Crystallization through metastable phases, such as polymorphism, plays an important role in chemical manufacture, biomineralization, and protein crystallization. However, the kinetics creating the final stable crystalline phase from metastable phases has so far remained unclear. In this study, crystallization via an amorphous precursor, the so-called multistep crystallization (MSC), is studied quantitatively in a colloidal model system. In MSC, amorphous dense droplets are first nucleated from the mother phase. Subsequently, a few unstable subcrystalline nuclei can be created simultaneously by fluctuation from the tiny dense droplets, which is different from previous theoretical predictions. It is necessary for these crystalline nuclei to reach a critical size N*(crys) to become stable. However, in contrast to subcrystalline nuclei, a stable mature crystalline nucleus is not created by fluctuation but by coalescence of subcrystalline nuclei, which is unexpected. To accommodate a mature crystalline nucleus larger than the critical size N*(crys), the dense droplets have to first acquire a critical size N*. This implies that only a fraction of amorphous dense droplets can serve as a precursor of crystal nucleation. As an outcome, the overall nucleation rate of the crystalline phase is, to a large extent, determined by the nucleation rate of crystals in the dense droplets, which is much lower than the previous theoretical expectation. Furthermore, it is surprising to see that MSC will promote the production of defect-free crystals. The knowledge acquired in this study will also significantly advance our understandings in polymorphism related processes.

Cluster formation and gelation are studied in a colloidal model system with competing short-range attractions and long-range repulsions. In contrast to predictions by equilibrium theory, the size of clusters spontaneously formed at low colloidal volume fractions decreases with increasing strength of the short-range attraction. Moreover, the microstructure and shape of the clusters sensitively depend on the strength of the short-range attraction: from compact and crystalline clusters at relatively weak attractions to disordered and quasi-linear clusters at strong attractions. By systematically varying attraction strength and colloidal volume fraction, we observe gelation at relatively high volume fraction. The structure of the gel depends on attraction strength: in systems with the lowest attraction strength, crowding of crystalline clusters leads to microcrystalline gels. In contrast, in systems with relatively strong attraction strength, percolation of quasi-linear clusters leads to low-density gels. In analyzing the results we show that nucleation and rearrangement processes play a key role in determining the properties of clusters and the mechanism of gelation. This study implies that by tuning the strength of short-range attractions, the growth mechanism as well as the structure of clusters can be controlled, and thereby the route to a gel state.

Crystallizing growth: The initial structure of crystal nuclei is supersaturation-dependent. At low degrees of supersaturation, liquid-like nuclei are formed initially, which undergo a continuous structure transition from liquid-like to crystal-like as the size N increases. This gradual structure evolution substantially lowers the nucleation barrier DeltaG* and facilitates the nucleation relative to the formation of crystal-like clusters from the beginning.

In the last few decades, the controlled colloidal assembly was adopted as a new modelling technology for the study of the crystallization mechanism. In colloidal systems, the movement of particles is slow enough to follow and the particle dynamics can be monitored at the single-particle level using normal optical microscopes. So far, the studies of colloidal crystallization have produced a number of insights, which have significantly improved our understanding of crystallization. In this review, we summarize the recent advances in understanding the mechanism of crystallization, which were achieved using colloidal model systems, i.e., the kinetics of nucleation, growth and defect formation. Such model systems allow us to not only visualize some "atomic" details of nucleation and surface processes of crystallization, but also quantify previous models to such an extent that has never been achieved before by other approaches. In the case of nucleation, the quantitative observation of the kinetic process was made at the single-particle level; the results include the ideal case and the deviations from classical theories. The deviations include multi-step crystallization, supersaturation-driven structural mismatch nucleation, defect creation and migration kinetics, surface roughening, etc. It can be foreseen that this approach will become a powerful tool to study the fundamental process of crystallization and other phase transitions.

Crystallization via an amorphous precursor, the so-called multistep crystallization (MSC), plays a key role in biomineralization and protein crystallization. MSC has attracted much attention in the past decade, but a quantitative understanding of it has so far not been available. The major challenge is that the kinetics governing the nucleation of crystals occurring in the metastable amorphous precursor remains unclear. In this study, the kinetics of MSC is addressed experimentally. Most importantly, a mathematical method is developed to calculate the local nucleation rate of the crystals in the amorphous precursor, which is not accessible to conventional methods. This local nucleation rate is critical to the understanding of MSC, but it has never been dealt with experimentally because of the difficulties of in situ observation. With the local crystal nucleation rates, the supersaturation for crystallization and the crystal-liquid interfacial free energy in the amorphous precursor are evaluated.

A stable short-range crystalline structure is observed in colloidal systems with competing short-range attractions and long-range repulsions. We term these structures ''microcrystalline gels'' as the microcrystals are embedded in a dense disordered network.

We report qualitatively on the differences between colloidal systems left to evolve in the Earth's gravitational field and the same systems for which a slow continuous rotation averaged out the effects of particle sedimentation on a distance scale small compared to the particle size. Several systems of micron-sized colloidal particles were studied: a hard sphere fluid, colloids interacting via long-range electrostatic repulsion above the freezing volume fraction, an oppositely charged colloidal system close to either gelation and/or crystallization, colloids with a competing short-range depletion attraction and a long-range electrostatic repulsion, colloidal dipolar chains, and colloidal gold platelets under conditions where they formed stacks. Important differences in structure formation were observed between the experiments where the particles were allowed to sediment and those where sedimentation was averaged out. For instance, in the case of colloids interacting via long-range electrostatic repulsion, an unusual sequence of dilute-fluid-dilute-crystal-dense-fluid-dense-crystal phases was observed throughout the suspension under the effect of gravity. This was related to the volume fraction dependence of the colloidal interactions, whereas the system stayed homogeneously crystallized with rotation. For the oppositely charged colloids, a gel-like structure was found to collapse under the influence of gravity with a few crystalline layers grown on top of the sediment, whereas when the colloidal sedimentation was averaged out, the gel completely transformed into crystallites that were oriented randomly throughout the sample. Rotational averaging out of gravitational sedimentation is an effective and cheap way to estimate the importance of gravity for colloidal self-assembly processes.

Virtually all of the many active matter systems studied so far are made of units (biofilaments, cells, colloidal particles, robots, animals, etc.) that move even when they are alone or isolated. Their collective properties continue to fascinate, and we now understand better how they are unique to the bulk transduction of energy into work. Here we demonstrate that systems in which isolated but potentially active particles do not move can exhibit specific and remarkable collective properties. Combining experiments, theory, and numerical simulations, we show that such subcritical active matter can be realized with Quincke rollers, that is, dielectric colloidal particles immersed in a conducting fluid subjected to a vertical DC electric field. Working below the threshold field value marking the onset of motion for a single colloid, we find fast activity waves, reminiscent of excitable systems, and stable, arbitrarily large self-standing vortices made of thousands of particles moving at the same speed. Our theoretical model accounts for these phenomena and shows how they can arise in the absence of confining boundaries and individual chirality. We argue that our findings imply that a faithful description of the collective properties of Quincke rollers need to consider the fluid surrounding particles.