Diffusive growth of polydisperse hard-sphere crystals

Evans, R. M. L.; Holmes, C. B.

doi:10.1103/physreve.64.011404

Cited by 30 publications

(36 citation statements)

References 38 publications

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“…One illustration of the importance of the kinetics and mechanisms to an actual experiment is recent work on the diffusive growth of crystals from polydisperse spheres 17 . The essence is that because smaller spheres move fastest, they arrive at the crystal surface ®rst and the resulting crystal has more small particles than one might otherwise expect.…”

Section: Predictions From Phase Diagrams and Free Energymentioning

confidence: 99%

Insights into phase transition kinetics from colloid science

Anderson

Lekkerkerker

2002

Nature

910

845

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Colloids display intriguing transitions between gas, liquid, solid and liquid crystalline phases. Such phase transitions are ubiquitous in nature and have been studied for decades. However, the predictions of phase diagrams are not always realized; systems often become undercooled, supersaturated, or trapped in gel-like states. In many cases the end products strongly depend on the starting position in the phase diagram and discrepancies between predictions and actual observations are due to the intricacies of the dynamics of phase transitions. Colloid science aims to understand the underlying mechanisms of these transitions. Important advances have been made, for example, with new imaging techniques that allow direct observation of individual colloidal particles undergoing phase transitions, revealing some of the secrets of the complex pathways involved.F igure 1 illustrates three types of phase diagram. The ®rst (Fig. 1a) is a simple system of hard spheres. Introducing attractions results in three-phase equilibria, as in atomic systems such as argon (Fig. 1b). With shorter-range attractions the gas±liquid (or¯uid±¯uid) equilibrium becomes metastable (Fig. 1c). This is often observed in protein systems. One might assume equilibrium diagrams show the complete picture, with perhaps the initial distance from the phase boundary (indicative of the distance to equilibrium) controlling the speed with which the equilibrium phases are attained; however, this is the exception rather than the rule.Hard-sphere colloids suspended in a solvent provide an excellent illustration of the dif®culties involved in understanding the equilibrium states and the mechanisms by which systems evolve. Entropy considerations predict that these systems will form crystals if the volume fraction is increased. Above the`freezing' volume fraction, f f 0:494, it is entropically favourable if some spheres are in a crystal, but above the`melting' volume fraction, f m 0:545, all spheres should be in a crystal (Fig. 1a). However this is not always the situation found experimentally, either because the conditions the theory assumes (low polydispersity, for example) are not satis®ed, or the dynamics of the system have dictated a different structure (note that we cannot say that this structure is the equilibrium structureÐif entropy favours crystal formation then a crystal will form eventually, however the system may remain in the less-favoured state for a signi®cant amount of time). This crystallization process is often interpreted within the familiar framework of nucleation and growth. There has been renewed interest in this mechanism recently, both with simulations 1 and experimentally 2,3 : by monitoring the individual particles undergoing the transition it is possible to evaluate and improve the model.The classical theory predicts that the free energy cost, DG, of forming a nucleus of radius r is:where g is the surface free energy, r is the density of the bulk liquid, and Dm is the chemical potential difference between the bulk solid and bulk liquid...

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Section: Predictions From Phase Diagrams and Free Energymentioning

confidence: 99%

Insights into phase transition kinetics from colloid science

Anderson

Lekkerkerker

2002

Nature

910

845

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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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“…One complicating factor behind this is that, for the normal case of length polydispersity, the simplifications brought about by the moment structure in the excess free energy do not lead to any obvious simplification of the dynamical equations: the natural coordinates for dynamics are not the moment densities, but the species monomer densities. (See ref 6 for a related discussion, in the context of colloids, addressed there via a perturbation theory in the narrowness of the size distribution.) Previous treatments of length polydispersity mapped the polydisperse situation into that of a mixture with a finite set of components by matching the lowest moments of the distribution [7].…”

Section: Introductionmentioning

confidence: 99%

Dynamics of Polydisperse Polymer Mixtures

Pagonabarraga

Cates

2003

Macromolecules

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We develop a general analysis of the diffusive dynamics of polydisperse polymers in the presence of chemical potential gradients, within the context of the tube model (with all species entangled). We obtain a set of coupled dynamical equations for the time evolution of the polymeric densities in a form proposed phenomenologically in recent work by N. Clarke, but with explicitly derived coefficients. For the case of chemical polydispersity (a set of chains that are identical except for having a continuous spectrum of enthalpic interaction strengths) the coupled equations can be fully solved in certain cases. For these we study the linearised mode spectrum following a quench through the spinodal, with and without a passive (polymeric) solvent. We also study the more conventional case of length polydisperse chains in a poor solvent. Here the mode structure is more complicated and exact analysis difficult, but enough progress can still be made to gain some qualitative insight. We briefly discuss the modifications required to allow for the presence of unentangled, low molecular weight species in the system.

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Diffusive growth of polydisperse hard-sphere crystals

Cited by 30 publications

References 38 publications

Insights into phase transition kinetics from colloid science

Insights into phase transition kinetics from colloid science

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

Dynamics of Polydisperse Polymer Mixtures

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