Binary colloidal structures assembled through Ising interactions

Lattice Model Results for Pattern Formation in a Mixture with Competing Interactions

A monolayer consisting of two types of particles, with energetically favored alternating stripes of the two components, is studied by Monte Carlo simulations and within a mesoscopic theory. We consider a triangular lattice model and assume short-range attraction and long-range repulsion between particles of the same kind, as well as short-range repulsion and long-range attraction for the cross-interaction. The structural evolution of the model upon increasing temperature is studied for equal chemical potentials of the two species. We determine the structure factor, the chemical potential-density isotherms, the specific heat, and the compressibility, and show how these thermodynamic functions are associated with the spontaneous formation of stripes with varying degrees of order.

Magnetic field directed assembly of magnetic non-spherical microparticles

This study reports on the fabrication and assembly of anisotropic microparticles as versatile building blocks for directed magnetic assemblies. Although spherical microparticles have received extensive attention, the assembly of non-spherical magnetic microparticles remains underexplored. Herein, we present a fabrication approach that utilizes photolithography and soft lithography to create prism-shaped magnetic microparticles. In order to investigate their assembly, a switching rotating magnetic field was employed. To support our experimental findings, a numerical model which takes into account the magnetic dipole moments induced by the field of other particles was developed. This model helps in understanding the forces and torques governing particle behavior during assembly. Simulations were conducted using the numerical model to complement our experimental findings. In the two particle experiments, attractive magnetic interactions led to various configurations depending on initial positions. For three particles, a tip-to-tip configuration suggested closed or stable ring-like structures. Our work highlights the feasibility of producing highly responsive, non-spherical magnetic microparticles and their potential for assemblies. The versatile fabrication method, coupled with the added degree of freedom conferred by prismatic shapes, opens promising avenues for applications in biology and material science.

Colloidal Self-Assembly: From Passive to Active Systems

Self-assembly fundamentally implies the organization of small sub-units into large structures or patterns without the intervention of specific local interactions. This process is commonly observed in nature, occurring at various scales ranging from atomic/molecular assembly to the formation of complex biological structures. Colloidal particles may serve as micrometer-scale surrogates for studying assembly, particularly for the poorly understood kinetic and dynamic processes at the atomic scale. Recent advances in colloidal self-assembly have enabled the programmable creation of novel materials with tailored properties. We here provide an overview and comparison of both passive and active colloidal self-assembly, with a discussion on the energy landscape and interactions governing both types. In the realm of passive colloidal assembly, many impressive and important structures have been realized, including colloidal molecules, one-dimensional chains, two-dimensional lattices, and three-dimensional crystals. In contrast, active colloidal self-assembly, driven by optical, electric, chemical, or other fields, involves more intricate dynamic processes, offering more flexibility and potential new applications. A comparative analysis underscores the critical distinctions between passive and active colloidal assemblies, highlighting the unique collective behaviors emerging in active systems. These behaviors encompass collective motion, motility-induced phase segregation, and exotic properties arising from out-of-equilibrium thermodynamics. Through this comparison, we aim to identify the future opportunities in active assembly research, which may suggest new application domains.

Motility-induced phase separation and frustration in active matter swarmalators

We introduce a two dimensional system of active matter swarmalators composed of elastically interacting run-and-tumble active disks with an internal parameter ϕ_{i}. The disks experience an additional attractive or repulsive force with neighboring disks depending upon their relative difference in ϕ_{i}, making them similar to swarmalators used in robotic systems. In the absence of the internal parameter, the system forms a motility-induced phase separated (MIPS) state, but when the swarmalator interactions are present, a wide variety of other active phases appear depending upon whether the interaction is attractive or repulsive and whether the particles act to synchronize or ant-synchronize their internal parameter values. These phases include a gas-free gel regime, arrested clusters, a labyrinthine state, a regular MIPS state, a frustrated MIPS state for attractive antisynchronization, and a superlattice MIPS state for attractive synchronization.

A density functional theory and simulation study of stripe phases in symmetric colloidal mixtures

In a binary mixture, stripes refer to a one-dimensional periodicity of the composition, namely, a regular alternation of layers filled with particles of mostly one species. We have recently introduced [Munaò et al., Phys. Chem. Chem. Phys. 25, 16227 (2023)] a model that possibly provides the simplest binary mixture endowed with stripe order. The model consists of two species of identical hard spheres with equal concentration, which mutually interact through a square-well potential. In that paper, we have numerically shown that stripes are present in both liquid and solid phases when the attraction range is rather long. Here, we study the phase behavior of the model in terms of a density functional theory capable to account for the existence of stripes in the dense mixture. Our theory is accurate in reproducing the phases of the model, at least insofar as the composition inhomogeneities occur on length scales quite larger than the particle size. Then, using Monte Carlo simulations, we prove the existence of solid stripes even when the square well is much thinner than the particle diameter, making our model more similar to a real colloidal mixture. Finally, when the width of the attractive well is equal to the particle diameter, we observe a different and more complex form of compositional order in the solid, where each species of particle forms a regular porous matrix holding in its holes the other species, witnessing a surprising variety of emergent behaviors for a very basic model of interaction.

A multiscale generative model to understand disorder in domain boundaries

A continuing challenge in atomic resolution microscopy is to identify significant structural motifs and their assembly rules in synthesized materials with limited observations. Here, we propose and validate a simple and effective hybrid generative model capable of predicting unseen domain boundaries in a potassium sodium niobate thin film from only a small number of observations, without expensive first-principles calculations or atomistic simulations of domain growth. Our results demonstrate that complicated domain boundary structures spanning 1 to 100 nanometers can arise from simple interpretable local rules played out probabilistically. We also found previously unobserved, significant, tileable boundary motifs that may affect the piezoelectric response of the material system, and evidence that our system creates domain boundaries with the highest configurational entropy. More broadly, our work shows that simple yet interpretable machine learning models could pave the way to describe and understand the nature and origin of disorder in complex materials, therefore improving functional materials design.

A Paramagnetic Compass Based on Lanthanide Metal-Organic Framework

Macroscopic compass-like magnetic alignment at low magnetic fields is natural for ferromagnetic materials but is seldomly observed in paramagnetic materials. Herein, we report a "paramagnetic compass" that magnetically aligns under ∼mT fields based on the single-crystalline framework constructed by lanthanide ions and organic ligands (Ln-MOF). The magnetic alignment is attributed to the Ln-MOF's strong macroscopic anisotropy, where the highly-ordered structure allows the Ln-ions' molecular anisotropy to be summed according to the crystal symmetry. In tetragonal Ln-MOFs, the alignment is either parallel or perpendicular to the field depending on the easiest axis of the molecular anisotropy. Reversible switching between the two alignments is realized upon the removal and re-adsorption of solvent molecules filled in the framework. When the crystal symmetry is lowered in monoclinic Ln-MOFs, the alignments become even inclined (47°-66°) to the field. These fascinating properties of Ln-MOFs would encourage further explorations of framework materials containing paramagnetic centers.

Like aggregation from unlike attraction: stripes in symmetric mixtures of cross-attracting hard spheres

Self-assembly of colloidal particles into striped phases is at once a process of relevant technological interest-just think about the possibility to realise photonic crystals with a dielectric structure modulated along a specific direction-and a challenging task, since striped patterns emerge in a variety of conditions, suggesting that the connection between the onset of stripes and the shape of the intermolecular potential is yet to be fully unravelled. Hereby, we devise an elementary mechanism for the formation of stripes in a basic model consisting of a symmetric binary mixture of hard spheres that interact via a square-well cross attraction. Such a model would mimic a colloid in which the interspecies affinity is of longer range and significantly stronger than the intraspecies interaction. For attraction ranges shorter enough than the particle size the mixture behaves like a compositionally-disordered simple fluid. Instead, for wider square-wells, we document by numerical simulations the existence of striped patterns in the solid phase, where layers of particles of one species are interspersed with layers of the other species; increasing the attraction range stabilises the stripes further, in that they also appear in the bulk liquid and become thicker in the crystal. Our results lead to the counterintuitive conclusion that a flat and sufficiently long-ranged unlike attraction promotes the aggregation of like particles into stripes. This finding opens a novel way for the synthesis of colloidal particles with interactions tailored at the development of stripe-modulated structures.

Self-assembly and percolation in two dimensional binary magnetic colloids

We study the self-assembly of branching-chain networks and crystals in a binary colloidal system with tunable interactions. The particle positions are extracted from microscopy images and order parameters are extracted by image processing and statistical analysis. With these, we construct phase diagrams with respect to particle density, ratio and interaction. In order to draw a more complete picture, we complement the experiments with computer simulations. We establish a region in the phase diagram, where bead ratios and interactions are symmetric, promoting percolated structures.

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.

Ferrofluids and bio-ferrofluids: looking back and stepping forward

Ferrofluids investigated along for about five decades are ultrastable colloidal suspensions of magnetic nanoparticles, which manifest simultaneously fluid and magnetic properties. Their magnetically controllable and tunable feature proved to be from the beginning an extremely fertile ground for a wide range of engineering applications. More recently, biocompatible ferrofluids attracted huge interest and produced a considerable increase of the applicative potential in nanomedicine, biotechnology and environmental protection. This paper offers a brief overview of the most relevant early results and a comprehensive description of recent achievements in ferrofluid synthesis, advanced characterization, as well as the governing equations of ferrohydrodynamics, the most important interfacial phenomena and the flow properties. Finally, it provides an overview of recent advances in tunable and adaptive multifunctional materials derived from ferrofluids and a detailed presentation of the recent progress of applications in the field of sensors and actuators, ferrofluid-driven assembly and manipulation, droplet technology, including droplet generation and control, mechanical actuation, liquid computing and robotics.

Magnetowetting dynamics of sessile ferrofluid droplets: a review

The fascinating behavior of ferrofluids in a magnetic field has been intriguing researchers for many years. With the advancement in digital microfluidics, ferrofluid droplets have been extensively used in different applications ranging from biomedical to mechanical systems. Notably, the magnetic field can change the wetting dynamics of sessile ferrofluid droplets, leading to a plethora of interesting hydrodynamic phenomena. In the recent past, the spatiotemporal evolution of the droplet shape and contact line dynamics of a ferrofluid droplet in different magnetowetting scenarios has been explored widely. The relevant studies elucidate several critical aspects, such as the role of magnetic nanoparticles, carrier fluid, and the interaction of the magnetic fluid with the solid surface, among many others. Hence a systematic review of the progress made in understanding the fundamental and practical aspects of magnetowetting in the past decade (2010-2020) would be a helpful resource to the scientific community in the near future. Drawn by this motivation, an honest effort has been made in this Review to highlight the significant scientific findings concerning the sessile droplet magnetowetting phenomena within the timeline of interest. Several cutting-edge applications developed from the scientific findings in the purview of magnetowetting have also been discussed before outlining the conclusions and future areas of scope.

From dynamic self-organization to avalanching instabilities in soft-granular threads

We study the dynamics of threads of monodisperse droplets, including droplet chains and multi-chains, in which the droplets are interconnected by capillary bridges of another immiscible liquid phase. This system represents wet soft-granular matter - a class of granular materials in which the grains are soft and wetted by thin fluid films-with other examples including wet granular hydrogels or foams. In contrast to wet granular matter with rigid grains (e.g., wet sand), studied previously, the deformability of the grains raises the number of available metastable states and facilitates rearrangements which allow for reorganization and self-assembly of the system under external drive, e.g., applied via viscous forces. We use a co-flow configuration to generate a variety of unique low-dimensional regular granular patterns, intermediate between 1D and 2D, ranging from linear chains and chains with periodically occurring folds to multi-chains and segmented structures including chains of finite length. In particular, we observe that the partially folded chains self-organize via limit cycle of displacements and rearrangements occurring at a frequency self-adapted to the rate of build-up of compressive strain in the chain induced by the viscous forces. Upon weakening of the capillary arrest of the droplets, we observe spontaneous fluidization of the quasi-solid structures and avalanches of rearrangements. We identify two types of fluidization-induced instabilities and rationalize them in terms of a competition between advection and propagation. While we use aqueous droplets as the grains we demonstrate that the reported mechanisms of adaptive self-assembly apply to other types of soft granular systems including foams and microgels. We discuss possible application of the reported quasi-1D compartmentalized structures in tissue engineering, bioprinting and materials science.

Rotation dynamics and internal structure of self-assembled binary paramagnetic colloidal clusters

We study experimentally and theoretically the dynamics of two-dimensional self-assembled binary clusters of paramagnetic colloids of two different sizes and magnetic susceptibilities under a time-varying magnetic field. Due to the continuous energy input by the rotating field, these clusters are at a state of dissipative nonequilibrium. Dissipative viscoelastic shear waves traveling around their interface enable the rotation of isotropic binary clusters. The angular velocity of a binary cluster is much slower than that of the magnetic field; it increases with the concentration of big particles, and it saturates at a concentration threshold. We generalize an earlier theoretical model to successfully account for the observed effect of cluster composition on cluster rotation. We also investigate the evolution of the internal distribution of the two particle types, reminiscent of segregation in a drop of two immiscible liquids, and the effect of this internal structure on rotation dynamics. The binary clusters exhibit short-range order, which rapidly vanishes at a larger scale, consistent with the clusters' viscoelastic liquid behavior.

Unconventional-Phase Crystalline Materials Constructed from Multiscale Building Blocks

Crystal phase, an intrinsic characteristic of crystalline materials, is one of the key parameters to determine their physicochemical properties. Recently, great progress has been made in the synthesis of nanomaterials with unconventional phases that are different from their thermodynamically stable bulk counterparts via various synthetic methods. A nanocrystalline material can also be viewed as an assembly of atoms with long-range order. When larger entities, such as nanoclusters, nanoparticles, and microparticles, are used as building blocks, supercrystalline materials with rich phases are obtained, some of which even have no analogues in the atomic and molecular crystals. The unconventional phases of nanocrystalline and supercrystalline materials endow them with distinctive properties as compared to their conventional counterparts. This Review highlights the state-of-the-art progress of nanocrystalline and supercrystalline materials with unconventional phases constructed from multiscale building blocks, including atoms, nanoclusters, spherical and anisotropic nanoparticles, and microparticles. Emerging strategies for engineering their crystal phases are introduced, with highlights on the governing parameters that are essential for the formation of unconventional phases. Phase-dependent properties and applications of nanocrystalline and supercrystalline materials are summarized. Finally, major challenges and opportunities in future research directions are proposed.

Mechanisms of Nucleation and Solid-Solid-Phase Transitions in Triblock Janus Assemblies

A model, including the chemical details of core nanoparticles as well as explicit surface charges and hydrophobic patches, of triblock Janus particles is employed to simulate nucleation and solid-solid phase transitions in two-dimensional layers. An explicit solvent and a substrate are included in the model, and hydrodynamic and many-body interactions were taken into account within many-body dissipative particle dynamics simulation. In order not to impose a mechanism a priori, we performed free (unbiased) simulations, leaving the system the freedom to choose its own pathways. In agreement with the experiment and previous biased simulations, a two-step mechanism for the nucleation of a kagome lattice from solution was detected. However, a distinct feature of the present unbiased versus biased simulations is that multiple nuclei emerge from the solution; upon their growth, the aligned and misaligned facets at the grain boundaries are introduced into the system. The liquid-like particles trapped between the neighboring nuclei connect them together. A mismatch in the symmetry planes of neighboring nuclei hinders the growth of less stable (smaller) nuclei. Unification of such nuclei at the grain boundaries of misaligned facets obeys a two-step mechanism: melting of the smaller nuclei, followed by subsequent nucleation of liquid-like particles at the interface of bigger neighboring nuclei. Besides, multiple postcritical nuclei are formed in the simulation box; the growth of some of which stops due to introduction of a strain in the system. Such an incomplete nucleation/growth mechanism is in complete agreement with the recent experiments. The solid-solid (hexagonal-to-kagome) phase transition, at weak superheatings, obeys a two-step mechanism: a slower step (formation of a liquid droplet), followed by a faster step (nucleation of kagome from the liquid droplet).

Simulated clustering dynamics of colloidal magnetic nanoparticles

Magnetically guided self-assembly of nanoparticles is a promising bottom-up method to fabricate novel materials and superstructures, such as, for example, magnetic nanoparticle clusters for biomedical applications. The existence of assembled structures has been verified by numerous experiments, yet a comprehensive theoretical framework to explore design possibilities and predict emerging properties is missing. Here we present a model of magnetic nanoparticle interactions built upon a Langevin dynamics algorithm to simulate the time evolution and aggregation of colloidal suspensions. We recognise three main aggregation regimes: non-aggregated, linear and clustered. Through systematic simulations we have revealed the link between single particle parameters and which aggregates are formed, both in terms of the three regimes and the chance of finding specific aggregates, which we characterise by nanoparticle arrangement and net magnetic moment. Our findings are shown to agree with past experiments and may serve as a stepping stone to guide the design and interpretation of future studies.

Layering of magnetic nanoparticles at amorphous magnetic templates with perpendicular anisotropy

We reveal the assembly of magnetite nanoparticles of sizes 5 nm, 15 nm and 25 nm from dilute water-based ferrofluids onto an amorphous magnetic template with out-of-plane anisotropy. From neutron reflectometry experiments we extract density profiles and show that the particles self-assemble into layers at the magnetic surface. The layers are extremely stable against cleaning and rinsing of the substrate. The density of the layers is determined by and increases with the remanent magnetic moment of the particles.

Grand canonical inverse design of multicomponent colloidal crystals

Inverse design methods are powerful computational approaches for creating colloidal systems which self-assemble into a target morphology by reverse engineering the Hamiltonian of the system. Despite this, these optimization procedures tend to yield Hamiltonians which are too complex to be experimentally realized. An alternative route to complex structures involves the use of several different components, however, conventional inverse design methods do not explicitly account for the possibility of phase separation into compositionally distinct structures. Here, we present an inverse design scheme for multicomponent colloidal systems by combining active learning with a method to directly compute their ground state phase diagrams. This explicitly accounts for phase separation and can locate stable regions of Hamiltonian parameter space which grid-based surveys are prone to miss. Using this we design low-density, binary structures with Lennard-Jones-like pairwise interactions that are simpler than in the single component case and potentially realizable in an experimental setting. This reinforces the concept that ground states of simple, multicomponent systems might be rich with previously unappreciated diversity, enabling the assembly of non-trivial structures with only few simple components instead of a single complex one.

Flexible Ferrofluids: Design and Applications

Ferrofluids, also known as ferromagnetic particle suspensions, are materials with an excellent magnetic response, which have attracted increasing interest in both industrial production and scientific research areas. Because of their outstanding features, such as rapid magnetic reaction, flexible flowability, as well as tunable optical and thermal properties, ferrofluids have found applications in various fields, including material science, physics, chemistry, biology, medicine, and engineering. Here, a comprehensive, in-depth insight into the diverse applications of ferrofluids from material fabrication, droplet manipulation, and biomedicine to energy and machinery is provided. Design of ferrofluid-related devices, recent developments, as well as present challenges and future prospects are also outlined.

Magnetic quadrupole assemblies with arbitrary shapes and magnetizations

Magnetic dipole-dipole interactions govern the behavior of magnetic matter across scales from micrometer colloidal particles to centimeter magnetic soft robots. This pairwise long-range interaction creates rich emergent phenomena under both static and dynamic magnetic fields. However, magnetic dipole particles, from either ferromagnetic or paramagnetic materials, tend to form chain-like structures as low-energy configurations due to dipole symmetry. The repulsion force between two magnetic dipoles raises challenges for creating stable magnetic assemblies with complex two-dimensional (2D) shapes. In this work, we propose a magnetic quadrupole module that is able to form stable and frustration-free magnetic assemblies with arbitrary 2D shapes. The quadrupole structure changes the magnetic particle-particle interaction in terms of both symmetry and strength. Each module has a tunable dipole moment that allows the magnetization of overall assemblies to be programmed at the single module level. We provide a simple combinatorial design method to reach both arbitrary shapes and arbitrary magnetizations concurrently. Last, by combining modules with soft segments, we demonstrate programmable actuation of magnetic metamaterials that could be used in applications for soft robots and electromagnetic metasurfaces.

Effect of volume fraction on chains of superparamagnetic colloids at equilibrium

For a few decades, the influence of a magnetic field on the aggregation process of superparamagnetic colloids has been well known on short time scale. However, the accurate study of the equilibrium state is still challenging on some aspects. On the numerical aspect, current simulations have only access to a restricted set of experimental conditions due to the computational cost of long-range interactions in many-body systems. In the present paper, we numerically explore a new range of parameters thanks to sped up numerical simulations validated by a recent experimental and numerical study. We first show that our simulations reproduce results from previous study in well-established conditions. Then we show that unexpectedly long chains are observed for higher volume fractions and intermediate fields. We also present theoretical developments taking into account the interaction between the chains which are able to reproduce the data that we obtained with our simulations. We finally confirm this model thanks to experimental data.

Self-assembled multi-layer simple cubic photonic crystals of oppositely charged colloids in confinement

Designing and fabricating self-assembled open colloidal crystals have become one major direction in the soft matter community because of many promising applications associated with open colloidal crystals. However, most of the self-assembled crystals found in experiments are not open but close-packed. Here, by using computer simulation, we systematically investigate the self-assembly of oppositely charged colloidal hard spheres confined between two parallel hard walls, and we find that the confinement can stabilize multi-layer NaCl-like (simple cubic) open crystals. The maximal number of layers of stable NaCl-like crystals increases with decreasing inverse screening length. More interestingly, at finite low temperature, the large vibrational entropy can stabilize some multi-layer NaCl-like crystals against the most energetically favoured close-packed crystals. In the parameter range studied, we find up to 4-layer NaCl-like crystals to be stable in confinement. Our photonic calculation shows that the inverse 4-layer NaCl-like crystal can already reproduce the large photonic band gaps of the bulk simple cubic crystal, which open in the low frequency range with a low dielectric contrast. This suggests new possibilities of using confined colloidal systems to fabricate open crystalline materials with novel photonic properties.

Moiré and honeycomb lattices through self-assembly of hard-core/soft-shell microgels: experiment and simulation

Moiré and honeycomb lattices result from the sequential double deposition of monolayers of core/shell microgels in dependence of the drying conditions.

Tools and Functions of Reconfigurable Colloidal Assembly

We review work in reconfigurable colloidal assembly, a field in which rapid, back-and-forth transitions between the equilibrium states of colloidal self-assembly are accomplished by dynamic manipulation of the size, shape, and interaction potential of colloids, as well as the magnitude and direction of the fields applied to them. It is distinguished from the study of colloidal phase transitions by the centrality of thermodynamic variables and colloidal properties that are time switchable; by the applicability of these changes to generate transitions in assembled colloids that may be spatially localized; and by its incorporation of the effects of generalized potentials due to, for example, applied electric and magnetic fields. By drawing upon current progress in the field, we propose a matrix classification of reconfigurable colloidal systems based on the tool used and function performed by reconfiguration. The classification distinguishes between the multiple means by which reconfigurable assembly can be accomplished (i.e., the tools of reconfiguration) and the different kinds of structural transitions that can be achieved by it (i.e., the functions of reconfiguration). In the first case, the tools of reconfiguration can be broadly classed as (i) those that control the colloidal contribution to the system entropy-as through volumetric and/or shape changes of the particles; (ii) those that control the internal energy of the colloids-as through manipulation of colloidal interaction potentials; and (iii) those that control the spatially resolved potential energy that is imposed on the colloids-as through the introduction of field-induced phoretic mechanisms that yield colloidal displacement and accumulation. In the second case, the functions of reconfiguration include reversible: (i) transformation between different phases-including fluid, cluster, gel, and crystal structures; (ii) manipulation of the spacing between colloids in crystals and clusters; and (iii) translation, rotation, or shape-change of finite-size objects self-assembled from colloids. With this classification in hand, we correlate the current limits on the spatiotemporal scales for reconfigurable colloidal assembly and identify a set of future research challenges.

Ising-like behaviour of mesoscopic magnetic chains

We demonstrate an experimental realization of the short range magnetic order in a one-dimensional Ising chain using fabricated mesospins. We confirm an excellent agreement between the experimental findings and simulations obtained using the original Ising model. In particular, we are able to show that the thermal behaviour of the mesoscopic Ising chain dominates over the thermal behaviour of the individual mesospins themselves, confirming that fabricated mesospins can be viewed as artificial magnetic atoms.

Recent Advances in Multicomponent Particle Assembly

Particle assembly and co-assembly have been research frontiers in chemistry and material science in the past few decades. To achieve a large variety of intricate structures and functional materials, remarkable progress has been made in particle assembly principles and strategies. Essentially, particle assembly is driven by intrinsic interparticle interactions or the external control. In this article, we focus on binary or ternary particle co-assembly and review the principles and feasible strategies. These advances have led to new disciplines of microfabrication technology and material engineering. Although significant achievement on particle-based structures has been made, it is still challenging to fully develop general and facile strategies to precisely control the one-dimensional (1D) co-assembly. This article reviews the recent development on multicomponent particle co-assembly, which significantly increases structural complexity and functional diversity. In particular, we highlight the advances in the particle co-assembly of well-ordered 1D binary superstructures by liquid soft confinement. Finally, prospective outlook for future trends in this field is proposed.

Electric Field Assembly of Colloidal Superstructures

The assembly of materials from building blocks has been in the core of a wide range of applications from catalysis to photonics and electronics. External electric fields enable the interactions between building blocks to be controlled via induced dipoles. Dipolar interactions were used so far to obtain one-dimensional chains or three-dimensional non-close-packed lattices. However, complex colloidal assemblies and clusters of simple spherical particles are rare. Here we demonstrate a novel self-assembly approach enabling the formation of regular axially symmetric clusters, an array of colloidal assemblies as per design of posts, and hierarchical complex assemblies by using posts and dipolar interactions or combining them. Regulating the polarization of the particles from positive to negative allows us to control the interparticle interactions from attractive to repulsive at the poles or equator of the particles. Therefore, such particle-particle interactions enable switching between Saturn ring-like and candle-flame-like axially symmetric assemblies, which could potentially be exploited for display applications.

From dynamic self-assembly to networked chemical systems

Although dynamic self-assembly, DySA, is a relatively new area of research, the past decade has brought numerous demonstrations of how various types of components - on scales from (macro)molecular to macroscopic - can be arranged into ordered structures thriving in non-equilibrium, steady states. At the same time, none of these dynamic assemblies has so far proven practically relevant, prompting questions about the field's prospects and ultimate objectives. The main thesis of this Review is that formation of dynamic assemblies cannot be an end in itself - instead, we should think more ambitiously of using such assemblies as control elements (reconfigurable catalysts, nanomachines, etc.) of larger, networked systems directing sequences of chemical reactions or assembly tasks. Such networked systems would be inspired by biology but intended to operate in environments and conditions incompatible with living matter (e.g., in organic solvents, elevated temperatures, etc.). To realize this vision, we need to start considering not only the interactions mediating dynamic self-assembly of individual components, but also how components of different types could coexist and communicate within larger, multicomponent ensembles. Along these lines, the review starts with the discussion of the conceptual foundations of self-assembly in equilibrium and non-equilibrium regimes. It discusses key examples of interactions and phenomena that can provide the basis for various DySA modalities (e.g., those driven by light, magnetic fields, flows, etc.). It then focuses on the recent examples where organization of components in steady states is coupled to other processes taking place in the system (catalysis, formation of dynamic supramolecular materials, control of chirality, etc.). With these examples of functional DySA, we then look forward and consider conditions that must be fulfilled to allow components of multiple types to coexist, function, and communicate with one another within the networked DySA systems of the future. As the closing examples show, such systems are already appearing heralding new opportunities - and, to be sure, new challenges - for DySA research.

Statistical analysis of phase formation in 2D colloidal systems

Colloidal systems offer unique opportunities for the study of phase formation and structure since their characteristic length scales are accessible to visible light. As a model system the two-dimensional assembly of colloidal magnetic and non-magnetic particles dispersed in a ferrofluid (FF) matrix is studied by transmission optical microscopy. We present a method to statistically evaluate images with thousands of particles and map phases by extraction of local variables. Different lattice structures and long-range connected branching chains are observed, when tuning the effective magnetic interaction and varying particle ratios.

Kinetics of doublet formation in bicomponent magnetic suspensions: The role of the magnetic permeability anisotropy

Micron-sized particles (microbeads) dispersed in a suspension of magnetic nanoparticles, i.e., ferrofluids, can be assembled into different types of structures upon application of an external magnetic field. This paper is devoted to theoretical modeling of a relative motion of a pair of microbeads (either soft ferromagnetic or diamagnetic) in the ferrofluid under the action of applied uniform magnetic field which induces magnetic moments in the microbeads making them attracting to each other. The model is based on a point-dipole approximation for the magnetic interactions between microbeads mediated by the ferrofluid; however, the ferrofluid is considered to possess an anisotropic magnetic permeability thanks to field-induced structuring of its nanoparticles. The model is tested against experimental results and shows generally better agreement with experiments than the model considering isotropic magnetic permeability of ferrofluids. The results could be useful for understanding kinetics of aggregation of microbeads suspended in a ferrofluid. From a broader perspective, the present study is believed to contribute to a general understanding of particle behaviors in anisotropic media.

Interference-like patterns of static magnetic fields imprinted into polymer/nanoparticle composites

Interference of waves is important and used in many areas of science and technology but does not extend to static magnetic fields which lack the wave structure. On the other hand, magnetic fields can be spatially modulated using microstructured materials comprising magnetic and non-magnetic domains. Here, we show that when such spatial modulation is coupled to the dynamics of magnetic particles, it can give rise to interference-like patterns. These patterns are imprinted into thin polymer films by overlaying “stamps” presenting periodic arrays of magnetic and nonmagnetic regions. The structures that emerge from such a superposition are sensitive to any motions of the stamps, can depend on the history of these motions, can produce features significantly smaller than those in the stamps, and can be either planar or three-dimensional.

For materials fabrication, it is most efficient to create various patterns from the same set of templates. Here, the authors show that when magnetic particles are exposed to stacks of periodic magnetic fields, they can form dynamic interference-like patterns that reflect where the magnetic fields overlap.

Assembly Modulated by Particle Position and Shape: A New Concept in Self-Assembly

In this communication we outline how the bespoke arrangements and design of micron-sized superparamagnetic shapes provide levers to modulate their assembly under homogeneous magnetic fields. We label this new approach, 'assembly modulated by particle position and shape' (APPS). Specifically, using rectangular lattices of superparamagnetic micron-sized cuboids, we construct distinct microstructures by adjusting lattice pitch and angle of array with respect to a magnetic field. Broadly, we find two modes of assembly: (1) immediate 2D jamming of the cuboids as they rotate to align with the applied field (rotation-induced jamming) and (2) aggregation via translation after their full alignment (dipole-dipole assembly). The boundary between these two assembly pathways is independent on field strength being solely a function of the cuboid's dimensions, lattice pitch, and array angle with respect to field-a relationship which we capture, along with other features of the assembly process, in a 'phase diagram'. In doing so, we set out initial design rules to build custom made assemblies. Moreover, these assemblies can be made flexible thanks to the hinged contacts of their particle building blocks. This flexibility, combined with the superparamagnetic nature of the architectures, renders our assembly method particularly appropriate for the construction of complex actuators at a scale hitherto not possible.

Hierarchically self-assembled hexagonal honeycomb and kagome superlattices of binary 1D colloids

Synthesis of binary nanoparticle superlattices has attracted attention for a broad spectrum of potential applications. However, this has remained challenging for one-dimensional nanoparticle systems. In this study, we investigate the packing behavior of one-dimensional nanoparticles of different diameters into a hexagonally packed cylindrical micellar system and demonstrate that binary one-dimensional nanoparticle superlattices of two different symmetries can be obtained by tuning particle diameter and mixing ratios. The hexagonal arrays of one-dimensional nanoparticles are embedded in the honeycomb lattices (for AB₂ type) or kagome lattices (for AB₃ type) of micellar cylinders. The maximization of free volume entropy is considered as the main driving force for the formation of superlattices, which is well supported by our theoretical free energy calculations. Our approach provides a route for fabricating binary one-dimensional nanoparticle superlattices and may be applicable for inorganic one-dimensional nanoparticle systems.

Binary mixtures of 1D particles are rarely observed to cooperatively self-assemble into binary superlattices, as the particle types separate into phases. Here, the authors design a system that avoids phase separation, obtaining binary superlattices with different symmetries by simply tuning the particle diameter and mixture composition.

Superparamagnetic colloids in viscous fluids

The influence of a magnetic field on the aggregation process of superparamagnetic colloids has been well known on short time for a few decades. However, the influence of important parameters, such as viscosity of the liquid, has received only little attention. Moreover, the equilibrium state reached after a long time is still challenging on some aspects. Indeed, recent experimental measurements show deviations from pure analytical models in extreme conditions. Furthermore, current simulations would require several years of computing time to reach equilibrium state under those conditions. In the present paper, we show how viscosity influences the characteristic time of the aggregation process, with experimental measurements in agreement with previous theories on transient behaviour. Afterwards, we performed numerical simulations on equivalent systems with lower viscosities. Below a critical value of viscosity, a transition to a new aggregation regime is observed and analysed. We noticed this result can be used to reduce the numerical simulation time from several orders of magnitude, without modifying the intrinsic physical behaviour of the particles. However, it also implies that, for high magnetic fields, granular gases could have a very different behaviour from colloidal liquids.

On the formation of stripe, sigma, and honeycomb phases in a core-corona system

Using Monte Carlo simulations and free-energy calculations, we investigate the phase behaviour of a two-dimensional core-corona system. We model this system as particles consisting of an impenetrable hard core of diameter σ_HD surrounded by a purely repulsive soft corona of diameter δ = 1.95σ_HD. At low densities, we observe the spontaneous formation of a phase with a stripe texture as well as a honeycomb-like phase driven by both energy and entropy considerations. At high densities, we find that a two-dimensional analogue of the periodic sigma phase, considered as an approximant of dodecagonal quasicrystals, is energetically stabilised with respect to two distinct dodecagonal quasicrystals, namely, a square-triangle tiling and a square-triangle-shield tiling. We also find the formation of stable hexagonal phases at three distinct density ranges, which are energetically driven, i.e. by minimising the overlap of coronas. Furthermore, our calculations show that the low-density dodecagonal quasicrystal that was previously reported by Dotera et al., [Nature, 2014, 506, 208] is kinetically formed in the coexistence region between the honeycomb and the medium-density hexagonal phase.

Formation of metastable phases by spinodal decomposition

Metastable phases may be spontaneously formed from other metastable phases through nucleation. Here we demonstrate the spontaneous formation of a metastable phase from an unstable equilibrium by spinodal decomposition, which leads to a transient coexistence of stable and metastable phases. This phenomenon is generic within the recently introduced scenario of the landscape-inversion phase transitions, which we experimentally realize as a structural transition in a colloidal crystal. This transition exhibits a rich repertoire of new phase-ordering phenomena, including the coexistence of two equilibrium phases connected by two physically different interfaces. In addition, this scenario enables the control of sizes and lifetimes of metastable domains. Our findings open a new setting that broadens the fundamental understanding of phase-ordering kinetics, and yield new prospects of applications in materials science.

Metastable phases are usually formed through nucleation, upon overcoming an energy barrier. Here, Alert et al. theoretically predict and experimentally verify the unexpected formation of a metastable phase by spinodal decomposition through direct phase separation from an unstable phase.

Two-dimensional assemblies of nematic colloids in homeotropic cells and their response to electric fields

Micrometer-sized colloidal particles dispersed in nematic liquid crystals interact with each other through anisotropic interactions induced by orientational deformation of the nematic field. In the case of so-called dipole nematic colloids, their interaction is of the dipole-dipole type. Two-dimensional, non-close-packed colloidal assemblies having various characteristics were fabricated using optical tweezers by exploiting the attraction between anti-parallel dipole nematic colloids in homeotropically aligned nematic cells. Structures comprising polygons, squares, and tetrahedra were built using equal-sized particles, and hexagonal structures were built using particles of two sizes. As the nematic field is sensitive to electric fields, the response of the fabricated assemblies toward an alternating electric field was also studied. All assemblies exhibited homogeneous reversible shrinkage, and their shrinkage rates were dependent on the structure. The maximum shrinkage rate in the linear dimension of the assemblies was over 20% at 5 Vrms for a hexagon comprising tetrahedral units.

Directed Assembly of Soft Anisotropic Nanoparticles by Colloid Electrospinning

Directed assembly of triblock copolymer worms to produce nanostructured fibers is achieved via colloid electrospinning. These copolymer worms are conveniently prepared by polymerization-induced self-assembly in concentrated aqueous dispersion. Addition of a second water-soluble component, poly(vinyl alcohol), is found to be critical for the production of well-defined fibers: trial experiments performed using the worms alone produce only spherical microparticles. Transmission electron microscopy studies confirm that the worm morphology survives electrospinning and the worms become orientated parallel to the main axis of the fibers during their generation. The average deviant angle (θ_dev ) between the worm orientation and fiber axis decreases from 17° to 9° as the worm/PVA mass ratio increases from 1.15:1 to 5:1, indicating a greater degree of worm alignment within fibers with higher worm contents and smaller fiber diameters. Thus triblock copolymer fibers of ≈300 ± 120 nm diameter can be readily produced that comprise aligned worms on the nanoscale.

Label-Free and Continuous-Flow Ferrohydrodynamic Separation of HeLa Cells and Blood Cells in Biocompatible Ferrofluids

In this study, a label-free, low-cost, and fast ferrohydrodynamic cell separation scheme is demonstrated using HeLa cells (an epithelial cell line) and red blood cells. The separation is based on cell size difference, and conducted in a custom-made biocompatible ferrofluid that retains the viability of cells during and after the assay for downstream analysis. The scheme offers moderate-throughput (≈106 cells h-1 for a single channel device) and extremely high recovery rate (>99%) without the use of any label. It is envisioned that this separation scheme will have clinical applications in settings where rapid cell enrichment and removal of contaminating blood will improve efficiency of screening and diagnosis such as cervical cancer screening based on mixed populations in exfoliated samples.

Ribbons of superparamagnetic colloids in magnetic field

While the aggregation process of superparamagnetic colloids in strong magnetic field is well known on short time since a few decades, recent theoretical works predicted an equilibrium state reached after a long time. In the present paper, we present experimental observations of this equilibrium state with a two-dimensional system and we compare our data with the predictions of a pre-existing model. Above a critical aggregation size, a deviation between the model and the experimental data is observed. This deviation is explained by the formation of ribbon-shaped aggregates. The ribbons are formed due to lateral aggregation of chains. An estimation of the magnetic energy for chains and ribbons shows that ribbons are stable structures when the number of magnetic grains is higher than N = 30 .

Highly parallel acoustic assembly of microparticles into well-ordered colloidal crystallites

The precise arrangement of microscopic objects is critical to the development of functional materials and ornately patterned surfaces. Here, we present an acoustics-based method for the rapid arrangement of microscopic particles into organized and programmable architectures, which are periodically spaced within a square assembly chamber. This macroscale device employs two-dimensional bulk acoustic standing waves to propel particles along the base of the chamber toward pressure nodes or antinodes, depending on the acoustic contrast factor of the particle, and is capable of simultaneously creating thousands of size-limited, isotropic and anisotropic assemblies within minutes. We pair experiments with Brownian dynamics simulations to model the migration kinetics and assembly patterns of spherical microparticles. We use these insights to predict and subsequently validate the onset of buckling of the assemblies into three-dimensional clusters by experiments upon increasing the acoustic pressure amplitude and the particle concentration. The simulations are also used to inform our experiments for the assembly of non-spherical particles, which are then recovered via fluid evaporation and directly inspected by electron microscopy. This method for assembly of particles offers several notable advantages over other approaches (e.g., magnetics, electrokinetics and optical tweezing) including simplicity, speed and scalability and can also be used in concert with other such approaches for enhancing the types of assemblies achievable.

Phase formation in colloidal systems with tunable interaction

Self-assembly is one of the most fascinating phenomena in nature and is one key component in the formation of hierarchical structures. The formation of structures depends critically on the interaction between the different constituents, and therefore the link between these interactions and the resulting structure is fundamental for the understanding of materials. We have realized a two-dimensional system of colloidal particles with tunable magnetic dipole forces. The phase formation is studied by transmission optical microscopy and a phase diagram is constructed. We report a phase transition from hexagonal to random and square arrangements when the magnetic interaction between the individual particles is tuned from antiferromagnetic to ferrimagnetic.

Magnetic field aligned assembly of nonmagnetic composite dumbbells in nanoparticle-based aqueous ferrofluid

Monodisperse, nonmagnetic, asymmetrical composite dumbbells in a suspension of magnetic nanoparticles (ferrofluid) were aligned by application of an external magnetic field to the ferrofluid. The asymmetrical composite dumbbells were prepared by two-step soap-free emulsion polymerization consisting of the first polymerization to coat spherical silica cores with cross-linked poly(methyl methacrylate) (PMMA) shell and the second polymerization to protrude a polystyrene (PSt) lobe from the core-shell particles. A chain structure of nonmagnetic dumbbells oriented to the applied magnetic field was observed at nanoparticle content of 2.0 vol % and field strengths higher than 1.0 mT. A similar chain structure of the dumbbells was observed under application of alternating electric field at strengths higher than 50 V/mm. Parallel and orthogonally combined applications of the electric and magnetic fields were also conducted to examine independence of the electric and magnetic applications as operational factors in the dumbbell assembling. Dumbbell chains stiffer than those in a single application of external field were formed in the parallel combined application of electric and magnetic fields. The orthogonal combination of the different applied fields could form a magnetically aligned chain structure of the nonmagnetic dumbbells oriented to the electric field. The present work experimentally indicated that the employment of inverse magnetorheological effect for nonmagnetic, anisotropic particles can be a useful method for the simultaneous controls over the orientation and the positon of anisotropic particles in their assembling.

Phase transformations in binary colloidal monolayers

Phase transformations can be difficult to characterize at the microscopic level due to the inability to directly observe individual atomic motions. Model colloidal systems, by contrast, permit the direct observation of individual particle dynamics and of collective rearrangements, which allows for real-space characterization of phase transitions. Here, we study a quasi-two-dimensional, binary colloidal alloy that exhibits liquid-solid and solid-solid phase transitions, focusing on the kinetics of a diffusionless transformation between two crystal phases. Experiments are conducted on a monolayer of magnetic and nonmagnetic spheres suspended in a thin layer of ferrofluid and exposed to a tunable magnetic field. A theoretical model of hard spheres with point dipoles at their centers is used to guide the choice of experimental parameters and characterize the underlying materials physics. When the applied field is normal to the fluid layer, a checkerboard crystal forms; when the angle between the field and the normal is sufficiently large, a striped crystal assembles. As the field is slowly tilted away from the normal, we find that the transformation pathway between the two phases depends strongly on crystal orientation, field strength, and degree of confinement of the monolayer. In some cases, the pathway occurs by smooth magnetostrictive shear, while in others it involves the sudden formation of martensitic plates.

Colloidal polymers with controlled sequence and branching constructed from magnetic field assembled nanoparticles

The assembly of nanoparticles into polymer-like architectures is challenging and usually requires highly defined colloidal building blocks. Here, we show that the broad size-distribution of a simple dispersion of magnetic nanocolloids can be exploited to obtain various polymer-like architectures. The particles are assembled under an external magnetic field and permanently linked by thermal sintering. The remarkable variety of polymer-analogue architectures that arises from this simple process ranges from statistical and block copolymer-like sequencing to branched chains and networks. This library of architectures can be realized by controlling the sequencing of the particles and the junction points via a size-dependent self-assembly of the single building blocks.

Non-additive simple potentials for pre-programmed self-assembly

A major goal in nanoscience and nanotechnology is the self-assembly of any desired complex structure with a system of particles interacting through simple potentials. To achieve this objective, intense experimental and theoretical efforts are currently concentrated in the development of the so-called "patchy" particles. Here we follow a completely different approach and introduce a very accessible model to produce a large variety of pre-programmed two-dimensional (2D) complex structures. Our model consists of a binary mixture of particles that interact through isotropic interactions that enable them to self-assemble into targeted lattices by the appropriate choice of a small number of geometrical parameters and interaction strengths. We study the system using Monte Carlo computer simulations and, despite its simplicity, we are able to self-assemble potentially useful structures such as chains, stripes, and Kagomé, twisted Kagomé, honeycomb, square, Archimedean and quasicrystalline tilings. Our model is designed in such a way that it may be implemented using discotic particles or, alternatively, using exclusively spherical particles interacting isotropically. Thus, it represents a promising strategy for bottom-up nano-fabrication.