Core-shell nanogels: the effects of morphology, electro- and magnetostatic interactions

We study the influence of core-shell morphology on the structural characteristics of nanogels. Using computer simulations, we examine three different types of systems, distinguished by their intermonomer interactions: those with excluded volume only; those with charged monomers and excluded volume; and those with excluded volume combined with a certain number of magnetised nanoparticles incorporated within the nanogel. We observe that if the polymers in the shell are short and dense, they tend to penetrate the core. This effect of backfolding is enhanced in charged nanogels, regardless of whether all monomers are charged, or only the core or shell ones. The presence of an experimentally available amount of magnetic nanoparticles in a gel, on the one hand, does not lead to any significant morphological changes. On the other hand, the morphology of the nanogel with magnetic particles has an impact on its magnetic susceptibility. Particular growth of the magnetic response is observed if a long shell of a nanogel is functionalised.

Phase separation of a magnetic fluid: Asymptotic states and nonequilibrium kinetics

We study self-assembly in a colloidal suspension of magnetic particles by performing comprehensive molecular dynamics simulations of the Stockmayer (SM) model, which comprises spherical particles decorated by a magnetic moment. The SM potential incorporates dipole-dipole interactions along with the usual Lennard-Jones interaction and exhibits a gas-liquid phase coexistence observed experimentally in magnetic fluids. When this system is quenched from the high-temperature homogeneous phase to the coexistence region, the nonequilibrium evolution to the condensed phase proceeds with the development of spatial as well as magnetic order. We observe density-dependent coarsening mechanisms-a diffusive growth law ℓ(t)∼t^{1/3} in the nucleation regime and hydrodynamics-driven inertial growth law ℓ(t)∼t^{2/3} in the spinodal regimes. [ℓ(t) is the average size of the condensate at time t after the quench.] While the spatial growth is governed by the expected conserved order parameter dynamics, the growth of magnetic order in the spinodal regime exhibits unexpected nonconserved dynamics. The asymptotic morphologies have density-dependent shapes which typically include the isotropic sphere and spherical bubble morphologies in the nucleation region, and the anisotropic cylinder, planar slab, cylindrical bubble morphologies in the spinodal region. The structures are robust and nonvolatile, and exhibit characteristic magnetic properties. For example, the oppositely magnetized hemispheres in the spherical morphology impart the characteristics of a Janus particle to it. The observed structures have versatile applications in catalysis, drug delivery systems, memory devices, and magnetic photonic crystals, to name a few.

The relevance of curvature-induced quadrupolar interactions in dipolar chain aggregation

The aggregation of dipolar chains driven by thermal fluctuations in an external strong (electric or magnetic) field is investigated theoretically. We discover a new simple electrostatic mechanism that rationalizes the counter-intuitive lateral coalescence of dipolar chains. There, we first demonstrate that two bent dipolar chains can either attract or repel each other depending if they possess similar or opposite curvatures, respectively. Upon bending, dipolar chains become the siege of polarization-induced local charges that in turn lead to quadrupolar couplings. This striking feature is then exploited to understand our conducted Monte Carlo simulations at finite temperature where thermal fluctuations cause local curvatures in the formed dipolar chains. The related quadrupolar attractive mode with correlated chain-curvatures is clearly identified in the simulation snapshots. Our findings shed new light on a longstanding problem in soft matter and related areas.

Controlling the coarsening dynamics of ferrogranular networks by means of a vertical magnetic field

We are exploring in experiments the aggregation process in a shaken granular mixture of glass and magnetized steel beads, filled in a horizontal vessel, after the shaking amplitude is suddenly decreased. Then the magnetized beads form a transient network that coarsens in time into compact clusters, resembling a viscoelastic phase separation [Tanaka, J. Phys.: Condens. Matter 12, R207 (2000)0953-898410.1088/0953-8984/12/15/201], where attached beads represent the slow phase. Here we investigate how a homogeneous magnetic field oriented in vertical direction impedes the emergence and growth of the networks. With increasing field amplitude this phase is replaced by a fluctuating arrangement of repelling, isolated steel beads. The experimental results are compared with those of computer simulations. Coarse-grained molecular dynamics confirms the impact of an applied magnetic field on the structural transitions and allows us to investigate long-time regimes and magnetic response not yet accessible in the experiment. It turns out that an applied magnetic field has different impacts, depending on it strength. It can be used either to slow down the dynamics of the structural transitions without changing the type of the resulting phases and only affecting the amount and sizes of clusters, or to fully impede the formation of network-like and compact aggregates of steel beads.

Self-assembly and percolation in two dimensional binary magnetic colloids

We study the self-assembly of branching-chain networks and crystals in a binary colloidal system with tunable interactions. The particle positions are extracted from microscopy images and order parameters are extracted by image processing and statistical analysis. With these, we construct phase diagrams with respect to particle density, ratio and interaction. In order to draw a more complete picture, we complement the experiments with computer simulations. We establish a region in the phase diagram, where bead ratios and interactions are symmetric, promoting percolated structures.

How chains and rings affect the dynamic magnetic susceptibility of a highly clustered ferrofluid

The dynamic magnetic susceptibility, χ(ω), of a model ferrofluid at a very low concentration (volume fraction, approximately 0.05%), and with a range of dipolar coupling constants (1≤λ≤8), is examined using Brownian dynamics simulations. With increasing λ, the structural motifs in the system change from unclustered particles, through chains, to rings. This gives rise to a nonmonotonic dependence of the static susceptibility χ(0) on λ and qualitative changes to the frequency spectrum. The behavior of χ(0) is already understood, and the simulation results are compared to an existing theory. The single-particle rotational dynamics are characterized by the Brownian time, τ_{B}, which depends on the particle size, carrier-liquid viscosity, and temperature. With λ≤5.5, the imaginary part of the spectrum, χ^{''}(ω), shows a single peak near ω∼τ_{B}^{-1}, characteristic of single particles. With λ≥5.75, the spectrum is dominated by the low-frequency response of chains. With λ≥7, new features appear at high frequency, which correspond to intracluster motions of dipoles within chains and rings. The peak frequency corresponding to these intracluster motions can be computed accurately using a simple theory.

Magnetic Coupling in Colloidal Clusters for Hierarchical Self-Assembly

Manipulating the way in which colloidal particles self-organize is a central challenge in the design of functional soft materials. Meeting this challenge requires the use of building blocks that interact with one another in a highly specific manner. Their fabrication, however, is limited by the complexity of the available synthesis procedures. Here, we demonstrate that, starting from experimentally available magnetic colloids, we can create a variety of complex building blocks suitable for hierarchical self-organization through a simple scalable process. Using computer simulations, we compress spherical and cubic magnetic colloids in spherical confinement, and investigate their suitability to form small clusters with reproducible structural and magnetic properties. We find that, while the structure of these clusters is highly reproducible, their magnetic character depends on the particle shape. Only spherical particles have the rotational degrees of freedom to produce consistent magnetic configurations, whereas cubic particles frustrate the minimization of the cluster energy, resulting in various magnetic configurations. To highlight their potential for self-assembly, we demonstrate that already clusters of three magnetic particles form highly nontrivial Archimedean lattices, namely, staggered kagome, bounce, and honeycomb, when focusing on different aspects of the same monolayer structure. The work presented here offers a conceptually different way to design materials by utilizing preassembled magnetic building blocks that can readily self-organize into complex structures.

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.

An Expanded State Diagram for the Directed Self-Assembly of Colloidal Suspensions in Toggled Fields

The suspension structure and assembly kinetics of micrometer-diameter paramagnetic spheres in toggled magnetic fields are investigated at a constant field strength H = 1750A·m^-1 while toggling the field on and off over the frequency range 0.3<f<5 Hz and duty ratio values (the fraction of time the field is on over one toggle period) 0.05 ≤ ξ ≤ 0.8. Five microstructures form after sufficient time in the toggled field, fluid, columnar, percolated, ellipsoidal-shaped, and perpendicular, and their kinetic pathways are identified. For ellipsoidal-shaped microstructures, diffusion-driven particle aggregation at early times gives way to a fluid-like breakup. For columnar and percolated structures, this coarsening arrests before breakup. As the toggling duty cycle decreases, the range of frequencies for each structure narrows, giving way to an unstructured fluid; below ξ<0.1, only the fluid state is observed. The existence of fluid, columnar, percolated, and ellipsoidal-shaped microstructures agrees well with those predicted by the theoretical and computational work of Sherman et al. (Sherman, Z. M.; Rosenthal, H.; Swan, J. W. Langmuir 2018, 34, 1029-1041). Microstructures that connect perpendicularly to the magnetic field are identified for 0.1 ≤ ξ ≤ 0.3 and 1.6<f<3.7 Hz. Perpendicular microstructures also exhibit emergent dynamics with continuous rotation, breakup, and coalescence events.

Clustering and phase separation in mixtures of dipolar and active particles

The self-assembly of colloidal particles in dynamic environments has become an important field of study because of potential applications in fabricating out-of-equilibrium materials. We investigate the phase behavior of mixtures of passive dipolar colloids and active soft spheres using Brownian dynamics simulations in two dimensions. The phase behaviors exhibited include dipolar percolated network, dipolar string-fluid, isotropic fluid, and a phase-separated state. We find that the clustering of dipolar colloids is enhanced in the presence of slow-moving active particles compared to the clustering of dipolar particles mixed with passive particles. When the active particle motility is high, the chains of dipolar particles are either broken into short chains or pushed into dense clusters. Motility-induced phase separation into dense and dilute phases is also present. The area fraction of particles in the dilute phase increases as the fraction of active particles in the system decreases, while the area fraction of particles in the dense phase remains constant. Our findings are relevant to the development of reconfigurable self-assembled materials.

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

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

The structure of clusters formed by Stockmayer supracolloidal magnetic polymers

Unlike Stockmayer fluids, that prove to undergo gas-liquid transition on cooling, the system of dipolar hard or soft spheres without any additional central attraction so far has not been shown to have a critical point. Instead, in the latter, one observes diverse self-assembly scenarios. Crosslinking dipolar soft spheres into supracolloidal magnetic polymer-like structures (SMPs) changes the self-assembly behaviour. Moreover, aggregation in systems of SMPs strongly depends on the constituent topology. For Y- and X-shaped SMPs, under the same conditions in which dipolar hard spheres would form chains, the formation of very large loose gel-like clusters was observed (E. Novak et al., J. Mol. Liq. 271, 631 (2018)). In this work, using molecular dynamics simulations, we investigate the self-assembly in suspensions of four topologically different SMPs --chains, rings, X and Y-- whose monomers interact via Stockmayer potential. As expected, compact drop-like clusters are formed by SMPs in all cases if the central isotropic attraction is introduced, however, their shape and internal structure turn out to depend on the SMPs topology.

Field-responsive colloidal assemblies defined by magnetic anisotropy

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

Zero-Field and Field-Induced Interactions between Multicore Magnetic Nanoparticles

In this paper, the Langevin dynamics simulation method is used to study magnetic interactions between a pair of multicore magnetic nanoparticles subjected to a uniform magnetic field. Multicore nanoparticles are modelled as spherical rigid clusters of single-domain superparamagnetic cores coupled via dipole-dipole interactions. It is shown that the magnetic force between two well-separated clusters in a strong applied field can be accurately described within the induced point-dipole approximation. However, this approximation also assumes that there are no interactions between clusters in the zero-field limit. On the contrary, simulations indicate the existence of a relatively small attractive magnetic force between clusters, even in the absence of an applied field. It is shown that this force is a direct superparamagnetic analog of the van der Waals interaction between a pair of dielectric spheres.

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.

Self-organization and stability of magnetosome chains-A simulation study

Magnetotactic bacteria orient in magnetic fields with the help of their magnetosome chain, a linear structure of membrane enclosed magnetic nanoparticles (magnetosomes) anchored to a cytoskeletal filament. Here, we use simulations to study the assembly and the stability of magnetosome chains. We introduce a computational model describing the attachment of the magnetosomes to the filament and their magnetic interactions. We show that the filamentous backbone is crucial for the robust assembly of the magnetic particles into a linear chain, which in turn is key for the functionality of the chain in cellular orientation and magnetically directed swimming. In addition, we simulate the response to an external magnetic field that is rotated away from the axis of the filament, an experimental method used to probe the mechanical stability of the chain. The competition between alignment along the filament and alignment with the external fields leads to the rupture of a chain if the applied field exceeeds a threshold value. These observations are in agreement with previous experiments at the population level. Beyond that, our simulations provide a detailed picture of chain rupture at the single cell level, which is found to happen through two abrupt events, which both depend on the field strength and orientation. The re-formation of the chain structure after such rupture is found to be strongly sped up in the presence of a magnetic field parallel to the filament, an observation that may also be of interest for the design of self-healing materials. Our simulations underline the dynamic nature of the magnetosome chain. More generally, they show the rich complexity of self-assembly in systems with competing driving forces for alignment.

Free energy calculations for rings and chains formed by dipolar hard spheres

We employ a method based on Monte Carlo grand-canonical simulations to precisely calculate partition functions of non-interacting chains and rings formed by dipolar hard spheres (DHS) at low temperature. The extended low temperature region offered by such cluster calculations, compared to what had been previously achieved with standard simulations, opens up the possibility of exploring a part of the DHS phase diagram which was inaccessible before. The reported results offer the unique opportunity of verifying well-established theoretical models based on the ideal gas of cluster approximation in order to clarify their range of validity. They also provide the basis for future studies in which cluster-cluster interactions will be included.

Scattering properties and internal structure of magnetic filament brushes

Practical applications of polymer brush-like systems rely on a clear understanding of their internal structure. In the case of magnetic nanoparticle filament brushes, the competition between bonding and nonbonding interactions-including long range magnetic dipole-dipole interactions-makes the microstructure of these polymer brush-like systems rather complex. On the other hand, the same interactions open up the possibility to manipulate the meso- and macroscopic responses of these systems by applying external magnetic fields or by changing the background temperature. In this study, we put forward an approach to extract information about the internal structure of a magnetic filament brush from scattering experiments. Our method is based on the mapping of the scattering profiles to the information about the internal equilibrium configurations of the brushes obtained from computer simulations. We show that the structure of the magnetic filament brush is strongly anisotropic in the direction perpendicular to the grafting surface, especially at low temperatures and external fields. This makes slice-by-slice scattering measurements a technique very useful for the study of such systems.

Monte Carlo simulation of magnetic domain structure and magnetic properties near the morphotropic phase boundary

The morphotropic phase boundary (MPB), which is the boundary separating a tetragonal phase from a rhombohedral phase by varying the composition or mechanical pressure in ferroelectrics, has been studied extensively for decades because it can lead to strong enhancement of piezoelectricity. Recently, a parallel ferromagnetic MPB was experimentally reported in the TbCo₂-DyCo₂ ferromagnetic system and this discovery proposes a new way to develop potential materials with giant magnetostriction. However, the role of magnetic domain switching and spin reorientation near the MPB region is still unclear. For the first time, we combine micromagnetic theory with Monte Carlo simulation to investigate the evolution of magnetic domain structures and the corresponding magnetization properties near the MPB region. It is demonstrated that the magnetic domain structure and the corresponding magnetization properties are determined by the interplay among anisotropy energy, magnetostatic energy and exchange energy. If the anisotropy energy barrier is large compared with the magnetostatic energy barrier and the exchange energy barrier, the MPB region is a T and R mixed structure and magnetic domain switching is the dominant mechanism. If the anisotropy energy barrier is small, the MPB region will also contain M phases and spin reorientation is the dominant mechanism. Our work could provide a guide for the design of advanced ferromagnetic materials with enhanced magnetostriction.

Self-Assembly of Colloidal Nanocrystals: From Intricate Structures to Functional Materials

Chemical methods developed over the past two decades enable preparation of colloidal nanocrystals with uniform size and shape. These Brownian objects readily order into superlattices. Recently, the range of accessible inorganic cores and tunable surface chemistries dramatically increased, expanding the set of nanocrystal arrangements experimentally attainable. In this review, we discuss efforts to create next-generation materials via bottom-up organization of nanocrystals with preprogrammed functionality and self-assembly instructions. This process is often driven by both interparticle interactions and the influence of the assembly environment. The introduction provides the reader with a practical overview of nanocrystal synthesis, self-assembly, and superlattice characterization. We then summarize the theory of nanocrystal interactions and examine fundamental principles governing nanocrystal self-assembly from hard and soft particle perspectives borrowed from the comparatively established fields of micrometer colloids and block copolymer assembly. We outline the extensive catalog of superlattices prepared to date using hydrocarbon-capped nanocrystals with spherical, polyhedral, rod, plate, and branched inorganic core shapes, as well as those obtained by mixing combinations thereof. We also provide an overview of structural defects in nanocrystal superlattices. We then explore the unique possibilities offered by leveraging nontraditional surface chemistries and assembly environments to control superlattice structure and produce nonbulk assemblies. We end with a discussion of the unique optical, magnetic, electronic, and catalytic properties of ordered nanocrystal superlattices, and the coming advances required to make use of this new class of solids.

Ring formation in the quasi-two-dimensional system of the patchy magnetic spheres

Fabricating new functional materials has always been at the center of colloidal science, and how to form circular rings is a meaningful challenge due to their special electronic, magnetic and optical properties. Magnetic colloidal spheres can self-assemble into rings, but these rings have an uncontrollable length and shape and also have to coexist with chains and defected clusters. To make the most of magnetic spheres being able to self-assemble into rings, a patch is added to the surface of the sphere to form a chiral link between particles. The structural transition in the system of patchy magnetic spheres is studied using the Monte Carlo simulation. When the patch angle is in the interval 60° to 75°, rings become the dominant structure if the strength of patchy interaction exceeds a particular threshold and the shape of these rings is close to the circle. With an increase in the patch angle, the threshold of patchy interaction decreases and the average length of the circular ring increases approximately from 5 to 8.5.

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

We consider a model of colloidal spherical particles carrying a permanent dipole moment which is laterally shifted out of the particles' geometrical centres, i.e. the dipole vector is oriented perpendicular to the radius of the particles. Varying the shift δ from the centre, we analyse ground state structures for two, three and four hard spheres, using a simulated annealing procedure. We also compare earlier ground state results. We then consider a bulk system at finite temperatures and different densities. Using molecular dynamics simulations, we examine the equilibrium self-assembly properties for several shifts. Our results show that the shift of the dipole moment has a crucial impact on both the ground state configurations as well as the self-assembled structures at finite temperatures.

Magnetic filament brushes: tuning the properties of a magnetoresponsive supracolloidal coating

We present a theoretical study on the design of a supramolecular magnetoresponsive coating. The coating is formed by a relatively dense array of supracolloidal magnetic filaments grafted to a surface in a polymer brush-like arrangement. In order to determine and optimise the properties of the magnetic filament brush, we perform extensive computer simulations with a coarse-grained model that takes into account the correlations between the magnetic moments of the particles and the backbone crosslinks. We show that the self-assembly of magnetic beads from neighbouring filaments defines the equilibrium structural properties of the complete brush. In order to control this self-assembly, we highlight two external stimuli that can lead to significant effects: temperature of the system and an externally applied magnetic field. Our study reveals self-assembly scenarios inherently driven by the crosslinking and grafting constraints. Finally, we explain the mechanisms of structural changeovers in the magnetic filament brushes and confirm the possibility of controlling them by changing the temperature or the intensity of an external magnetic field.

Temperature-dependent dynamic correlations in suspensions of magnetic nanoparticles in a broad range of concentrations: a combined experimental and theoretical study

We study the effects of temperature and concentration on the dynamic spectra of polydisperse magnetic nanoparticle suspensions.