Minimal Positive Design for Self-Assembly of the Archimedean Tilings

Hierarchical assembly is more robust than egalitarian assembly in synthetic capsids

Self-assembly of complex and functional materials remains a grand challenge in soft material science. Efficient assembly depends on a delicate balance between thermodynamic and kinetic effects, requiring fine-tuning affinities and concentrations of subunits. By contrast, we introduce an assembly paradigm that allows large error-tolerance in the subunit affinity and helps avoid kinetic traps. Our combined experimental and computational approach uses a model system of triangular subunits programmed to assemble into T = 3 icosahedral capsids comprising 60 units. The experimental platform uses DNA origami to create monodisperse colloids whose three-dimensional geometry is controlled to nanometer precision, with two distinct bonds whose affinities are controlled to kBT precision, quantified in situ by static light scattering. The computational model uses a coarse-grained representation of subunits, short-ranged potentials, and Langevin dynamics. Experimental observations and modeling reveal that when the bond affinities are unequal, two distinct hierarchical assembly pathways occur, in which the subunits first form dimers in one case and pentamers in another. These hierarchical pathways produce complete capsids faster and are more robust against affinity variation than egalitarian pathways, in which all binding sites have equal strengths. This finding suggests that hierarchical assembly may be a general engineering principle for optimizing self-assembly of complex target structures.

Two-Dimensional Noble Metal Chalcogenides in the Frustrated Snub-Square Lattice

We study two-dimensional noble metal chalcogenides, with compositions {Cu, Ag, Au}2{S, Se, Te}, crystallizing in a snub-square lattice. This is a semiregular two-dimensional tesselation formed by triangles and squares that exhibits geometrical frustration. We use for comparison a square lattice, from which the snub-square tiling can be derived by a simple rotation of the squares. The monolayer snub-square chalcogenides are very close to thermodynamic stability, with the most stable system (Ag2Se) a mere 7 meV/atom above the convex hull of stability. All compounds studied in the square and snub-square lattice are semiconductors, with band gaps ranging from 0.1 to more than 2.5 eV. Excitonic effects are strong, with an exciton binding energy of around 0.3 eV. We propose the Cu (001) surface as a possible substrate to synthesize Cu2Se, although many other metal and semiconducting surfaces can be found with very good lattice matching.

Predictive Theoretical Framework for Dynamic Control of Bioinspired Hybrid Nanoparticle Self-Assembly

At-will tailoring of the formation and reconfiguration of hierarchical structures is a key goal of modern nanomaterial design. Bioinspired systems comprising biomacromolecules and inorganic nanoparticles have potential for new functional material structures. Yet, consequential challenges remain because we lack a detailed understanding of the temporal and spatial interplay between participants when it is mediated by fundamental physicochemical interactions over a wide range of scales. Motivated by a system in which silica nanoparticles are reversibly and repeatedly assembled using a homobifunctional solid-binding protein and single-unit pH changes under near-neutral solution conditions, we develop a theoretical framework where interactions at the molecular and macroscopic scales are rigorously coupled based on colloidal theory and atomistic molecular dynamics simulations. We integrate these interactions into a predictive coarse-grained model that captures the pH-dependent reversibility and accurately matches small-angle X-ray scattering experiments at collective scales. The framework lays a foundation to connect microscopic details with the macroscopic behavior of complex bioinspired material systems and to control their behavior through an understanding of both equilibrium and nonequilibrium characteristics.

Tiling a tubule: how increasing complexity improves the yield of self-limited assembly

The ability to design and synthesize ever more complicated colloidal particles opens the possibility of self-assembling a zoo of complex structures, including those with one or more self-limited length scales. An undesirable feature of systems with self-limited length scales is that thermal fluctuations can lead to the assembly of nearby, off-target states. We investigate strategies for limiting off-target assembly by using multiple types of subunits. Using simulations and energetics calculations, we explore this concept by considering the assembly of tubules built from triangular subunits that bind edge to edge. While in principle, a single type of triangle can assemble into tubules with a monodisperse width distribution, in practice, the finite bending rigidity of the binding sites leads to the formation of off-target structures. To increase the assembly specificity, we introduce tiling rules for assembling tubules from multiple species of triangles. We show that the selectivity of the target structure can be dramatically improved by using multiple species of subunits, and provide a prescription for choosing the minimum number of subunit species required for near-perfect yield. Our approach of increasing the system's complexity to reduce the accessibility of neighboring structures should be generalizable to other systems beyond the self-assembly of tubules.

Neuroevolutionary Learning of Particles and Protocols for Self-Assembly

Within simulations of molecules deposited on a surface we show that neuroevolutionary learning can design particles and time-dependent protocols to promote self-assembly, without input from physical concepts such as thermal equilibrium or mechanical stability and without prior knowledge of candidate or competing structures. The learning algorithm is capable of both directed and exploratory design: it can assemble a material with a user-defined property, or search for novelty in the space of specified order parameters. In the latter mode it explores the space of what can be made, rather than the space of structures that are low in energy but not necessarily kinetically accessible.

Learning to grow: Control of material self-assembly using evolutionary reinforcement learning

We show that neural networks trained by evolutionary reinforcement learning can enact efficient molecular self-assembly protocols. Presented with molecular simulation trajectories, networks learn to change temperature and chemical potential in order to promote the assembly of desired structures or choose between competing polymorphs. In the first case, networks reproduce in a qualitative sense the results of previously known protocols, but faster and with higher fidelity; in the second case they identify strategies previously unknown, from which we can extract physical insight. Networks that take as input the elapsed time of the simulation or microscopic information from the system are both effective, the latter more so. The evolutionary scheme we have used is simple to implement and can be applied to a broad range of examples of experimental self-assembly, whether or not one can monitor the experiment as it proceeds. Our results have been achieved with no human input beyond the specification of which order parameter to promote, pointing the way to the design of synthesis protocols by artificial intelligence.

Exotic Vortex Lattices in Binary Repulsive Superfluids

We investigate a mixture of two repulsively interacting superfluids with different constituent particle masses: m_{1}≠m_{2}. Solutions to the Gross-Pitaevskii equation for homogeneous infinite vortex lattices predict the existence of rich vortex lattice configurations, a number of which correspond to Platonic and Archimedean planar tilings. Some notable geometries include the snub-square, honeycomb, kagome, and herringbone lattice configurations. We present a full phase diagram for the case m_{2}/m_{1}=2 and list a number of geometries that are found for higher integer mass ratios.

Designing Molecular Building Blocks for the Self-assembly of Complex Porous Networks

The creation of molecular or colloidal building blocks which can self-assemble into complex, ordered porous structures has been long sought-after, and so are the guiding principles behind this creation. The pursuit of this goal has led to the creation of novel classes of materials like metal organic frameworks (MOFs) and covalent organic frameworks (COFs). In theory, a tremendous number of structures can be formed by these materials due to the variety of geometries available to their building blocks. However, most realized crystal structures tend to be simple or homoporous and typically assemble from building blocks with high degrees of symmetry. Building blocks with low degrees of symmetry suitable for assembly into the more complex structures tend to assemble into polymorphous or disordered structures instead. In this work, we use Monte Carlo simulations of patchy vertex-like building blocks to show how the addition of chemical specificity via orthogonally reacting functional sites can allow vertex-like building blocks with even asymmetric geometries to self-assemble into ordered crystallites of various complex structures. In addition to demonstrating the utility of such a strategy in creating ordered, heteroporous structures, we also demonstrate that it can be used as a means for tuning specific features of the crystal structure, accomplishing such aims as the control of relative pore sizes. We also discuss heuristics for properly designing molecules so that they can assemble into target structures.

Multi-photon patterning of photoactive o-nitrobenzyl ligands bound to gold surfaces

We quantitatively investigate lithographic patterning of a thiol-anchored self-assembled monolayer (SAM) of photocleavable o-nitrobenzyl ligands on gold through a multi-photon absorption process at 1.7 eV (730 nm wavelength). The photocleaving rate increases faster than the square of the incident light intensity, indicating a process more complex than simple two-photon absorption. We tentatively ascribe this observation to two-photon absorption that triggers the formation of a long-lived intermediate aci-nitro species whose decomposition yield is partially determined either by absorption of additional photons or by a local temperature that is elevated by the incident light. At the highest light intensities, thermal processes compete with photoactivation and lead to damage of the SAM. The threshold is high enough that this destructive process can largely be avoided, even while power densities are kept sufficiently large that complete photoactivation takes place on time scales of tens of seconds to a few minutes. This means that this type of ligand can be activated at visible and near infrared wavelengths where plasmonic resonances can easily be engineered in metal nanostructures, even though their single-photon reactivity at these wavelengths is negligible. This will allow selective functionalization of plasmon hotspots, which in addition to high resolution lithographic applications would be of benefit to applications such as Surface Enhanced Raman Spectroscopy and plasmonic photocatalysis as well as directed bottom-up nanoassembly.

Topological flat band, Dirac fermions and quantum spin Hall phase in 2D Archimedean lattices

We've constructed a guide to the electronic properties and topological phases of Archimedean lattices. Within these lattices, a rich electronic structure emerges forming type-I and II Dirac fermions, topological flat bands and high-degeneracy points.

Nematic liquid crystals of bifunctional patchy spheres

Anisotropic interactions can bring about the formation, through self-assembly, of semi-flexible chains, which in turn can give rise to nematic phases for suitable temperatures and concentrations. A minimalist model constituted of hard cylinders decorated with attractive sites has been already extensively studied numerically. Simulation data shows that a theoretical approach recently proposed is able to properly capture the physical properties of these self-assembly-driven liquid crystals. Here, we investigated a simpler model constituted of bifunctional Kern-Frenkel hard spheres which does not possess steric anisotropy but which can undergo a istropic-nematic transition as a result of their self-assembly into semi-flexible chains. For this model we compare an accurate numerical estimate of isotropic-nematic phase boundaries with theoretical predictions. The theoretical treatment, originally proposed for cylinder-like particles, has been greatly simplified and its predictions are in good agreement with numerical results. Finally, we also assess a crucial, and not obvious, hypothesis used in the theory, i.e. the ability of the Onsager trial function to properly model particle orientation in the presence of aggregation, that has not been properly checked yet.

Molecular control over colloidal assembly

Contemporary chemical and material engineering often takes inspiration from nature, targeting for example strong yet light materials and materials composed of highly ordered domains at multiple different lengthscales for fundamental science and applications in e.g. sensing, catalysis, coating technology, and delivery. The preparation of such hierarchically structured functional materials through guided bottom-up assembly of synthetic building blocks requires a high level of control over their synthesis, interactions and assembly pathways. In this perspective we showcase recent work demonstrating how molecular control can be exploited to direct colloidal assembly into responsive materials with mechanical, optical or electrical properties that can be adjusted post-synthesis with external cues.

Irregular model DNA particles self-assemble into a regular structure

DNA nanoparticles with three-fold coordination have been observed to self-assemble in experiment into a network equivalent to the hexagonal (6.6.6) tiling, and a network equivalent to the 4.8.8 Archimedean tiling. Both networks are built from a single type of vertex. Here we use analytic theory and equilibrium and dynamic simulation to show that a model particle, whose rotational properties lie between those of the vertices of the 6.6.6 and 4.8.8 networks, can self-assemble into a network built from three types of vertex. Important in forming this network is the ability of the particle to rotate when bound, thereby allowing the formation of more than one type of binding motif. The network in question is equivalent to a false tiling, a periodic structure built from irregular polygons, and possesses 40 particles in its unit cell. The emergence of this complex structure, whose symmetry properties are not obviously related to those of its constituent particles, highlights the potential for creating new structures from simple variants of existing nanoparticles.

Assembly of trivalent particles under confinement: from an exotic solid phase to a liquid phase at low temperature

Using computer simulations, we study the phase diagram of a two-dimensional system of disk particles with three patches distributed symmetrically along the particle equator. The geometry of the particles is compatible with a honey-comb lattice at moderately low temperature and pressure, whereas it is expected that the system forms a close-packed triangular lattice at high temperature and pressure. The effect of patch size within the single bond per patch regime was investigated, and it was found that the topology of the phase diagram changes drastically with patch size. Interestingly, in particles with small patches (with a half opening angle of 10°), the fluid transforms upon increasing the pressure into a rather exotic phase that can be understood as a honey-comb lattice whose voids are filled continuously with additional particles that remain, on average, unbound. Eventually, all the voids are occupied so that particles are located at the positions of a triangular lattice, but only two thirds of the particles are orientationally ordered whereas the remaining one third can rotate almost freely as in a plastic crystal. At moderately low temperature, the fluid transforms into a nearly empty honey-comb lattice, whereas at high temperature it transforms directly into the almost filled lattice. Interestingly, for particles with big patches (with a half opening angle of 20°), the honey-comb and triangular lattices are separated by a liquid phase that remains stable down to fairly low temperatures. Less surprisingly, only particles with big patches exhibit an equilibrium gas-liquid separation.