Design of Patchy Rhombi: From Close-Packed Tilings to Open Lattices

Anisotropic functionalized platelets: percolation, porosity and network properties

Anisotropic functionalized platelets are able to model the assembly behaviour of molecular systems in two dimensions thanks to the unique combination of steric and bonding constraints. The assembly scenarios can vary from open to close-packed crystals, finite clusters and chains, according to the features of the imposed constraints. In this work, we focus on the assembly of equilibrium networks. These networks can be seen as disordered, porous monolayers and can be of interest for instance in nano-filtration and optical applications. We investigate the formation and properties of two dimensional networks from shape anisotropic colloids functionalized with four patches. We characterize the connectivity properties, the typical local bonding motives, as well as the geometric features of the emerging networks for a large variety of different systems. Our results show that networks of shape anisotropic colloids assemble into highly versatile network topologies, that may be utilized for applications at the nanoscale.

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.

Coarse-Grained Modeling of On-Surface Self-Assembly of Mixtures Comprising Di-Substituted Polyphenyl-Like Compounds and Metal Atoms of Different Sizes

We use coarse-grained molecular dynamics simulations to investigate the phase behavior of binary mixtures of di-substituted polyphenyl-like compounds and metal atoms of different sizes. We have estimated the possible on-surface behavior that could be useful for the target design of particular ordered networks. We have found that due to the variation of system conditions, we can observe the formation of the parallel, square, and triangular networks, Archimedean tessellation, and "spaghetti wires." All of these structures have been characterized by various order parameters.

Symmetry-derived structure directing agents for two-dimensional crystals of arbitrary colloids

We derive properties of self-assembling rings which can template the organization of an arbitrary colloid into any periodic symmetry in two Euclidean dimensions. By viewing this as a tiling problem, we illustrate how the shape and chemical patterning of these rings are derivable, and are explicitly reflected by the symmetry group's orbifold symbol. We performed molecular dynamics simulations to observe their self-assembly and found 5 different characteristics which could be easily rationalized on the basis of this symbol. These include systems which undergo chiral phase separation, are addressably complex, exhibit self-limiting growth into clusters, form ordered "rods" in only one-dimension akin to a smectic phase, and those from symmetry groups which are pluripotent and allow one to select rings which exhibit different behaviors. We discuss how the curvature of the ring's edges plays an integral role in achieving correct self-assembly, and illustrate how to obtain these shapes. This provides a method for patterning colloidal systems at interfaces without explicitly programming this information onto the colloid itself.

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).

A Matter of Size and Placement: Varying the Patch Size of Anisotropic Patchy Colloids

Non-spherical colloids provided with well-defined bonding sites—often referred to as patches—are increasingly attracting the attention of materials scientists due to their ability to spontaneously assemble into tunable surface structures. The emergence of two-dimensional patterns with well-defined architectures is often controlled by the properties of the self-assembling building blocks, which can be either colloidal particles at the nano- and micro-scale or even molecules and macromolecules. In particular, the interplay between the particle shape and the patch topology gives rise to a plethora of tilings, from close-packed to porous monolayers with pores of tunable shapes and sizes. The control over the resulting surface structures is provided by the directionality of the bonding mechanism, which mostly relies on the selective nature of the patches. In the present contribution, we investigate the effect of the patch size on the assembly of a class of anisotropic patchy colloids—namely, rhombic platelets with four identical patches placed in different arrangements along the particle edges. Larger patches are expected to enhance the bond flexibility, while simultaneously reducing the bond selectivity as the single bond per patch condition—which would guarantee a straightforward mapping between local bonding arrangements and long-range pattern formation—is not always enforced. We find that the non-trivial interplay between the patch size and the patch position can either promote a parallel particle arrangement with respect to a non-parallel bonding scenario or give rise to a variety a bonded patterns, which destroy the order of the tilings. We rationalize the occurrence of these two different regimes in terms of single versus multiple bonds between pairs of particles and/or patches.

Simulations of the 2D self-assembly of tripod-shaped building blocks

We introduce a molecular dynamics (MD) coarse-grained model for the description of tripod building blocks. This model has been used by us already for linear, V-shape, and tetratopic molecules. We wanted to further extend its possibilities to trifunctional molecules to prove its versatility. For the chosen systems we have also compared the MD results with Monte Carlo results on a triangular lattice. We have shown that the constraints present in the latter method can enforce the formation of completely different structures, not reproducible with off-lattice simulations. In addition to that, we have characterized the obtained structures regarding various parameters such as theoretical diffraction pattern and average association number.

How patchiness controls the properties of chain-like assemblies of colloidal platelets

Patchy colloidal platelets with non-spherical shapes have been realized with different materials at length scales ranging from nanometers to microns. While the assembly of these hard shapes tends to maximize edge-to-edge contacts, as soon as a directional attraction is added-by means of, e.g. specific ligands along the particle edges-a competition between shape and bonding anisotropy sets in, giving rise to a complex assembly scenario. Here we focus on a two-dimensional system of patchy rhombi, i.e. colloidal platelets with a regular rhombic shape decorated with bonding sites along their perimeter. Specifically, we consider rhombi with two patches, placed on either opposite or adjacent edges. While for the first particle class only chains can form, for the latter we observe the emergence of either chains or loops, depending on the system parameters. According to the patch positioning-classified in terms of different configurations, topologies and distances from the edge center-we are able to characterize the emerging chain-like assemblies in terms of length, packing abilities, flexibility properties and nematic ordering.

Hierarchical self-assembly of patchy colloidal platelets

Anisotropy at the level of the inter-particle interaction provides the particles with specific instructions for the self-assembly of target structures. The ability to synthesize non-spherical colloids, together with the possibility of controlling the particle bonding pattern via suitably placed interaction sites, is nowadays enlarging the playing field for materials design. We consider a model of anisotropic colloidal platelets with regular rhombic shape and two attractive sites placed along adjacent edges and we run Monte Carlo simulations in two-dimensions to investigate the two-stage assembly of these units into clusters with well-defined symmetries and, subsequently, into extended lattices. Our focus is on how the site positioning and site-site attraction strength can be tuned to obtain micellar aggregates that are robust enough to successively undergo to a second-stage assembly from sparse clusters into a stable hexagonal lattice.