Weakly Polydisperse Systems: Perturbative Phase Diagrams that Include the Critical Region

Sollich, Peter

doi:10.1103/physrevlett.100.035701

Cited by 4 publications

(5 citation statements)

References 14 publications

(35 reference statements)

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“…This is surprising given the presence of fractionation. But one can confirm by perturbation theory 72,73 that the behaviour we observe comes from the fact that in our models polydispersity enters only via the particle size and not the strength of the interaction. For the MFE results shown, symbols correspond to the scaled values of the polydispersity δ used in the simulations.…”

Section: Fluid-solid Coexistencesupporting

confidence: 70%

Phase behavior of polydisperse spheres: Simulation strategies and an application to the freezing transition

Wilding

Sollich

2010

The Journal of Chemical Physics

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The statistical mechanics of phase transitions in dense systems of polydisperse particles presents distinctive challenges to computer simulation and analytical theory alike. The core difficulty, namely, dealing correctly with particle size fractionation between coexisting phases, is set out in the context of a critique of previous simulation work on such systems. Specialized Monte Carlo simulation techniques and moment free energy method calculations, capable of treating fractionation exactly, are then described and deployed to study the fluid-solid transition of an assembly of repulsive spherical particles described by a top-hat "parent" distribution of particle sizes. The cloud curve delineating the solid-fluid coexistence region is mapped as a function of the degree of polydispersity δ, and the properties of the incipient "shadow" phases are presented. The coexistence region is found to shift to higher densities as δ increases, but does not exhibit the sharp narrowing predicted by many theories and some simulations.

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Section: Fluid-solid Coexistencesupporting

confidence: 70%

Phase behavior of polydisperse spheres: Simulation strategies and an application to the freezing transition

Wilding

Sollich

2010

The Journal of Chemical Physics

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“…17,[38][39][40] For instance, Evans has developed a perturbative approach for narrow distributions of the polydisperse attribute. 16,36,[41][42][43] This predicts, for example, that the difference in mean particle size between the two daughter phases is proportional to the variance of the parent distribution. It can also predict specific trends, e.g.…”

Section: Introductionmentioning

confidence: 99%

Phase separation dynamics of polydisperse colloids: a mean-field lattice-gas theory

Castro

Sollich

2017

Phys. Chem. Chem. Phys.

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New insights into phase separation in colloidal suspensions are provided via a new dynamical theory based on the Polydisperse Lattice-Gas model. The model gives a simplified description of polydisperse colloids, incorporating a hard-core repulsion combined with polydispersity in the strength of the attraction between neighbouring particles. Our mean-field equations describe the local concentration evolution for each of an arbitrary number of species, and for an arbitrary overall composition of the system. We focus on the predictions for the dynamics of colloidal gas-liquid phase separation after a quench into the coexistence region. The critical point and the relevant spinodal curves are determined analytically, with the latter depending only on three moments of the overall composition. The results for the early-time spinodal dynamics show qualitative changes as one crosses a 'quenched' spinodal that excludes fractionation and so allows only density fluctuations at fixed composition. This effect occurs for dense systems, in agreement with a conjecture by Warren that, at high density, fractionation should be generically slow because it requires inter-diffusion of particles. We verify this conclusion by showing that the observed qualitative changes disappear when direct particle-particle swaps are allowed in the dynamics. Finally, the rich behaviour beyond the spinodal regime is examined, where we find that the evaporation of gas bubbles with strongly fractionated interfaces causes long-lived composition heterogeneities in the liquid phase; we introduce a two-dimensional density histogram method that allows such effects to be easily visualized for an arbitrary number of particle species.

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“…But the pair correlation functions g ij (r) and hence the h ij (q) depend smoothly on particle size, so we expand the latter up to ǫ a i ǫ a j , taking e.g. for a = 1, h ij (q) = h 0 (q) + h 1 (q)(ǫ i + ǫ j ) + h 2 (q)ǫ i ǫ j [7]. This expansion is inserted into Eq.…”

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confidence: 99%

“…The compressibility from Eq. ( 3) can then be rewritten as ρk B T χ T (q) = S(q) − s T 0c (q)S −1 cc (q)s 0c (q) (7) where the (n − 1)-dimensional vector s 0c gathers the correlations between number and composition fluctuations, and the matrix S cc the correlations among the latter [14,16]. For the compressibility to vanish at jamming the two terms must cancel, which implies that local fluctuations in N become fully correlated with composition fluctuations.…”

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confidence: 99%

Suppressed Compressibility at Large Scale in Jammed Packings of Size-Disperse Spheres

et al. 2011

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We analyze the large-scale structure and fluctuations of jammed packings of size-disperse spheres, produced in a granular experiment as well as numerically. While the structure factor of the packings reveals no unusual behavior for small wave vectors, the compressibility displays an anomalous linear dependence at low wave vectors and vanishes when q→0. We show that such behavior occurs because jammed packings of size-disperse spheres have no bulk fluctuations of the volume fraction and are thus hyperuniform, a property not observed experimentally before. Our results apply to arbitrary particle size distributions. For continuous distributions, we derive a perturbative expression for the compressibility that is accurate for polydispersity up to about 30%.

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Weakly Polydisperse Systems: Perturbative Phase Diagrams that Include the Critical Region

Cited by 4 publications

References 14 publications

Phase behavior of polydisperse spheres: Simulation strategies and an application to the freezing transition

Phase behavior of polydisperse spheres: Simulation strategies and an application to the freezing transition

Phase separation dynamics of polydisperse colloids: a mean-field lattice-gas theory

Suppressed Compressibility at Large Scale in Jammed Packings of Size-Disperse Spheres

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