 (2004)]. Using particle-resolved colloid experiments in 3d we demonstrate that crossover exists and that its location in the phase diagram is in quantitative agreement with the results of both theory and our Monte-Carlo simulations. In contrast with previous work [J. Baumgartl, R. Dullens, M. Dijkstra, R. Roth & C. Bechinger, Phys.Rev.Lett. 98, 198303 (2007)], where a correspondence was drawn between crossover and percolation of both species, in our 3d study we find that structural crossover is unrelated to percolation.
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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.
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.
The structural properties of additive binary hard-sphere mixtures are addressed as a follow-up of a previous paper [S. Pieprzyk et al., Phys. Rev. E 101, 012117 (2020)]. The so-called rational-function approximation method and an approach combining accurate molecular dynamics simulation data, the pole structure representation of the total correlation functions, and the Ornstein-Zernike equation are considered. The density, composition, and size-ratio dependencies of the leading poles of the Fourier transforms of the total correlation functions $h_{ij} (r)$ of such mixtures are presented, those poles accounting for the asymptotic decay of $h_{ij} (r)$ for large $r$. Structural crossovers, in which the asymptotic wavelength of the oscillations of the total correlation functions changes discontinuously, are investigated. The behavior of the structural crossover lines as the size ratio and densities of the two species are changed is also discussed.
Although much is known about the metastable liquid branch of hard spheres--from low dimension $d$ up to $dtoinfty$--its crystal counterpart remains largely unexplored for $d>3$. In particular, it is unclear whether the crystal phase is thermodynamically stable in high dimensions and thus whether a mean-field theory of crystals can ever be exact. In order to determine the stability range of hard sphere crystals, their equation of state is here estimated from numerical simulations, and fluid-crystal coexistence conditions are determined using a generalized Frenkel-Ladd scheme to compute absolute crystal free energies. The results show that the crystal phase is stable at least up to $d=9$, and the dimensional trends suggest that crystal stability likely persists well beyond that point.
We simulate the motion of spherical particles in a phase-separating binary mixture. By combining cell dynamical equations with Langevin dynamics for particles, we show that the addition of hard particles significantly changes both the speed and the morphology of the phase separation. At the late stage of the spinodal decomposition process, particles significantly slow down the domain growth, in qualitative agreement with earlier experimental data.
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