How cube-like must magnetic nanoparticles be to modify their self-assembly?

Tuning higher order structure in colloidal fluids

Colloidal particles self assemble into a wide range of structures under external AC electric fields due to induced dipolar interactions [Yethiraj and Van Blaaderen, Nature, 2003, 421, 513]. As a result of these dipolar interactions, at low volume fraction the system is modulated between a hard-sphere like state (in the case of zero applied field) and a "string fluid" upon application of the field. Using both particle-resolved experiments and computer simulations, we investigate the emergence of the string fluid with a variety of structural measures including two-body and higher-order correlations. We probe the higher-order structure using three-body spatial correlation functions and a many-body approach based on minimum energy clusters of a dipolar-Lennard-Jones system. The latter constitutes a series of geometrically distinct minimum energy clusters upon increasing the strength of the dipolar interaction, which are echoed in the higher-order structure of the colloidal fluids we study here. We find good agreement between experiment and simulation at the two-body level. Higher-order correlations exhibit reasonable agreement between experiment and simulation, again with more discrepancy at higher field strength for three-body correlation functions. At higher field strength, the cluster population in our experiments and simulations is dominated by the minimum energy clusters for all sizes 8 ≤ m ≤ 12.

Chirality-Dependent Magnetization of Colloidal Squares with Offset Magnetic Dipoles

Colloidal particles with anisotropic geometries and interactions display rich phase behavior and hence have the potential to serve as the basis of functional materials, which can tunably and reversibly self-assemble into different configurations. External fields are one design parameter that can be used to manipulate how systems of colloidal particles assemble with one another. One challenge in designing new materials using anisotropic colloidal particles is understanding how an individual particle's various anisotropic features, like geometry, affect their overall self-assembly. Here, we present the results of simulation studies that explore the self-assembly of 2D colloidal squares with offset magnetic dipoles in the presence of an external field. Annealing simulations are used to measure the equilibrium-phase behavior of systems of these particles in the ground state, when the magnetic interactions dominate over the thermal forces of the system. We find that the magnetic properties of these systems are strongly influenced by the relative number of squares with opposite "handedness", or chirality, that are present within the system. Systems of squares that contain equal numbers of either chirality are extremely responsive to the external field; a relatively weak external field is required to magnetize them. In contrast, systems that contain only one chirality of squares are significantly less responsive to the external field; a significantly stronger external field is required to elicit the same magnetic response. Ultimately, the differing macroscopic magnetic properties of these systems are related to their microscopic self-assembly in an external field. Simulation snapshots and ground state phase diagrams illustrate how the absence of opposite chirality squares prevents systems of these particles from leaving an energetically favorable antiparallel configuration in the presence of an external field. When opposite chirality squares are present, these magnetic particles assemble into a head-to-tail configuration, therefore inducing a magnetic state.

Directed Assembly of Magnetic Colloidal Rods in an External Field

In fabricating new colloid-based materials via bottom-up design, particle-particle interactions are engineered to encourage the formation of the desired assemblies. One way to do this is to apply an external field, which orients magnetically polarized particles in the field direction. External fields have the advantage that they can be programmed to change in time (e.g., field rotation or toggling), tunably shifting the system away from equilibrium. Here, we apply a model for ferromagnetic colloidal rods that simulates their phase behavior in the presence of an external magnetic field with constant strength and direction. An annealing process slowly reduces the temperature during molecular dynamics simulations to estimate the system's equilibrium configuration in the ground state when the magnetic interactions between colloidal rods dominate the thermal forces. Numerous annealing simulations are performed at various particle densities and external field strengths. In the absence of an external field, the magnetic rods assemble into antiparallel configurations. When the strength of the external field is sufficiently strong, the magnetic rods are forced to orient in the direction of the field and therefore form head-to-tail structures. The formation of a head-to-tail state is associated with a net magnetic moment that results from the collective alignment of all magnetic particles in the field direction. Furthermore, when systems of magnetic rods assemble into a head-to-tail state, they occupy more space than they do in a phase in which most rods are assembled into antiparallel configurations. Phase diagrams predict that the magnetic properties of systems of rod-like magnetic particles can switch between magnetic and nonmagnetic states by tuning not only the external field strength but also the particle density.

Tuning the dimensional order in self-assembled magnetic nanostructures: theory, simulations, and experiments

A major obstacle to building nanoscale magnetic devices or even experimentally studying novel nanomagnetic spin textures is the present lack of a simple and robust method to fabricate various nano-structured alloys. Here, theoretical and experimental investigations were conducted to understand the underlying physical mechanisms of magnetic particle self-assembly in zero applied magnetic field. By changing the amount of NaOH added during the synthesis, we demonstrate that the resulting morphology of the assembled FeCo structure can be tuned from zero-dimensional (0D) nanoparticles to one-dimensional (1D) chains, and even three-dimensional (3D) networks. Two numerical simulations were developed to predict aspects of nanostructure formation by accounting for the magnetic interactions between individual magnetic nanoparticles. The first utilized the Boltzmann distribution to determine the equilibrium structure of a nanochain, iteratively predicting the local deviation angle θ of each particle as it attaches to a forming chain. The second simulation illustrates the differences in nanostructure arrangement and dimensionality (0D, 1D, or 3D) that arise from random interactions at various nanoparticle densities. The simulation results closely match the experimental findings, as seen from SEM images, demonstrating their ability to capture the system's structural properties. In addition, magnetic hysteresis measurements of the samples were performed along two orthogonal directions to show the influence of dimensional order on the magnetic behavior. The normalized remanence (MR/MS||) of the FeCo alloys increases as the dimensions of nanostructures are increased. Of the three cases, the FeCo 3D network structures exhibit the highest normalized nanostructure remanence of 0.33 and an increased coercivity to above 200 Oe at 300 K. This combined numerical and experimental investigation aims to shed light on the preparation of FeCo nanostructures with tailorable dimensional order and it opens new avenues for exploring the complex spin textures and coercive behavior of these multi-dimensional nanomagnetic structures.

Nanopolymers for magnetic applications: how to choose the architecture?

Directional assembly of nanoscale objects results in morphologies that can broadly be classified as supra-molecular nanopolymers. Such morphologies, given a functional choice of the monomers used as building blocks, can be of ubiquitous utility in optical, magnetic, rheological, and medical applications. These applications, however, require a profound understanding of the interplay between monomer shape and bonding on one side, and polymeric properties - on the other. Recently, we fabricated nanopolymers using cuboid DNA nanochambers, as they not only allow fine-tuning of the resulting morphologies but can also carry magnetic nanoparticles. However, it is not known if the cuboid shape and inter-cuboid connectivity restrict the equilibrium confirmations of the resulting nanopolymers, making them less responsive to external stimuli. In this work, using Molecular Dynamics simulations, we perform an extensive comparison between various nanopolymer architectures to explore their polymeric properties, and their response to an applied magnetic field if magnetic nanoparticles are embedded. We explain the impact of monomer shape and bonding on the mechanical and magnetic properties and show that DNA nanochambers can build highly responsive and magnetically controllable nanopolymers.

Rheology of a Nanopolymer Synthesized through Directional Assembly of DNA Nanochambers, for Magnetic Applications

We present a numerical study of the effects of monomer shape and magnetic nature of colloids on the behavior of a single magnetic filament subjected to the simultaneous action of shear flow and a stationary external magnetic field perpendicular to the flow. We find that based on the magnetic nature of monomers, magnetic filaments exhibit a completely different phenomenology. Applying an external magnetic field strongly inhibits tumbling only for filaments with ferromagnetic monomers. Filament orientation with respect to the flow direction is in this case independent of monomer shape. In contrast, reorientational dynamics in filaments with superparamagnetic monomers are not inhibited by applied magnetic fields, but enhanced. We find that the filaments with spherical, superparamagnetic monomers, depending on the flow and external magnetic field strength, assume semipersistent, collapsed, coiled conformations, and their characteristic time of tumbling is a function of field strength. However, external magnetic fields do not affect the characteristic time of tumbling for filaments with cubic, superparamagnetic monomers, but increase how often tumbling occurs.

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.

Energetically favorable configurations of hematite cube chains

Hematite at room temperature is a weak ferromagnetic material. Its permanent magnetization is three orders smaller than for magnetite. Thus, hematite colloids allow us to explore a different physical range of particle interaction parameters compared to ordinary ferromagnetic particle colloids. In this paper we investigate a colloid consisting of hematite particles with cubic shape. We search for energetically favorable structures in an external magnetic field with analytical and numerical methods and molecular dynamics simulations and analyze whether it is possible to observe them in experiments. We find that energetically favorable configurations are observable only for short chains. Longer chains usually contain kinks which are formed in the process of chain formation due to the interplay of energy and thermal fluctuations as an individual cube can be in one of two alignments with an equal probability.

Divalent Multilinking Bonds Control Growth and Morphology of Nanopolymers

Assembly of nanoscale objects into linear architectures resembling molecular polymers is a basic organization resulting from divalent interactions. Such linear architectures occur for particles with two binding patches on opposite sides, known as Janus particles. However, unlike molecular systems where valence bonds can be envisioned as pointlike interactions nanoscale patches are often realized through multiple molecular linkages. The relationship between the characteristics of these linkages, the resulting interpatch connectivity, and assembly morphology is not well-explored. Here, we investigate assembly behavior of model divalent nanomonomers, DNA nanocuboid with tailorable multilinking bonds. Our study reveals that the characteristics of individual molecular linkages and their collective properties have a profound effect on nanomonomer reactivity and resulting morphologies. Beyond linear nanopolymers, a common signature of divalent nanomonomers, we observe an effective valence increase as linkages lengthened, leading to the nanopolymer bundling. The experimental findings are rationalized by molecular dynamics simulations.

Self-assembly of polymer-tethered nanoparticles with uniform and Janus surfaces in nanotubes

In this study, a coarse-grained molecular simulation was performed to investigate the morphologies and phase diagrams of self-assembled polymer-tethered nanoparticles (NPs) confined in nanotubes (NTs). Unlike ordinary NPs, polymer-tethered NPs have two distinct characteristic lengths, which are key factors that determine their self-assembly. Herein, two distinct types of NT walls and three types of polymer-tethered NPs were considered: hydrophilic and hydrophobic walls, and hydrophilic, hydrophobic, and Janus surfaces. First, the qualitative phase diagrams of the axial pressure, Pz, versus the ratio of the NT radius to the NP radius, L, were derived. The results revealed that diverse self-assembled morphologies, which are not formed in non-tethered NPs, were observed in the polymer-tethered NPs. For example, three types of ordered structures with different structural characteristic lengths, depending on Pz, were obtained. In addition, the effect of the chemical nature of the polymer-tethered NP surface on the self-assembled morphology confined in NTs was investigated. Clusters of water molecules were formed, particularly in the hydrophobic polymer-tethered NPs, and these clusters caused the structural distortion of the NP. Moreover, in the polymer-tethered NPs with the Janus amphiphilic surface, the hydrophobic and hydrophilic polymer tethered NPs assembled in the axial direction to form an ordered structure, and a double-helix structure was formed at L = 3.0 in the hydrophobic NT. The results of these simulations indicate that the self-assembly behaviours of polymer-tethered NPs can be qualitatively predicted based on the chemical nature of the NT walls and the surface design of the polymer-tethered NP.

Magnetic Coupling in Colloidal Clusters for Hierarchical Self-Assembly

Manipulating the way in which colloidal particles self-organize is a central challenge in the design of functional soft materials. Meeting this challenge requires the use of building blocks that interact with one another in a highly specific manner. Their fabrication, however, is limited by the complexity of the available synthesis procedures. Here, we demonstrate that, starting from experimentally available magnetic colloids, we can create a variety of complex building blocks suitable for hierarchical self-organization through a simple scalable process. Using computer simulations, we compress spherical and cubic magnetic colloids in spherical confinement, and investigate their suitability to form small clusters with reproducible structural and magnetic properties. We find that, while the structure of these clusters is highly reproducible, their magnetic character depends on the particle shape. Only spherical particles have the rotational degrees of freedom to produce consistent magnetic configurations, whereas cubic particles frustrate the minimization of the cluster energy, resulting in various magnetic configurations. To highlight their potential for self-assembly, we demonstrate that already clusters of three magnetic particles form highly nontrivial Archimedean lattices, namely, staggered kagome, bounce, and honeycomb, when focusing on different aspects of the same monolayer structure. The work presented here offers a conceptually different way to design materials by utilizing preassembled magnetic building blocks that can readily self-organize into complex structures.

Chains of cubic colloids at fluid-fluid interfaces

Inspired by recent experimental observations of spontaneous chain formation of cubic particles adsorbed at a fluid-fluid interface, we theoretically investigate whether capillary interactions can be responsible for this self-assembly process. We calculate adsorption energies, equilibrium particle orientations, and interfacial deformations, not only for a variety of contact angles but also for single cubes as well as an infinite 2D lattice of cubes at the interface. This allows us to construct a ground-state phase diagram as a function of areal density for several contact angles, and upon combining the capillary energy of a 2D lattice with a simple expression for the entropy of a 2D fluid we also construct temperature-density or size-density phase diagrams that exhibit large two-phase regions and triple points. We identify several regimes with stable chainlike structures, in line with the experimental observations.

Self-assembly of charged colloidal cubes

In this work, we show how and why the interactions between charged cubic colloids range from radially isotropic to strongly directionally anisotropic, depending on tuneable factors. Using molecular dynamics simulations, we illustrate the effects of typical solvents to complement experimental investigations of cube assembly. We find that in low-salinity water solutions, where cube self-assembly is observed, the colloidal shape anisotropy leads to the strongest attraction along the corner-to-corner line, followed by edge-to-edge, with a face-to-face configuration of the cubes only becoming energetically favorable after the colloids have collapsed into the van der Waals attraction minimum. Analysing the potential of mean force between colloids with varied cubicity, we identify the origin of the asymmetric microstructures seen in experiment.

Morphology and kinetics of random sequential adsorption of superballs: From hexapods to cubes

Superballs represent a class of particles whose shapes are defined by the domain |x|^{2p}+|y|^{2p}+|z|^{2p}≤R^{2p}, with p∈(0,∞) being the deformation parameter. 0<p<0.5 represents a family of hexapodlike (concave octahedral-like) particles, 0.5≤p<1 and p>1 represent, respectively, families of convex octahedral-like and cubelike particles, with p=1,0.5, and ∞ representing spheres, octahedra, and cubes. Colloidal zeolite suspensions, catalysis, and adsorption, as well as biomedical magnetic nanoparticles are but a few of the applications of packing of superballs. We introduce a universal method for simulating random sequential adsorption of superballs, which we refer to as the low-entropy algorithm, which is about two orders of magnitude faster than the conventional algorithms that represent high-entropy methods. The two algorithms yield, respectively, precise estimates of the jamming fraction ϕ_{∞}(p) and ν(p), the exponent that characterizes the kinetics of adsorption at long times t, ϕ_{∞}(p)-ϕ(p,t)∼t^{-ν(p)}. Precise estimates of ϕ_{∞}(p) and ν(p) are obtained and shown to be in agreement with the existing analytical and numerical results for certain types of superballs.

Manifestation of dipole-induced disorder in self-assembly of ferroelectric and ferromagnetic nanocubes

The colloidal processing of nearly monodisperse and highly crystalline single-domain ferroelectric or ferromagnetic nanocubes is a promising route to produce superlattice structures for integration into next-generation devices, whereas controlling the local behaviour of nanocrystals is imperative for fabricating highly-ordered assemblies. The current picture of nanoscale polarization in individual nanocrystals suggests a potential presence of a significant dipolar interaction, but its role in the condensation of nanocubes is unknown. We simulate the self-assembly of colloidal dipolar nanocubes under osmotic compression and perform the microstructural characterization of their densified ensembles. Our results indicate that the long-range positional and orientational correlations of perovskite nanocubes are highly sensitive to the presence of dipoles.

A platform for nanomagnetism - assembled ferromagnetic and antiferromagnetic dipolar tubes

We report an interesting case where magnetic phenomena can transcend mesoscopic scales. Our system consists of tubes created by the assembly of dipolar spheres. The cylindrical topology results in the breakup of degeneracy observed in planar square and triangular packings. As far as the ground state is concerned, the tubes switch from circular to axial magnetization with increasing tube length. All magnetostatic properties found in magnetic nanotubes, in which the dipolar interaction is comparable to or dominant over the exchange interaction, are reproduced by the dipolar tubes including an intermediary helically magnetized state. Besides, we discuss the antiferromagnetic phase resulting from the square arrangement of the dipolar spheres and its interesting vortex state.

Interplay between spherical confinement and particle shape on the self-assembly of rounded cubes

Self-assembly of nanoparticles (NPs) inside drying emulsion droplets provides a general strategy for hierarchical structuring of matter at different length scales. The local orientation of neighboring crystalline NPs can be crucial to optimize for instance the optical and electronic properties of the self-assembled superstructures. By integrating experiments and computer simulations, we demonstrate that the orientational correlations of cubic NPs inside drying emulsion droplets are significantly determined by their flat faces. We analyze the rich interplay of positional and orientational order as the particle shape changes from a sharp cube to a rounded cube. Sharp cubes strongly align to form simple-cubic superstructures whereas rounded cubes assemble into icosahedral clusters with additionally strong local orientational correlations. This demonstrates that the interplay between packing, confinement and shape can be utilized to develop new materials with novel properties.

Colloidal nanoparticles self-assembled under spherical confinement can form a rich variety of structures. Here, the authors study the self-assembly of sharp and rounded nanocubes under such confinement, revealing the influence of particle and face geometry on positional and orientational behavior.

Catalytic Nanotruss Structures Realized by Magnetic Self-Assembly in Pulsed Plasma

Tunable nanostructures that feature a high surface area are firmly attached to a conducting substrate and can be fabricated efficiently over significant areas, which are of interest for a wide variety of applications in, for instance, energy storage and catalysis. We present a novel approach to fabricate Fe nanoparticles using a pulsed-plasma process and their subsequent guidance and self-organization into well-defined nanostructures on a substrate of choice by the use of an external magnetic field. A systematic analysis and study of the growth procedure demonstrate that nondesired nanoparticle agglomeration in the plasma phase is hindered by electrostatic repulsion, that a polydisperse nanoparticle distribution is a consequence of the magnetic collection, and that the formation of highly networked nanotruss structures is a direct result of the polydisperse nanoparticle distribution. The nanoparticles in the nanotruss are strongly connected, and their outer surfaces are covered with a 2 nm layer of iron oxide. A 10 μm thick nanotruss structure was grown on a lightweight, flexible and conducting carbon-paper substrate, which enabled the efficient production of H₂ gas from water splitting at a low overpotential of 210 mV and at a current density of 10 mA/cm².

Self-organization in dipolar cube fluids constrained by competing anisotropies

For magnetite spherical nanoparticles, the orientation of the dipole moment in the crystal does not affect the morphology of either zero field or field induced structures. For non-spherical particles however, an interplay between particle shape and direction of the magnetic moment can give rise to unusual behaviors, in particular when the moment is not aligned along a particle symmetry axis. Here we disclose for the first time the unique magnetic properties of hematite cubic particles and show the exact orientation of the cubes' dipole moment. Using a combination of experiments and computer simulations, we show that dipolar hematite cubes self-organize into dipolar chains with morphologies remarkably different from those of spheres, and demonstrate that the emergence of these structures is driven by competing anisotropic interactions caused by the particles' shape anisotropy and their fixed dipole moment. Furthermore, we have analytically identified a specific interplay between energy, and entropy at the microscopic level and found that an unorthodox entropic contribution mediates the organization of particles into the kinked nature of the dipolar chains.

Directed Self-Assembly of Polarizable Ellipsoids in an External Electric Field

The interplay between shape anisotropy and directed long-range interactions enables the self-assembly of complex colloidal structures. As a recent highlight, ellipsoidal particles polarized in an external electric field were observed to associate into well-defined tubular structures. In this study, we systematically investigate such directed self-assembly using Monte Carlo simulations of a two-point-charge model of polarizable prolate ellipsoids. In spite of its simplicity and computational efficiency, we demonstrate that the model is capable of capturing the complex structures observed in experiments on ellipsoidal colloids at low volume fractions. We show that, at sufficiently high electric field strength, the anisotropy in shape and electrostatic interactions causes a transition from three-dimensional crystal structures observed at low aspect ratios to two-dimensional sheets and tubes at higher aspect ratios. Our work thus illustrates the rich self-assembly behavior accessible when exploiting the interplay between competing long- and short-range anisotropic interactions in colloidal systems.

Nanoparticle Shape Influences the Magnetic Response of Ferro-Colloids

The interesting magnetic response of conventional ferro-colloid has proved extremely useful in a wide range of technical applications. Furthermore, the use of nano/micro- sized magnetic particles has proliferated cutting-edge medical research, such as drug targeting and hyperthermia. In order to diversify and improve the application of such systems, new avenues of functionality must be explored. Current efforts focus on incorporating directional interactions that are surplus to the intrinsic magnetic one. This additional directionality can be conveniently introduced by considering systems composed of magnetic particles of different shapes. Here we present a combined analytical and simulation study of permanently magnetized dipolar superball particles; a geometry that closely resembles magnetic cubes synthesized in experiments. We have focused on determining the initial magnetic susceptibility of these particles in dilute suspensions, seeking to quantify the effect of the superball shape parameter on the system response. In turn, we linked the computed susceptibilities to the system microstructure by analyzing cluster composition using a connectivity network analysis. Our study has shown that by increasing the shape parameter of these superball particles, one can alter the outcome of self-assembly processes, leading to the observation of an unanticipated decrease in the initial static magnetic susceptibility.