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

Dynamic response of a ferromagnetic nanofilament under rotating fields: effects of flexibility, thermal fluctuations and hydrodynamics

Using nonequilibrium computer simulations, we study the response of ferromagnetic nanofilaments, consisting of stabilized one dimensional chains of ferromagnetic nanoparticles, under external rotating magnetic fields. In difference with their analogous microscale and stiff counterparts, which have been actively studied in recent years, nonequilibrium properties of rather flexible nanoparticle filaments remain mostly unexplored. By progressively increasing the modeling details, we are able to evidence the qualitative impact of main interactions that can not be neglected at the nanoscale, showing that filament flexibility, thermal fluctuations and hydrodynamic interactions contribute independently to broaden the range of synchronous frequency response in this system. Furthermore, we also show the existence of a limited set of characteristic dynamic filament configurations and discuss in detail the asynchronous response, which at finite temperature becomes probabilistic.

Relating the length of a magnetic filament with solvophobic, superparamagnetic colloids to its properties in applied magnetic fields

The idea of creating polymer-like structures by crosslinking magnetic nanoparticles (MNPs) opened an alternative perspective on controlling the rheological properties of magnetoresponsive systems, because unlike suspensions of self-assembled MNPs, whose cluster sizes are sensitive to temperature, magnetic filaments (MFs) preserve their initial topology. Considering the length scales characteristic of single-domain nanoparticles used to create MFs, the MNPs can be both ferro- and superparamagnetic. Moreover, steric or electrostatic stabilization might not fully screen van der Waals interactions. In this paper, using coarse-grained molecular dynamics simulations, we investigate the influence of susceptibility of superparamagnetic MNPs-their number and central attraction forces between them-on the polymeric, structural, and magnetic properties of MFs with varied backbone rigidity. We find that, due to the general tendency of MFs with superparamagnetic monomers to bend, reinforced for colloids with a high susceptibility, properties of MFs vary greatly with chain length.

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.

Coiling of semiflexible paramagnetic colloidal chains

Semiflexible filaments deform into a variety of configurations that dictate different phenomena manifesting at low Reynolds number. Harnessing the elasticity of these filaments to perform transport-related processes at the microfluidic scale requires structures that can be directly manipulated to attain controllable geometric features during their deformation. The configuration of semiflexible chains assembled from paramagnetic colloids can be readily controlled upon the application of external time-varying magnetic fields. In circularly rotating magnetic fields, these chains undergo coiling dynamics in which their ends close into loops that wrap inward, analogous to the curling of long nylon filaments under shear. The coiling is promising for the precise loading and targeted transport of small materials, however effective implementation requires an understanding of the role that field parameters and chain properties play on the coiling features. Here, we investigate the formation of coils in semiflexible paramagnetic chains using numerical simulations. We demonstrate that the size and shape of the initial coils are governed by the Mason and elastoviscous numbers, related to the field parameters and the chain bending stiffness. The size of the initial coil follows a nonmonotonic behavior with Mason number from which two regions are identified: (1) an elasticity-dependent nonlinear regime in which the coil size decreases with increasing field strength and for which loop shape tends to be circular, and (2) an elasticity-independent linear regime where the size increases with field strength and the shape become more elliptical. From the time scales associated to these regimes, we identify distinct coiling mechanisms for each case that relate the coiling dynamics to two other configurational dynamics of paramagnetic chains: wagging and folding behaviors.

Accelerating the Design of Self-Guided Microrobots in Time-Varying Magnetic Fields

Mobile robots combine sensory information with mechanical actuation to move autonomously through structured environments and perform specific tasks. The miniaturization of such robots to the size of living cells is actively pursued for applications in biomedicine, materials science, and environmental sustainability. Existing microrobots based on field-driven particles rely on knowledge of the particle position and the target destination to control particle motion through fluid environments. Often, however, these external control strategies are challenged by limited information and global actuation where a common field directs multiple robots with unknown positions. In this Perspective, we discuss how time-varying magnetic fields can be used to encode the self-guided behaviors of magnetic particles conditioned on local environmental cues. Programming these behaviors is framed as a design problem: we seek to identify the design variables (e.g., particle shape, magnetization, elasticity, stimuli-response) that achieve the desired performance in a given environment. We discuss strategies for accelerating the design process using automated experiments, computational models, statistical inference, and machine learning approaches. Based on the current understanding of field-driven particle dynamics and existing capabilities for particle fabrication and actuation, we argue that self-guided microrobots with potentially transformative capabilities are close at hand.

Positional ordering induced by dynamic steric interactions in superparamagnetic rods

The dynamic motion produced by precessing magnetic fields can drive matter into far-from-equilibrium states. We predict 1D periodic ordering in systems of precessing rods when magnetic interactions between rods remain insignificant. The precession angle of the rods is completely determined by the field's precession angle and the ratio of the field's precession frequency and the characteristic response frequency of the rods. We develop a molecular dynamics model that explicitly calculates magnetic interactions between particles, and we also simulate rods in the limit of a strong and fast precessing magnetic field where inter-rod magnetic interactions are negligible, using a purely steric model. Our simulations show how steric interactions drive the rods from a positionally disordered phase (nematic) to a layered (smectic) phase. As the rod precession angle increases, the nematic-smectic transition density significantly decreases. The minimization of unfavorable steric interactions also induces phase separation in binary mixtures of rods of different lengths. This effect is general to any force that produces precession in elongated particles. This work will advance the understanding and control of out-of-equilibrium soft matter systems.

Elasticity of Semiflexible ZigZag Nanosprings with a Point Magnetic Moment

Kinks can appear along the contour of semiflexible polymers (biopolymers or synthetic ones), and they affect their elasticity and function. A regular sequence of alternating kink defects can form a semiflexible nanospring. In this article, we theoretically analyze the elastic behavior of such a nanospring with a point magnetic dipole attached to one end while the other end is assumed to be grafted to a rigid substrate. The rod-like segments of the nanospring are treated as weakly bending wormlike chains, and the propagator (Green's function) method is used in order to calculate the conformational and elastic properties of this system. We analytically calculate the distribution of orientational and positional fluctuations of the free end, the force-extension relation, as well as the compressional force that such a spring can exert on a planar wall. Our results show how the magnetic interaction affects the elasticity of the semiflexible nanospring. This sensitivity, which is based on the interplay of positional and orientational degrees of freedom, may prove useful in magnetometry or other applications.

Nanopolymers for magnetic applications: how to choose the architecture?

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

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

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

Periodic deformation of semiflexible colloidal chains in eccentric time-varying magnetic fields

Elastic filaments driven out of equilibrium display complex phenomena that involve periodic changes in their shape. Here, the periodic deformation dynamics of semiflexible colloidal chains in an eccentric magnetic field are presented. This field changes both its magnitude and direction with time, leading to novel nonequilibrium chain structures. Deformation into S-, Z-, and 4-mode shapes arises via the propagation and growth of bending waves. Transitions between these morphologies are governed by an interplay among magnetic, viscous, and elastic forces. Furthermore, the periodic behavior leading to these structures is described by four distinct stages of motion that include rotation, arrest, bending, and stretching of the chain. These stages correspond to specific intervals of the eccentric field's period. A scaling analysis that considers the relative ratio of viscous to magnetic torques via a critical frequency illustrates how to maximize the bending energy. These results provide new insights into controlling colloidal assemblies by applying complex magnetic fields.

Colloidal magnetic brushes: influence of the magnetic content and presence of short-range attractive forces in the micro-structure and field response

The behaviour of supramolecular brushes, whose filaments are composed of sequences of magnetic and non-magnetic colloidal particles, has been studied using Langevin dynamics simulations. Two types of brushes have been considered: sticky or Stockmayer brushes (SB) and non-sticky magnetic brushes (NSB). In both cases, the microstructure and the collective behaviour have been analysed for a wide range of magnetic field strengths including the zero-field case, and negative fields. The results show that, for the same magnetic content, SB placed in a magnetic field present an extensibility up to two times larger than NSB. The analysis of the microstructure of SB at zero field shows that magnetic particles belonging to different filaments in the brush self-organize into ring and chain aggregates, while magnetic colloids in NSB mainly remain in a non-aggregated state. Clustering among magnetic particles belonging to different filaments is observed to gradually fade away as the magnetic content of SB filaments increases towards 100%. Under an external field, SB are observed to form chains, threads and sheets depending on the magnetic content and the applied field strength. The chain-like clusters in SB are observed to decrease in size as the magnetic content in the filaments increases. A non-monotonic field dependence is observed for the average size of these clusters. In spite of the very different microstructure, both NSB and SB are observed to have a very similar magnetization, especially in high strength fields.

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.

Reconfigurable microbots folded from simple colloidal chains

To overcome the reversible nature of low-Reynolds-number flow, a variety of biomimetic microrobotic propulsion schemes and devices capable of rapid transport have been developed. However, these approaches have been typically optimized for a specific function or environment and do not have the flexibility that many real organisms exhibit to thrive in complex microenvironments. Here, inspired by adaptable microbes and using a combination of experiment and simulation, we demonstrate that one-dimensional colloidal chains can fold into geometrically complex morphologies, including helices, plectonemes, lassos, and coils, and translate via multiple mechanisms that can be varied with applied magnetic field. With chains of multiblock asymmetry, the propulsion mode can be switched from bulk to surface-enabled, mimicking the swimming of microorganisms such as flagella-rotating bacteria and tail-whipping sperm and the surface-enabled motion of arching and stretching inchworms and sidewinding snakes. We also demonstrate that reconfigurability enables navigation through three-dimensional and narrow channels simulating capillary blood vessels. Our results show that flexible microdevices based on simple chains can transform both shape and motility under varying magnetic fields, a capability we expect will be particularly beneficial in complex in vivo microenvironments.

Adsorption transition of a grafted ferromagnetic filament controlled by external magnetic fields

Extensive Langevin dynamics simulations are used to characterize the adsorption transition of a flexible magnetic filament grafted onto an attractive planar surface. Our results identify different structural transitions at different ratios of the thermal energy to the surface attraction strength: filament straightening, adsorption, and the magnetic flux closure. The adsorption temperature of a magnetic filament is found to be higher in comparison to an equivalent nonmagnetic chain. The adsorption has been also investigated under the application of a static homogeneous external magnetic field. We found that the strength and the orientation of the field can be used to control the adsorption process, providing a precise switching mechanism. Interestingly, we have observed that the characteristic field strength and tilt angle at the adsorption point are related by a simple power law.

Characterisation of the magnetic response of nanoscale magnetic filaments in applied fields

Incorporating magnetic nanoparticles (MNPs) within permanently crosslinked polymer-like structures opens up the possibility for synthesis of complex, highly magneto-responsive systems. Among such structures are chains of prealigned magnetic (ferro- or super-paramagnetic) monomers, permanently crosslinked by means of macromolecules, which we refer to as magnetic filaments (MFs). In this paper, using molecular dynamics simulations, we encompass filament synthesis scenarios, with a compact set of easily tuneable computational models, where we consider two distinct crosslinking approaches, for both ferromagnetic and super-paramagnetic monomers. We characterise the equilibrium structure, correlations and magnetic properties of MFs in static magnetic fields. Calculations show that MFs with ferromagnetic MNPs in crosslinking scenarios where the dipole moment orientations are decoupled from the filament backbone, have similar properties to MFs with super-paramagnetic monomers. At the same time, magnetic properties of MFs with ferromagnetic MNPs are more dependent on the crosslinking approach than they are for ones with super-paramagnetic monomers. Our results show that, in a strong applied field, MFs with super-paramagnetic MNPs have similar magnetic properties to ferromagnetic ones, while exhibiting higher susceptibility in low fields. We find that MFs with super-paramagnetic MNPs have a tendency to bend the backbone locally rather than to fully stretch along the field. We explain this behaviour by supplementing Flory theory with an explicit dipole-dipole interaction potential, with which we can take in to account folded filament configurations. It turns out that the entropy gain obtained through bending compensates an insignificant loss in dipolar energy for the filament lengths considered in the manuscript.

Crystalline membrane morphology beyond polyhedra

Elastic crystalline membranes exhibit a buckling transition from sphere to polyhedron. However, their morphologies are restricted to convex polyhedra and are difficult to externally control. Here we study morphological changes of closed crystalline membranes of superparamagnetic particles. The competition of magnetic dipole-dipole interactions with the elasticity of this magnetoelastic membrane leads to concave morphologies. Interestingly, as the magnetic field strength increases, the symmetry of the buckled membrane decreases from 5-fold to 3-fold, to 2-fold and, finally, to 1-fold rotational symmetry. This gives the ability to switch the membrane morphology between convex and concave shapes with specific symmetry and provides promising applications for membrane shape control in the design of actuatable microcontainers for targeted delivery systems.

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.

Nonlinear multimode buckling dynamics examined with semiflexible paramagnetic filaments

We present the contractile buckling dynamics of superparamagnetic filaments using experimental, theoretical, and simulation approaches. Under the influence of an orthogonal magnetic field, flexible magnetic filaments exhibit higher-order buckling dynamics that can be identified as occurring in three stages: initiation, development, and decay. Unlike initiation and decay stages where the balance between magnetic interactions and elastic forces is dominant, in the development stage, the influence of hydrodynamic drag results in transient buckling dynamics that is nonlinear along the filament contour. The inhomogeneous temporal evolution of the buckling wavelength is analyzed and the contractions under various conditions are compared.