Crystal growth kinetics of triblock Janus colloids

Self-Assembly of Model Three- and Four-Patch Colloidal Particles in Two Dimensions

A coarse-grained effective solvent model of two-patch particles is extended to study the self-assembly of three- and four-patch particles to two-dimensional honeycomb and square lattices, respectively. Employing this model, grand canonical ensemble simulations are done to calculate vapor-liquid equilibria and the critical temperatures for patchy particles of various patch widths. The range of stability of the liquid, although very limited compared to isotropic particles, which interact through a longer-range potential, depends on the patch width and on the number of patches. Biased sampling and unbiased simulations are also done to investigate the mechanism of nucleation and crystal growth for honeycomb and square lattices, self-assembled from three- and four-patch particles, respectively. A two-step mechanism governs the nucleation of both lattices. In the first step, the particles form a dense amorphous network, and in the second step, the particles inside the amorphous network reorient to form crystalline nuclei. Barrier heights for the nucleation of honeycomb and square lattices are 7.8 kBT and 7.4 kBT, which are close to the reported values for the nucleation of the kagome lattice. In agreement with confocal microscopy experiments, the self-assembly in a honeycomb lattice involves the formation of 5- to 7-membered rings. The 5- and 7-membered rings hamper the nucleation of the honeycomb lattice, through defect formation and rotation of the symmetry planes of crystals that form at their surfaces. With the progress of self-assembly, a substantial amount of restructuring of the defects and crystals in their vicinity is needed to heal the defects.

Self-Assembly Pathways of Triblock Janus Particles into 3D Open Lattices

The self-assembly of triblock Janus particles is simulated from a fluid to 3D open lattices: pyrochlore, perovskite, and diamond. The coarse-grained model explicitly takes into account the chemical details of the Janus particles (attractive patches at the poles and repulsion around the equator) and it contains explicit solvent particles. Hydrodynamic interactions are accounted for by dissipative particle dynamics. The relative stability of the crystals depends on the patch width. Narrow, intermediate, and wide patches stabilize the pyrochlore-, the perovskite-, and the diamond-lattice, respectively. The nucleation of all three lattices follows a two-step mechanism: the particles first agglomerate into a compact and disordered liquid cluster, which does not crystallize until it has grown to a threshold size. Second, the particles reorient inside this cluster to form crystalline nuclei. The free-energy barriers for the nucleation of pyrochlore and perovskite are ≈10 kBT, which are close to the nucleation barriers of previously studied 2D kagome lattices. The barrier height for the nucleation of diamond, however, is much larger (>20 kBT), as the symmetry of the triblock Janus particles is not perfect for a diamond structure. The large barrier is associated with the reorientation of particles, i.e., the second step of the nucleation mechanism.

Bottom-Up Construction of the Interaction between Janus Particles

While the interaction between two uniformly charged spheres─viz colloids─is well-known, the interaction between nonuniformly charged spheres such as Janus particles is not. Specifically, the Derjaguin approximation relates the potential energy between two spherical particles with the interaction energy Vpl per unit area between two planar surfaces. The formalism has been extended to obtain a quadrature expression for the screened electrostatic interaction between Janus colloids with variable relative orientations. The interaction is decomposed into three zones in the parametric space, distinguished by their azimuthal symmetry. Different specific situations are examined to estimate the contributions of these zones to the total energy. The effective potential Vpl is renormalized such that the resulting potential energy is identical with the actual one for the most preferable relative orientations between the Janus particles. The potential energy as a function of the separation distance and the mutual orientation of a pair of particles compares favorably between the analytical (but approximate) form and the rigorous point-wise computational model used earlier. Coarse-grained models of Janus particles can thus implement this potential model efficiently without loss of generality.

Two-Dimensional Structures Formed by Triblock Patchy Particles with Two Different Patches

Two-dimensional structures formed by spherical triblock patchy particles are examined by performing Monte Carlo simulations. In the model, the triblock patchy particles have two different types of patches at the polar positions. The patch sizes are different from each other, and the attractive interaction acts only between the same types of patches. The particles translate on a flat plane and rotate three-dimensionally. When varying the two patch sizes, the pressure, and interaction energy, various structures are observed. When the difference between two patch sizes is small, kagome lattices, hexagonal structures, and two-dimensional dodecagonal quasi-crystal structures are observed. When the difference between two patch sizes is large, chain-like structures are created. With lower temperature, sparse structures such as ring-like structures form.

Colloidal cubic diamond photonic crystals through cooperative self-assembly

Colloidal cubic diamond crystals with low-coordinated and staggered structures could display a wide photonic bandgap at low refractive index contrasts, which makes them extremely valuable for photonic applications. However, self-assembly of cubic diamond crystals using simple colloidal building blocks is still considerably challenging, due to their low packing fraction and mechanical instability. Here we propose a new strategy for constructing colloidal cubic diamond crystals through cooperative self-assembly of surface-anisotropic triblock Janus colloids and isotropic colloidal spheres into superlattices. In self-assembly, cooperativity is achieved by tuning the interaction and particle size ratio of colloidal building blocks. The pyrochlore lattice formed by self-assembly of triblock Janus colloids acts as a soft template to direct the packing of colloidal spheres into cubic diamond lattices. Numerical simulations show that this cooperative self-assembly strategy works well in a large range of particle size ratio of these two species. Moreover, photonic band structure calculations reveal that the resulting cubic diamond lattices exhibit wide and complete photonic bandgaps and the width and frequency of the bandgaps can also be easily adjusted by tuning the particle size ratio. Our work will open up a promising avenue toward photonic bandgap materials by cooperative self-assembly employing surface-anisotropic Janus or patchy colloids as a soft template.

Self-Assembly of Model Triblock Janus Colloidal Particles in Two Dimensions

A simplified two-dimensional effective-solvent model of triblock Janus particles, consisting of three interaction sites in a linear configuration, a core particle, and two particles modeling the attractive patches at the poles, is developed to study the mechanism of nucleation and self-assembly in triblock Janus particles. The potential energy parameters are tuned against phase transition temperatures and free energy barriers to the nucleation of crystalline phases, calculated from our previous detailed model of Janus particles. Vapor-liquid equilibria and critical temperatures are calculated by grand-canonical molecular dynamics simulations for particles of different patch widths. With metadynamics, phase equilibria, mechanism of nucleation, and free energy barriers to nucleation are investigated. The minimum free energy path to nucleation indicates two steps. The first step, with a higher free energy increase, consists of the densification of the fluid into a disordered cluster. In the second step, of a lower free energy barrier, the inner particles of the disordered cluster reorient to form a crystalline nucleus. This two-step mechanism of nucleation of a kagome lattice is in complete agreement with the experiment and with our previous simulations using a detailed model of Janus particles. Large systems at a slight supersaturation generate multiple crystalline domains, which are misaligned at the grain boundaries. In complete agreement with the experiment and with previous simulation results, we observe a two-step mechanism for crystal growth: melting of the smaller (less stable) crystallites to a fluid followed by recrystallization at the surface of neighboring bigger (more stable) crystallites. A comparison of the present softer modeling of a Janus particle with harder models in the literature for self-assembly of Janus particles indicates that softer potentials stabilize open lattices (e.g., kagome) more than dense lattices (e.g., hexagonal). Also, experimental locations of phase transition points and barrier heights to nucleation are better reproduced by the present model than by the existing simple models.

Softness-Enhanced Self-Assembly of Pyrochlore- and Perovskite-like Colloidal Photonic Crystals from Triblock Janus Particles

It remains extremely challenging to build three-dimensional photonic crystals with complete photonic bandgaps by simple and experimentally realizable colloidal building blocks. Here, we demonstrate that particle softness can enhance both the self-assembly of pyrochlore- and perovskite-like lattice structures from simple deformable triblock Janus colloids and their photonic bandgap performances. Dynamics simulation results show that the region of stability of pyrochlore lattices can be greatly expanded by appropriately increasing softness, and the perovskite lattices are unexpectedly obtained at enough high softness. Photonic calculations show that the direct pyrochlore lattices formed from overlapping soft triblock Janus particles exhibit even larger photonic bandgaps than the ideal nonoverlapping pyrochlore lattice, and proper overlap arising from softness can also dramatically improve the photonic properties of the inverse pyrochlore and perovskite lattices. Our study offers a new and feasible self-assembly path toward three-dimensional photonic crystals with large and robust photonic bandgaps.

Mechanisms of Nucleation and Solid-Solid-Phase Transitions in Triblock Janus Assemblies

A model, including the chemical details of core nanoparticles as well as explicit surface charges and hydrophobic patches, of triblock Janus particles is employed to simulate nucleation and solid-solid phase transitions in two-dimensional layers. An explicit solvent and a substrate are included in the model, and hydrodynamic and many-body interactions were taken into account within many-body dissipative particle dynamics simulation. In order not to impose a mechanism a priori, we performed free (unbiased) simulations, leaving the system the freedom to choose its own pathways. In agreement with the experiment and previous biased simulations, a two-step mechanism for the nucleation of a kagome lattice from solution was detected. However, a distinct feature of the present unbiased versus biased simulations is that multiple nuclei emerge from the solution; upon their growth, the aligned and misaligned facets at the grain boundaries are introduced into the system. The liquid-like particles trapped between the neighboring nuclei connect them together. A mismatch in the symmetry planes of neighboring nuclei hinders the growth of less stable (smaller) nuclei. Unification of such nuclei at the grain boundaries of misaligned facets obeys a two-step mechanism: melting of the smaller nuclei, followed by subsequent nucleation of liquid-like particles at the interface of bigger neighboring nuclei. Besides, multiple postcritical nuclei are formed in the simulation box; the growth of some of which stops due to introduction of a strain in the system. Such an incomplete nucleation/growth mechanism is in complete agreement with the recent experiments. The solid-solid (hexagonal-to-kagome) phase transition, at weak superheatings, obeys a two-step mechanism: a slower step (formation of a liquid droplet), followed by a faster step (nucleation of kagome from the liquid droplet).

Directed assembly of photonic crystals through simple substrate patterning

We present molecular dynamics simulations of the epitaxial growth of high quality crystalline films for photonics applications from triblock Janus colloids. With a featureless substrate, the film morphologies were qualitatively similar to previously reported experimental results, with two stacking polymorphs appearing in nearly equal proportion. However, with a patterned substrate deliberately designed to be easy to fabricate by standard photolithography techniques, both the grain size and selectivity towards the photonically active polymorph were greatly improved. We also evaluated the effect of particle flux to find that lower flux led to higher quality crystals, while higher flux led to frustrated films with smaller crystalline domains. Our results suggest that carefully engineered but simple to manufacture patterned substrates could yield self-assembled single crystals of sufficient quality to exhibit a complete photonic bandgap.