Early-stage bifurcation of crystallization in a sphere.

Bifurcations in kinetic pathways decide the evolution of a system. An example is crystallization, in which the thermodynamically stable polymorph may not form due to kinetic hindrance. Here, we use confined self-assembly to investigate the interplay of thermodynamics and kinetics in the crystallization pathways of finite clusters. We report the observation of decahedral clusters from colloidal particles in emulsion droplets and show that these decahedral clusters can be thermodynamically stable, just like icosahedral clusters. Our hard sphere simulations reveal how the development of the early nucleus shape passes through a bifurcation that decides the cluster symmetry. A geometric argument explains why decahedral clusters are kinetically hindered and why icosahedral clusters can be dominant even if they are not in the thermodynamic ground state.

Spontaneous Crystallization in Systems of Binary Hard Sphere Colloids.

Computer simulations of the fluid-to-solid phase transition in the hard sphere system were instrumental for our understanding of crystallization processes. But while colloid experiments and theory have been predicting the stability of several binary hard sphere crystals for many years, simulations were not successful to confirm this phenomenon. Here, we report the growth of binary hard sphere crystals isostructural to Laves phases, AlB_{2}, and NaZn_{13} in simulation directly from the fluid. We analyze particle kinetics during Laves phase growth using event-driven molecular dynamics simulations with and without swap moves that speed up diffusion. The crystallization process transitions from nucleation and growth to spinodal decomposition already deep within the fluid-solid coexistence regime. Finally, we present packing fraction-size ratio state diagrams in the vicinity of the stability regions of three binary crystals.

Complex Crystals from Size-Disperse Spheres.

Colloids are rarely perfectly uniform but follow a distribution of sizes, shapes, and charges. This dispersity can be inherent (static) or develop and change over time (dynamic). Despite a long history of research, the conditions under which nonuniform particles crystallize and which crystal forms is still not well understood. Here, we demonstrate that hard spheres with Gaussian radius distribution and dispersity up to 19% always crystallize if compressed slowly enough, and they do so in surprisingly complex ways. This result is obtained by accelerating event-driven simulations with particle swap moves for static dispersity and particle resize moves for dynamic dispersity. Above 6% dispersity, AB_{2} Laves, AB_{13}, and a region of Frank-Kasper phases are found. The Frank-Kasper region includes a quasicrystal approximant with Pearson symbol oS276. Our findings are relevant for ordering phenomena in soft matter and alloys.

Molecular simulation of homogeneous crystal nucleation of AB2 solid phase from a binary hard sphere mixture.

Co-crystal formation from fluid-mixtures is quite common in a large number of systems. The simplest systems that show co-crystal (also called substitutionally ordered solids) formation are binary hard sphere mixtures. In this work, we study the nucleation of AB2 type solid compounds using Monte Carlo molecular simulations in binary hard sphere mixtures with the size ratio of 0.55. The conditions chosen for the study lie in the region where nucleation of an AB2 type solid competes with that of a pure A solid with a face-centered-cubic structure. The fluid phase composition is kept equal to that of the AB2 type solid. The nucleation free-energy barriers are computed using the seeding technique of Sanz et al. [J. Am. Chem. Soc. 135, 15008 (2013)]. Our simulation results show that the nucleation of the AB2 type solid is favored even under conditions where the pure A solid is more stable. This is primarily due to the similarity in the composition of the fluid phase and the AB2 type solid which in turn leads to much lower interfacial tension between the crystal nucleus and the fluid phase. This system is an example of how the fluid phase composition affects the structure of the nucleating solid phase during crystallization and has relevance to crystal polymorphism during crystallization processes.

Enhancement of nucleation of protein crystals on nano-wrinkled surfaces.

The synthesis of high quality protein crystals is essential for determining their structure. Hence the development of strategies to facilitate the nucleation of protein crystals is of prime importance. Recently, Ghatak and Ghatak [Langmuir 2013, 29, 4373] reported heterogeneous nucleation of protein crystals on nano-wrinkled surfaces. Through a series of experiments on different proteins, they were able to obtain high quality protein crystals even at low protein concentrations and sometimes without the addition of a precipitant. In this study, the mechanism of protein crystal nucleation on nano-wrinkled surfaces is studied through Monte Carlo simulations. The wrinkled surface is modeled by a sinusoidal surface. Free-energy barriers for heterogeneous crystal nucleation on flat and wrinkled surfaces are computed and compared. The study reveals that the enhancement of nucleation is closely related to the two step nucleation process seen during protein crystallization. There is an enhancement of protein concentration near the trough of the sinusoidal surface which aids in nucleation. However, the high curvature at the trough acts as a deterrent to crystal nucleus formation. Hence, significant lowering of the free-energy barrier is seen only if the increase in the protein concentration at the trough is very high.