Orientational dynamics of colloidal ribbons self-assembled from microscopic magnetic ellipsoids

Synergistic interactions of binary suspensions of magnetic anisotropic particles

We report the effect of the dipole-dipole interaction and shape anisotropy in suspensions of permanently magnetized anisotropic particles. We quantify the dipolar interaction energy using an ellipsoid-dipole model to describe particles with similar or dissimilar shapes. The expression captures the physics of the point-dipole interaction energy between uniformly magnetized spherical particles. Additionally, we report Monte Carlo simulations to describe the effect of dipolar interaction and shape anisotropy under different field strengths. Results show that the shape anisotropy and dipolar interactions modify the head-to-tail interaction with respect to spheres, promoting dendritic and barbed-wire structures in uniform ellipsoids and binary mixtures, respectively. Furthermore, competing entropic and energy interactions generate a synergistic effect reducing the magnetic response of binary suspensions.

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.

Highly Efficient Magnetic Propulsion of NiFe Nanorod-Based Miniature Swimmers in Three Dimensions

Magnetically actuated miniature robots have attracted the attention of the scientific community over the past two decades, but the confined workspace of their manipulation system (typically a tri-axial coil or eight electromagnetic coils) and the low efficiency of propulsion have limited their utility. Here, we describe a highly efficient NiFe nanorod-based magnetic miniature swimmer that can be manipulated in 3D spaces using two pairs of coils placed in the x-y horizontal plane. In the new swimmer, the shape symmetry is broken along its body, and the asymmetry in magnetizations is introduced perpendicular to the long axis of its body simultaneously. Such a combined asymmetry design offers favorable controllability in planar magnetic fields, which relaxes the multi-axial coil requirement of the commonly used manipulation system and thus reduces the restriction on the shape and size of the workspaces. The new swimmers display efficient 3D propulsion, with a speed of over 5000 μm s^-1 (∼3 body length s^-1) and powerful locomotion in biological media such as raw human blood. The fuel utilization efficiency of the swimmer, defined as the ratio of the distance to the net input work in one period, was estimated to be approximately from 10^-2 to 10^-3 m/J, which is significantly higher than that of magnetic motors with a slender body. Moreover, to provide practical support for further potential use, we demonstrated that the swimmer is able to perform incision operations as a minimally invasive microsurgical tool. Such a swimmer actuation strategy provides a simple and efficient way for 3D manipulation of magnetic miniature robots, offering great potential for future biomedical and other applications.

Collective hydrodynamic transport of magnetic microrollers

We investigate the collective transport properties of microscopic magnetic rollers that propel close to a surface due to a circularly polarized, rotating magnetic field. The applied field exerts a torque to the particles, which induces a net rolling motion close to a surface. The collective dynamics of the particles result from the balance between magnetic dipolar interactions and hydrodynamic ones. We show that, when hydrodynamics dominate, i.e. for high particle spinning, the collective mean velocity linearly increases with the particle density. In this regime we analyse the clustering kinetics, and find that hydrodynamic interactions between the anisotropic, elongated particles, induce preferential cluster growth along a direction perpendicular to the driving one, leading to dynamic clusters that easily break and reform during propulsion.

Static and Dynamic Self-Assembly of Pearl-Like-Chains of Magnetic Colloids Confined at Fluid Interfaces

Magnetic colloids adsorbed at a fluid interface are unique model systems to understand self-assembly in confined environments, both in equilibrium and out of equilibrium, with important potential applications. In this work the pearl-chain-like self-assembled structures of superparamagnetic colloids confined to a fluid-fluid interface under static and time-dependent actuations are investigated. On the one hand, it is found that the structures generated by static fields transform as the tilt angle of the field with the interface is increased, from 2D crystals to separated pearl-chains in a process that occurs through a controllable and reversible zip-like thermally activated mechanism. On the other hand, the actuation with precessing fields about the axis perpendicular to the interface induces dynamic self-assembled structures with no counterpart in non-confined systems, generated by the interplay of averaged magnetic interactions, interfacial forces, and hydrodynamics. Finally, how these dynamic structures can be used as remotely activated roller conveyors, able to transport passive colloidal cargos at fluid interfaces and generate parallel viscous flows is shown. The latter can be used in the mixture of adsorbed molecules and the acceleration of surface-chemical reactions, overcoming diffusion limitations.

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.

Preparation, properties, and applications of magnetic hematite microparticles

Hematite microparticles are becoming increasingly important components in the soft matter field. The remarkable combination of magnetic and photocatalytic properties that characterize them, coupled with the variety of uniform and monodisperse shapes that they can be synthesized in, makes them a one of a kind colloidal model system. Thanks to these properties, hematite microparticles have been recently applied in several important soft matter applications, spanning from novel colloidal building blocks for self-assembly to necessary tools to investigate and understand fundamental problems. In this review article we provide a detailed overview of the traditional methods available for the preparation of hematite microparticles of different shapes, devoting special attention on some of the most common hiccups that could hider a successful synthesis. We furthermore review the particles' most important physico-chemical properties and their most relevant applications in the soft matter field.

Hierarchical assemblies of superparamagnetic colloids in time-varying magnetic fields

Magnetically-guided colloidal assembly has proven to be a versatile method for building hierarchical particle assemblies. This review describes the dipolar interactions that govern superparamagnetic colloids in time-varying magnetic fields, and how such interactions have guided colloidal assembly into materials with increasing complexity that display novel dynamics. The assembly process is driven by magnetic dipole-dipole interactions, whose strength can be tuned to be attractive or repulsive. Generally, these interactions are directional in static external magnetic fields. More recently, time-varying magnetic fields have been utilized to generate dipolar interactions that vary in both time and space, allowing particle interactions to be tuned from anisotropic to isotropic. These interactions guide the dynamics of hierarchical assemblies of 1-D chains, 2-D networks, and 2-D clusters in both static and time-varying fields. Specifically, unlinked and chemically-linked colloidal chains exhibit complex dynamics, such as fragmentation, buckling, coiling, and wagging phenomena. 2-D networks exhibit controlled porosity and interesting coarsening dynamics. Finally, 2-D clusters have shown to be an ideal model system for exploring phenomena related to statistical thermodynamics. This review provides recent advances in this fast-growing field with a focus on its scientific potential.

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.

Static and dynamic behavior of magnetic particles at fluid interfaces

This perspective work reviews the current status of research on magnetic particles at fluid interfaces. The article gives both a unified overview of recent experimental advances and theoretical studies centered on very different phenomena that share a common characteristic: they involve adsorbed magnetic particles that range in size from a few nanometers to several millimeters. Because of their capability of being remotely piloted through controllable external fields, magnetic particles have proven essential as building blocks in the design of new techniques, smart materials and micromachines, with new tunable properties and prospective applications in engineering and biotechnology. Once adsorbed at a fluid-fluid interfase, in a process that can be facilitated via the application of magnetic field gradients, these particles often result sorely confined to two dimensions (2D). In this configuration, inter-particle forces directed along the perpendicular to the interface are typically very small compared to the surface forces. Hence, the confinement and symmetry breaking introduced by the presence of the surface play an important role on the response of the system to the application of an external field. In monolayers of particles where the magnetic is predominant interaction, the states reached are strongly determined by the mode and orientation of the applied field, which promote different patterns and processes. Furthermore, they can reproduce some of the dynamic assemblies displayed in bulk or form new ones, that take advantage of the interfacial phenomena or of the symmetry breaking introduce by the confining boundary. Magnetic colloids are also widely used for unraveling the guiding principles of 2D dynamic self-assembly, in designs devised for producing interface transport, as tiny probes for assessing interfacial rheological properties, neglecting the bulk and inertia contributions, as well as actuated stabilizing agents in foams and emulsions.

Propulsion and energetics of a minimal magnetic microswimmer

In this manuscript we describe the realization of a minimal hybrid microswimmer, composed of a ferromagnetic nanorod and a paramagnetic microsphere. The unbounded pair is propelled in water upon application of a swinging magnetic field that induces a periodic relative movement of the two composing elements, where the nanorod rotates and slides on the surface of the paramagnetic sphere. When taken together, the processes of rotation and sliding describe a finite area in the parameter space, which increases with the frequency of the applied field. We develop a theoretical approach and combine it with numerical simulations, which allow us to understand the dynamics of the propeller and explain the experimental observations. Furthermore, we demonstrate a reversal of the microswimmer velocity by varying the length of the nanorod, as predicted by the model. Finally, we determine theoretically and in experiments the Lighthill's energetic efficiency of this minimal magnetic microswimmer.

Direct measurement of Lighthill's energetic efficiency of a minimal magnetic microswimmer

The realization of artificial microscopic swimmers able to propel in viscous fluids is an emergent research field of fundamental interest and vast technological applications. For certain functionalities, the efficiency of the microswimmer in converting the input power provided through an external actuation into propulsive power output can be critical. Here we use a microswimmer composed by a self-assembled ferromagnetic rod and a paramagnetic sphere and directly determine its swimming efficiency when it is actuated by a swinging magnetic field. Using fast video recording and numerical simulations we fully characterize the dynamics of the propeller and identify the two independent degrees of freedom which allow its propulsion. We then obtain experimentally the Lighthill's energetic efficiency of the swimmer by measuring the power consumed during propulsion and the energy required to translate the propeller at the same speed. Finally, we discuss how the efficiency of our microswimmer could be increased upon suitable tuning of the different experimental parameters.

Rotating-field-driven ensembles of magnetic particles

Vortex patterns in ensembles of magnetic particles driven by a rotating field are studied. The driving arises due to the lubrication forces between the rotating particles acting in the direction perpendicular to the radius vector between the particles. Since the lubrication forces cannot be equilibrated by the radial forces due to the dipolar attraction and steric repulsion, the ensemble is in a nonequilibrium state. Different regimes are found for the dynamics of the driven ensembles-solid-body rotation at low frequency of the rotating field and stick-slip motion of the external layers of the aggregate with respect to the internal structure as the frequency is increased. The relation obtained for describing the angular velocity of the solid-body rotation is in good agreement with existing experimental data.

Self-assembling outside equilibrium: emergence of structures mediated by dissipation

Self-assembly under non-equilibrium conditions may give rise to the formation of structures not available at equilibrium.

Active apolar doping determines routes to colloidal clusters and gels

Collections of polar active particles have been unable to form stable and long-living structures due to the presence of self-propulsion. We solve this timely issue by introducing the concept of “active doping” and show that a few light-activated apolar, i.e., non–self-propelling, units can be used to rapidly trigger the formation of solid clusters and gels composed of passive colloidal particles. Our active doping can be used to assemble disparate microscopic objects, including synthetic or biological ones, paving the way toward the extension of fundamental concepts of gel and glass formation to active out-of-equilibrium systems.

Collections of interacting active particles, self-propelling or not, have shown remarkable phenomena including the emergence of dynamic patterns across different length scales, from animal groups to vibrated grains, microtubules, bacteria, and chemical- or field-driven colloids. Burgeoning experimental and simulation activities are now exploring the possibility of realizing solid and stable structures from passive elements that are assembled by a few active dopants. Here we show that such an elusive task may be accomplished by using a small amount of apolar dopants, namely synthetic active but not self-propelling units. We use blue light to rapidly assemble 2D colloidal clusters and gels via nonequilibrium diffusiophoresis, where microscopic hematite dockers form long-living interstitial bonds that strongly glue passive silica microspheres. By varying the relative fraction of doping, we uncover a rich phase diagram including ordered and disordered clusters, space-filling gels, and bicontinuous structures formed by filamentary dockers percolating through a solid network of silica spheres. We characterize the slow relaxation and dynamic arrest of the different phases via correlation and scattering functions. Our findings provide a pathway toward the rapid engineering of mesoscopic gels and clusters via active colloidal doping.

Physico-chemical foundations of particle-laden fluid interfaces

Particle-laden interfaces are ubiquitous nowadays. The understanding of their properties and structure is essential for solving different problems of technological and industrial relevance; e.g. stabilization of foams, emulsions and thin films. These rely on the response of the interface to mechanical perturbations. The complex mechanical response appearing in particle-laden interfaces requires deepening on the understanding of physico-chemical mechanisms underlying the assembly of particles at interface which plays a central role in the distribution of particles at the interface, and in the complex interfacial dynamics appearing in these systems. Therefore, the study of particle-laden interfaces deserves attention to provide a comprehensive explanation on the complex relaxation mechanisms involved in the stabilization of fluid interfaces.

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.

Advances in colloidal manipulation and transport via hydrodynamic interactions

In this review article, we highlight many recent advances in the field of micromanipulation of colloidal particles using hydrodynamic interactions (HIs), namely solvent mediated long-range interactions. At the micrsocale, the hydrodynamic laws are time reversible and the flow becomes laminar, features that allow precise manipulation and control of colloidal matter. We focus on different strategies where externally operated microstructures generate local flow fields that induce the advection and motion of the surrounding components. In addition, we review cases where the induced flow gives rise to hydrodynamic bound states that may synchronize during the process, a phenomenon essential in different systems such as those that exhibit self-assembly and swarming.

Orientational dynamics of fluctuating dipolar particles assembled in a mesoscopic colloidal ribbon

We combine experiments and theory to investigate the dynamics and orientational fluctuations of ferromagnetic microellipsoids that form a ribbonlike structure due to attractive dipolar forces. When assembled in the ribbon, the ellipsoids display orientational thermal fluctuations with an amplitude that can be controlled via application of an in-plane magnetic field. We use video microscopy to investigate the orientational dynamics in real time and space. Theoretical arguments are used to derive an analytical expression that describes how the distribution of the different angular configurations depends on the strength of the applied field. The experimental data are in good agreement with the developed model for all the range of field parameters explored. Understanding the role of fluctuations in chains composed of dipolar particles is important not only from a fundamental point of view, but it may also help understanding the stability of such structures against thermal noise, which is relevant in microfluidics and laboratory-on-a-chip applications.

Magneto-induced anisotropy in magnetic colloids of superparamagnetic magnetite nanoparticles in an external magnetic field

Here we report a study of chain formation and the magnetic anisotropy induced by them in suspensions of slightly anisotropic Fe₃O₄ nanoparticles in water and in aqueous V₂O₅ suspensions. An investigation into the magnetization of the fluid and frozen suspensions, the application of dynamic light scattering techniques and the observation of the magnetic anisotropy in the frozen magnetically aligned samples allowed us to confirm the existence of chains of Fe₃O₄ in both suspensions. Our study shows that the magneto-induced anisotropy appearing in magnetic fields in colloids with Fe₃O₄ particles is mainly due to many particle (chain) magneto-induced anisotropy, but not due to single particle magneto-induced anisotropy connected with particle shape anisotropy. In other words, the single particle magneto-induced anisotropy is much smaller than the many particle (chain) anisotropy. The anisometry of the chains provides effective coupling with the nonmagnetic V₂O₅ component of the suspension and results in its strong sensitivity to the magnetic field.

Separation of two attractive ferromagnetic ellipsoidal particles by hydrodynamic interactions under alternating magnetic field

In applications where magnetic particles are used to detect and dose targeted molecules, it is of major importance to prevent particle clustering and aggregation during the capture stage in order to maximize the capture rate. Elongated ferromagnetic particles can be more interesting than spherical ones due to their large magnetic moment, which facilitates their separation by magnets or the detection by optical measurement of their orientation relaxation time. Under alternating magnetic field, the rotational dynamics of elongated ferromagnetic particles results from the balance between magnetic torque that tends to align the particle axis with the field direction and viscous torque. As for their translational motion, it results from a competition between direct magnetic particle-particle interactions and solvent-flow-mediated hydrodynamic interactions. Due to particle anisotropy, this may lead to intricate translation-rotation couplings. Using numerical simulations and theoretical modeling of the system, we show that two ellipsoidal magnetic particles, initially in a head-to-tail attractive configuration resulting from their remnant magnetization, can repel each other due to hydrodynamic interactions when alternating field is operated. The separation takes place in a range of low frequencies f_{c1}<f<f_{c2}. The upper frequency limit f_{c2}τ_{r}≈0.04 (where τ_{r} is the rotation time scale) depends weakly on the ratio of magnetic field to particle magnetization strength, whereas f_{c1} tends to zero when this ratio increases.

Assembly and Transport of Microscopic Cargos via Reconfigurable Photoactivated Magnetic Microdockers

The realization of micromotors able to dock and transport microscopic objects in a fluid medium has direct applications toward the delivery of drugs and chemicals in small channels and pores, and the realization of functional wireless microrobots in lab-on-a-chip technology. A simple and general method to tow microscopic particles in water by using remotely controllable light-activated hematite microdockers is demonstrated. These anisotropic ferromagnetic particles can be synthesized in bulk and present the remarkable ability to be activated by light while independently manipulated via external fields. The photoactivation process induces a phoretic flow capable to attract cargos toward the surface of the propellers, while a rotating magnetic field is used to transport the composite particles to any location of the experimental platform. The method allows the assembling of small colloidal clusters of various sizes, composed by a skeleton of mobile magnetic dockers, which cooperatively keep, transport, and release the microscopic cargos. The possibility to easily reconfigure in situ the location of the docker above the cargo is demonstrated, which enables optimize transport and cargo release operations.

Multidirectional colloidal assembly in concurrent electric and magnetic fields

Dipolar interactions between nano- and micron sized colloids lead to their assembly into domains with well-defined local order. The particles with a single dipole induced by an external field assemble into linear chains and clusters. However, to achieve the formation of multidirectionally organized nano- or microassemblies with tunable physical characteristics, more sophisticated interaction tools are needed. Here we demonstrate that such complex interactions can be introduced in the form of two independent, non-interacting dipoles (double-dipoles) within a microparticle. We show how this can be achieved by the simultaneous application of alternating current (AC)-electric field and uniform magnetic field to dispersions of superparamagnetic microspheres. Depending on their timing and intensity, concurrent electric and magnetic fields lead to the formation of bidirectional particle chains, colloidal networks, and discrete crystals. We investigate the mechanistic details of the assembly process, and identify and classify the non-equilibrium states formed. The morphologies of different experimental states are in excellent correlation with our theoretical predictions based on Brownian dynamics simulations combined with a structural analysis based on local energy parameters. This novel methodology of introducing and interpreting double-dipolar particle interactions may assist in the assembly of colloidal coatings, dynamically reconfigurable particle networks, and bidirectional active structures.