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Physics Department, Bar-Ilan University

Sloutskin Lab: Soft Condensed Matter Physics

We study crystal nucleation from within a metastable fluid.

Crystal nucleation is ubiquitous, playing important role in diverse processes, such as limescale and kidney stone formation, protein crystallization, food processing, and igneous rock solidification in geophysics, to mention a few.

Our particles are imaged in-vivo by confocal microscopy, in three dimensions. We follow the positions of ~5e4 particles inside our sample, detect the formation of early nuclei, and measure the morphology of these nuclei. Note, that none of the existing experimental techniques allows the morphology of atomic or molecular nuclei to be determined, at single-particle resolution, in vivo, in three dimensions. The thermodynamic state of hard spheres is fully determined by their density η, and their phase diagram is well known.

In glass industry, crystal nucleation is undesirable, competing with glassification.

Formation of crystals with tunable concentration of defects, a ‘holy grail’ for nano-fabrication of photonic crystals, requires nucleation and growth to be understood and controlled.

A widely-used framework describing the nucleation process is the “classical nucleation theory”. Appealingly simple, classical nucleation theory nevertheless mispredicts the observed rate at which these nuclei actually form by orders of magnitude; this severely limits its real-world usefulness.

A suspension of hard spheres is one of the simplest systems exhibiting crystal nucleation.  The liquid-solid interfacial tension per particle in many of the abundant atomic and molecular systems is of the same range as that of the hard spheres. Therefore, we expect our results to be applicable to crystal nucleation in a wide range of liquids. Being thermodynamically simple, a system of hard spheres is well suited for nucleation studies. Colloidal particles, suspended in a density-matched  solvent, undergo Brownian motion, and do not sediment, probing the phase space akin to atoms or molecules.

Fluid of colloids

Phase diagram of hard spheres

Crystallites nucleate in the fluid phase, as it is densified beyond η=0.494. The nuclei subsequently grow, as the thermodynamic equilibrium is being established.

A reconstruction of a portion of our sample, at η=0.53. The particles which are associated with the crystalline phase are shown in red. Particles which belong to the fluid phase are shown in blue, half their size, slightly transparent. Three hours after sample preparation, only small crystalline nuclei are present, as shown in the left panel. Then occurs nucleation, followed by rapid growth of the crystalline phase. The right panel shows the same sample, 13 hours later, at thermodynamical equilibrium: ~60% of the volume is filled by the crystalline phase.

We use our three-dimensional reconstruction of the nuclei, to measure their radius of gyration R_g, their mass M, their surface area, and their size distribution.We track individual nuclei, to test directly the predictions of classical nucleation theory.

Our results indicate, that morphology of nuclei plays important role in nucleation process, and modifies the chances of a given nucleus to grow.
The fractal dimension of nuclei dim is defined by the scaling relation M~R_g^dim. Experimentally dim≈2 for small nuclei, with a crossover to dim =3 exhibited at M≈30.

We have developed theoretical arguments which may be used to account for this crossover, as also for the lower fractal dimension observed for the nuclei in charged colloids, where long-range Coulombic interactions dominate. The same theory allows to account for size distribution of the nuclei, which is significantly different from predictions of the classical nucleation theory.

1.   E. Sloutskin, P. J. Lu, T. Kanai, A. Schofield, and D. A. Weitz, in preparation.
2.   U. Gasser, E. R. Weeks, A. Schofield, P. N. Pusey, and D. A. Weitz, Science 292, 258 (2001).

References for more information

Copyright Eli Sloutskin, Bar-Ilan University (2011)

Colloidal ellipsoids: 3d reconstruction

aspect ratio = 3.

Note several pair formation events; these events may indicate short-range attractive interactions.

Sedimentation of granular materials is abundant. The structure of granular sediments plays an important role in various industrial processes; for example, it determines the density of randomly close-packed materials, such as flour or sugar, if these are poured to fill a container. The physics of sedimentation determines the mechanical strength of various construction materials; in microelectronics, it controls the electronic properties of thin layers, which are typically formed by deposition techniques. Slow sedimentation processes form rocks and minerals; faster sedimentation forms snowdrifts, disastrous for the traffic flow in the major cities of the world. Last, but not the least, the physics of randomly close-packed materials must be deeply related to the physics of glass formation; both of these phenomena remain poorly understood, after many decades of an intensive scientific research.

Recently, significant scientific efforts were devoted to measure the density of various randomly close-packed materials, such as the M&M candies filling a container [Donev et al., Nature 303, 590 (2004)]. Recent analytical theories suggest that quasi-long-range density correlations exist in materials formed by sedimentation [Katzav et al., EPL 75, 29 (2006)] . Such correlations are highly counterintuitive; a quasi-long-range order forms out of a completely random “rain” of particles, falling on a solid substrate. Yet, these theories employ a continuum approximation, which is not necessarily valid for granular materials. To test the validity of these approximations, computer simulations of sedimentation were attempted; these simulations are highly demanding, limiting these studies to a two-dimensional space. Strikingly, these simulations support the presence of quasi-long-range density correlations. However, there are three spatial dimensions in nature, and an experimental evidence for spontaneous quasi-long-ranged ordering in sediments is still lacking. Careful measurements of the quasi-long-range order in experimental systems are non-trivial. Moreover, the conventional experimental techniques provide only sample-averaged quantities, such that the detailed three-dimensional structure of random close-packed materials is unknown.

Colloidal particles, density mismatched with their solvent, sediment under centrifugation. We measure the structure of colloidal sediments by confocal microscopy. Confocal microscopy provides the local structure of the sediment with a single particle (100 nm) resolution. Yet, a large field of view is accessible; this allows the correlation between points separated by several millimeters to be measured. In our system, both the short range and the long-range structural information is accessible, allowing a deeper insight into the physics of sedimentation.

A small (90 x 90 microns sq.) portion of a confocal image, which shows a sediment of colloidal particles (<diameter> ≈ 2.4 micron).

Most molecules in nature are spherically anisotropic, which gives rise to unique types of collective behavior both in the bulk material and within the various interfacial phases. In bulk phases, the anisotropy may give rise to liquid crystalline phases; at the interfaces, the anisotropy is suggested to be responsible the formation of quasi-two-dimensional surface-frozen phases. The formation of liquid-crystalline phases and the surface freezing transitions were intensively studied during the last decades, yet the conventional techniques do not allow the individual particles to be imaged in real-time, during the kinetics of these phase transitions. Thus, the physical mechanism driving these phase transitions is obscure.

We employ colloidal spheroids (ellipsoids of revolution) to mimic the behavior of spherically anisotropic atoms and molecules. These particles undergo Brownian motion, thus tending to minimize their free energy, akin to atoms and molecules; yet, these particles are visible for optical microscopy. We track these particles in real time, in three dimensions, employing confocal microscopy. We fine-tune the interactions between these particles, which is impossible with the conventional molecules. These studies should shed light onto the physics of formation of liquid crystalline phases, and provide a deeper physical understanding of the surface freezing phenomena.

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