Driving self-assembly and emergent dynamics in colloidal suspensions by time-dependent magnetic fields

Field-Driven Out-of-Equilibrium Collective Patterns for Swarm Micro-Robotics

Soft robotics has been rapidly advancing, offering significant improvements over traditional rigid robotic systems through the use of compliant materials that enhance adaptability and interaction with the environment. However, current approaches face critical challenges, including the reliance on complex "top-down" fabrication techniques and the difficulty of wireless powering and control at the microscale. Swarm robotics introduces a paradigm shift, leveraging collective dynamics to achieve cooperative and adaptable behaviors among multiple robotic units. Inspired by nature, this "bottom-up" approach enables swarm robots to execute task-specific reconfigurations, enhancing flexibility and robustness. Field-driven active colloids emerge as a promising platform for swarm microrobotics, capable of self-propulsion and self-organization into dynamic collective patterns under external field excitation and manipulation. These systems mimic biologically inspired swarm behaviors, such as flocking and vortex formation, providing a versatile foundation for designing innovative swarm microrobots. This review discusses the principles of electric and magnetic field-driven collective self-organization, focusing on the particle dynamics, the emergence of collective swarm patterns, and illustrative examples of functional swarm microrobots. It concludes with future perspectives on harnessing these systems for adaptive, scalable, and multifunctional microrobotic applications.

High-speed videomicroscopy and magnetorheology under triaxial unsteady magnetic fields

We describe a custom-built device that is capable of superimposing triaxial unsteady magnetic fields on a sample at the same time that its microstructure is visualized using a high-speed camera and its rheological properties are measured with a commercial rheometer. The device reaches field strengths up to 5 kA·m^{-1}, frequencies up to 4 kHz, and its functionality is evaluated by testing magnetorheological fluids under steady shear flow and field transients. Striking differences are found at small Mason numbers by changing the field configuration.

Robotic Microcapsule Assemblies with Adaptive Mobility for Targeted Treatment of Rugged Biological Microenvironments

Microrobots are poised to transform biomedicine by enabling precise, noninvasive procedures. However, current magnetic microrobots, composed of solid monolithic particles, present fundamental challenges in engineering intersubunit interactions, limiting their collective effectiveness in navigating irregular biological terrains and confined spaces. To address this, we design hierarchically assembled microrobots with multiaxis mobility and collective adaptability by engineering the potential magnetic interaction energy between subunits to create stable, self-reconfigurable structures capable of carrying and protecting cargo internally. Using double emulsion templates and magnetic control techniques, we confine 10 nm iron oxide and 15 nm silica nanoparticles within the shell of 100 μm microcapsules that form multiunit robotic collectives. Unexpectedly, we find that asymmetric localization of iron oxide nanoparticles in the microcapsules enhances the intercapsule potential energy, creating stable connections under rotating magnetic fields without altering the magnetic susceptibility. These robotic microcapsule collectives exhibit emergent behaviors, self-reconfiguring into kinematic chain-like structures to traverse complex obstacles, arched confinements, and adhesive, rugged biological tissues that typically impede microscale systems. By harnessing these functions, we demonstrate targeted antifungal delivery using a localized biofilm model on mucosal tissues, showing effective killing ofCandida without binding or causing physical damage to host cells. Our findings show how hierarchical assembly can produce cargo-carrying microrobots with collective, self-adaptive mobility for traversing complex biological environments, advancing targeted delivery for biomedical applications.

Emergence of synchronization-induced patterns in two-dimensional magnetic rod systems under rotating magnetic fields

We investigate the dynamics of two-dimensional assemblies of rod-shaped magnetic colloids under the influence of an external rotating magnetic field. Using molecular dynamics, we simulate the formation of patterns that emerge based on the synchronization degree between the magnetic rods and the rotating field. We then explore the structural and dynamic characteristics of the resulting steady states, examining their evolution as a function of changes in the rods' aspect ratio, the strength of the external magnetic field, and its rotation frequency. Three distinct synchronization regimes of the rods with the magnetic field are clearly observed. A detailed set of phase diagrams illustrates the complex relationship between the magnitude of the external magnetic field and its rotation frequency and how these parameters govern the formation of unique self-organized structures.

High-Density and Well-Aligned Hierarchical Structures of Colloids Assembled under Orthogonal Magnetic and Electric Fields

Colloids can be used either as model systems for directed assembly or as the necessary building blocks for making functional materials. Previous work primarily focused on assembling colloids under a single external field, where controlling particle-particle interactions is limited. This work presents results under a combination of electric and magnetic fields. When these two fields are orthogonally applied, we can independently tune the magnitude and direction of the dipolar attraction and repulsion between the particles. As a result, we obtain well-aligned, highly dense, but individually separated linear chains at intermediate particle concentrations. Both the inter- and intrachain spacings can be tuned by adjusting the particle concentration and relative strengths of both fields. At high particle concentrations and by tuning the electric field frequency, the individual microspheres can assemble into colloidal oligomers such as trimers, tetramers, heptamers, and nonamers in response to the electric field due to the synergy between dipolar and electrohydrodynamic interactions. These oligomers, in turn, serve as building blocks for making hierarchical structures with finer architectures upon superimposing a one-dimensional (1D) magnetic field. In addition to experiments, Monte Carlo (MC) simulations have been performed on colloids confined near the electrode, interacting through a Stockmayer-like potential. They faithfully reproduce key observations in the experiments. Our work demonstrates the potential of using orthogonal electric and magnetic fields to assemble diversified types of highly aligned structures for applications in high-strength composites, optical materials, or structured battery electrodes.

Rhythmic states and first-order phase transitions in adaptive coupled three-dimensional limit-cycle oscillators

This paper reports a phase transition in coupled three-dimensional limit-cycle oscillators with an adaptive coupling. We reveal that the multiple-cluster rhythmic states emerge when natural frequencies of oscillators follow uniform distribution (case I), but disappear for Gaussian distribution (case II). Furthermore, as the coupling strength K increases, two first-order phase transitions occur sequentially. When K→0^{+}, an inevitable and nonhysteretic discontinuous phase transition occurs. For K>0, another discontinuous phase transition with a hysteresis loop emerges, and its occurrence depends on the width of the natural frequency distribution. From the microscopic perspective of the system, there are double switches between suppression and revival of oscillations as K varies in case I, but only one switch occurs in case II. Theoretical analyses of the incoherent states and the fixed points are given, which can be accurately verified by numerical simulations. This paper provides insights into our understanding of high-dimensional oscillators and their variants.

Molecular dynamics simulations of microscopic structural transition and macroscopic mechanical properties of magnetic gels

Magnetic gels with embedded micro-/nano-sized magnetic particles in cross-linked polymer networks can be actuated by external magnetic fields, with changes in their internal microscopic structures and macroscopic mechanical properties. We investigate the responses of such magnetic gels to an external magnetic field, by means of coarse-grained molecular dynamics simulations. We find that the dynamics of magnetic particles are determined by the interplay of magnetic dipole-dipole interactions, polymer elasticity, and thermal fluctuations. The corresponding microscopic structures formed by the magnetic particles, such as elongated chains, can be controlled by the external magnetic field. Furthermore, the magnetic gels can exhibit reinforced macroscopic mechanical properties, where the elastic modulus increases algebraically with the magnetic moments of the particles in the form of ∝(m-mc)2 when magnetic chains are formed. This simulation work can not only serve as a tool for studying the microscopic and the macroscopic responses of the magnetic gels, but also facilitate future fabrications and practical controls of magnetic composites with desired physical properties.

Advances in Nanoarchitectonics: A Review of "Static" and "Dynamic" Particle Assembly Methods

Particle assembly is a promising technique to create functional materials and devices from nanoscale building blocks. However, the control of particle arrangement and orientation is challenging and requires careful design of the assembly methods and conditions. In this study, the static and dynamic methods of particle assembly are reviewed, focusing on their applications in biomaterial sciences. Static methods rely on the equilibrium interactions between particles and substrates, such as electrostatic, magnetic, or capillary forces. Dynamic methods can be associated with the application of external stimuli, such as electric fields, magnetic fields, light, or sound, to manipulate the particles in a non-equilibrium state. This study discusses the advantages and limitations of such methods as well as nanoarchitectonic principles that guide the formation of desired structures and functions. It also highlights some examples of biomaterials and devices that have been fabricated by particle assembly, such as biosensors, drug delivery systems, tissue engineering scaffolds, and artificial organs. It concludes by outlining the future challenges and opportunities of particle assembly for biomaterial sciences. This review stands as a crucial guide for scholars and professionals in the field, fostering further investigation and innovation. It also highlights the necessity for continuous research to refine these methodologies and devise more efficient techniques for nanomaterial synthesis. The potential ramifications on healthcare and technology are substantial, with implications for drug delivery systems, diagnostic tools, disease treatments, energy storage, environmental science, and electronics.

Bioinspired self-assembled colloidal collectives drifting in three dimensions underwater

Active matter systems feature a series of unique behaviors, including the emergence of collective self-assembly structures and collective migration. However, realizing collective entities formed by synthetic active matter in spaces without wall-bounded support makes it challenging to perform three-dimensional (3D) locomotion without dispersion. Inspired by the migration mechanism of plankton, we propose a bimodal actuation strategy in the artificial colloidal systems, i.e., combining magnetic and optical fields. The magnetic field triggers the self-assembly of magnetic colloidal particles to form a colloidal collective, maintaining numerous colloids as a dynamically stable entity. The optical field allows the colloidal collectives to generate convective flow through the photothermal effect, enabling them to use fluidic currents for 3D drifting. The collectives can perform 3D locomotion underwater, transit between the water-air interface, and have a controlled motion on the water surface. Our study provides insights into designing smart devices and materials, offering strategies for developing synthetic active matter capable of controllable collective movement in 3D space.

Spontaneous shock waves in pulse-stimulated flocks of Quincke rollers

Active matter demonstrates complex spatiotemporal self-organization not accessible at equilibrium and the emergence of collective behavior. Fluids comprised of microscopic Quincke rollers represent a popular realization of synthetic active matter. Temporal activity modulations, realized by modulated external electric fields, represent an effective tool to expand the variety of accessible dynamic states in active ensembles. Here, we report on the emergence of shockwave patterns composed of coherently moving particles energized by a pulsed electric field. The shockwaves emerge spontaneously and move faster than the average particle speed. Combining experiments, theory, and simulations, we demonstrate that the shockwaves originate from intermittent spontaneous vortex cores due to a vortex meandering instability. They occur when the rollers' translational and rotational decoherence times, regulated by the electric pulse durations, become comparable. The phenomenon does not rely on the presence of confinement, and multiple shock waves continuously arise and vanish in the system.

Magnetically Induced Anisotropic Interaction in Colloidal Assembly

The wide accessibility to nanostructures with high uniformity and controllable sizes and morphologies provides great opportunities for creating complex superstructures with unique functionalities. Employing anisotropic nanostructures as the building blocks significantly enriches the superstructural phases, while their orientational control for obtaining long-range orders has remained a significant challenge. One solution is to introduce magnetic components into the anisotropic nanostructures to enable precise control of their orientations and positions in the superstructures by manipulating magnetic interactions. Recognizing the importance of magnetic anisotropy in colloidal assembly, we provide here an overview of magnetic field-guided self-assembly of magnetic nanoparticles with typical anisotropic shapes, including rods, cubes, plates, and peanuts. The Review starts with discussing the magnetic energy of nanoparticles, appreciating the vital roles of magneto-crystalline and shape anisotropies in determining the easy magnetization direction of the anisotropic nanostructures. It then introduces superstructures assembled from various magnetic building blocks and summarizes their unique properties and intriguing applications. It concludes with a discussion of remaining challenges and an outlook of future research opportunities that the magnetic assembly strategy may offer for colloidal assembly.

Active Colloids as Models, Materials, and Machines

Active colloids use energy input at the particle level to propel persistent motion and direct dynamic assemblies. We consider three types of colloids animated by chemical reactions, time-varying magnetic fields, and electric currents. For each type, we review the basic propulsion mechanisms at the particle level and discuss their consequences for collective behaviors in particle ensembles. These microscopic systems provide useful experimental models of nonequilibrium many-body physics in which dissipative currents break time-reversal symmetry. Freed from the constraints of thermodynamic equilibrium, active colloids assemble to form materials that move, reconfigure, heal, and adapt. Colloidal machines based on engineered particles and their assemblies provide a basis for mobile robots with increasing levels of autonomy. This review provides a conceptual framework for understanding and applying active colloids to create material systems that mimic the functions of living matter. We highlight opportunities for chemical engineers to contribute to this growing field.

Electric and Magnetic Field-Driven Dynamic Structuring for Smart Functional Devices

The field of soft matter is rapidly growing and pushing the limits of conventional materials science and engineering. Soft matter refers to materials that are easily deformed by thermal fluctuations and external forces, allowing for better adaptation and interaction with the environment. This has opened up opportunities for applications such as stretchable electronics, soft robotics, and microfluidics. In particular, soft matter plays a crucial role in microfluidics, where viscous forces at the microscale pose a challenge to controlling dynamic material behavior and operating functional devices. Field-driven active colloidal systems are a promising model system for building smart functional devices, where dispersed colloidal particles can be activated and controlled by external fields such as magnetic and electric fields. This review focuses on building smart functional devices from field-driven collective patterns, specifically the dynamic structuring of hierarchically ordered structures. These structures self-organize from colloidal building blocks and exhibit reconfigurable collective patterns that can implement smart functions such as shape shifting and self-healing. The review clarifies the basic mechanisms of field-driven particle dynamic behaviors and how particle-particle interactions determine the collective patterns of dynamic structures. Finally, the review concludes by highlighting representative application areas and future directions.

Solvable Dynamics of Coupled High-Dimensional Generalized Limit-Cycle Oscillators

We introduce a new model consisting of globally coupled high-dimensional generalized limit-cycle oscillators, which explicitly incorporates the role of amplitude dynamics of individual units in the collective dynamics. In the limit of weak coupling, our model reduces to the D-dimensional Kuramoto phase model, akin to a similar classic construction of the well-known Kuramoto phase model from weakly coupled two-dimensional limit-cycle oscillators. For the practically important case of D=3, the incoherence of the model is rigorously proved to be stable for negative coupling (K<0) but unstable for positive coupling (K>0); the locked states are shown to exist if K>0; in particular, the onset of amplitude death is theoretically predicted. For D≥2, the discrete and continuous spectra for both locked states and amplitude death are governed by two general formulas. Our proposed D-dimensional model is physically more reasonable, because it is no longer constrained by fixed amplitude dynamics, which puts the recent studies of the D-dimensional Kuramoto phase model on a stronger footing by providing a more general framework for D-dimensional limit-cycle oscillators.

Motility of acoustically powered micro-swimmers in a liquid crystalline environment

Suspensions of microswimmers in liquid crystals demonstrate remarkably complex dynamics and serve as a model system for studying active nematics. So far, experimental realization of microswimmers suspended in liquid crystalline media has relied on biological microorganisms that impose strict limitations on the compatible media and makes it difficult to regulate activity. Here, we demonstrate that acoustically powered bubble microswimmers can efficiently self-propel in a lyotropic liquid crystal. The velocity of the swimmers is controlled by the amplitude of the acoustic field. Histograms of swimming directions with respect to the local nematic field reveal a bimodal distribution: the swimmers tend to either fully align with or swim perpendicular to the director field of the liquid crystal, occasionally switching between these two states. The bubble-induced streaming from a swimmer locally melts the liquid crystal and produces topological defects at the tail of the swimmer. We show that the defect proliferation rate increases with the angle between the swimmer's velocity and the local orientation of the director field.

Superparamagnetic colloids in a rotating field: Transition state from chains to disks

When exposed to an external magnetic field, 2D layers of spherical superparamagnetic colloids form specific structures which depend on the features of the external field. If the magnetic field is constant along time, superparamagnetic colloids self-organize into chains oriented in the direction of the field. If the magnetic field is rotating in the plane of the suspension, below a critical frequency, the superparamagnetic beads still aggregate into chains, but these chains rotate with the magnetic field. When the rotation reaches a certain speed, the colloids aggregate in rotating disklike clusters. In this work, we focused on the early stages of the disklike clusters' aggregation and the dynamics of this process. In particular, we observed experimentally that before clustering into disklike structures, the colloids were aggregating into rotating chains, just as they did in suspensions submitted to a magnetic field rotating at a lower rate. Over time, the chains interact with one another and aggregate into disklike clusters, resulting in a mixture of chains and disks in the sample. Finally, we propose a model to characterize the suspension over time in terms of the proportion of chains and disklike clusters, and report its deduced temporal evolution for different frequencies and volume fractions.

Elastically-mediated collective organisation of magnetic microparticles

Gels are soft elastic materials made of a three-dimensional cross-linked polymer network and featuring both elastic and dissipative responses under external mechanical stimuli. Here we investigate how such gels mediate the organization of embedded magnetic microparticles when driven by an external field. By constructing a continuum theory, we demonstrate that the collective dynamics of the embedded particles result from the delicate balance between magnetic dipole-dipole interactions, thermal fluctuations and elasticity of the polymer network, verified by our experiments. The proposed model could be extended to other soft magnetic composites in order to predict how the elastic interactions mediate the aggregation of the embedded elements, fostering technological implications for multifunctional hydrogel materials.

Treating random sequential addition via the replica method

While many physical processes are non-equilibrium in nature, the theory and modeling of such phenomena lag behind theoretical treatments of equilibrium systems. The diversity of powerful theoretical tools available to describe equilibrium systems has inspired strategies that map non-equilibrium systems onto equivalent equilibrium analogs so that interrogation with standard statistical mechanical approaches is possible. In this work, we revisit the mapping from the non-equilibrium random sequential addition process onto an equilibrium multi-component mixture via the replica method, allowing for theoretical predictions of non-equilibrium structural quantities. We validate the above approach by comparing the theoretical predictions to numerical simulations of random sequential addition.

Grain boundary dynamics driven by magnetically induced circulation at the void interface of 2D colloidal crystals

The complexity of shear-induced grain boundary dynamics has been historically difficult to view at the atomic scale. Meanwhile, two-dimensional (2D) colloidal crystals have gained prominence as model systems to easily explore grain boundary dynamics at single-particle resolution but have fallen short at exploring these dynamics under shear. Here, we demonstrate how an inherent interfacial shear in 2D colloidal crystals drives microstructural evolution. By assembling paramagnetic particles into polycrystalline sheets using a rotating magnetic field, we generate a particle circulation at the interface of particle-free voids. This circulation shears the crystalline bulk, operating as both a source and sink for grain boundaries. Furthermore, we show that the Read-Shockley theory for hard-condensed matter predicts the misorientation angle and energy of shear-induced low-angle grain boundaries based on their regular defect spacing. Model systems containing shear provide an ideal platform to elucidate shear-induced grain boundary dynamics for use in engineering improved/advanced materials.

A broad perspective to particle-laden fluid interfaces systems: from chemically homogeneous particles to active colloids

Particles adsorbed to fluid interfaces are ubiquitous in industry, nature or life. The wide range of properties arising from the assembly of particles at fluid interface has stimulated an intense research activity on shed light to the most fundamental physico-chemical aspects of these systems. These include the mechanisms driving the equilibration of the interfacial layers, trapping energy, specific inter-particle interactions and the response of the particle-laden interface to mechanical perturbations and flows. The understanding of the physico-chemistry of particle-laden interfaces becomes essential for taking advantage of the particle capacity to stabilize interfaces for the preparation of different dispersed systems (emulsions, foams or colloidosomes) and the fabrication of new reconfigurable interface-dominated devices. This review presents a detailed overview of the physico-chemical aspects that determine the behavior of particles trapped at fluid interfaces. This has been combined with some examples of real and potential applications of these systems in technological and industrial fields. It is expected that this information can provide a general perspective of the topic that can be exploited for researchers and technologist non-specialized in the study of particle-laden interfaces, or for experienced researcher seeking new questions to solve.

Extension of Kelvin's equation to dipolar colloids

Suspensions of colloids driven out-of-equilibrium demonstrate interesting collective behavior, such as organized and directed clustering and swarming. These systems require continuous energy input, yet some of the dynamics of these driven systems resemble the equilibrium-phase behavior of molecular fluids, such as crystallization, condensation, and phase separation. Consequently, there has been significant interest in exploring the applicability of thermodynamic concepts, such as pressure and surface tension, to describe nonequilibrium phenomena. Here, we show how rotating magnetic fields can drive superparamagnetic particles to form steady-state vapor–liquid coexistence that can be analyzed with Kelvin’s equation to determine an “effective vapor pressure” for this active colloidal system. These results illustrate the convergence of statistical physics of simple liquids to nonequilibrium colloidal fluids.

Vapor pressure refers to the pressure exerted by the vapor phase in thermodynamic equilibrium with either its liquid or solid phase. An important class of active matter is field-driven colloids. A suspension of dipolar colloids placed in a high-frequency rotating magnetic field undergoes a nonequilibrium phase transition into a dilute and dense phase, akin to liquid–vapor coexistence in a simple fluid. Here, we compute the vapor pressure of this colloidal fluid. The number of particles that exist as the dilute bulk phase versus condensed cluster phases can be directly visualized. An exponential relationship between vapor pressure and effective temperature is determined as a function of applied field strength, analogous to the thermodynamic expression between vapor pressure and temperature found for pure liquids. Additionally, we demonstrate the applicability of Kelvin’s equation to this field-driven system. In principle, this appears to be in conflict with macroscopic thermodynamic assumptions due to the nonequilibrium and discrete nature of this colloidal system. However, the curvature of the vapor–liquid interface provides a mechanical equilibrium characterized by interfacial tension that connects the condensed clusters observed with these active fluids to classical colligative fluid properties.

The role of attraction in the phase diagrams and melting scenarios of generalized 2D Lennard-Jones systems

Monolayer and two-dimensional (2D) systems exhibit rich phase behavior, compared with 3D systems, in particular, due to the hexatic phase playing a central role in melting scenarios. The attraction range is known to affect critical gas–liquid behavior (liquid–liquid in protein and colloidal systems), but the effect of attraction on melting in 2D systems remains unstudied systematically. Here, we have revealed how the attraction range affects the phase diagrams and melting scenarios in a 2D system. Using molecular dynamics simulations, we have considered the generalized Lennard-Jones system with a fixed repulsion branch and different power indices of attraction from long-range dipolar to short-range sticky-sphere-like. A drop in the attraction range has been found to reduce the temperature of the gas–liquid critical point, bringing it closer to the gas–liquid–solid triple point. At high temperatures, attraction does not affect the melting scenario that proceeds through the cascade of solid–hexatic (Berezinskii–Kosterlitz–Thouless) and hexatic–liquid (first-order) phase transitions. In the case of dipolar attraction, we have observed two triple points inherent in a 2D system: hexatic–liquid–gas and crystal–hexatic–gas, the temperature of the crystal–hexatic–gas triple point is below the hexatic–liquid–gas triple point. This observation may have far-reaching consequences for future studies, since phase diagrams determine possible routes of self-assembly in molecular, protein, and colloidal systems, whereas the attraction range can be adjusted with complex solvents and external electric or magnetic fields. The results obtained may be widely used in condensed matter, chemical physics, materials science, and soft matter.

Emergence and dynamics of unconfined self-organised vortices in active magnetic roller liquids

Actively driven colloids demonstrate complex out-of-equilibrium dynamics often rivaling self-organized patterns and collective behavior observed in living systems. Recent studies revealed the emergence of steady macroscopic states with multiple interacting vortices in an unconfined environment that emerge from the coupling between microscale particle rotation and translation. Yet, insights into the microscopic behavior during the vortex emergence, growth, and formation of a multi-vortical state remain lacking. Here, we investigate in experiments and simulations how the microscale magnetic roller behavior leads to the emergence of seed vortices, their aggregation or annihilation, and the formation of stable large-scale vortical structures. We reveal that the coupling of roller-induced hydrodynamic flows guides the local self-densifications and self-organization of the micro-rollers into seed vortices. The resulting multi-vortical state is sensitive to the external magnetic field amplitude and allows tuning the rollers' number density in a vortex and its characteristic size.

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.

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.

2D colloids in rotating electric fields: A laboratory of strong tunable three-body interactions

Many-body forces play a prominent role in structure and dynamics of matter, but their role is not well understood in many cases due to experimental challenges. Here, we demonstrate that a novel experimental system based on rotating electric fields can be utilised to deliver unprecedented degree of control over many-body interactions between colloidal silica particles in water. We further show that we can decompose interparticle interactions explicitly into the leading terms and study their specific effects on phase behaviour. We found that three-body interactions exert critical influence over the phase diagram domain boundaries, including liquid-gas binodal, critical and triple points. Phase transitions are shown to be reversible and fully controlled by the magnitude of external rotating electric field governing the tunable interactions. Our results demonstrate that colloidal systems in rotating electric fields are a unique laboratory to study the role of many-body interactions in physics of phase transitions and in applications, such as self-assembly, offering exciting opportunities for studying generic phenomena inherent to liquids and solids, from atomic to protein and colloidal systems.

Core-shell particles in rotating electric and magnetic fields: Designing tunable interactions via particle engineering

Tunable interactions between colloidal particles, governed by external rotating electric or magnetic fields, yield rich capabilities for prospective self-assembly technologies of materials and fundamental particle-resolved studies of phase transitions and transport phenomena in soft matter. However, the role of the internal structure of colloidal particles in the tunable interactions has never been systematically investigated. Here, we study the tunable interactions between composite particles with core-shell structure in a rotating electric field and show that the engineering of their internal structure provides an effective tool for designing the interactions. We generalized an integral theory and studied the tunable interactions between core-shell particles with homogeneous cores (layered particles) and cores with nano-inclusions to reveal the main trends in the interactions influenced by the structure. We found that depending on the materials of the core, shell, and solvent, the interactions with the attractive pairwise part and positive or negative three-body part can be obtained, as well as pairwise repulsion with attractive three-body interactions (for triangular triplets). The latter case is observed for the first time, being unattainable for homogeneous particles but feasible with core-shell particles: Qualitatively similar interactions are inherent to charged colloids (repulsive pairwise and attractive three-body energies), known as a model system of globular proteins. The methods and conclusions of our paper can be generalized for magnetic and 3D colloidal systems. The results make a significant advance in the analysis of tunable interactions in colloidal systems, which are of broad interest in condensed matter, chemical physics, physical chemistry, materials science, and soft matter.

Neuroevolutionary Learning of Particles and Protocols for Self-Assembly

Within simulations of molecules deposited on a surface we show that neuroevolutionary learning can design particles and time-dependent protocols to promote self-assembly, without input from physical concepts such as thermal equilibrium or mechanical stability and without prior knowledge of candidate or competing structures. The learning algorithm is capable of both directed and exploratory design: it can assemble a material with a user-defined property, or search for novelty in the space of specified order parameters. In the latter mode it explores the space of what can be made, rather than the space of structures that are low in energy but not necessarily kinetically accessible.

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.

Persistence length regulates emergent dynamics in active roller ensembles

Active colloidal fluids, biological and synthetic, often demonstrate complex self-organization and the emergence of collective behavior. Spontaneous formation of multiple vortices has been recently observed in a variety of active matter systems, however, the generation and tunability of the active vortices not controlled by geometrical confinement remain challenging. Here, we exploit the persistence length of individual particles in ensembles of active rollers to tune the formation of vortices and to orchestrate their characteristic sizes. We use two systems and employ two different approaches exploiting shape anisotropy or polarization memory of individual units for control of the persistence length. We characterize the dynamics of emergent multi-vortex states and reveal a direct link between the behavior of the persistence length and properties of the emergent vortices. We further demonstrate common features between the two systems including anti-ferromagnetic ordering of the neighboring vortices and active turbulent behavior with a characteristic energy cascade in the particles velocity field energy spectra. Our findings provide insights into the onset of spatiotemporal coherence in active roller systems and suggest a control knob for manipulation of dynamic self-assembly in active colloidal ensembles.

Dissipative non-equilibrium dynamics of self-assembled paramagnetic colloidal clusters

We study experimentally and theoretically the dynamics of two-dimensional clusters of paramagnetic colloids under a time-varying magnetic field. These self-assembled clusters are a dissipative non-equilibrium system with shared features with aggregates of living matter. We investigate the dynamics of cluster rotation and develop a theoretical model to explain the emergence of collective viscoelastic properties. The model successfully captures the observed dependence on particle, cluster, and field characteristics, and it provides an estimate of cluster viscoelasticity. We also study the rapid cluster disassembly in response to a change in the external field. The experimentally observed disassembly dynamics are successfully described by a model, which also allows estimating the particle-substrate friction coefficient. Our study highlights physical mechanisms that may be at play in biological aggregates, where similar dynamical behaviors are observed.

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.

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.

Counterrotation of magnetic beads in spinning fields

A magnetic stirrer, an omnipresent device in the laboratory, generates a spinning magnetic dipolelike field that drives in a contactless manner the rotation of a ferromagnetic bead on top of it. We investigate here the surprisingly complex dynamics displayed by the spinning magnetic bead emerging from its dissipatively driven, coupled translation and rotation. A particularly stunning and counterintuitive phenomenon is the sudden inversion of the bead's rotational direction, from corotation to counterrotation, acting seemingly against the driving field, when the stirrer's frequency surpasses a critical value. The bead counterrotation effect, experimentally described by Chau et al. [J. Magn. Magn. Mater. 476, 376 (2019)JMMMDC0304-885310.1016/j.jmmm.2018.12.073], is here comprehensively studied, with numerical simulations and a theoretical approach complementing experimental observations.

Colloids in rotating electric and magnetic fields: designing tunable interactions with spatial field hodographs

Opening a way to designing tunable interactions between colloidal particles in rotating electric and magnetic fields provides rich opportunities both for fundamental studies of phase transitions and engineering of soft materials. Spatial hodographs, showing the distribution of the field magnitude and orientation, allow the adjustment of interactions and can be an extremely potent tool for prospective experiments, but remain unstudied systematically. Here, we calculate the tunable interactions between spherical particles in rhodonea, conical, cylindrical, and ellipsoidal field hodographs, as the most experimentally important cases. We discovered that spatial hodographs are reduced to each other, providing a plethora of interactions, e.g., repulsive, attractive, barrier-like, and double-scale repulsive ones. Complementing the "magic" conical angle, the "magic" compression and ellipticity of cylindrical and ellipsoidal hodographs are introduced. In the "magic" hodographs, the interactions become spatially isotropic and attain dispersion-force-like asymptotic (the same for pairwise and many-body energies), being attractive or repulsive, if the particle permittivity is larger or smaller than that of the solvent. With the diagrammatic method and numerical calculations, we obtained physically meaningful fits to the many-body tunable potentials for silica (iron oxide) particles in deionised water in the rotating electric (magnetic) fields. Our results provide essential guidance for future experiments and simulations of colloidal liquids, crystals, gels, and glasses, important for a broad range of problems in condensed matter, chemical physics, physical chemistry, materials science, and soft matter.

Guided Self-Assembly and Control of Vortices in Ensembles of Active Magnetic Rollers

Active magnetic colloids are capable of rich collective behavior and complex self-organization. The interplay between short- and long-range interactions taking place away from equilibrium often results in a spontaneous formation of localized dynamic microstructures. Here we report a method for guided self-assembly and control of self-organized colloidal vortices emerging in a ferromagnetic particle ensemble energized by a uniaxial alternating (ac) magnetic field. The structure of a vortex composed of rolling magnetic particles can be stabilized and manipulated by means of an additional strongly localized alternating magnetic field provided by a minicoil. By tuning the parameters of the localized field, we effectively control the dimensions and particle number density in the vortex. We find that the roller vortex self-organization is assisted by field-induced magnetic "steering" rather than magnetic field gradients and is only possible while the system is in the active (magnetic rollers) state. We demonstrate that parameters of the emergent vortex are efficiently tuned by a phase shift between alternating magnetic fields. The method for assisted self-organization of rolling magnetic colloids into a vortex with on-demand characteristics suggests a new tool for active matter control and manipulation that may lead to a development of new approaches toward the guided microscopic transport in active particle systems.

Reconfigurable structure and tunable transport in synchronized active spinner materials

Ensembles of actuated colloids are excellent model systems to explore emergent out-of-equilibrium structures, complex collective dynamics, and design rules for the next generation materials. Here, we demonstrate that ferromagnetic microparticles suspended at an air-water interface and energized by an external rotating magnetic field spontaneously form dynamic ensembles of synchronized spinners in a certain range of the excitation field parameters. Each spinner generates strong hydrodynamic flows, and collective interactions of the multiple spinners promote a formation of dynamic lattices. On the basis of experiments and simulations, we reveal structural transitions from liquid to nearly crystalline states in this novel active spinner material and demonstrate that dynamic spinner lattices are reconfigurable, capable of self-healing behavior and that the transport of embedded inert cargo particles can be remotely tuned by the parameters of the external excitation field. Our findings provide insights into the behavior of active spinner materials with reconfigurable structural order and tunable functionalities.

Enhanced diffusion and magnetophoresis of paramagnetic colloidal particles in rotating magnetic fields

Dispersions of paramagnetic colloids can be manipulated with external magnetic fields to assemble structures via dipolar assembly and control transport via magnetophoresis. For fields held steady in time, the dispersion structure and dynamic properties are coupled. This coupling can be problematic when designing processes involving field-induced forces, as particle aggregation competes against and hinders particle transport. Time-varying fields drive dispersions out-of-equilibrium, allowing the structure and dynamics to be tuned independently. Rotating the magnetic field direction using two biaxial fields is a particularly effective mode of time-variation and has been used experimentally to enhance particle transport. Fundamental transport properties, like the diffusivity and magnetophoretic mobility, dictate dispersions' out-of-equilibrium responses to such time-varying fields, and are therefore crucial to understand to effectively design processes utilizing rotating fields. However, a systematic study of these dynamic quantities in rotating fields has not been performed. Here, we investigate the transport properties of dispersions of paramagnetic colloids in rotating magnetic fields using dynamic simulations. We find that self-diffusion of particles is enhanced in rotating fields compared to steady fields, and that the self-diffusivity in the plane of rotation reaches a maximum value at intermediate rotation frequencies that is larger than the Stokes-Einstein diffusivity of an isolated particle. We also show that, while the magnetophoretic velocity of particles through the bulk in a field gradient decreases with increasing rotation frequency, the enhanced in-plane diffusion allows for faster magnetophoretic transport through porous materials in rotating fields. We examine the effect of porous confinement on the transport properties in rotating fields and find enhanced diffusion at all pore sizes. The confined and bulk values of the transport properties are leveraged in simple models of magnetophoresis through tortuous porous media.

Non-equilibrium steady-state colloidal assembly dynamics

Simulations and experiments are reported for nonequilibrium steady-state assembly of small colloidal crystal clusters in rotating magnetic fields vs frequency and amplitude. High-dimensional trajectories of particle coordinates from image analysis of experiments and from Stokesian Dynamic computer simulations are fit to low-dimensional reaction coordinate based Fokker-Planck and Langevin equations. The coefficients of these equations are effective energy and diffusivity landscapes that capture configuration-dependent energy and friction for nonequilibrium steady-state dynamics. Two reaction coordinates that capture condensation and anisotropy of dipolar chains folding into crystals are sufficient to capture high-dimensional experimental and simulated dynamics in terms of first passage time distributions. Our findings illustrate how field-mediated nonequilibrium steady-state colloidal assembly dynamics can be modeled to interpret and design pathways toward target microstructures and morphologies.

Aggregation dynamics of active rotating particles in dense passive media

Active matter systems are able to exhibit emergent non-equilibrium behavior due to activity-induced effective interactions between the active particles. Here we study the aggregation and dynamical behavior of active rotating particles, spinners, embedded in 2D passive colloidal monolayers. Using both experiments and simulations we observe aggregation of active particles or spinners whose behavior resembles classical 2D Cahn-Hilliard coarsening. The aggregation behavior and spinner attraction depend on the mechanical properties of the passive monolayer and the activity of spinners. Spinner aggregation only occurs when the passive monolayer behaves elastically and when the spinner activity exceeds a minimum activity threshold. Interestingly, for the spinner concentrations investigated here, the spinner concentration does not seem to change the dynamics of the aggregation behavior. There is a characteristic cluster size which maximizes spinner aggregation by minimizing the drag through the passive monolayer and maximizing the stress applied on the passive medium. We also show a ternary mixture of passive particles and co-rotating and counter-rotating spinners that aggregate into clusters of co and counter-rotating spinners respectively.

Hydrodynamic interaction induced breakdown of the state properties of active fluids

The mechanical pressure of active fluids in which swimmers are modeled by soft run-and-tumble spheres is investigated by dissipative particle dynamics simulations. The incremental pressure (Π) with respect to the system pressure with inactive swimmers comprises the direct contribution of the swimmers (π) and the indirect contribution of fluids associated with hydrodynamic interactions (HIs). The pressure can be determined from the bulk and confining wall and the former is always less than the latter. The π of dilute active dispersions is proportional to their active diffusivity while Π grows generally with propulsive force and run time. However, Π is always substantially less than π because of negative contributions to pressure by HIs. The wall pressure depends on the swimmer-wall interactions, verifying that pressure is not a state function for active spheres due to the HIs. Owing to the distinct flow patterns, Π varies with the swim-type (pusher and puller) subject to the same run-and-tumble parameters at high concentrations.

Manipulation of emergent vortices in swarms of magnetic rollers

Active colloids are an emergent class of out-of-equilibrium materials demonstrating complex collective phases and tunable functionalities. Microscopic particles energized by external fields exhibit a plethora of fascinating collective phenomena, yet mechanisms of control and manipulation of active phases often remains lacking. Here we report the emergence of unconfined macroscopic vortices in a system of ferromagnetic rollers energized by a vertical alternating magnetic field and elucidate the complex nature of a magnetic roller-vortex interactions with inert scatterers. We demonstrate that active self-organized vortices have an ability to spontaneously switch the direction of rotation and move across the surface. We reveal the capability of certain non-active particles to pin the vortex and manipulate its dynamics. Building on our findings, we demonstrate the potential of magnetic roller vortices to effectively capture and transport inert particles at the microscale.

Ferumoxytol of ultrahigh magnetization produced by hydrocooling and magnetically internal heating co-precipitation

Ferumoxytol, which is originally intended for MRI and anemia treatment, is currently the only inorganic nanodrug approved by FDA for clinical application in vivo. Common ferumoxytol seems incapable of meeting the requirements for diverse applications. Thus, the development of a novel strategy based on co-precipitation to produce ferumoxytol with high quality is an imminent task. Herein, we proposed a physically assisted strategy, namely hydrocooling and magnetically internal heating co-precipitation, to optimize the properties of ferumoxytol and thus significantly enhance its magnetic performance. Magnetization of the newly developed ferumoxytol can reach 104-105 emu g-1 Fe, which is the highest value among the reported results. It has been found that the crystalline structures of the newly developed ferumoxytol have been greatly improved on the basis of pharmaceutical quality criteria.

Paramagnetic colloids: Chaotic routes to clusters and molecules

We present computer simulations and experiments on dilute suspensions of superparamagnetic particles subject to rotating magnetic fields. We focus on chains of four particles and their decay routes to stable structures. At low rates, the chains track the external field. At intermediate rates, the chains break up but perform a periodic (albeit complex) motion. At sufficiently high rates, the chains generally undergo chaotic motion at short times and decay to either closely packed clusters or more dispersed, colloidal molecules at long times. We show that the transition out of the chaotic states can be described as a Poisson process in both simulation and experiment.