Field-induced self-assembly of suspended colloidal membranes

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.

Assembly and manipulation of responsive and flexible colloidal structures by magnetic and capillary interactions

The long-ranged interactions induced by magnetic fields and capillary forces in multiphasic fluid-particle systems facilitate the assembly of a rich variety of colloidal structures and materials. We review here the diverse structures assembled from isotropic and anisotropic particles by independently or jointly using magnetic and capillary interactions. The use of magnetic fields is one of the most efficient means of assembling and manipulating paramagnetic particles. By tuning the field strength and configuration or by changing the particle characteristics, the magnetic interactions, dynamics, and responsiveness of the assemblies can be precisely controlled. Concurrently, the capillary forces originating at the fluid-fluid interfaces can serve as means of reconfigurable binding in soft matter systems, such as Pickering emulsions, novel responsive capillary gels, and composites for 3D printing. We further discuss how magnetic forces can be used as an auxiliary parameter along with the capillary forces to assemble particles at fluid interfaces or in the bulk. Finally, we present examples how these interactions can be used jointly in magnetically responsive foams, gels, and pastes for 3D printing. The multiphasic particle gels for 3D printing open new opportunities for making of magnetically reconfigurable and "active" structures.

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.

Field-Pulse-Induced Annealing of 2D Colloidal Polycrystals

Two-dimensional colloidal crystals are of considerable fundamental and practical importance. However, their quality is often low due to the widespread presence of domain walls and defects. In this work, we explored the annealing process undergone by monolayers of superparamagnetic colloids adsorbed onto fluid interfaces in the presence of magnetic field pulses. These systems present the extraordinary peculiarity that both the extent and the character of interparticle interactions can be adjusted at will by simply varying the strength and orientation of the applied field so that the application of field pulses results in a sudden input of energy. Specifically, we have studied the effect of polycrystal size, pulse duration, slope and frequency on the efficiency of the annealing process and found that (i) this strategy is only effective when the polycrystal consists of less than approximately 10 domains; (ii) that the pulse duration should be of the order of magnitude of the time required for the outer particles to travel one diameter during the heating step; (iii) that the quality of larger polycrystals can be slightly improved by applying tilted pulses. The experimental results were corroborated by Brownian dynamics simulations.

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.

First-passage statistics of colloids on fractals: Theory and experimental realization

In nature and technology, particle dynamics frequently occur in complex environments, for example in restricted geometries or crowded media. These dynamics have often been modeled invoking a fractal structure of the medium although the fractal structure was only indirectly inferred through the dynamics. Moreover, systematic studies have not yet been performed. Here, colloidal particles moving in a laser speckle pattern are used as a model system. In this case, the experimental observations can be reliably traced to the fractal structure of the underlying medium with an adjustable fractal dimension. First-passage time statistics reveal that the particles explore the speckle in a self-similar, fractal manner at least over four decades in time and on length scales up to 20 times the particle radius. The requirements for fractal diffusion to be applicable are laid out, and methods to extract the fractal dimension are established.

Increasing efficiency and accuracy of magnetic interaction calculations in colloidal simulation through machine learning

Calculating the magnetic interaction between magnetic particles that are positioned in close proximity to one another is a surprisingly challenging task. Exact solutions for this interaction exist either through numerical expansion of multipolar interactions or through solving Maxwell's equations with a finite element solver. These approaches can take hours for simple configurations of three particles. Meanwhile, across a range of scientific and engineering problems, machine learning approaches have been developed as fast computational platforms for solving complex systems of interest when large data sets are available. In this paper, we bring the touted benefits of recent advances in science-based machine learning algorithms to bear on the problem of modeling the magnetic interaction between three particles. We investigate this approach using diverse machine learning systems including physics informed neural networks. We find that once the training data has been collected and the model has been initiated, simulation times are reduced from hours to mere seconds while maintaining remarkable accuracy. Despite this promise, we also try to lay bare the current challenges of applying machine learning to these and more complex colloidal systems.

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.

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.

Diagrammatics of tunable interactions in anisotropic colloids in rotating electric or magnetic fields: New kind of dipole-like interactions

Anisotropic particles are widely presented in nature, from colloidal to bacterial systems, and control over their interactions is of crucial importance for many applications, from self-assembly of novel materials to microfluidics. Placed in rapidly rotating external electric fields, colloidal particles attain a tunable long-range and many-body part in their interactions. For spherical colloids, this approach has been shown to offer rich capabilities to construct the tunable interactions via designing the internal structure of particles and spatial hodographs of external rotating fields, but in the case of anisotropic particles, the interactions remain poorly understood. Here, we show that tunable interactions between anisotropic rod-like and spheroidal colloidal particles in rotating electric or magnetic fields can be calculated and analyzed with the diagrammatic technique we developed in the present work. With this technique, we considered an in-plane rotating electric field, obtained the long-range asymptotics of the anisotropic interactions, calculated the tunable interactions between particles rotating synchronously, and found conditions for rotator repulsion. We compared the mechanisms providing tunable interactions to those for orientational (Keesom), induction (Debye), and dispersion (London) interactions in molecular systems and found that the tunable interactions between anisotropic particles represent a novel kind of dipole-like interaction. The method can be directly generalized for magnetically induced interactions, 3D systems, and fields with spatial hodographs. The results provide significant advance in theoretical methods for tunable interactions in colloids and, therefore, are of broad interest in condensed matter, chemical physics, physical chemistry, materials science, and soft matter.

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.

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.

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.

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.

Active microrheology in two-dimensional magnetic networks

We study active microrheology in two-dimensional (2D) magnetic networks. To this end, we use Langevin dynamics computer simulations where single non-magnetic or magnetic tracer particles are pulled through the network structures via a constant force f. Structural changes in the network around the pulled tracer particle are characterized in terms of pair correlation functions. These functions indicate that the non-magnetic tracer particles tend to strongly affect the network structure leading to the formation of channels at sufficiently high forces, while the magnetic tracer particles modify the network structure only slightly. At zero pulling force, f = 0, both non-magnetic and magnetic tracer particles are localized, i.e. they do not show diffusive behavior in the long-time limit. Nevertheless, the friction coefficient, as obtained from the steady-state velocity of the tracer particles, seems to indicate a linear-response regime at small values of f. Beyond the latter linear response regime, the diffusion dynamics of the tracer particles are anisotropic with superdiffusive behavior in force direction. This transport anomaly is investigated via van Hove correlation functions and residence time distributions.

Actuation of magnetoelastic membranes in precessing magnetic fields

Superparamagnetic nanoparticles incorporated into elastic media offer the possibility of creating actuators driven by external fields in a multitude of environments. Here, magnetoelastic membranes are studied through a combination of continuum mechanics and molecular dynamics simulations. We show how induced magnetic interactions affect the buckling and the configuration of magnetoelastic membranes in rapidly precessing magnetic fields. The field, in competition with the bending and stretching of the membrane, transmits forces and torques that drives the membrane to expand, contract, or twist. We identify critical field values that induce spontaneous symmetry breaking as well as field regimes where multiple membrane configurations may be observed. Our insights into buckling mechanisms provide the bases to develop soft, autonomous robotic systems that can be used at micro- and macroscopic length scales.

Tunable interactions between particles in conically rotating electric fields

Tunable interactions between colloidal particles in external conically rotating electric fields are calculated, while the (vertical) axis of the field rotation is normal to the (horizontal) particle motion plane. The comparison of different approaches, including the methods of noninteracting, self-consistent dipoles, and the boundary element method, indicates that the last method is the most suitable for tunable interaction analysis. Thorough analysis, performed for interactions in pairs and clusters of colloidal particles, indicate that two- and three-body interactions make the main contributions in the interaction energy, while the effect of high-order terms is negligible. The tunable interactions are determined by the dielectric properties of the particles and solvent and can be changed in a wide range, providing a rich variety for the experimental "design" of different interactions, including repulsion, attraction, combination of short-range repulsion with long-range attraction, barrier-type interactions with short-range attraction and long-range repulsion, and double-scale repulsive (core-shoulder) interactions. These conclusions can be generalized for magnetically induced tunable interactions. The results indicate that tunable interactions can be widely applied in self-assembly and particle-resolved studies of generic phenomena in fluids and crystals, and, therefore, are of broad interest in the fields of chemical physics, physical chemistry, materials science, and soft matter.

Reconfiguring ferromagnetic microrod chains by alternating two orthogonal magnetic fields

It is well-known that ferromagnetic microrods form linear chains under an external uniform magnetic field B and the chain length is strongly dependent on the applied field, the applied time duration, and the microrod density. When the chains become long enough and the B-field switches to its orthogonal direction, an irreversible morphological transition, i.e. a parallel linear chain array to a 2D network, is observed. The formation of the network depends on the ratio of the average chain length L and separation D, L/D, as well as the magnitude of the changed B-field. When the chain pattern has an L/D larger than a critical value, the network structure will be formed. Such a critical L/D ratio is a monotonic function of B, which determines the bending length of each magnetic chain during the change of B-fields. This morphological change triggered by external magnetic field can be used as scaffolds or building blocks for biological applications or design smart materials.

Self-Assembly of Ionic Microgels Driven by an Alternating Electric Field: Theory, Simulations, and Experiments

The structural properties of a system of ionic microgels under the influence of an alternating electric field are investigated both theoretically and experimentally. This combined investigation aims to shed light on the structural transitions that can be induced by changing either the driving frequency or the strength of the applied field, which range from string-like formation along the field to crystal-like structures across the orthogonal plane. In order to highlight the physical mechanisms responsible for the observed particle self-assembly, we develop a coarse-grained description, in which effective interactions among the charged microgels are induced by both equilibrium ionic distributions and their time-averaged hydrodynamic responses to the applied field. These contributions are modeled by the buildup of an effective dipole moment at the microgels backbones, which is partially screened by their ionic double layer. We show that this description is able to capture the structural properties of this system, allowing for very good agreement with the experimental results. The model coarse-graining parameters are indirectly obtained via the measured pair distribution functions and then further assigned with a clear physical interpretation, allowing us to highlight the main physical mechanisms accounting for the observed self-assembly behavior.

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.

Coarsening dynamics of ferromagnetic granular networks-experimental results and simulations

We investigate the phase separation of a shaken mixture of glass and magnetised steel spheres after a sudden quench of the shaker amplitude. After quenching, transient networks of steel spheres emerge in the experiment. For the developing network clusters we estimate the number of spheres in them, and the characteristic path lengths. We find that both quantities follow a log-normal distribution function. Moreover, we study the temporal evolution of the networks. In the sequence of snapshots we observe an initial regime, where the network incubates, followed by a temporal regime where network structures are elongated and broken, and finally a regime where the structures have relaxed to compact clusters of rounded shapes. This phaenomenology resembles the initial, elastic and hydrodynamic regimes observed by H. Tanaka [J. Phys.: Condens. Matter, 2000, 12, R207] during the viscoelastic phase separation for dynamically asymmetric mixtures of polymers. In order to discriminate the three regimes we investigate in the experiment order parameters like the mean number of neighbors and the efficiency of the networks. In order to capture the origin for a viscoelastic phase separation in our granular mixture, we use a simple simulation approach. Not aiming at a quantitative description of the experimental results, we rather use the simulations to define the key interactions in the experimental system. This way, we discover that along with dipolar and steric interactions, there is an effective central attraction between the magnetised spheres that is responsible for the coarsening dynamics. Our simulations show as well three regimes in the evolution of characteristic order parameters.

Temperature- and field-induced structural transitions in magnetic colloidal clusters

Magnetic colloidal clusters can form chain, ring, and more compact structures depending on their size. In the present investigation we examine the combined effects of temperature and external magnetic field on these configurations by means of extensive Monte Carlo simulations and a dedicated analysis based on inherent structures. Various thermodynamical, geometric, and magnetic properties are calculated and altogether provide evidence for possibly multiple structural transitions at low external magnetic field. Temperature effects are found to overcome the ordering effect of the external field, the melted stated being associated with low magnetization and a greater compactness. Tentative phase diagrams are proposed for selected sizes.

Resonant reshaping of colloidal clusters on a current carrying wire

Colloids in confined geometries promise a path towards tailored microscopic superstructures. Yet, a major roadblock is posed by kinetically trapped states that prevent the assemblies from reaching their anticipated shapes. We investigate magnetic colloids trapped on a cylindrical surface of a current carrying wire. If kinetic traps could be avoided the wire's surface would act as an ideal mold for colloidal rings and helical fibers. We devise here a way to dynamically shake down the clusters and avoid kinetic traps in their energy landscape. A low frequency magnetic modulation wave around the wire axis effectively eliminates defects from the clusters and stretches them into slender rings and helical filaments. A theoretical model is developed that qualitatively explains the observed resonant reshaping response of clusters.

Tunable two-dimensional assembly of colloidal particles in rotating electric fields

Tunable interparticle interactions in colloidal suspensions are of great interest because of their fundamental and practical significance. In this paper we present a new experimental setup for self-assembly of colloidal particles in two-dimensional systems, where the interactions are controlled by external rotating electric fields. The maximal magnitude of the field in a suspension is 25 V/mm, the field homogeneity is better than 1% over the horizontal distance of 250 μm, and the rotation frequency is in the range of 40 Hz to 30 kHz. Based on numerical electrostatic calculations for the developed setup with eight planar electrodes, we found optimal experimental conditions and performed demonstration experiments with a suspension of 2.12 μm silica particles in water. Thanks to its technological flexibility, the setup is well suited for particle-resolved studies of fundamental generic phenomena occurring in classical liquids and solids, and therefore it should be of interest for a broad community of soft matter, photonics, and material science.

Emergence of an enslaved phononic bandgap in a non-equilibrium pseudo-crystal

Material systems that reside far from thermodynamic equilibrium have the potential to exhibit dynamic properties and behaviours resembling those of living organisms. Here we realize a non-equilibrium material characterized by a bandgap whose edge is enslaved to the wavelength of an external coherent drive. The structure dynamically self-assembles into an unconventional pseudo-crystal geometry that equally distributes momentum across elements. The emergent bandgap is bestowed with lifelike properties, such as the ability to self-heal to perturbations and adapt to sudden changes in the drive. We derive an exact analytical solution for both the spatial organization and the bandgap features, revealing the mechanism for enslavement. This work presents a framework for conceiving lifelike non-equilibrium materials and emphasizes the potential for the dynamic imprinting of material properties through external degrees of freedom.

Phase diagram and aggregation dynamics of a monolayer of paramagnetic colloids

We have developed a tunable colloidal system and a corresponding theoretical model for studying the phase behavior of particles assembling under the influence of long-range magnetic interactions. A monolayer of paramagnetic particles is subjected to a spatially uniform magnetic field with a static perpendicular component and a rapidly rotating in-plane component. The sign and strength of the interactions vary with the tilt angle θ of the rotating magnetic field. For a purely in-plane field, θ=90^{∘}, interactions are attractive and the experimental results agree well with both equilibrium and out-of-equilibrium predictions based on a two-body interaction model. For tilt angles 50^{∘}≲θ≲55^{∘}, the two-body interaction gives a short-range attractive and long-range repulsive interaction, which predicts the formation of equilibrium microphases. In experiments, however, a different type of assembly is observed. Inclusion of three-body (and higher-order) terms in the model does not resolve the discrepancy. We further characterize the anomalous regime by measuring the time-dependent cluster size distribution.

Contractile actuation and dynamical gel assembly of paramagnetic filaments in fast precessing fields

Flexible superparamagnetic filaments are studied under the influence of fast precessing magnetic fields using simulations and a continuum approximation analysis. We find that individual filaments can be made to exert controllable tensile forces along the precession axis. These forces are exploited for microscopic actuation. In bulk, the filaments can be rapidly assembled into different configurations whose material properties depend on the field parameters. The precession frequency affects filament aggregation and conformation by changing the net torques on the filament ends. Using a time-dependent precession angle allows considerable freedom in choosing properties for filament aggregates. As an example, we design a field that twists chains together to dynamically assemble a self-healing gel.

Contractile actuation and dynamical gel assembly of paramagnetic filaments in fast precessing fields

Flexible superparamagnetic filaments are studied under the influence of fast precessing magnetic fields using simulations and a continuum approximation analysis. We find that individual filaments can be made to exert controllable tensile forces along the precession axis. These forces are exploited for microscopic actuation. In bulk, the filaments can be rapidly assembled into different configurations whose material properties depend on the field parameters. The precession frequency affects filament aggregation and conformation by changing the net torques on the filament ends. Using a time-dependent precession angle allows considerable freedom in choosing properties for filament aggregates. As an example, we design a field that twists chains together to dynamically assemble a self-healing gel.

Two-dimensional melting of colloids with long-range attractive interactions

The solid-liquid melting transition in a two-dimensional (2-D) attractive colloidal system is visualized using superparamagnetic colloids that interact through a long-range isotropic attractive interaction potential, which is induced using a high-frequency rotating magnetic field. Various experiments, supported by Monte Carlo simulations, are carried out over a range of interaction potentials and densities to determine structure factors, Lindermann parameters, and translational and orientational order parameters. The system shows a first-order solid-liquid melting transition. Simulations and experiments suggest that dislocations and disclinations simultaneously unbind during melting. This is in direct contrast with reports of 2-D melting of paramagnetic particles that interact with a repulsive interaction potential.

Many-body interactions in soft jammed materials

In jammed packings of soft frictionless particles such as foams or emulsions, stress is transmitted via a network of mechanical contacts between neighbors. In generic simplified models of such materials, particle interaction energies are assumed to be pairwise additive. We report ab initio simulations of foam microstructures, showing that in general, this fundamental assumption is not justified: the conservation of bubble volumes introduces a many-body coupling between all the contacts of a given particle. It strongly modifies the relation between forces and displacements at individual contacts, in a way that cannot be captured by an effective two-body interaction. We report the impact of this effect on the linear and nonlinear elastic response of ordered bubble packings with coordination numbers ranging from 6 to 12, used as simple model systems, and we present an analytical model without free parameters which is valid as long as bubbles have an approximately spherical shape. It predicts the many-body coupling of particle contact forces, as well as the macroscopic mechanical response. For packing fractions approaching the jamming transition where contact forces go to zero, we derive an asymptotic two-body interaction law. It contains a logarithmic term, yielding a critical scaling that cannot be approximated by a power law.

Assembly of Superparamagnetic Filaments in External Field

We present a theoretical and simulation study of anchored magneto-elastic filaments in external magnetic field. The filaments are composed of a mixture of superparamagnetic and nonmagnetic colloidal beads interlinked with elastic springs. We explore the steady-state structures of filaments with various composition and bending rigidity subject to external magnetic field parallel to the surface. The interplay of elastic and induced magnetic interactions results in a rich phase behavior with morphologies reminiscent of macromolecular folding: bent filaments, loops, sheets, helicoids, and other collapsed structures. Our results provide new insights into the design of hierarchically assembled supramolecular structures with controlled response to external stimuli.

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.

Modified Mason number for charged paramagnetic colloidal suspensions

The dynamics of magnetorheological fluids have typically been described by the Mason number, a governing parameter defined as the ratio between viscous and magnetic forces in the fluid. For most experimental suspensions of magnetic particles, surface forces, such as steric and electrostatic interactions, can significantly influence the dynamics. Here we propose a theory of a modified Mason number that accounts for surface forces and show that this modified Mason number is a function of interparticle distance. We demonstrate that this modified Mason number is accurate in describing the dynamics of a rotating pair of paramagnetic colloids of identical or mismatched sizes in either high or low salt solutions. The modified Mason number is confirmed to be pseudoconstant for particle pairs and particle chains undergoing a stable-metastable transition during rotation. The interparticle distance term can be calculated using theory or can be measured experimentally. This modified Mason number is more applicable to magnetorheological systems where surface forces are not negligible.

Dynamic Assembly of Magnetic Colloidal Vortices

Magnetic colloids in external time-dependent fields are subject to complex induced many-body interactions governing their self-assembly into a variety of equilibrium and out-of-equilibrium structures such as chains, networks, suspended membranes, and colloidal foams. Here, we report experiments, simulations, and theory probing the dynamic assembly of superparamagnetic colloids in precessing external magnetic fields. Within a range of field frequencies, we observe dynamic large-scale structures such as ordered phases composed of precessing chains, ribbons, and rotating fluidic vortices. We show that the structure formation is inherently coupled to the buildup of torque, which originates from internal relaxation of induced dipoles and from transient correlations among the particles as a result of short-lived chain formation. We discuss in detail the physical properties of the vortex phase and demonstrate its potential in particle-coating applications.

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

We combine experiments and theory to investigate the orientational dynamics of dipolar ellipsoids, which self-assemble into elongated ribbon-like structures due to the presence of a permanent magnetic moment, perpendicular to the long axis in each particle. Monodisperse hematite ellipsoids are synthesized via the sol-gel technique and arrange into ribbons in the presence of static or time-dependent magnetic fields. We find that under an oscillating field, the ribbons reorient perpendicular to the field direction, in contrast with the behaviour observed under a static field. This observation is explained theoretically by treating a chain of interacting ellipsoids as a single particle with orientational and demagnetizing field energy. The model allows us to describe the orientational behaviour of the chain and captures well its dynamics at different strengths of the actuating field. The understanding of the complex dynamics and assembly of anisotropic magnetic colloids is a necessary step for controlling the structure formation, which has direct applications in different fluid-based microscale technologies.

Two-dimensional magnetic colloids under shear

Complex rheological properties of soft disordered solids, such as colloidal gels or glasses, inspire a range of novel applications. However, the microscopic mechanisms of their response to mechanical loading are not well understood. Here, we elucidate some aspects of these mechanisms by studying a versatile model system, i.e. two-dimensional superparamagnetic colloids in a precessing magnetic field, whose structure can be tuned from a hexagonal crystal to a disordered gel network by varying the external field opening angle θ. We perform Langevin dynamics simulations subjecting these structures to a constant shear rate and observe three qualitatively different types of material response. In hexagonal crystals (θ = 0°), at a sufficiently low shear rate, plastic flow occurs via successive stress drops at which the stress releases due to the formation of dislocation defects. The gel network at θ = 48°, on the contrary, via bond rearrangement and transient shear banding evolves into a homogeneously stretched network at large strains. The latter structure remains metastable after switching off of the shear. At θ = 50°, the external shear makes the system unstable against phase separation and causes a failure of the network structure leading to the formation of hexagonal close packed clusters interconnected by particle chains. At a microcopic level, our simulations provide insight into some of the mechanisms by which strain localization as well as material failure occur in a simple gel-like network. Furthermore, we demonstrate that new stretched network structures can be generated by the application of shear.

Minimal model for dynamic bonding in colloidal transient networks

We investigate a model for colloidal network formation using Brownian dynamics computer simulations. Hysteretic springs establish transient bonds between particles with repulsive cores. If a bonded pair of particles is separated by a cutoff distance, the spring vanishes and reappears only if the two particles contact each other. We present results for the bond lifetime distribution and investigate the properties of the van Hove dynamical two-body correlation function. The model displays crossover from fluidlike dynamics, via transient network formation, to arrested quasistatic network behavior.