Using shape for self-assembly

Dumbbells, chains, and ribbons: anisotropic self-assembly of isotropic nanoparticles

Functionalizing the surface of metal nanoparticles can assure their stability in solution or mediate their self-assembly into aggregates with controlled shapes. Here we present a computational study of the colloidal aggregation of gold nanoparticles (Au NPs) isotropically functionalized by a mixture of charged and hydrophobic ligands. We show that, by varying the relative proportion of the two ligands, the NPs form anisotropic aggregates with markedly different topologies: dumbbells, chains, or ribbons. In all cases, two kinds of connections keep the aggregates together: hydrophobic bonds and ion bridges. We show that the anisotropy of the aggregates derives from the NP shell reshaping due to the formation of the hydrophobic links, while ion bridges are accountable for the "secondary structure" of the aggregates. Our findings provide a general physical principle that can also be exploited in different self-assembled systems: anisotropic/directional aggregation can be achieved starting from isotropic objects with a soft, deformable surface.

Synthesis of patchy particles using gaseous ligands

The collective self-assembly of colloidal particles can be influenced by the composition of the suspending medium, the bulk material of the particles themselves and, importantly, by their surface chemistry. This can be inhomogeneous or patchy to give an orientational dependence to the interaction potential between the particles. These additional constraints to the energy landscape then steer the self-assembly towards configurations of fundamental or applicational interest. We present a novel approach to modify the surface chemistry of colloidal particles to give them two polar patches, using gaseous ligands. In particular, we synthesize polar inverse patchy colloids, i.e., charged particles with two (fluorescent) patches of the opposite charge on their poles. We characterize the dependence of these charges on the pH of the suspending solution.

Solvent-induced assembly of mono- and divalent silica nanoparticles

Particles with attractive patches are appealing candidates to be used as building units to fabricate novel colloidal architectures by self-assembly. Here, we report the synthesis of one-patch silica nanoparticles, which consist of silica half-spheres whose concave face carries in its center a polymeric patch made of grafted polystyrene chains. The multistage synthesis allows for a fine control of the patch-to-particle size ratio from 0.23 to 0.57. The assembly of the patchy nanoparticles can be triggered by reducing the solvent quality for the polystyrene chains. Dimers or trimers can be obtained by tuning the patch-to-particle size ratio. When mixed with two-patch nanoparticles, one-patch nanoparticles control the length of the resulting chains by behaving as colloidal chain stoppers. The present strategy allows for future elaboration of novel colloidal structures by controlled assembly of nanoparticles.

Molecular Engineering of Noncovalent Dimerization

Dimers are probably the simplest model to facilitate the understanding of fundamental physical and chemical processes that take place in much-expanded systems like aggregates, crystals, and other solid states. The molecular interplay within a dimer differentiates it from the corresponding monomeric state and determines its features. Molecular engineering of noncovalent dimerization through applied supramolecular restrictions enables additional control over molecular interplay, particularly over its dynamic aspect. This Perspective introduces the recent effort that has been made in the molecular engineering of noncovalent dimerization, including supramolecular dimers, folda-dimers, and macrocyclic dimers. It showcases how the variation in supramolecular restrictions endows molecular-based materials with improved performance and/or functions like enhanced emission, room-temperature phosphorescence, and effective catalysis. We particularly discuss pseudostatic dimers that can sustain molecular interplay for a long period of time, yet are still flexible enough to adapt to variations. The pseudostatic feature allows for active species to decay along an alternate pathway, thereby spinning off emerging features that are not readily accessible from conventional dynamic systems.

Manipulating the morphology of colloidal particles via ion beam irradiation: A route to anisotropic shaping

Ion beam irradiation of spherical colloidal particles is a viable route to induce particle deformation, especially to get anisotropic shapes. Even though less common in comparison with dry etching techniques, different types of morphological changes can be attained depending on the process parameters (angle of incidence, energy, fluence of the ion beam, type of ion, temperature) and on particle material and initial particle arrangement (crystalline or disordered, made up of isolated or closely-packed particles). The technique can be harnessed to get anisotropic deformation of spherical colloidal particles into an ellipsoidal shape, but also to tailor the interstices between closely-packed colloidal particles, to get particle necking and coalescence as well as particle rearrangement. As such, particle deformation based on ion irradiation can find diverse applications from synthesis of ellipsoidal particles to modified templates for colloidal lithography. In this review, we examine in detail the principles and models of colloidal particle shaping via ion beam irradiation, the influence of process parameters on particle morphology and the applications of irradiated particles.

1D Colloidal chains: recent progress from formation to emergent properties and applications

Integrating nanoscale building blocks of low dimensionality (0D; i.e., spheres) into higher dimensional structures endows them and their corresponding materials with emergent properties non-existent or only weakly existent in the individual building blocks. Constructing 1D chains, 2D arrays and 3D superlattices using nanoparticles and colloids therefore continues to be one of the grand goals in colloid and nanomaterial science. Amongst these higher order structures, 1D colloidal chains are of particular interest, as they possess unique anisotropic properties. In recent years, the most relevant advances in 1D colloidal chain research have been made in novel synthetic methodologies and applications. In this review, we first address a comprehensive description of the research progress concerning various synthetic strategies developed to construct 1D colloidal chains. Following this, we highlight the amplified and emergent properties of the resulting materials, originating from the assembly of the individual building blocks and their collective behavior, and discuss relevant applications in advanced materials. In the discussion of synthetic strategies, properties, and applications, particular attention will be paid to overarching concepts, fresh trends, and potential areas of future research. We believe that this comprehensive review will be a driver to guide the interdisciplinary field of 1D colloidal chains, where nanomaterial synthesis, self-assembly, physical property studies, and material applications meet, to a higher level, and open up new research opportunities at the interface of classical disciplines.

Triangles on a triangular lattice: Insights into self-assembly in two dimensions driven by shape complementarity

A series of models for reversible filling of a triangular lattice with equilateral triangles has been developed and investigated. There are eight distinct models that vary in the set of prohibitions. In zeroth approximation, these models allow one to estimate the influence of the particles' shape and complementarity of their pair configurations on the self-assembly of dense monolayers formed by reversible filling. The most symmetrical models were found to be equivalent to hard-disk models on the hexagonal lattice. When any contact of hard triangles by vertices is prohibited, the dense monolayers are disordered, and their entropy tends to the constant. If only one pair configuration is prohibited, the close-packed layer appears through the continuous phase transition. In other cases, the weak first-order transition resulting in the self-assembly of close-packed layers is observed.

Shape-Changing Particles: From Materials Design and Mechanisms to Implementation

Demands for next-generation soft and responsive materials have sparked recent interest in the development of shape-changing particles and particle assemblies. Over the last two decades, a variety of mechanisms that drive shape change have been explored and integrated into particulate systems. Through a combination of top-down fabrication and bottom-up synthesis techniques, shape-morphing capabilities extend from the microscale to the nanoscale. Consequently, shape-morphing particles are rapidly emerging in a variety of contexts, including photonics, microfluidics, microrobotics, and biomedicine. Herein, the key mechanisms and materials that facilitate shape changes of microscale and nanoscale particles are discussed. Recent progress in the applications made possible by these particles is summarized, and perspectives on their promise and key open challenges in the field are discussed.

Low Interfacial Free Energy Describes the Bulk Ordering Transition in Colloidal Cubes

Many hard faceted nanoparticles are known to undergo disorder-to-order phase transitions following a classical nucleation and growth mechanism. In a previous study [J. Phys. Chem. B 2018, 122, 9264-9273], it was shown that hard cubes undergo a nonclassical phase transition with a bulk character instead of originating from consolidated nuclei. Significantly, an unusually high fraction of ordered particles was observed in the metastable basin of the disordered phase, even for very low degrees of supersaturation. This work aims to substantiate the conjecture that these unique properties originate from a comparatively low interfacial free energy between the disordered and ordered phases for hard cubes relative to other hard particle systems. Using the cleaving wall method to directly measure the interfacial free energy for cubes, it is found that its values are indeed small; e.g., at phase coexistence conditions, it is only one-fifth that for hard spheres. A theoretical nucleation model is used to explore the broader implications of low interfacial tension values and how this could result in a bulk ordering mechanism.

Self-assembly of colloidal inorganic nanocrystals: nanoscale forces, emergent properties and applications

The self-assembly of colloidal nanoparticles has made it possible to bridge the nanoscopic and macroscopic worlds and to make complex nanostructures. The nanoparticle-mediated assembly enables many potential applications, from biodetection and nanomedicine to optoelectronic devices. Properties of assembled materials are determined not only by the nature of nanoparticle building blocks, but also by spatial positions of nanoparticles within the assemblies. A deep understanding of nanoscale interactions between nanoparticles is a prerequisite to controlling nanoparticle arrangement during assembly. In this review, we present an overview of interparticle interactions governing their assembly in a liquid phase. Considerable attention is devoted to examples that illustrate nanoparticle assembly into ordered superstructures using different types of building blocks, including plasmonic nanoparticles, magnetic nanoparticles, lanthanide-doped nanophosphors, and quantum dots. We also cover the physicochemical properties of nanoparticle ensembles, especially those arising from particle coupling effects. We further discuss future research directions and challenges in controlling self-assembly at a level of precision that is most crucial to technology development.

Quantifying patterns in optical micrographs of one- and two-dimensional ellipsoidal particle assemblies

Current developments in colloidal science include the assembly of anisotropic colloids with broad geometric diversity. As the complexity of particle assemblies increases, the need for ubiquitous algorithms that quantitatively analyze images of the assemblies to deliver key information such as quantification of crystal structures becomes more urgent. This contribution describes algorithms capable of image analysis for classifying colloidal structures based on abstracted interparticle relationship information and quantitatively analyzing the abundance of each structure in mixed pattern assemblies. The algorithm parameters can be adjusted, allowing for the algorithms to be adapted for different image analyses. Three different ellipsoidal particle assembly images are presented to demonstrate the effectiveness of the algorithms: a one-dimensional (1D) particle chain assembly and two two-dimensional (2D) polymorphic crystals each consisting of assemblies of two distinct plane symmetry groups. Angle relationships between neighbouring particles are calculated and neighbour counts of each particle are determined. Combining these two parameters as rules for classification criteria allows for the labeling and quantification of each particle into a defined symmetry class within an assembly. The algorithms provide a labelled image comprising classification results and particle counts of each defined class. For multiple images or individual frames from a video, the script can be looped to achieve automatic processing. The yielded classification data allow for more in-depth image analysis of mixed pattern particle assemblies. We envision that these algorithms will have utility in quantitative analysis of images comprising ellipsoidal colloidal materials, nanoparticles, or biological matter.

Quantitative Supramolecular Heterodimerization for Efficient Energy Transfer

The challenge of quantitatively forming self-assembled heterodimers without other equilibrium by-products is overcome through self-sorting favored by the introduction of designed shape-complementary moieties. Such a supramolecular strategy based on cucurbit[8]uril-directed dimerization is further applied to generate hetero-chromophore dimers quantitatively, leading to efficient energy transfer (>85 %) upon photoexcitation.

Role of Entropy in Colloidal Self-Assembly

Entropy plays a key role in the self-assembly of colloidal particles. Specifically, in the case of hard particles, which do not interact or overlap with each other during the process of self-assembly, the free energy is minimized due to an increase in the entropy of the system. Understanding the contribution of entropy and engineering it is increasingly becoming central to modern colloidal self-assembly research, because the entropy serves as a guide to design a wide variety of self-assembled structures for many technological and biomedical applications. In this work, we highlight the importance of entropy in different theoretical and experimental self-assembly studies. We discuss the role of shape entropy and depletion interactions in colloidal self-assembly. We also highlight the effect of entropy in the formation of open and closed crystalline structures, as well as describe recent advances in engineering entropy to achieve targeted self-assembled structures.

On Markov blankets and hierarchical self-organisation

Biological self-organisation can be regarded as a process of spontaneous pattern formation; namely, the emergence of structures that distinguish themselves from their environment. This process can occur at nested spatial scales: from the microscopic (e.g., the emergence of cells) to the macroscopic (e.g. the emergence of organisms). In this paper, we pursue the idea that Markov blankets - that separate the internal states of a structure from external states - can self-assemble at successively higher levels of organisation. Using simulations, based on the principle of variational free energy minimisation, we show that hierarchical self-organisation emerges when the microscopic elements of an ensemble have prior (e.g., genetic) beliefs that they participate in a macroscopic Markov blanket: i.e., they can only influence - or be influenced by - a subset of other elements. Furthermore, the emergent structures look very much like those found in nature (e.g., cells or organelles), when influences are mediated by short range signalling. These simulations are offered as a proof of concept that hierarchical self-organisation of Markov blankets (into Markov blankets) can explain the self-evidencing, autopoietic behaviour of biological systems.

Preparation of colloidal molecules with temperature-tunable interactions from oppositely charged microgel spheres

The self-assembly of small colloidal clusters, so-called colloidal molecules, into crystalline materials has proven extremely challenging, the outcome often being glassy, amorphous states where positions and orientations are locked. In this paper, a new type of colloidal molecule is therefore prepared, assembled from poly(N-isopropylacrylamide) (PNIPAM)-based microgels that due to their well documented softness and temperature-response allow for greater defect tolerance compared to hard spheres and for convenient in situ tuning of size, volume fraction and inter-particle interactions with temperature. The microgels (B) are assembled by electrostatic adsorption onto oppositely charged, smaller-sized microgels (A), where the relative size of the two determines the valency (n) of the resulting core-satellite ABn-type colloidal molecules. Following assembly, a microfluidic deterministic lateral displacement (DLD) device is used to effectively isolate AB4-type colloidal molecules of tetrahedral geometry that possess a repulsive-to-attractive transition on crossing the microgels' volume phase transition temperature (VPTT). These soft, temperature-responsive colloidal molecules constitute highly promising building blocks for the preparation of new materials with emergent properties, and their optical wavelength-size makes them especially interesting for optical applications.

Looking for alternatives to the superspace description of icosahedral quasicrystals

A multiple-cell approach is discussed as a possible alternative to the higher dimensional crystallography of icosahedral quasicrystals. It is based on the Socolar-Steinhardt tiling combined with the quasi-unit cell model. Quasi-unit cells fill the space without gaps and overlappings similar to those in periodic crystals. Similarly, the atoms can occupy general and special positions. The alloy stoichiometry and the packing density can be calculated through the relative tile frequencies, which in turn are determined as the components of the Perron-Frobenius eigenvector of the corresponding substitution matrix. The calculation of the diffraction pattern reduces to the Perron projection of a special matrix, the entries of which reflect the contribution of each type of quasi-unit cell to the coherent scattering.

Binary colloidal crystals (BCCs): Interactions, fabrication, and applications

The organization of matter into hierarchical structures is a fundamental characteristic of functional materials and living organisms. Binary colloidal crystal (BCC) systems present a diversified range of nanotopographic structures where large and small colloidal particles simultaneously self-assemble into either 2D monolayer or 3D hierarchical crystal lattices. More importantly, understanding how BCCs form opens up the possibility to fabricate more complex systems such as ternary or quaternary colloidal crystals. Monolayer BCCs can also offer the possibility to achieve surface micro- and nano-topographies with heterogeneous chemistries, which can be challenging to achieve with other traditional fabrication tools. A number of fabrication methods have been reported that enable generation of BCC structures offering high accuracy in growth with controllable stoichiometries; however, it is still a challenge to make uniform BCC structures over large surface areas. Therefore, fully understand the mechanism of binary colloidal self-assembly is crucial and new/combinational methods are needed. In this review, we summarize the recent advances in BCC fabrication using particles made of different materials, shapes, and dispersion medium. Depending on the potential application, the degree of order and efficiency of crystal formation has to be determined in order to induce variability in the intended lattice structures. The mechanisms involved in the formation of highly ordered lattice structures from binary colloidal suspensions and applications are discussed. The generation of BCCs can be controlled by manipulation of their extensive phase behavior, which facilitates a wide range potential applications in the fields of both material and biointerfacial sciences including photonics, biosensors, chromatography, antifouling surfaces, biomedical devices, and cell culture tools.

Expected Free Energy Formalizes Conflict Underlying Defense in Freudian Psychoanalysis

Freud's core interest in the psyche was the dynamic unconscious: that part of the psyche which is unconscious due to conflict (Freud, 1923/1961). Over the course of his career, Freud variously described conflict as an opposition to the discharge of activation (Freud, 1950), opposition to psychic activity due to the release of unpleasure (Freud, 1990/1991), opposition between the primary principle and the reality principle (Freud, 1911/1963), structural conflict between id, ego, and superego (Freud, 1923/1961), and ambivalence (Freud, 1912/1963). Besides this difficulty of the shifting description of conflict, an underlying question remained the specific shared terrain in which emotions, thoughts, intentions or wishes could come into conflict with one another (the neuronal homolog of conflict), and most especially how they may exist as quantities in opposition within that terrain. Friston's free-energy principle (FEP henceforth) connected to the work of Friston (Friston et al., 2006; Friston, 2010) has provided the potential for a powerful unifying theory in psychology, neuroscience, and related fields that has been shown to have tremendous consilience with psychoanalytic concepts (Hopkins, 2012). Hopkins (2016), drawing on a formulation by Hobson et al. (2014), suggests that conflict may be potentially quantifiable as free energy from a FEP perspective. More recently, work by Friston et al. (2017a) has framed the selection of action as a gradient descent of expected free energy under different policies of action. From this perspective, the article describes how conflict could potentially be formalized as a situation where opposing action policies have similar expected free energy, for example between actions driven by competing basic prototype emotion systems as described by Panksepp (1998). This conflict state may be avoided in the future through updating the relative precision of a particular set of prior beliefs about outcomes: this has the result of tending to favor one of the policies of action over others in future instances, a situation analogous to defense. Through acting as a constraint on the further development of the person, the defensive operation can become entrenched, and resistant to alteration. The implications that this formalization has for psychoanalysis is explored.

Solvent-Assisted Surface Engineering for High-Performance All-Inorganic Perovskite Nanocrystal Light-Emitting Diodes

All-inorganic cesium halide perovskite nanocrystals have attracted much interest in optoelectronic applications for the sake of the readily adjustable band gaps, high photoluminescence quantum yield, pure color emission, and affordable cost. However, because of the ineluctable utilization of organic surfactants during the synthesis, the structural and optical properties of CsPbBr₃ nanocrystals degrade upon transforming from colloidal solutions to solid thin films, which plagues the device operation. Here, we develop a novel solvent-assisted surface engineering strategy, producing high-quality CsPbBr₃ thin films for device applications. A good solvent is first introduced as an assembly trigger to conduct assembly in a one-dimensional direction, which is then interrupted by adding a nonsolvent. The nonsolvent drives the adjacent nanoparticles connecting in a two-dimensional direction. Assembled CsPbBr₃ nanocrystal thin films are densely packed and very smooth with a surface roughness of ∼4.8 nm, which is highly desirable for carrier transport in a light-emitting diode (LED) device. Meanwhile, the film stability is apparently improved. Benefiting from this facile and reliable strategy, we have achieved remarkably improved performance of CsPbBr₃ nanocrystal-based LEDs. Our results not only enrich the methods of nanocrystal surface engineering but also shed light on developing high-performance LEDs.

Mix-and-Melt Colloidal Engineering

Increasing significance is being placed on the synthesis of smart colloidal particles, since the route to various meta-materials has been outlined through their bottom-up self-assembly. Unfortunately, making particles with well-defined shape and surface chemistry often requires considerable effort and time, and as such, they are available only in restrictive yields. Here we report a synthetic methodology, which we refer to as mix-and-melt reactions (MMR), that allows for rapid prototyping and mass production of anisotropic core-shell colloids. MMR take advantage of the synergistic properties between common colloidal suspensions by aggregating then reconfiguring polystyrene shell particles onto core particle substrates. By systematically exchanging cores and shells, the resultant core-shell particle's properties are manipulated in a modular fashion. The influence of the constituent particles' size ratio is extensively explored, which is shown to tune shell thickness, change the aspect ratio of shells on anisotropic cores, and access specific shapes such as tetrahedra. Beyond particle shape, mixed shell systems are utilized to create regular surface patches. Surface Evolver simulations are used to demonstrate how randomly packed clusters melt into regular shapes via a shell compartmentalization mechanism.

Shape-directed dynamics of active colloids powered by induced-charge electrophoresis

The symmetry and shape of colloidal particles can direct complex particle motions through fluid environments powered by simple energy inputs. The ability to rationally design or "program" the dynamics of such active colloids is an important step toward the realization of colloidal machines, in which components assemble spontaneously in space and time to perform dynamic (dissipative) functions such as actuation and transport. Here, we systematically investigate the dynamics of polarizable particles of different shapes moving in an oscillating electric field via induced-charge electrophoresis (ICEP). We consider particles from each point group in three dimensions (3D) and identify the different rotational and translational motions allowed by symmetry. We describe how the 3D shape of rigid particles can be tailored to achieve desired dynamics including oscillatory motions, helical trajectories, and complex periodic orbits. The methodology we develop is generally applicable to the design of shape-directed particle motions powered by other energy inputs.

Buckling Instability Causes Inertial Thrust for Spherical Swimmers at All Scales

Microswimmers, and among them aspirant microrobots, generally have to cope with flows where viscous forces are dominant, characterized by a low Reynolds number (Re). This implies constraints on the possible sequences of body motion, which have to be nonreciprocal. Furthermore, the presence of a strong drag limits the range of resulting velocities. Here, we propose a swimming mechanism which uses the buckling instability triggered by pressure waves to propel a spherical, hollow shell. With a macroscopic experimental model, we show that a net displacement is produced at all Re regimes. An optimal displacement caused by nontrivial history effects is reached at intermediate Re. We show that, due to the fast activation induced by the instability, this regime is reachable by microscopic shells. The rapid dynamics would also allow high-frequency excitation with standard traveling ultrasonic waves. Scale considerations predict a swimming velocity of order 1  cm/s for a remote-controlled microrobot, a suitable value for biological applications such as drug delivery.

Direct Observation of Interactions between Nanoparticles and Nanoparticle Self-Assembly in Solution

Hierarchically organized nanoparticles (NPs) possess unique properties and are relevant to various technological applications. An important "bottom-up" strategy for building such hierarchical nanostructures is to guide the individual NPs into ordered nanoarchitectures using intermolecular interactions and external forces. However, our current understanding of the nanoscale interactions that govern such self-assembly processes usually relies on post-synthesis/assembly or indirect characterization. Theoretical models that can derive these interactions are presently constrained to systems with only a few particles or on short time scales. Hence, except for a number of special cases, a description that captures the detailed mechanisms of NP self-assembly still eludes us. By imaging the assembly of NPs in solution with subnanometer resolution and in real-time, in situ liquid cell transmission electron microscopy (LC-TEM) can identify previously unknown intermediate stages and improve our understanding of such processes. Here, we review recent studies where we explored NP self-assembly at different organization length scales using LC-TEM: (1) we followed the transformation of atoms into crystalline NPs in solution, (2) we highlighted the role of solvation forces on interaction dynamics between NPs, and (3) we described the assembly dynamics of NPs in solution. In the case of nanocrystal nucleation, we identified the existence of three distinct steps that lead to the formation of crystalline nuclei in solution. These steps are spinodal decomposition of the precursor solution into solute-rich and solute-poor liquid phases, nucleation of amorphous clusters within the solute-rich liquid phase, followed by crystallization of these amorphous clusters into crystalline NPs. The next question we ask is how NPs interact in solution once they form. It turns out that the hydration layer surrounding each NP acts as a repulsive barrier that prevents NPs from readily attaching to each other due to attractive vdW forces. Consequently, two interacting NPs form a metastable pair separated by their one water molecule thick hydration shell and they undergo attachment only when this water between them is drained. Next, we explore the self-assembly of many NP systems where the formation of linear chains from spherical NPs or nanorods (NRs) is mediated by linker molecules. At low linker concentration, both spherical NPs and NRs tend to form linear chains because of the need to reduce electrostatic repulsion between NP building blocks. When the concentration of linkers is increased, the attachment of NPs is no longer linear. For example, we find that two NRs undergo side-to-side assembly due to decreased electrostatic repulsion and the anisotropic distribution of linkers on NR surfaces at high linker concentration. Lastly, we look at the formation of NP nanorings directed by ethylenediaminetetraacetic acid (EDTA) nanodroplets in water. Our study shows that nanoring assemblies form via sequential attachment of NPs to binding sites located along the circumference of the EDTA nanodroplet, followed by rearrangement and reorientation of the attached NPs. Our approach based on real-time visualization of nanoscale processes not only reveals all the intermediate steps of NP assembly, but also provides quantitative description on the interactions between nanoscale objects in solution.

Spinning Hierarchical Gold Nanowire Microfibers by Shear Alignment and Intermolecular Self-Assembly

Hierarchical structures lend strength to natural fibers made of soft nanoscale building blocks. Intermolecular interactions connect the components at different levels of hierarchy, distribute stresses, and guarantee structural integrity under load. Here, we show that synthetic ultrathin gold nanowires with interacting ligand shells can be spun into biomimetic, free-standing microfibers. A solution spinning process first aligns the wires, then lets their ligand shells interact, and finally converts them into a hierarchical superstructure. The resulting fiber contained 80 vol % organic ligand but was strong enough to be removed from the solution, dried, and mechanically tested. Fiber strength depended on the wire monomer alignment. Shear in the extrusion nozzle was systematically changed to obtain process-structure-property relations. The degree of nanowire alignment changed breaking stresses by a factor of 1.25 and the elongation at break by a factor of 2.75. Plasma annealing of the fiber to form a solid metal shell decreased the breaking stress by 65%.

Depletion-driven crystallization of cubic colloids sedimented on a surface

Cubic colloids, sedimented on a surface and immersed in a solution of depletant molecules, were modeled with a family of shapes which smoothly varies from squares to circles. Using Wang-Landau simulations with expanded ensembles, we observe the formation of rhombic lattices, square lattices, hexagonal lattices, and a fluid phase. This systematic investigation includes locating transitions between all combinations of the three lattice structures upon changing the shape and transitions between the fluid and crystal upon changing the depletant concentration. The rhombic lattice deforms smoothly between square-like and hexagonal-like angles, depending on both the shape and the depletant concentration. Our results on the effect of the depletant concentration, depletant size, and colloid shape to influence the stability of the fluid and the lattice structures may help guide experimental studies with recently synthesized cubic colloids.

Chiral self-assembly of helical particles

The shape of the building blocks plays a crucial role in directing self-assembly towards desired architectures. Out of the many different shapes, the helix has a unique position. Helical structures are ubiquitous in nature and a helical shape is exhibited by the most important biopolymers like polynucleotides, polypeptides and polysaccharides as well as by cellular organelles like flagella. Helical particles can self-assemble into chiral superstructures, which may have a variety of applications, e.g. as photonic (meta)materials. However, a clear and definite understanding of these structures has not been entirely achieved yet. We have recently undertaken an extensive investigation on the phase behaviour of hard helical particles, using numerical simulations and classical density functional theory. Here we present a detailed study of the phase diagram of hard helices as a function of their morphology. This includes a variety of liquid-crystal phases, with different degrees of orientational and positional ordering. We show how, by tuning the helix parameters, it is possible to control the organization of the system. Starting from slender helices, whose phase behaviour is similar to that of rodlike particles, an increase in curliness leads to the onset of azimuthal correlations between the particles and the formation of phases specific to helices. These phases feature a new kind of screw order, of which there is experimental evidence in colloidal suspensions of helical flagella.

Rich Polymorphic Behavior of Wigner Bilayers

Self-assembly into target structures is an efficient material design strategy. Combining analytical calculations and computational techniques of evolutionary and Monte Carlo types, we report about a remarkable structural variability of Wigner bilayer ground states, when charges are confined between parallel charged plates. Changing the interlayer separation, or the plate charge asymmetry, a cascade of ordered patterns emerges. At variance with the symmetric case phenomenology, the competition between commensurability features and charge neutralization leads to long range attraction, appearance of macroscopic charges, exotic phases, and nonconventional phase transitions with distinct critical indices, offering the possibility of a subtle, but precise and convenient control over patterns.

Self-Assembly of Colloidal Nanocrystals: From Intricate Structures to Functional Materials

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.

Shape-shifting colloids via stimulated dewetting

The ability to reconfigure elementary building blocks from one structure to another is key to many biological systems. Bringing the intrinsic adaptability of biological systems to traditional synthetic materials is currently one of the biggest scientific challenges in material engineering. Here we introduce a new design concept for the experimental realization of self-assembling systems with built-in shape-shifting elements. We demonstrate that dewetting forces between an oil phase and solid colloidal substrates can be exploited to engineer shape-shifting particles whose geometry can be changed on demand by a chemical or optical signal. We find this approach to be quite general and applicable to a broad spectrum of materials, including polymers, semiconductors and magnetic materials. This synthetic methodology can be further adopted as a new experimental platform for designing and rapidly prototyping functional colloids, such as reconfigurable micro swimmers, colloidal surfactants and switchable building blocks for self-assembly.

Mimicking the intrinsic adaptability of biological systems in synthetic materials has been a challenge. Here, Sacanna and co-workers have used dewetting forces between an oil phase and solid colloidal substrate to facilitate shape shifting particles that can change geometry by chemical and optical signals.

Self-assembly of trimer colloids: effect of shape and interaction range

Trimers with one attractive bead and two repulsive beads, similar to recently synthesized trimer patchy colloids, were simulated with flat-histogram Monte Carlo methods to obtain the stable self-assembled structures for different shapes and interaction potentials. Extended corresponding states principle was successfully applied to self-assembling systems in order to approximately collapse the results for models with the same shape, but different interaction range. This helps us directly compare simulation results with previous experiment, and good agreement was found between the two. In addition, a variety of self-assembled structures were observed by varying the trimer geometry, including spherical clusters, elongated clusters, monolayers, and spherical shells. In conclusion, our results help to compare simulations and experiments, via extended corresponding states, and we predict the formation of self-assembled structures for trimer shapes that have not been experimentally synthesized.

Computational study of trimer self-assembly and fluid phase behavior

The fluid phase diagram of trimer particles composed of one central attractive bead and two repulsive beads was determined as a function of simple geometric parameters using flat-histogram Monte Carlo methods. A variety of self-assembled structures were obtained including spherical micelle-like clusters, elongated clusters, and densely packed cylinders, depending on both the state conditions and shape of the trimer. Advanced simulation techniques were employed to determine transitions between self-assembled structures and macroscopic phases using thermodynamic and structural definitions. Simple changes in particle geometry yield dramatic changes in phase behavior, ranging from macroscopic fluid phase separation to molecular-scale self-assembly. In special cases, both self-assembled, elongated clusters and bulk fluid phase separation occur simultaneously. Our work suggests that tuning particle shape and interactions can yield superstructures with controlled architecture.

Multivalent bonds in self-assembled bundles of ultrathin gold nanowires

We describe solvent effects in the self-assembly of ultrathin gold nanowires and highlight the role of intermolecular ligand–solvent interactions.

Knowing one's place: a free-energy approach to pattern regulation

Understanding how organisms establish their form during embryogenesis and regeneration represents a major knowledge gap in biological pattern formation. It has been recently suggested that morphogenesis could be understood in terms of cellular information processing and the ability of cell groups to model shape. Here, we offer a proof of principle that self-assembly is an emergent property of cells that share a common (genetic and epigenetic) model of organismal form. This behaviour is formulated in terms of variational free-energy minimization-of the sort that has been used to explain action and perception in neuroscience. In brief, casting the minimization of thermodynamic free energy in terms of variational free energy allows one to interpret (the dynamics of) a system as inferring the causes of its inputs-and acting to resolve uncertainty about those causes. This novel perspective on the coordination of migration and differentiation of cells suggests an interpretation of genetic codes as parametrizing a generative model-predicting the signals sensed by cells in the target morphology-and epigenetic processes as the subsequent inversion of that model. This theoretical formulation may complement bottom-up strategies-that currently focus on molecular pathways-with (constructivist) top-down approaches that have proved themselves in neuroscience and cybernetics.

Toward coordinated colloids: site-selective growth of titania on patchy silica particles

Rational synthesis of coordinated spherical colloids is reported by site-selective growth of secondary hemispherical patches on primary spherical particles with quasi-defined coordination numbers and positions. We clarify the importance of mass transport phenomena on the site-specific secondary nucleation/growth in nanoparticulate colloidal systems. By comparing ultrasonic and conventional agitation during patch growth, we found that enhanced mass transfer is the key to controlled, homogeneous transport of the molecular precursors in a solvent onto the nanoparticles. With chemically defined nucleation sites, the surfaces of spherical silica particles were modified for use as a new kind of colloid with patches at desired coordination positions. Our observations represent a significant breakthrough in colloidal chemistry and self-assembly.

Polymorphic Ring-Shaped Molecular Clusters Made of Shape-Variable Building Blocks

Self-assembling molecular building blocks able to dynamically change their shapes, is a concept that would offer a route to reconfigurable systems. Although simulation studies predict novel properties useful for applications in diverse fields, such kinds of building blocks, have not been implemented thus far with molecules. Here, we report shape-variable building blocks fabricated by DNA self-assembly. Blocks are movable enough to undergo shape transitions along geometrical ranges. Blocks connect to each other and assemble into polymorphic ring-shaped clusters via the stacking of DNA blunt-ends. Reconfiguration of the polymorphic clusters is achieved by the surface diffusion on mica substrate in response to a monovalent salt concentration. This work could inspire novel reconfigurable self-assembling systems for applications in molecular robotics.

Thermodynamic insights into the self-assembly of capped nanoparticles using molecular dynamic simulations

Although the molecular modeling of self-assembling processes stands as a challenging research issue, there have been a number of breakthroughs in recent years. This report describes the use of large-scale molecular dynamics simulations with coarse grained models to study the spontaneous self-assembling of capped nanoparticles in chloroform suspension. A model system comprising 125 nanoparticles in chloroform evolved spontaneously from a regular array of independent nanoparticles to a single thread-like, ramified superstructure spanning the whole simulation box. The aggregation process proceeded by means of two complementary mechanisms, the first characterized by reactive collisions between monomers and oligomers, which were permanently trapped into the growing superstructure, and the second a slow structural reorganization of the nanoparticle packing. Altogether, these aggregation processes were over after ca. 0.6 μs and the system remained structurally and energetically stable until 1 μs. The thread-like structure closely resembles the TEM images of capped ZrO2, but a better comparison with experimental results was obtained by the deposition of the suspension over a graphene solid substrate, followed by the complete solvent evaporation. The agreement between the main structural features from this simulation and those from the TEM experiment was excellent and validated the model system. In order to shed further light on the origins of the stable aggregation of the nanoparticles, the Gibbs energy of aggregation was computed, along with its enthalpy and entropy contributions, both in chloroform and in a vacuum. The thermodynamic parameters arising from the modeling are consistent with larger nanoparticles in chloroform due to the solvent-swelled organic layer and the overall effect of the solvent was the partial destabilization of the aggregated state as compared to the vacuum system. The modeling strategy has been proved effective and reliable to describe the self-assembling of capped nanoparticles, but we must acknowledge the fact that larger model systems and longer timescales will be necessary in future investigations in order to assess structural and dynamical information approaching the behavior of macroscopic systems.

Understanding shape entropy through local dense packing

Many natural systems are structured by the ordering of repeated, distinct shapes. Understanding how this happens is difficult because shape affects structure in two ways. One is how the shape of a cell or nanoparticle, for example, affects its surface, chemical, or other intrinsic properties. The other is an emergent, entropic effect that arises from the geometry of the shape itself, which we term “shape entropy,” and is not well understood. In this paper, we determine how shape entropy affects structure. We quantify the mechanism and determine when shape entropy competes with intrinsic shape effects. Our results show that in a wide class of systems, shape affects bulk structure because crowded particles optimize their local packing.

Self-assembly of nanoparticle amphiphiles with adaptive surface chemistry

We investigate the self-assembly of amphiphilic nanoparticles (NPs) functionalized with mixed monolayers of hydrophobic and hydrophilic ligands in water. Unlike typical amphiphilic particles with "fixed" surface chemistries, the ligands used here are not bound irreversibly but can rearrange dynamically on the particles' surface during their assembly from solution. Depending on the assembly conditions, these adaptive amphiphiles form compact micellar clusters or extended chain-like assemblies in aqueous solution. By controlling the amount of hydrophobic ligands on the particles' surface, the average number of nearest neighbors--that is, the preferred coordination number--can be varied systematically from ∼ 1 (dimers) to ∼ 2 (linear chains) to ∼ 3 (extended clusters). To explain these experimental findings, we present an assembly mechanism in which hydrophobic ligands organize dynamically to form discrete patches between proximal NPs to minimize contact with their aqueous surroundings. Monte Carlo simulations incorporating these adaptive hydrophobic interactions reproduce the three-dimensional assemblies observed in experiment. These results suggest a general strategy based on reconfigurable "sticky" patches that may allow for tunable control over particle coordination number within self-assembled structures.

Understanding shape entropy through local dense packing

Entropy drives the phase behavior of colloids ranging from dense suspensions of hard spheres or rods to dilute suspensions of hard spheres and depletants. Entropic ordering of anisotropic shapes into complex crystals, liquid crystals, and even quasicrystals was demonstrated recently in computer simulations and experiments. The ordering of shapes appears to arise from the emergence of directional entropic forces (DEFs) that align neighboring particles, but these forces have been neither rigorously defined nor quantified in generic systems. Here, we show quantitatively that shape drives the phase behavior of systems of anisotropic particles upon crowding through DEFs. We define DEFs in generic systems and compute them for several hard particle systems. We show they are on the order of a few times the thermal energy ([Formula: see text]) at the onset of ordering, placing DEFs on par with traditional depletion, van der Waals, and other intrinsic interactions. In experimental systems with these other interactions, we provide direct quantitative evidence that entropic effects of shape also contribute to self-assembly. We use DEFs to draw a distinction between self-assembly and packing behavior. We show that the mechanism that generates directional entropic forces is the maximization of entropy by optimizing local particle packing. We show that this mechanism occurs in a wide class of systems and we treat, in a unified way, the entropy-driven phase behavior of arbitrary shapes, incorporating the well-known works of Kirkwood, Onsager, and Asakura and Oosawa.

Electrostatics-driven shape transitions in soft shells

Manipulating the shape of nanoscale objects in a controllable fashion is at the heart of designing materials that act as building blocks for self-assembly or serve as targeted drug delivery carriers. Inducing shape deformations by controlling external parameters is also an important way of designing biomimetic membranes. In this paper, we demonstrate that electrostatics can be used as a tool to manipulate the shape of soft, closed membranes by tuning environmental conditions such as the electrolyte concentration in the medium. Using a molecular dynamics-based simulated annealing procedure, we investigate charged elastic shells that do not exchange material with their environment, such as elastic membranes formed in emulsions or synthetic nanocontainers. We find that by decreasing the salt concentration or increasing the total charge on the shell's surface, the spherical symmetry is broken, leading to the formation of ellipsoids, discs, and bowls. Shape changes are accompanied by a significant lowering of the electrostatic energy and a rise in the surface area of the shell. To substantiate our simulation findings, we show analytically that a uniformly charged disc has a lower Coulomb energy than a sphere of the same volume. Further, we test the robustness of our results by including the effects of charge renormalization in the analysis of the shape transitions and find the latter to be feasible for a wide range of shell volume fractions.

Rod hydrodynamics and length distributions of single-wall carbon nanotubes using analytical ultracentrifugation

Because of their repetitive chemical structure, extreme rigidity, and the separability of populations with varying aspect ratio, SWCNTs are excellent candidates for use as model rodlike colloids. In this contribution, the sedimentation velocities of length and density sorted single-wall carbon nanotubes (SWCNTs) are compared to predictions from rod hydrodynamic theories of increasing complexity over a range of aspect ratios from <50 to >400. Independently measuring all contributions to the sedimentation velocity besides the shape factor, excellent agreement is found between the experimental findings and theoretical predictions for numerically calculated hydrodynamic radius values and for multiterm analytical expansion approximations; values for the hydrodynamic radii in these cases are additionally found to be consistent with the apparent hydrated particle radius determined independently by buoyancy measurements. Lastly, we utilize this equivalency to calculate the apparent distribution of nanotube lengths in each population from their sedimentation coefficient distribution without adjustable parameters, achieving excellent agreement with distributions from atomic force microscopy. The method developed herein provides an alternative for the ensemble measurement of SWCNT length distributions and others rodlike particles.

Percolation Diffusion into Self-Assembled Mesoporous Silica Microfibres

Percolation diffusion into long (11.5 cm) self-assembled, ordered mesoporous microfibres is studied using optical transmission and laser ablation inductive coupled mass spectrometry (LA-ICP-MS). Optical transmission based diffusion studies reveal rapid penetration (<5 s, D > 80 μm²∙s^-¹) of Rhodamine B with very little percolation of larger molecules such as zinc tetraphenylporphyrin (ZnTPP) observed under similar loading conditions. The failure of ZnTPP to enter the microfibre was confirmed, in higher resolution, using LA-ICP-MS. In the latter case, LA-ICP-MS was used to determine the diffusion of zinc acetate dihydrate, D~3 × 10^-4 nm²∙s^-1. The large differences between the molecules are accounted for by proposing ordered solvent and structure assisted accelerated diffusion of the Rhodamine B based on its hydrophilicity relative to the zinc compounds. The broader implications and applications for filtration, molecular sieves and a range of devices and uses are described.