Self-assembly of three-dimensional ensembles of magnetic particles with laterally shifted dipoles

Fabrication of strong magnetic micron-sized supraparticles with anisotropic magnetic properties for magnetorheology

We propose three different techniques to synthesize anisotropic magnetic supraparticles for their incorporation in the formulation of magnetorheological fluids with novel potential applications. The techniques include microtransfer molding, electrodeposition and microfluidic flow-focusing devices. Although the yield of these methods is not large, with their use, it is possible to synthesize supraparticles with anisotropy in both their magnetic content and shape. The magnetorheological characteristics (yield stress) of the resulting field-induced structures were computed using finite element method simulations and demonstrated to be strongly dependent on the microstructural anisotropy of the supraparticles. In anisotropic particles, the simulated yield stress is always larger than that of the isotropic ones consisting of magnetically homogeneous spherical particles.

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.

Structure and rheology of soft hybrid systems of magnetic nanoparticles in liquid-crystalline matrices: results from particle-resolved computer simulations

Hybrid mixtures composed of magnetic nanoparticles (MNP) in liquid crystalline (LC) matrices are a fascinating class of soft materials with intriguing physical properties and a wide range of potential applications, e.g., as stimuli-responsive and adaptive materials. Already in the absence of an external stimulus, these systems can display various types of orientationally disordered and ordered phases, which are enriched by self-assembled structures formed by the MNPs. In the presence of external fields, one typically observes highly nonlinear macroscopic behavior. However, an understanding of the structure and dynamics of such systems on the particle level has, so far, remained elusive. In the present paper we review recent computer simulation studies targeting the structure, equilibrium dynamics and rheology of LC-MNP systems, in which the particle sizes of the two components are comparable. As a numerically tractable model system we consider mixtures of soft spherical or elongated particles with a permanent magnetic dipole moment and ellipsoidal non-magnetic particles interacting via a Gay-Berne potential. We address, first, equilibrium aspects such as structural organization and self-assembly (cluster formation) of the MNPs in dependence of the orientational state of the matrix, the role of the size ratio, the impact of an external magnetic field, and the translational and orientational diffusion of the two components. Second, we discuss the non-equilibrium dynamics of LC-MNP mixtures under planar shear flow, considering both, spherical and non-spherical MNPs. Our results contribute to a detailed understanding of these intriguing hybrid materials, and they may serve as a guide for future experiments.

Self-assembly of magnetic colloids with radially shifted dipoles

Anisotropic potentials in Janus colloids provide additional freedom to control particle aggregation into structures of different sizes and morphologies. In this work, we perform Brownian dynamics simulations of a dilute suspension of magnetic spherical Janus colloids with their magnetic dipole moments shifted radially towards the surface of the particle in order to gain valuable microstructural insight. Properties such as the mean cluster size, orientational ordering, and nucleation and growth are examined dynamically. Differences in the structure of clusters and in the aggregation process are observed depending on the dipolar shift (s)-the ratio between the displacement of the dipole and the particle radius-and the dipolar coupling constant (λ)-the ratio between the magnetic dipole-dipole and Brownian forces. Using these two dimensionless quantities, a structural "phase" diagram is constructed. Each phase corresponds to unique nucleation and growth behavior and orientational ordering of dipoles inside clusters. At small λ, the particles aggregate and disaggregate resulting in short-lived clusters at small s, while at high s the particles aggregate in permanent triplets (long-lived clusters). At high λ, the critical nuclei formed during the nucleation process are triplets and quadruplets with unique orientational ordering. These small clusters then serve as building blocks to form larger structures, such as single-chain, loop-like, island-like, worm-like, and antiparallel-double-chain clusters. This study shows that dipolar shifts in colloids can serve as a control parameter in applications where unique size, morphology, and aggregation kinetics of clusters are required.

Dynamical self-assembly of dipolar active Brownian particles in two dimensions

Based on Brownian Dynamics (BD) simulations, we study the dynamical self-assembly of active Brownian particles with dipole-dipole interactions, stemming from a permanent point dipole at the particle center. The propulsion direction of each particle is chosen to be parallel to its dipole moment. We explore a wide range of motilities and dipolar coupling strengths and characterize the corresponding behavior based on several order parameters. At low densities and low motilities, the most important structural phenomenon is the aggregation of the dipolar particles into chains. Upon increasing the particle motility, these chain-like structures break, and the system transforms into a weakly correlated isotropic fluid. At high densities, we observe that the motility-induced phase separation is strongly suppressed by the dipolar coupling. Once the dipolar coupling dominates the thermal energy, the phase separation disappears, and the system rather displays a flocking state, where particles form giant clusters and move collective along one direction. We provide arguments for the emergence of the flocking behavior, which is absent in the passive dipolar system.

Steady states of non-axial dipolar rods driven by rotating fields

We investigate a two-dimensional system of magnetic colloids with anisotropic geometry (rods) subjected to an oscillating external magnetic field. The structural and dynamical properties of the steady states are analyzed, by means of Langevin dynamics simulations, as a function of the misalignment of the intrinsic magnetic dipole moment of the rods with respect to their axial direction, and also in terms of the strength and rotation frequency of an external magnetic field. The misalignment of the dipole relative to their axial direction is inspired by recent studies, and this is extremely relevant in the microscopic aggregation states of the system. The dynamical response of the magnetic rods to the external magnetic field is strongly affected by such a misalignment. Concerning the synchronization between the magnetic rods and the direction of the external magnetic field, we define three distinct regimes of synchronization. A set of steady states diagrams are presented, showing the magnitude and rotation frequency intervals in which the distinct self-organized structures are observed.

Field-responsive colloidal assemblies defined by magnetic anisotropy

Particle dispersions provide a promising tool for the engineering of functional materials that exploit self-assembly of complex structures. Dispersion made from magnetic colloidal particles is a great choice; they are biocompatible and remotely controllable among many other advantages. However, their dominating dipolar interaction typically limits structural complexity to linear arrangements. This paper shows how a magnetostatic equilibrium state with noncollinear arrangement of the magnetic moments, as reported for ferromagnetic Janus particles, enables the controlled self-organization of diverse structures in two dimensions via constant and low-frequency external magnetic fields. Branched clusters of staggered chains, compact clusters, linear chains, and dispersed single particles can be formed and interconverted reversibly in a controlled way. The structural diversity is a consequence of both the inhomogeneity and the spatial extension of the magnetization distribution inside the particles. We draw this conclusion from calculations based on a model of spheres with multiple shifted dipoles. The results demonstrate that fundamentally new possibilities for responsive magnetic materials can arise from interactions between particles with a spatially extended, anisotropic magnetization distribution.

Self-assembly of magnetic colloids with shifted dipoles

The self-assembly of colloidal magnetic Janus particles with a laterally displaced (or shifted), permanent dipole in a quasi-two-dimensional system is studied using Brownian dynamics simulations. The rate of formation of clusters and their structures are quantified for several values of dipolar shift from the particle center, which is nondimensionalized using the particle's radius so that it takes values ranging from 0 to 1, and examined under different magnetic interaction strengths relative to Brownian motion. For dipolar shifts close to 0, chain-like structures are formed, which grow at long times following a power law, while particles of shift higher than 0.2 generally aggregate in ring-like clusters that experience limited growth. In the case of shifts between 0.4 and 0.5, the particles tend to aggregate in clusters of 3 to 6, while for all shifts higher than 0.6 clusters rarely contain more than 3 particles due to the antiparallel dipole orientations that are most stable at those shifts. The strength of the magnetic interactions hastens the rate at which clusters are formed; however, the effect it has on cluster size is lessened by increases in the shift of the dipoles. These results contribute to better understand the dynamics of magnetic Janus particles and can help the synthesis of functionalized materials for specific applications such as drug delivery.

Ground state of dipolar hard spheres confined in channels

We investigate the ground state of a classical two-dimensional system of hard-sphere dipoles confined between two hard walls. Using lattice sum minimization techniques we reveal that at fixed wall separations, a first-order transition from a vacuum to a straight one-dimensional chain of dipoles occurs upon increasing the density. Further increase in the density yields the stability of an undulated chain as well as nontrivial buckling structures. We explore the close-packed configurations of dipoles in detail, and we find that, in general, the densest packings of dipoles possess complex magnetizations along the principal axis of the slit. Our predictions serve as a guideline for experiments with granular dipolar and magnetic colloidal suspensions confined in slitlike channel geometry.

Self-assembly and clustering of magnetic peapod-like rods with tunable directional interaction

Based on extensive Langevin Dynamics simulations we investigate the structural properties of a two-dimensional ensemble of magnetic rods with a peapod-like morphology, i.e, rods consisting of aligned single dipolar beads. Self-assembled configurations are studied for different directions of the dipole with respect to the rod axis. We found that with increasing misalignment of the dipole from the rod axis, the smaller the packing fraction at which the percolation transition is found. For the same density, the system exhibits different aggregation states for different misalignment. We also study the stability of the percolated structures with respect to temperature, which is found to be affected by the microstructure of the assembly of rods.

Wrinkled labyrinths in critical demixing ferrofluid

A thin film of a critical ferrofluid mixture undergoes a sequence of transitions in a magnetic field. First the application of a field induces a critical demixing of the fluid into cylindrical droplets of the minority phase immersed in an extended majority phase. At a second critical field the cylindrical shape is destabilized and transforms into a labyrinth pattern. A third wrinkling transition occurs at even higher field if the liquid has a liquid/air interface. The wrinkling is absent if the droplet has a cover-slide on top. We explain the wrinkling by the wetting behavior of the liquid/air interface that shifts the surface region away from a critical demixing point.

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

Systems whose magnetic response can be finely tuned using control parameters, such as temperature and external magnetic field strength, are extremely desirable, functional materials. Magnetic nanoparticles, in particular suspensions thereof, offer opportunities for this controllability to be realised. Cube-like particles are particularly mono-disperse examples that, together with their favourable packing behaviour, make them of significant interest for study. Using a combination of analytical calculations and molecular dynamics we have studied the self-assembly of permanently magnetised dipolar superballs. The superball shape parameter was varied in order to interpolate the region between the already well-studied sphere system and that of the recently investigated cube. Our findings show that as a superball particle becomes more cubic the chain to ring transition, observed in the ground state of spherical particles, occurs at an increasingly larger cluster size. This effect is mitigated, however, by the appearance of a competing configuration; asymmetric rings, a conformation that we show superballs can readily adopt.

Simulation study on the structural properties of colloidal particles with offset dipoles

A major research theme in materials science is determining how the self-assembly of new generations of colloidal particles of complex shape and surface charge is guided by their interparticle interactions. In this paper, we describe results from quasi-2D Monte Carlo simulations of systems of colloidal particles with offset transversely-oriented extended dipole-like charge distributions interacting via an intermediate-ranged Yukawa potential. The systems are cooled slowly through an annealing procedure during which the temperature is lowered in discrete steps, allowing the system to equilibrate. We perform ground state calculations for two, three and four particles at several shifts of the dipole vector from the particle center. We create state diagrams in the plane spanned by the temperature and the area fraction outlining the boundaries between fluid, string-fluid and percolated states at various values of the shift. Remarkably we find that the effective cooling rate in our simulations has an impact on the structures formed, with chains being more prevalent if the system is cooled quickly and cyclic structures more prevalent if the system is cooled slowly. As the dipole is further shifted from the center, there is an increased tendency to assemble into small cyclic structures at intermediate temperatures. These systems further self-assemble into open lattice-like arrangements at very low temperatures. The novel structures identified might be useful for photonic applications, new types of porous media for filtration and catalysis, and gel matrices with unusual properties.

Supracolloidal reconfigurable polyhedra via hierarchical self-assembly

Enclosed three-dimensional structures with hollow interiors have been attractive targets for the self-assembly of building blocks across different length scales. Colloidal self-assembly, in particular, has enormous potential as a bottom-up means of structure fabrication exploiting a priori designed building blocks because of the scope for tuning interparticle interactions. Here we use computer simulation study to demonstrate the self-assembly of designer charge-stabilised colloidal magnetic particles into a series of supracolloidal polyhedra, each displaying a remarkable two-level structural hierarchy. The parameter space for design supports thermodynamically stable polyhedra of very different morphologies, namely tubular and hollow spheroidal structures, involving the formation of subunits of four-fold and three-fold rotational symmetry, respectively. The spheroidal polyhedra are chiral, despite having a high degree of rotational symmetry. The dominant pathways for self-assembly into these polyhedra reveal two distinct mechanisms - a growth mechanism via sequential attachment of the subunits for a tubular structure and a staged or hierarchical pathway for a spheroidal polyhedron. These supracolloidal architectures open up in response to an external magnetic field. Our results suggest design rules for synthetic reconfigurable containers at the microscale exploiting a hierarchical self-assembly scheme.

Non-equilibrium dynamics of magnetically anisotropic particles under oscillating fields

In this article, we demonstrate how magnetic anisotropy of colloidal particles can give rise to unusual dynamics and controllable rearrangements under time-dependent fields. As an example, we study spherical particles with a radially off-centered net magnetic moment in an oscillating field. Based on complementary data from a numerical simulation of spheres with shifted dipole and experimental observations from particles with hemispherical ferromagnetic coating, it is explained on a two particle basis how this magnetic anisotropy causes nontrivial rotational motion and magnetic reorientation. We further present the behavior of larger ensembles of coated particles. It illustrates the potential for controlled reconfiguration based on the presented two-particle dynamics.