Design of patchy rhombi: from close-packed tilings to open lattices.

In the realm of functional materials, the production of two-dimensional structures with tunable porosity is of paramount relevance for many practical applications: surfaces with regular arrays of pores can be used for selective adsorption or immobilization of guest units that are complementary in shape and/or size to the pores, thus achieving, for instance, selective filtering or well-defined responses to external stimuli. The principles that govern the formation of such structures are valid at both the molecular and the colloidal scale. Here we provide simple design directions to combine the anisotropic shape of the building units -- either molecules or colloids -- and selective directional bonding. Using extensive computer simulations we show that regular rhombic platelets decorated with attractive and repulsive interaction sites lead to specific tilings, going smoothly from close-packed arrangements to open lattices. The rationale behind the rich tiling scenario observed can be described in terms of steric incompatibilities, unsatisfied bonding geometries and interplays between local and long-range order.

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title: Molecular templates and nano-reactors: two-dimensional hydrogen bonded supramolecular networks on solid/liquid interfaces
abstract: With tunable cavities, the two-dimensional (2D) hydrogen bonded supramolecular networks are receiving increasing attention in surface supramolecular chemistry during the past decade. Herein, we give a brief account of our efforts on the 2D supramolecular host–guest chemistry based on molecular networks connected by hydrogen bonds, with an aid of scanning tunnelling microscopy (STM) technique. Following the molecular assembling, we have constructed a group of two-dimensional H-bonded supramolecular networks with cavities of different sizes, shapes, and symmetry characteristics on HOPG surface. Our researches have reported that these open porous structures could serve as molecular templates to host alien ensembles, as molecular sieves for molecular separation and recognition, as molecular sensors for ion detections, and as spatial confiners to control chemical reactions. It can be noticed that the interactions between host templates and guest molecules are emphasized throughout this review. On the basis of the confinement of supramolecular networks, it could be less problematic to explore the controllability, predictability, stability and applicability of the ordered structures.

title: Periodic potentials in hybrid van der Waals heterostructures formed by supramolecular lattices on graphene
abstract: The rise of 2D materials made it possible to form heterostructures held together by weak interplanar van der Waals interactions. Within such van der Waals heterostructures, the occurrence of 2D periodic potentials significantly modifies the electronic structure of single sheets within the stack, therefore modulating the material properties. However, these periodic potentials are determined by the mechanical alignment of adjacent 2D materials, which is cumbersome and time-consuming. Here we show that programmable 1D periodic potentials extending over areas exceeding 104 nm2 and stable at ambient conditions arise when graphene is covered by a self-assembled supramolecular lattice. The amplitude and sign of the potential can be modified without altering its periodicity by employing photoreactive molecules or their reaction products. In this regard, the supramolecular lattice/graphene bilayer represents the hybrid analogue of fully inorganic van der Waals heterostructures, highlighting the rich prospects that molecular design offers to create ad hoc materials.

title: From soft to hard: the generation of functional and complex colloidal monolayers for nanolithography
abstract: Take polymer colloids—simple to make and ubiquitously available—let them self-assemble into a monolayer and you have, readily engineered, a sophisticated mask to create highly symmetric surface patterns with nanometre precision. Thirty years after its invention, this process, commonly referred to as colloidal lithography, is far from being old news and an ever-increasing range of scientists continues to use their creativity to come up with increasingly more complex surface patterns. As intriguing this technique is, the devil is in the details and it is far from trivial to achieve high order in a colloidal monolayer. This article reviews available crystallization techniques and discusses their scope and limitations in order to provide just the right method for your next experiment.

title: Advanced colloidal lithography: From patterning to applications
abstract: This article presents a comprehensive review about the current research activities on colloidal lithography, a highly efficient technology for fabricating large-area patterned functional nanostructures. Three aspects are elaborated: i) self-assembly of monolayer of colloidal crystals (MCCs) and their modifications; ii) lithographic patterning methods, including deposition and patterning of functional materials and pattern transfer onto the underlying substrates; iii) promising applications, especially in the optical and photonic-related fields in the past several years. Finally, perspectives on the current challenges and future trends in this area are given. The present review intends to inspire more ingenious designs and exciting research in colloidal lithography for advanced nanofabrication.

title: Template-directed colloidal crystallization
abstract: Colloidal crystals are three-dimensional periodic structures formed from small particles suspended in solution. They have important technological uses as optical filters1–3, switches4 and materials with photonic band gaps5,6, and they also provide convenient model systems for fundamental studies of crystallization and melting7–10. Unfortunately, applications of colloidal crystals are greatly restricted by practical difficulties encountered in synthesizing large single crystals with adjustable crystal orientation11. Here we show that the slow sedimentation of colloidal particles onto a patterned substrate (or template) can direct the crystallization of bulk colloidal crystals, and so permit tailoring of the lattice structure, orientation and size of the resulting crystals: we refer to this process as 'colloidal epitaxy'. We also show that, by using silica spheres synthesized with a fluorescent core12,13, the defect structures in the colloidal crystals that result from an intentional lattice mismatch of the template can be studied by confocal microscopy14. We suggest that colloidal epitaxy will open new ways to design and fabricate materials based on colloidal crystals and also allow quantitative studies of heterogeneous crystallization in real space.

title: Diffusion and filtration properties of self-assembled gold nanocrystal membranes.
abstract: Close-packed nanoparticle monolayers have recently been shown to form mechanically robust, free-standing membranes. We report the first measurements of molecular transport through such ultrathin sheets, self-assembled from dodecanethiol-ligated gold nanocrystals. For aqueous solutions we find filtration coefficients 2 orders of magnitude larger than those observed in polymer-based filters, sieving of large solutes, and for smaller solutes a pronounced dependence of rejection on being charged. These results open up new possibilities for controlled delivery and separation of nano-objects.

title: Functional membranes via nanoparticle self-assembly.
abstract: This article summarizes a recently developed approach for the preparation of membrane materials by the self-assembly of inorganic, polymeric or hybrid nanoparticles, with the focus on functional membranes possessing permselectivity. Two types of such membranes are discussed, those possessing size and charge selectivity suitable for ultra- and nanofiltration and chemoselective separation, and those possessing proton or lithium transport properties suitable for fuel cell and lithium battery applications, respectively. This article describes the preparation methods of nanoparticle membranes, as well as their mechanical, molecular, and ionic transport properties.

title: Switching light with light--advanced functional colloidal monolayers.
abstract: Colloidal monolayers comprising of highly ordered two dimensional crystals are of high interest to generate surface patterns for a variety of different applications. Mostly, unfunctionalized polymer or silica colloids are assembled into monolayers. However, the incorporation of functional molecules into such colloids offers a convenient possibility of implementing additional properties to the two-dimensional crystal. Here, we present the formation of novel functional colloidal monolayers with photoswitchable fluorescence. The miniemulsion polymerization technique was used to incorporate an appropriate dye system of a perylene-based fluorophore and a bis-arylethene as a photochrome in polymeric colloids in defined ratios. Upon irradiation with UV or visible light the photochrome reversibly isomerizes from the ring-closed form, which is able to absorb light of the emission wavelength of the fluorescent dye and the ring-open form, which is not. The fluorescence emission of the dye can thus be reversibly switched on and off with light even when embedded in colloids. The colloids were self-assembled at the air-water interface to produce hexagonally ordered functional monolayers and more complex binary crystals. We investigate in detail the influence of the polymeric matrix on the switching properties of the fluorophore/photochrome system and find that the rate constants for the photoswitching, which all lie in the same range, are less influenced by the polymeric environment than expected. We demonstrate the reversible switching of the fluorescence emission in self-assembled colloidal monolayers. The arrangement of broadly distributed functional colloids into ordered monolayers with high addressability was obtained by the formation of binary colloidal monolayers.

title: Recent advances in solution-processed inorganic nanofilm photodetectors.
abstract: As important opto-electronical devices, nanofilm photodetectors constructed from inorganic low-dimensional nanostructures have drawn prime attention due to their significance in basic scientific research and potential technological applications. This review highlights a selection of important topics pertinent to inorganic nanofilm photodetectors processed via solution strategies. This article begins with a description of the advantages and drawbacks of nanofilm-based photodetectors versus 1D nanostructure-based ones, and then introduces rational design and controlled syntheses of various nanofilms via different wet-chemical routes, and then mainly focuses on their optoelectronic properties and applications in photodetectors based on the different types of nanofilms. Finally, the general challenges and the potential future directions of this exciting research and technology area are presented.

title: Self-Assembly of Colloidal Nanocrystals: From Intricate Structures to Functional Materials.
abstract: Chemical methods developed over the past two decades enable preparation of colloidal nanocrystals with uniform size and shape. These Brownian objects readily order into superlattices. Recently, the range of accessible inorganic cores and tunable surface chemistries dramatically increased, expanding the set of nanocrystal arrangements experimentally attainable. In this review, we discuss efforts to create next-generation materials via bottom-up organization of nanocrystals with preprogrammed functionality and self-assembly instructions. This process is often driven by both interparticle interactions and the influence of the assembly environment. The introduction provides the reader with a practical overview of nanocrystal synthesis, self-assembly, and superlattice characterization. We then summarize the theory of nanocrystal interactions and examine fundamental principles governing nanocrystal self-assembly from hard and soft particle perspectives borrowed from the comparatively established fields of micrometer colloids and block copolymer assembly. We outline the extensive catalog of superlattices prepared to date using hydrocarbon-capped nanocrystals with spherical, polyhedral, rod, plate, and branched inorganic core shapes, as well as those obtained by mixing combinations thereof. We also provide an overview of structural defects in nanocrystal superlattices. We then explore the unique possibilities offered by leveraging nontraditional surface chemistries and assembly environments to control superlattice structure and produce nonbulk assemblies. We end with a discussion of the unique optical, magnetic, electronic, and catalytic properties of ordered nanocrystal superlattices, and the coming advances required to make use of this new class of solids.

title: Tailoring molecular layers at metal surfaces.
abstract: The design of networks of organic molecules at metal surfaces, highly attractive for a variety of applications ranging from molecular electronics to gas sensors to protective coatings, has matured to a degree that patterns with multinanometre unit cells and almost any arbitrary geometry can be fabricated. This Review provides an overview of vacuum-deposited organic networks at metal surfaces, using intermolecular hydrogen bonding, metal-atom coordination and in situ polymerization. Recent progress in these areas highlights how the design of surface patterns can benefit from the wealth of information available from solution- and bulk-phase chemistry, while at the same time providing novel insights into the nature of such bonds through the applicability of direct scanning probe imaging at metal surfaces.

title: Broken symmetry and the variation of critical properties in the phase behaviour of supramolecular rhombus tilings.
abstract: The tiling of surfaces has long attracted the attention of scientists, not only because it is intriguing intrinsically, but also as a way to control the properties of surfaces. However, although random tiling networks are studied increasingly, their degree of randomness (or partial order) has remained notoriously difficult to control, in common with other supramolecular systems. Here we show that the random organization of a two-dimensional supramolecular array of isophthalate tetracarboxylic acids varies with subtle chemical changes in the system. We quantify this variation using an order parameter and reveal a phase behaviour that is consistent with long-standing theoretical studies on random tiling. The balance between order and randomness is driven by small differences in intermolecular interaction energies, which can be related by numerical simulations to the experimentally measured order parameter. Significant variations occur with very small energy differences, which highlights the delicate balance between entropic and energetic effects in complex self-assembly processes.

title: Controlling molecular deposition and layer structure with supramolecular surface assemblies
abstract: Selective non-covalent interactions have been widely exploited in solution-based chemistry to direct the assembly of molecules into nanometre-sized functional structures such as capsules, switches and prototype machines. More recently, the concepts of supramolecular organization have also been applied to two-dimensional assemblies on surfaces stabilized by hydrogen bonding, dipolar coupling or metal co-ordination. Structures realized to date include isolated rows, clusters and extended networks, as well as more complex multi-component arrangements. Another approach to controlling surface structures uses adsorbed molecular monolayers to create preferential binding sites that accommodate individual target molecules. Here we combine these approaches, by using hydrogen bonding to guide the assembly of two types of molecules into a two-dimensional open honeycomb network that then controls and templates new surface phases formed by subsequently deposited fullerene molecules. We find that the open network acts as a two-dimensional array of large pores of sufficient capacity to accommodate several large guest molecules, with the network itself also serving as a template for the formation of a fullerene layer.

title: Random Tiling and Topological Defects in a Two-Dimensional Molecular Network
abstract: A molecular network that exhibits critical correlations in the spatial order that is characteristic of a random, entropically stabilized, rhombus tiling is described. Specifically, we report a random tiling formed in a two-dimensional molecular network of p-terphenyl-3,5,3′,5′-tetracarboxylic acid adsorbed on graphite. The network is stabilized by hexagonal junctions of three, four, five, or six molecules and may be mapped onto a rhombus tiling in which an ordered array of vertices is embedded within a nonperiodic framework with spatial fluctuations in a local order characteristic of an entropically stabilized phase. We identified a topological defect that can propagate through the network, giving rise to a local reordering of molecular tiles and thus to transitions between quasi-degenerate local minima of a complex energy landscape. We draw parallels between the molecular tiling and dynamically arrested systems, such as glasses.

title: Concentration-dependent supramolecular engineering of hydrogen-bonded nanostructures at surfaces: predicting self-assembly in 2D.
abstract: We report a joint computational and experimental study on the concentration-dependent self-assembly of a flat C3-symmetric molecule at surfaces. As a model system we have chosen a rigid molecular module, 1,3,5-tris(pyridine-4-ylethynyl)benzene, which can undergo self-association via hydrogen bonding (H-bonding) to form ordered 2D nanostructures. In particular, the lattice Monte Carlo method, combined with density functional calculations, was employed to explore the spontaneous supramolecular organization of this tripod-shaped molecule under surface confinement. We analyzed the stability of different weak H-bonded patterns and the influence of the concentration of the starting molecule on the 2D supramolecular packing. We found that ordered, densely packed monolayers and 2D porous networks are obtained at high and low concentrations, respectively. A concentration-dependent scanning tunneling microscopy investigation of the molecular self-assembly at a graphite-solution interface revealed supramolecular motifs, which are in perfect agreement with those obtained by simulations. Therefore, our computational approach represents a step forward toward the deterministic prediction of molecular self-assembly at surfaces and interfaces.

title: Self-assembly of hydrogen-bonded two-dimensional quasicrystals
abstract: The process of molecular self-assembly on solid surfaces is essentially one of crystallization in two dimensions, and the structures that result depend on the interplay between intermolecular forces and the interaction between adsorbates and the underlying substrate. Because a single hydrogen bond typically has an energy between 15 and 35 kilojoules per mole, hydrogen bonding can be a strong driver of molecular assembly; this is apparent from the dominant role of hydrogen bonding in nucleic-acid base pairing, as well as in the secondary structure of proteins. Carboxylic acid functional groups, which provide two hydrogen bonds, are particularly promising and reliable in creating and maintaining surface order, and self-assembled monolayers of benzoic acids produce structure that depends on the number and relative placement of carboxylic acid groups. Here we use scanning tunnelling microscopy to study self-assembled monolayers of ferrocenecarboxylic acid (FcCOOH), and find that, rather than producing dimeric or linear structures typical of carboxylic acids, FcCOOH forms highly unusual cyclic hydrogen-bonded pentamers, which combine with simultaneously formed FcCOOH dimers to form two-dimensional quasicrystallites that exhibit local five-fold symmetry and maintain translational and rotational order (without periodicity) for distances of more than 400 ångströms.

title: Halogen-Bond-Based Molecular Self-Assembly on Graphene Surface: A First-Principles Study
abstract: The formation of halogen-bond-based 2D supramolecular assemblies on solid surfaces has become a hot research topic in recent years. Herein, we report a theoretical study of the halogen-bonded network formation of pyridine derivatives and aryl–halide molecules on graphene surface using first-principles density functional theory (DFT) calculations. To unravel the characteristics of molecule–molecule and molecule–substrate interactions, the noncovalent interaction index (NCI), electron density difference (EDD), density of state (DOS), and topographical scan tunneling microscopy (STM) image analyses were undertaken. The N···I interactions between terminal pyridyl groups and iodoperfluorobenzenes are predicted to be somewhat stronger than the molecule–surface stacking interactions and appear to be the primary interactions in the self-assembled networks, with geometries in good agreement with the experimental STM images. The results reported in this work should be of great importance in the applications of thes...

title: Two-dimensional tessellation by molecular tiles constructed from halogen–halogen and halogen–metal networks
abstract: Molecular tessellations are often discovered serendipitously, and the mechanisms by which specific molecules can be tiled seamlessly to form periodic tessellation remain unclear. Fabrication of molecular tessellation with higher symmetry compared with traditional Bravais lattices promises potential applications as photonic crystals. Here, we demonstrate that highly complex tessellation can be constructed on Au(111) from a single molecular building block, hexakis(4-iodophenyl)benzene (HPBI). HPBI gives rise to two self-assembly phases on Au(111) that possess the same geometric symmetry but different packing densities, on account of the presence of halogen-bonded and halogen–metal coordinated networks. Sub-domains of these phases with self-similarity serve as tiles in the periodic tessellations to express polygons consisting of parallelograms and two types of triangles. Our work highlights the important principle of constructing multiple phases with self-similarity from a single building block, which may constitute a new route to construct complex tessellations.Molecular tessellations of complex tilings are difficult to design and construct. Here, the authors show that molecular tessellations can be formed from a single building block that gives rise to two distinct supramolecular phases, whose self-similar subdomains serve as tiles in the periodic tessellations.

title: One building block, two different nanoporous self-assembled monolayers: a combined STM and Monte Carlo study.
abstract: With the use of a single building block, two nanoporous patterns with nearly equal packing density can be formed upon self-assembly at a liquid-solid interface. Moreover, the formation of both of these porous networks can be selectively and homogenously induced by changing external parameters like solvent, concentration, and temperature. Finally, their porous properties are exploited to host up to three different guest molecules in a spatially resolved way.

title: Surface-supported supramolecular pentamers.
abstract: Chiral pentamers of all-trans-retinoic acid molecules have been prepared on Au(111) surfaces and on a molecular monolayer. Over a range of coverages, pentamers are the building blocks of larger arrays that become increasingly enantiopure. The stability of pentamers is analyzed from experiments on an isomer and a more reactive substrate as well as from density functional theory. The linear shape of the molecule and suitable densities are crucial for the formation of pentamers, driven by cyclic hydrogen bonding between carboxylic acid moieties.

title: Random and ordered phases of off-lattice rhombus tiles.
abstract: We study the covering of the plane by nonoverlapping rhombus tiles, a problem well studied only in the limiting case of dimer coverings of regular lattices. We go beyond this limit by allowing tiles to take any position and orientation on the plane, to be of irregular shape, and to possess different types of attractive interactions. Using extensive numerical simulations, we show that at large tile densities there is a phase transition from a fluid of rhombus tiles to a solid packing with broken rotational symmetry. We observe self-assembly of broken-symmetry phases, even at low densities, in the presence of attractive tile-tile interactions. Depending on the tile shape and interactions, the solid phase can be random, possessing critical orientational fluctuations, or crystalline. Our results suggest strategies for controlling tiling order in experiments involving "molecular rhombi."

title: Emergent rhombus tilings from molecular interactions with M-fold rotational symmetry.
abstract: We show that model molecules with particular rotational symmetries can self-assemble into network structures equivalent to rhombus tilings. This assembly happens in an emergent way, in the sense that molecules spontaneously select irregular fourfold local coordination from a larger set of possible local binding geometries. The existence of such networks can be rationalized by simple geometrical arguments, but the same arguments do not guarantee a network's spontaneous self-assembly. This class of structures must in certain regimes of parameter space be able to reconfigure into networks equivalent to triangular tilings.

title: Influence of molecular shape and interaction anisotropy on the self-assembly of tripod building blocks on solid surfaces
abstract: Molecular shape and directionality of intermolecular interactions are important factors which affect structure formation in adsorbed overlayers. In this contribution, using theoretical methods we demonstrate the importance of these factors in the surface-confined self-assembly of tripod-shaped organic molecules with reduced symmetry. To that end a lattice Monte Carlo model is proposed in which the molecules are represented in a coarse grained way, as flat rigid structures comprising a few connected segments adsorbed on a triangular lattice. The calculations are performed for the molecules equipped with terminal active centers providing directional intermolecular interactions. These results are compared with analogous data obtained for C 3 -symmetric units and Y-shaped molecules whose all composite segments are active. The simulated results show that for the directional interactions, the reduction of molecular symmetry leads to the formation of disordered, glassy, porous networks with hexagonal nanovoids of different shapes. Moreover, it is demonstrated that the interaction mode involving all molecular segments of the asymmetric building blocks is responsible for the formation of compact patterns. Relative thermal stability of the simulated assemblies is also compared, highlighting deciding role of the interaction mode in stabilization of the adsorbed superstructures. The findings of our theoretical investigations can be helpful in designing new molecular blocks and programming their interactions to create 2D molecular superstructures with tunable morphology and functions.

title: Synthesis and site-specific functionalization of tetravalent, hexavalent, and dodecavalent silica particles.
abstract: Different shapes: Tetravalent, hexavalent, and dodecavalent silica particles were obtained by the growth of the silica core of binary tetrapods, hexapods, and dodecapods, respectively. The surface of the multivalent particles can be regioselectively functionalized, thereby leading to particles with anisotropic geometry and chemistry.

title: Fabrication of Polyhedral Particles from Spherical Colloids and Their Self-Assembly into Rotator Phases**
abstract: Particle shape is a critical parameter that plays an important role in self-assembly, for example, in designing targeted complex structures with desired properties. Over the last decades, an unprecedented range of monodisperse nanoparticle systems with control over the shape of the particles have become available. In contrast, the choice of micrometer-sized colloidal building blocks of particles with flat facets, that is, particles with polygonal shapes, is significantly more limited. This can be attributed to the fact that in contrast to nanoparticles, the larger colloids are significantly harder to synthesize as single crystals. It is now shown that a very simple building block, such as a micrometer-sized polymeric spherical colloidal particle, is already enough to fabricate particles with regularly placed flat facets, including completely polygonal shapes with sharp edges. As an illustration that the yields are high enough for further self-assembly studies, the formation of three-dimensional rotator phases of fluorescently labelled, micrometer-sized, and charged rhombic dodecahedron particles was demonstrated. This method for fabricating polyhedral particles opens a new avenue for designing new materials.

title: Shape-Anisotropic Polyimide Particles by Solid-State Polycondensation of Monomer Salt Single Crystals
abstract: Shape-anisotropic particles are of broad interest, e.g., for colloidal crystals or applications at interfaces such as particle-stabilized emulsions. Despite the wealth of accessible shapes of inorganic particles, anisotropic homopolymer particles are to date mostly limited to objects derived from spheres (e.g., ellipsoidal or disk-shaped particles). Here, we report the synthesis of shape-anisotropic, angular polyimide particles by thermal solid-state polycondensation (SSP) of monomer salts. We prepare monomer salt single crystals of relatively narrow size and shape distribution by growth inside hydrogels, and solve their crystal structure. Polyimide particles are obtained by simple heating and retain the shape of the initial salt crystals. Using high-temperature X-ray diffraction, thermal analyses and microscopy techniques, we investigate the mechanism of the transformation. The obtained polyimide particles are temperature-stable up to 640 °C and virtually insoluble in any solvent. This work sheds more li...

title: Colloidal Assembly Approaches to Micro/Nanostructures of Complex Morphologies.
abstract: The ability to programmatically assemble colloidal micro/nanostructures into highly ordered superstructures is of great importance in both fundamental studies and practical applications. In addition to the sophisticated manipulation of the short-range and long-range interactions imposed on the colloidal building blocks, the intrinsic shape elements including face, edge, corner, concave, convex, and curvature also play very important roles in solving the "jigsaw puzzle" of the superstructures. Here, the recent progress in the development of colloidal assembly strategies for the formation of complex superstructures is reviewed, with a primary focus on the unique effects of the morphology of the building blocks to the assembly processes and the final structures. Overall, this Review aims to shed light on the fundamental understanding of the colloidal behaviors of complex micro/nanostructures and promote the continued development of effective strategies for the creation of functional materials with complex compositions and morphologies.

title: A Roadmap for the Assembly of Polyhedral Particles
abstract: How particles pack together as a solid can often be predicted just from their shape and how many neighbors they have in the fluid phase. Self-assembly of atomic, molecular, or artificial nanoscale units into superstructures is a prevalent topic in science. Advances in control over the synthesis of colloidal nanoparticles (1, 2), in their organization into ordered structures (3–7), and in modeling of assembly (8–10) have boosted interest in this topic. Yet predicting what types of superstructures will be formed from specific building blocks according to the shape of the blocks and their interactions remains an open problem (11). Even if the shape is spherical and interactions between blocks do not depend on their mutual orientation, one cannot model the finite-pressure assembly on the basis of simple close-packing arguments; more elaborate approaches are required. On page 453 of this issue, Damasceno et al. (12) report the most extensive and systematic study thus far on the assembly behavior of polyhedral “hard” particles of many different shapes. The study exploits a large set of shapes to determine simple predictive criteria for assembly.

title: Predictive Self-Assembly of Polyhedra into Complex Structures
abstract: Getting Packed If one neglects the role of specific interactions, the packing of similar-shaped objects will depend only on the particular shape of the object. Damasceno et al. (p. 453; see the Perspective by de Graaf and Manna) present computer simulations of the behavior of different types of polyhedra with simple and complex shapes that are packed under thermal equilibrium into various structures, from crystals to amorphous materials through liquid crystals. Despite the wide variety of starting shapes, the packing behavior could be quantitatively described using just two criteria; one for the particle shape as a function of its volume and surface area, and one for the number of nearest neighbors. Two parameters relating to particle shape and nearest neighbors reveal the preferred packing of complex structures. Predicting structure from the attributes of a material’s building blocks remains a challenge and central goal for materials science. Isolating the role of building block shape for self-assembly provides insight into the ordering of molecules and the crystallization of colloids, nanoparticles, proteins, and viruses. We investigated 145 convex polyhedra whose assembly arises solely from their anisotropic shape. Our results demonstrate a remarkably high propensity for thermodynamic self-assembly and structural diversity. We show that from simple measures of particle shape and local order in the fluid, the assembly of a given shape into a liquid crystal, plastic crystal, or crystal can be predicted.

title: Competition of shape and interaction patchiness for self-assembling nanoplates.
abstract: Progress in nanocrystal synthesis and self-assembly enables the formation of highly ordered superlattices. Recent studies focused on spherical particles with tunable attraction and polyhedral particles with anisotropic shape, and excluded volume repulsion, but the effects of shape on particle interaction are only starting to be exploited. Here we present a joint experimental-computational multiscale investigation of a class of highly faceted planar lanthanide fluoride nanocrystals (nanoplates, nanoplatelets). The nanoplates self-assemble into long-range ordered tilings at the liquid-air interface formed by a hexane wetting layer. Using Monte Carlo simulation, we demonstrate that their assembly can be understood from maximization of packing density only in a first approximation. Explaining the full phase behaviour requires an understanding of nanoplate-edge interactions, which originate from the atomic structure, as confirmed by density functional theory calculations. Despite the apparent simplicity in particle geometry, the combination of shape-induced entropic and edge-specific energetic effects directs the formation and stabilization of unconventional long-range ordered assemblies not attainable otherwise.

title: Self-assembly of Archimedean tilings with enthalpically and entropically patchy polygons.
abstract: Considerable progress in the synthesis of anisotropic patchy nanoplates (nanoplatelets) promises a rich variety of highly ordered two-dimensional superlattices. Recent experiments of superlattices assembled from nanoplates confirm the accessibility of exotic phases and motivate the need for a better understanding of the underlying self-assembly mechanisms. Here, we present experimentally accessible, rational design rules for the self-assembly of the Archimedean tilings from polygonal nanoplates. The Archimedean tilings represent a model set of target patterns that (i) contain both simple and complex patterns, (ii) are comprised of simple regular shapes, and (iii) contain patterns with potentially interesting materials properties. Via Monte Carlo simulations, we propose a set of design rules with general applicability to one- and two-component systems of polygons. These design rules, specified by increasing levels of patchiness, correspond to a reduced set of anisotropy dimensions for robust self-assembly of the Archimedean tilings. We show for which tilings entropic patches alone are sufficient for assembly and when short-range enthalpic interactions are required. For the latter, we show how patchy these interactions should be for optimal yield. This study provides a minimal set of guidelines for the design of anisostropic patchy particles that can self-assemble all 11 Archimedean tilings.

title: Capillarity-induced directed self-assembly of patchy hexagram particles at the air-water interface.
abstract: Directed self-assembly can produce ordered or organized superstructures from pre-existing building blocks through pre-programmed interactions. Encoding desired information into building blocks with specific directionality and strength, however, poses a significant challenge for the development of self-assembled superstructures. Here, we demonstrate that controlling the shape and patchiness of particles trapped at the air-water interface can represent a powerful approach for forming ordered macroscopic complex structures through capillary interactions. We designed hexagram particles using a micromolding method that allowed for precise control over the shape and, more importantly, the chemical patchiness of the particles. The assembly behaviors of these hexagram particles at the air-water interface were strongly affected by chemical patchiness. In particular, two-dimensional millimeter-scale ordered structures could be formed by varying the patchiness of the hexagram particles, and we attribute this effect to the delicate balance between the attractive and repulsive interactions among the patchy hexagram particles. Our results provide important clues for encoding information into patchy particles to achieve macroscopic assemblies via a simple molding technique and potentially pave a new pathway for the programmable assembly of particles at the air-water interface.

title: Directed self-assembly of a colloidal kagome lattice
abstract: A challenging goal in materials chemistry and physics is spontaneously to form intended superstructures from designed building blocks. In fields such as crystal engineering and the design of porous materials, this typically involves building blocks of organic molecules, sometimes operating together with metallic ions or clusters. The translation of such ideas to nanoparticles and colloidal-sized building blocks would potentially open doors to new materials and new properties, but the pathways to achieve this goal are still undetermined. Here we show how colloidal spheres can be induced to self-assemble into a complex predetermined colloidal crystal—in this case a colloidal kagome lattice—through decoration of their surfaces with a simple pattern of hydrophobic domains. The building blocks are simple micrometre-sized spheres with interactions (electrostatic repulsion in the middle, hydrophobic attraction at the poles, which we call ‘triblock Janus’) that are also simple, but the self-assembly of the spheres into an open kagome structure contrasts with previously known close-packed periodic arrangements of spheres. This open network is of interest for several theoretical reasons. With a view to possible enhanced functionality, the resulting lattice structure possesses two families of pores, one that is hydrophobic on the rims of the pores and another that is hydrophilic. This strategy of ‘convergent’ self-assembly from easily fabricated colloidal building blocks encodes the target supracolloidal architecture, not in localized attractive spots but instead in large redundantly attractive regions, and can be extended to form other supracolloidal networks.

title: Frustrated 2D molecular crystallization.
abstract: Grafting isophthalic acid groups to linear connectors produces tetracarboxylic acids 2−4, which are extended analogues of trimesic acid (1). Normal pairwise association of -COOH groups induces trimesic acid to form a hexagonal network held together by six hydrogen bonds per molecule. In contrast, analogues 2−4 are designed to form two polymorphs, parallel network II and Kagome network III, which are linked by eight hydrogen bonds per molecule. The particular connectivity of these networks allows a smooth transition from one to the other without introducing discontinuities in hydrogen bonding. DFT calculations suggest that subtle differences in hydrogen bonding favor parallel motif II for short tetraacid 2 and Kagome motif III for long tetraacid 4, whereas the two motifs are closely similar in energy for intermediate tetraacid 3. These preferences were confirmed by using STM to image the adsorption of compounds 2−4 on graphite. 2D crystallization of tetraacid 3 is frustrated, presumably because the two mot...

title: Directing two-dimensional molecular crystallization using guest templates.
abstract: The use of a coronene guest template directs the formation of a 2D Kagomé network in preference to alternative close packed and parallel hydrogen-bonded structures of tetracarboxylic acid tectons self-assembled from solution on a graphite surface.

title: Site-selective fabrication of two-dimensional fullerene arrays by using a supramolecular template at the liquid-solid interface.
abstract: have been successfully used to direct theformation of ordered fullerene arrays. In this way theinterfullerene distance and symmetry of the arrangementaresolelydeterminedbythemoleculartemplateandcanbechanged by adjusting its structure. More importantly, inter-actions between fullerenes can also be modified with thisstrategy.Wehavedesignedandsynthesizedatetraacidicazoben-zene molecule NN4A (Figure1a) that exclusively formsKagomopennetworkswithtwotypesofcavitiesthathavedifferent size and symmetry at the liquid–solid interface.These cavities are capable of accommodating fullerenemolecules as guest species. Herein, we examine the siteselectivityofthenetworksfordifferentfullerenes,afeaturewhichhasnotbeenobservedforothersystemsatliquid–solidinterfaces.Azobenzenederivativesaretypicalphotochromiccompoundsthathaveawiderangeofpotentialapplications,including for optical switching, holographic storage, lightharvesting, long-term energy storage, and nonlinear opticalmaterials.

title: Periodic and nonperiodic chiral self-assembled networks from 1,3,5-benzenetricarboxylic acid on Ag(111).
abstract: Surface-catalyzed reactions provide a versatile route to synthesizing new 2D materials. Here, we show that the statistical nature of an activated reaction can lead to a diversity of intermolecular bonding motifs through partially-reacted molecules. With increasing annealing, we observe different periodic, well-defined phases of 1,3,5-benzenetricarboxylic acid on Ag(111), where the surface structure in each case is defined by the degree of deprotonation of the carboxylic groups. Over a wide range of deprotonation levels (∼50% to near 100%), we observe a granular alloy comprising two distinct phases in a continuous network. This ordered phase lacks well-defined translational symmetry, is stabilized through both intermolecular interactions and epitaxy, and demonstrates a design approach to creating non-crystalline phases by capitalizing on the chemical diversity of partially reacted molecules on a surface.

title: Do hierarchical structures assemble best via hierarchical pathways
abstract: Hierarchically structured natural materials possess functionalities unattainable to the same components organized or mixed in simpler ways. For instance, the bones and teeth of mammals are far stronger and more durable than the mineral phases from which they are derived because their constituents are organized hierarchically from the molecular scale to the macroscale. Making similarly functional synthetic hierarchical materials will require an understanding of how to promote the self-assembly of structure on multiple length scales, without falling foul of numerous possible kinetic traps. Here we use computer simulation to study the self-assembly of a simple hierarchical structure, a square crystal lattice whose repeat unit is a tetramer. Although the target material is organized hierarchically, it self-assembles most reliably when its dynamic assembly pathway consists of the sequential addition of monomers to a single structure. Hierarchical dynamic pathways via dimer and tetramer intermediates are also viable modes of assembly, but result in general in lower yield: these intermediates have a stronger tendency than monomers to associate in ways not compatible with the target structure. In addition, assembly via tetramers results in a kinetic trap whereby material is sequestered in trimers that cannot combine to form the target crystal. We use analytic theory to relate dynamical pathways to the presence of equilibrium phases close in free energy to the target structure, and to identify the thermodynamic principles underpinning optimum self-assembly in this model: (1) make the free energy gap between the target phase and the most stable fluid phase of order kBT, and (2) ensure that no other dense phases (liquids or close-packed solids of monomers or oligomers) or fluids of incomplete building blocks fall within this gap.

title: Colloids with valence and specific directional bonding
abstract: The ability to design and assemble three-dimensional structures from colloidal particles is limited by the absence of specific directional bonds. As a result, complex or low-coordination structures, common in atomic and molecular systems, are rare in the colloidal domain. Here we demonstrate a general method for creating the colloidal analogues of atoms with valence: colloidal particles with chemically distinct surface patches that imitate hybridized atomic orbitals, including sp, sp2, sp3, sp3d, sp3d2 and sp3d3. Functionalized with DNA with single-stranded sticky ends, patches on different particles can form highly directional bonds through programmable, specific and reversible DNA hybridization. These features allow the particles to self-assemble into ‘colloidal molecules’ with triangular, tetrahedral and other bonding symmetries, and should also give access to a rich variety of new microstructured colloidal materials.

title: Colloidal joints with designed motion range and tunable joint flexibility.
abstract: The miniaturization of machines towards the micron and nanoscale requires the development of joint-like elements that enable and constrain motion. We present a facile method to create colloidal joints, that is, anisotropic colloidal particles functionalized with surface mobile DNA linkers that control the motion range of bonded particles. We demonstrate quantitatively that we can control the flexibility of these colloidal joints by tuning the DNA linker concentration in the bond area. We show that the shape of the colloidal joint controls the range of motion of bonded particles through a maximisation of the bond area. Using spheres, cubes, and dumbbells, we experimentally realize spherical joints, planar sliders, and hinges, respectively. Finally we demonstrate the potential of the colloidal joints for programmable bottom-up self-assembly by creating flexible colloidal molecules and colloidal polymers. The reconfigurability and motion constraint offered by our colloidal joints make them promising building blocks for the development of switchable materials and nanorobots.

title: Modified Lagrangians and monotone maps in optimization
abstract: Monotone Maps Gradient-Type Methods and Modification of a Monotone Map Saddle Gradient Methods Modified Lagrangian Functions for Smooth Mathematical Programming Problems and Related Dual Methods Bibliographic Comments References Index.

title: Avoiding unphysical kinetic traps in Monte Carlo simulations of strongly attractive particles.
abstract: We introduce a "virtual-move" Monte Carlo algorithm for systems of pairwise-interacting particles. This algorithm facilitates the simulation of particles possessing attractions of short range and arbitrary strength and geometry, an important realization being self-assembling particles endowed with strong, short-ranged, and angularly specific ("patchy") attractions. Standard Monte Carlo techniques employ sequential updates of particles and can suffer from low acceptance rates when attractions are strong. In this event, collective motion can be strongly suppressed. Our algorithm avoids this problem by proposing simultaneous moves of collections (clusters) of particles according to gradients of interaction energies. One particle first executes a "virtual" trial move. We determine which of its neighbors move in a similar fashion by calculating individual bond energies before and after the proposed move. We iterate this procedure and update simultaneously the positions of all affected particles. Particles move according to an approximation of realistic dynamics without requiring the explicit computation of forces and without the step size restrictions required when integrating equations of motion. We employ a size- and shape-dependent damping of cluster movements, motivated by collective hydrodynamic effects neglected in simple implementations of Brownian dynamics. We discuss the virtual-move algorithm in the context of other Monte Carlo cluster-move schemes and demonstrate its utility by applying it to a model of biological self-assembly.

title: Approximating the dynamical evolution of systems of strongly interacting overdamped particles
abstract: We describe collective-move Monte Carlo (MC) algorithms designed to approximate the overdamped dynamics of self-assembling nanoscale components equipped with strong, short-ranged and anisotropic interactions. Conventional MC simulations comprise sequential moves of single particles, proposed and accepted so as to satisfy detailed balance. Under certain circumstances such simulations provide an approximation of overdamped dynamics, but the accuracy of this approximation can be poor if, for example, particle–particle interactions vary strongly with distance or angle. The twin requirements of simulation efficiency (trial moves of appreciable scale are needed to ensure reasonable sampling) and dynamical fidelity (true in the limit of vanishingly small trial moves) then become irreconcilable. As a result, single-particle moves can under-represent important collective modes of relaxation, such as self-diffusion of particle clusters. However, one way of using MC simulation to mimic real collective modes of motion, retaining the ability to make trial moves of reasonable scale, is to make explicit moves of collections of particles. We outline ways of doing so by iteratively linking particles to their environment. Linking criteria can be static, conditioned upon properties of the current state of a system, or dynamic, conditioned upon energy changes resulting from trial virtual moves of particles. We argue that the latter protocol is better suited to approximating real dynamics.