Assembly of clathrates from tetrahedral patchy colloids with narrow patches

Interplay between the Formation of Colloidal Clathrate and Cubic Diamond Crystals

Controlling the valency of directional interactions of patchy particles is insufficient for the selective formation of target crystalline structures due to the competition between phases of similar free energy. Examples of such are stacking hybrids of interwoven hexagonal and cubic diamonds with (i) its liquid phase, (ii) arrested glasses, or (iii) clathrates, all depending on the relative patch size, despite being within the one-bond-per-patch regime. Herein, using molecular dynamics simulations, we demonstrate that although tetrahedral patchy particles with narrow patches can assemble into clathrates or stacking hybrids in the bulk, this behavior can be suppressed by the application of external surface potential. Depending on its strength, the selective growth of either cubic diamond crystals or empty sII clathrate cages can be achieved. The formation of a given ordered network depends on the structure of the first adlayer, which is commensurate with the emerging network.

Spearheading a new era in complex colloid synthesis with TPM and other silanes

Colloid science has recently grown substantially owing to the innovative use of silane coupling agents (SCAs), especially 3-trimethoxysilylpropyl methacrylate (TPM). SCAs were previously used mainly as modifying agents, but their ability to form droplets and condense onto pre-existing structures has enabled their use as a versatile and powerful tool to create novel anisotropic colloids with increasing complexity. In this Review, we highlight the advances in complex colloid synthesis facilitated by the use of TPM and show how this has driven remarkable new applications. The focus is on TPM as the current state-of-the-art in colloid science, but we also discuss other silanes and their potential to make an impact. We outline the remarkable properties of TPM colloids and their synthesis strategies, and discuss areas of soft matter science that have benefited from TPM and other SCAs.

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.

Pursuing colloidal diamonds

The endeavor to selectively fabricate a cubic diamond is challenging due to the formation of competing phases such as its hexagonal polymorph or others possessing similar free energy. The necessity to achieve this is of paramount importance since the cubic diamond is the only polymorph exhibiting a complete photonic bandgap, making it a promising candidate in view of photonic applications. Herein, we demonstrate that due to the presence of an external field and delicate manipulation of its strength we can attain selectivity in the formation of a cubic diamond in a one-component system comprised of designer tetrahedral patchy particles. The driving force of such a phenomenon is the structure of the first adlayer which is commensurate with the (110) face of the cubic diamond. Moreover, after a successful nucleation event, once the external field is turned off, the structure remains stable, paving an avenue for further post-synthetic treatment.

Phases of surface-confined trivalent colloidal particles

Patchy colloids promise the design and modelling of complex materials, but the realization of equilibrium patchy particle structures remains challenging. Here, we assemble pseudo-trivalent particles and elucidate their phase behaviour when confined to a plane. We observe the honeycomb phase, as well as more complex amorphous network and triangular phases. Structural analysis performed on the three condensed phases reveals their shared structural motifs. Using a combined experimental and simulation approach, we elucidate the energetics of these phases and construct the phase diagram of this system, using order parameters to determine the phase coexistence lines. Our results reveal the rich phase behaviour that a relatively simple patchy particle system can display, and open the door to a larger joined simulation and experimental exploration of the full patchy-particle phase space.

Visualizing defect dynamics by assembling the colloidal graphene lattice

Graphene has been under intense scientific interest because of its remarkable optical, mechanical and electronic properties. Its honeycomb structure makes it an archetypical two-dimensional material exhibiting a photonic and phononic band gap with topologically protected states. Here, we assemble colloidal graphene, the analogue of atomic graphene using pseudo-trivalent patchy particles, allowing particle-scale insight into crystal growth and defect dynamics. We directly observe the formation and healing of common defects, like grain boundaries and vacancies using confocal microscopy. We identify a pentagonal defect motif that is kinetically favoured in the early stages of growth, and acts as seed for more extended defects in the later stages. We determine the conformational energy of the crystal from the bond saturation and bond angle distortions, and follow its evolution through the energy landscape upon defect rearrangement and healing. These direct observations reveal that the origins of the most common defects lie in the early stages of graphene assembly, where pentagons are kinetically favoured over the equilibrium hexagons of the honeycomb lattice, subsequently stabilized during further growth. Our results open the door to the assembly of complex 2D colloidal materials and investigation of their dynamical, mechanical and optical properties.

The physics of empty liquids: from patchy particles to water

Empty liquids represent a wide class of materials whose constituents arrange in a random network through reversible bonds. Many key insights on the physical properties of empty liquids have originated almost independently from the study of colloidal patchy particles on one side, and a large body of theoretical and experimental research on water on the other side. Patchy particles represent a family of coarse-grained potentials that allows for a precise control of both the geometric and the energetic aspects of bonding, while water has arguably the most complex phase diagram of any pure substance, and a puzzling amorphous phase behavior. It was only recently that the exchange of ideas from both fields has made it possible to solve long-standing problems and shed new light on the behavior of empty liquids. Here we highlight the connections between patchy particles and water, focusing on the modelling principles that make an empty liquid behave like water, including the factors that control the appearance of thermodynamic and dynamic anomalies, the possibility of liquid-liquid phase transitions, and the crystallization of open crystalline structures.

Facile self-assembly of colloidal diamond from tetrahedral patchy particles via ring selection

The self-assembly of colloidal diamond–a classic example of an open crystal with the low coordination number of four and much sought after due to its applications in visible light management–from designer spherical colloidal particles has proved challenging over the years. The formation of the diamond lattice from tetrahedral patchy particles is hampered by the propensity to form competing open periodic structures for narrow patches or dynamically arrested states for wider patches, leaving a narrow window in design space where diamond crystals may be realized. Our two-component system of designer tetrahedral patchy particles supports a significantly wider range for patch sizes for programmed self-assembly, thus facilitating experimental fabrication, and offers fundamental insight into crystallization into open lattices.

Diamond-structured crystals, particularly those with cubic symmetry, have long been attractive targets for the programmed self-assembly of colloidal particles, due to their applications as photonic crystals that can control the flow of visible light. While spherical particles decorated with four patches in a tetrahedral arrangement—tetrahedral patchy particles—should be an ideal building block for this endeavor, their self-assembly into colloidal diamond has proved elusive. The kinetics of self-assembly pose a major challenge, with competition from an amorphous glassy phase, as well as clathrate crystals, leaving a narrow widow of patch widths where tetrahedral patchy particles can self-assemble into diamond crystals. Here we demonstrate that a two-component system of tetrahedral patchy particles, where bonding is allowed only between particles of different types to select even-member rings, undergoes crystallization into diamond crystals over a significantly wider range of patch widths conducive for experimental fabrication. We show that the crystallization in the two-component system is both thermodynamically and kinetically enhanced, as compared to the one-component system. Although our bottom-up route does not lead to the selection of the cubic polytype exclusively, we find that the cubicity of the self-assembled crystals increases with increasing patch width. Our designer system not only promises a scalable bottom-up route for colloidal diamond but also offers fundamental insight into crystallization into open lattices.

Colloidal Self-Assembly Approaches to Smart Nanostructured Materials

Colloidal self-assembly refers to a solution-processed assembly of nanometer-/micrometer-sized, well-dispersed particles into secondary structures, whose collective properties are controlled by not only nanoparticle property but also the superstructure symmetry, orientation, phase, and dimension. This combination of characteristics makes colloidal superstructures highly susceptible to remote stimuli or local environmental changes, representing a prominent platform for developing stimuli-responsive materials and smart devices. Chemists are achieving even more delicate control over their active responses to various practical stimuli, setting the stage ready for fully exploiting the potential of this unique set of materials. This review addresses the assembly of colloids into stimuli-responsive or smart nanostructured materials. We first delineate the colloidal self-assembly driven by forces of different length scales. A set of concepts and equations are outlined for controlling the colloidal crystal growth, appreciating the importance of particle connectivity in creating responsive superstructures. We then present working mechanisms and practical strategies for engineering smart colloidal assemblies. The concepts underpinning separation and connectivity control are systematically introduced, allowing active tuning and precise prediction of the colloidal crystal properties in response to external stimuli. Various exciting applications of these unique materials are summarized with a specific focus on the structure-property correlation in smart materials and functional devices. We conclude this review with a summary of existing challenges in colloidal self-assembly of smart materials and provide a perspective on their further advances to the next generation.

Colloidal Particles with Triangular Patches

Self-assembling colloidal particles into clathrate hydrates requires the particles to have tetrahedral bonds in the eclipsed conformation. It has been suggested that colloidal particles with eclipsed triangular-shaped patches can form clusters in the eclipsed conformation that leads to colloidal clathrate hydrates. However, in experiments, patches have been limited to circular shapes due to surface energy minimization. Here, we extend the particle synthesis strategy and show that colloidal particles with triangular patches can be readily fabricated by controlling the viscosity of the liquid oil droplets during a colloidal fusion process. The position, orientation, curvature, shape, and size of the patches are all exclusively determined by the intrinsic symmetry of the colloidal clusters, resulting in dipatch particles with eclipsed patches and tetrahedral patchy particles with patch vertices pointing toward each other. Patch curvature can be controlled by tuning the viscosity of the oil droplets and using different surfactants. Using strain-promoted azide-alkyne cycloaddition, single-stranded DNA can be selectively functionalized on the patches. However, after annealing these particles, dipatch particles form chains because the patches are too small to form clathrate hydrates. Under certain conditions, tetrahedral triangular patchy particles should prefer the eclipsed conformation, as it maximizes DNA hybridization. However, we observe random aggregates, which result from having triangular patches that are too big. We estimate that tetrahedral patchy particles that can crystallize need to be less than 1 μm in diameter.

From colloidal particles to photonic crystals: advances in self-assembly and their emerging applications

Over the last three decades, photonic crystals (PhCs) have attracted intense interests thanks to their broad potential applications in optics and photonics. Generally, these structures can be fabricated via either "top-down" lithographic or "bottom-up" self-assembly approaches. The self-assembly approaches have attracted particular attention due to their low cost, simple fabrication processes, relative convenience of scaling up, and the ease of creating complex structures with nanometer precision. The self-assembled colloidal crystals (CCs), which are good candidates for PhCs, have offered unprecedented opportunities for photonics, optics, optoelectronics, sensing, energy harvesting, environmental remediation, pigments, and many other applications. The creation of high-quality CCs and their mass fabrication over large areas are the critical limiting factors for real-world applications. This paper reviews the state-of-the-art techniques in the self-assembly of colloidal particles for the fabrication of large-area high-quality CCs and CCs with unique symmetries. The first part of this review summarizes the types of defects commonly encountered in the fabrication process and their effects on the optical properties of the resultant CCs. Next, the mechanisms of the formation of cracks/defects are discussed, and a range of versatile fabrication methods to create large-area crack/defect-free two-dimensional and three-dimensional CCs are described. Meanwhile, we also shed light on both the advantages and limitations of these advanced approaches developed to fabricate high-quality CCs. The self-assembly routes and achievements in the fabrication of CCs with the ability to open a complete photonic bandgap, such as cubic diamond and pyrochlore structure CCs, are discussed as well. Then emerging applications of large-area high-quality CCs and unique photonic structures enabled by the advanced self-assembly methods are illustrated. At the end of this review, we outlook the future approaches in the fabrication of perfect CCs and highlight their novel real-world applications.

Revealing pseudorotation and ring-opening reactions in colloidal organic molecules

Colloids have a rich history of being used as 'big atoms' mimicking real atoms to study crystallization, gelation and the glass transition of condensed matter. Emulating the dynamics of molecules, however, has remained elusive. Recent advances in colloid chemistry allow patchy particles to be synthesized with accurate control over shape, functionality and coordination number. Here, we show that colloidal alkanes, specifically colloidal cyclopentane, assembled from tetrameric patchy particles by critical Casimir forces undergo the same chemical transformations as their atomic counterparts, allowing their dynamics to be studied in real time. We directly observe transitions between chair and twist conformations in colloidal cyclopentane, and we elucidate the interplay of bond bending strain and entropy in the molecular transition states and ring-opening reactions. These results open the door to investigate complex molecular kinetics and molecular reactions in the high-temperature classical limit, in which the colloidal analogue becomes a good model.

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.

Colloidal diamond

Self-assembling colloidal particles in the cubic diamond crystal structure could potentially be used to make materials with a photonic bandgap^1-3. Such materials are beneficial because they suppress spontaneous emission of light¹ and are valued for their applications as optical waveguides, filters and laser resonators⁴, for improving light-harvesting technologies^{5-7 and for other applications4,8}. Cubic diamond is preferred for these applications over more easily self-assembled structures, such as face-centred-cubic structures^9,10, because diamond has a much wider bandgap and is less sensitive to imperfections^11,12. In addition, the bandgap in diamond crystals appears at a refractive index contrast of about 2, which means that a photonic bandgap could be achieved using known materials at optical frequencies; this does not seem to be possible for face-centred-cubic crystals^3,13. However, self-assembly of colloidal diamond is challenging. Because particles in a diamond lattice are tetrahedrally coordinated, one approach has been to self-assemble spherical particles with tetrahedral sticky patches^14-16. But this approach lacks a mechanism to ensure that the patchy spheres select the staggered orientation of tetrahedral bonds on nearest-neighbour particles, which is required for cubic diamond^15,17. Here we show that by using partially compressed tetrahedral clusters with retracted sticky patches, colloidal cubic diamond can be self-assembled using patch-patch adhesion in combination with a steric interlock mechanism that selects the required staggered bond orientation. Photonic bandstructure calculations reveal that the resulting lattices (direct and inverse) have promising optical properties, including a wide and complete photonic bandgap. The colloidal particles in the self-assembled cubic diamond structure are highly constrained and mechanically stable, which makes it possible to dry the suspension and retain the diamond structure. This makes these structures suitable templates for forming high-dielectric-contrast photonic crystals with cubic diamond symmetry.

Designing Patchy Interactions to Self-Assemble Arbitrary Structures

One of the fundamental goals of nanotechnology is to exploit selective and directional interactions between molecules to design particles that self-assemble into desired structures, from capsids, to nanoclusters, to fully formed crystals with target properties (e.g., optical, mechanical, etc.). Here, we provide a general framework which transforms the inverse problem of self-assembly of colloidal crystals into a Boolean satisfiability problem for which solutions can be found numerically. Given a reference structure and the desired number of components, our approach produces designs for which the target structure is an energy minimum, and also allows us to exclude solutions that correspond to competing structures. We demonstrate the effectiveness of our approach by designing model particles that spontaneously nucleate milestone structures such as the cubic diamond, the pyrochlore, and the clathrate lattices.

Surveying the free energy landscape of clusters of attractive colloidal spheres

Controlling the assembly of colloidal particles into specific structures has been a long-term goal of the soft materials community. Much can be learned about the process of self-assembly by examining the early stage assembly into clusters. For the simple case of hard spheres with short-range attractions, the rigid clusters of N particles (where N is small) have been enumerated theoretically and tested experimentally. Less is known, however, about how the free energy landscapes are altered when the inter-particle potential is long-ranged. In this work, we demonstrate how adaptive biasing in molecular simulations may be used to pinpoint shifts in the stability of colloidal clusters as the inter-particle potential is varied. We also discuss the generality of our techniques and strategies for application to related molecular systems.