Multicore-based ferrofluids in zero field: initial magnetic susceptibility and self-assembly mechanisms.

The necessity to improve magnetic building blocks in magnetic nano-structured soft materials stems from a fascinating potential these materials have in bio-medical applications and nanofluidics. Along with practical reasons, the interplay of magnetic and steric interactions on one hand, and entropy, on the other, makes magnetic soft matter fundamentally challenging. Recently, in order to tailor magnetic response of the magnetic particle suspensions, the idea arose to replace standard single-core nanoparticles with nano-sized clusters of single-domain nanoparticles (grains) rigidly bound together by solid polymer matrix - multicore magnetic nanoparticles (MMNPs). To pursue this idea, a profound understanding of the MMNP interactions and self-assembly is required. In this work we present a computational study of the MMNP suspensions and elucidate their self-assembly and magnetic susceptibility. We show that depending on the magnetic moment of individual grains the suspensions exhibit qualitatively distinct regimes. Firstly, if the grains are moderately interacting, they contribute to a significant decrease of the remanent magnetisation of MMNPs and as such to a decrease of the magnetic susceptibility, this way confirming previous findings. If the grains are strongly interacting, instead, they serve as anchor points and support formation of grain clusters that span through several MMNPs, leading to MMNP cluster formation and a drastic increase of the initial magnetic response. Both the topology of the clusters and their size distribution in MMNP suspensions is found to be notably different from those formed in conventional magnetic fluids or magnetorheological suspensions.

Flux and separation of magneto-active superballs in applied fields.

The term "active matter" describes a class of out-of-equilibrium systems, whose ability to transform environmental to kinetic energy is sought after in multiple fields of science. A challenge that still remains is to craft nanometer-sized active particles, whose motion can be efficiently directed by externally applied bio-noninvasive stimuli. Adding a magnetic component and therefore being able to direct the motion of active nanoparticles with an applied magnetic field is one of the promising solutions in the field. In this study, we employ molecular dynamics simulations to predict an external field-induced flow that arises in mixtures of magneto-active nanosized cubic and spherical particles with distinct mutual orientations between magnetization and propulsion. We explain why the flux of the suspended particles in the field direction does not only depend on the angle between the active force, driving a particle forward, and the orientation of its magnetization, but also on particle shape and inter-particle interactions. Our results show that by tuning those parameters, one can achieve complete separation of particles according to their magnetization orientation. Based on our findings, along with optimizing the cargo properties of magneto-active nano-units, the actual composition of the magneto-active particle suspension can be characterized.

Self-assembly of charged colloidal cubes.

In this work, we show how and why the interactions between charged cubic colloids range from radially isotropic to strongly directionally anisotropic, depending on tuneable factors. Using molecular dynamics simulations, we illustrate the effects of typical solvents to complement experimental investigations of cube assembly. We find that in low-salinity water solutions, where cube self-assembly is observed, the colloidal shape anisotropy leads to the strongest attraction along the corner-to-corner line, followed by edge-to-edge, with a face-to-face configuration of the cubes only becoming energetically favorable after the colloids have collapsed into the van der Waals attraction minimum. Analysing the potential of mean force between colloids with varied cubicity, we identify the origin of the asymmetric microstructures seen in experiment.

Modeling the magnetostriction effect in elastomers with magnetically soft and hard particles.

We analyze theoretically the field-induced microstructural deformations in a hybrid elastomer, that consists of a polymer matrix filled with a mixture of magnetically soft and magnetically hard spherical microparticles. These composites were introduced recently in order to obtain a material that allows the tuning of its properties by both, magnetically active and passive control. Our theoretical analysis puts forward two complementary models: a continuum magnetomechanical model and a bead-spring computer simulation model. We use both approaches to describe qualitatively the microstructural response of such elastomers to applied external fields, showing that the combination of magnetically soft and hard particles may lead to an unusual magnetostriction effect: either an elongation or a shrinking in the direction of the applied field depending on its magnitude. This behavior is observed for conditions (moderate particle densities, fields and deformations) under which the approximations of our models (linear response regime, negligible mutual magnetization between magnetically soft particles) are physically valid.

Surface relief of magnetoactive elastomeric films in a homogeneous magnetic field: molecular dynamics simulations.

The structure of a thin magnetoactive elastomeric (MAE) film adsorbed on a solid substrate is studied by molecular dynamics simulations. Within the adopted coarse-grained approach, a MAE film consists of magnetic particles modeled as soft-core spheres, carrying point dipoles, connected by elastic springs representing a polymer matrix. MAE films containing 20, 25 and 30 vol% of randomly distributed magnetic particles are simulated. Once a magnetic field is applied, the competition between dipolar, elastic and Zeeman forces leads to the restructuring of the layer. The distribution of the magnetic particles as well as elastic strains within the MAE films are calculated for various magnetic fields applied perpendicular to the film surface. It is shown that the surface roughness increases strongly with growing magnetic field. For a given magnetic field, the roughness is larger for the softer polymeric matrix and exhibits a nonmonotonic dependence on the magnetic particle concentration. The obtained results provide a better understanding of the MAE surface structuring as well as possible guidelines for fabrication of MAE films with a tunable surface topology.

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.

Importance of matrix inelastic deformations in the initial response of magnetic elastomers.

Being able to predict and understand the behaviour of soft magnetic materials paves the way to their technological applications. In this study we analyse the magnetic response of soft magnetic elastomers (SMEs) with magnetically hard particles. We present experimental evidence of a difference between the first and next magnetisation loops exhibited by these SMEs, which depends non-monotonically on the interplay between the rigidity of the polymer matrix, its mechanical coupling with the particles, and the magnetic interactions in the system. In order to explain the microstructural mechanism behind this behaviour, we used a minimal computer simulation model whose results evidence the importance of irreversible matrix deformations due to both translations and rotations of the particles. To confirm the simulation findings, computed tomography (CT) was used. We conclude that the initial exposure to the field triggers the inelastic matrix relaxation in the SMEs, as particles attempt to reorient. However, once the necessary degree of freedom is achieved, both the rotations and the magnetisation behaviour become stationary. We expect this scenario not only to be limited to the materials studied here, but also to apply to a broader class of hybrid SMEs.

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 in dipolar cube fluids constrained by competing anisotropies.

For magnetite spherical nanoparticles, the orientation of the dipole moment in the crystal does not affect the morphology of either zero field or field induced structures. For non-spherical particles however, an interplay between particle shape and direction of the magnetic moment can give rise to unusual behaviors, in particular when the moment is not aligned along a particle symmetry axis. Here we disclose for the first time the unique magnetic properties of hematite cubic particles and show the exact orientation of the cubes' dipole moment. Using a combination of experiments and computer simulations, we show that dipolar hematite cubes self-organize into dipolar chains with morphologies remarkably different from those of spheres, and demonstrate that the emergence of these structures is driven by competing anisotropic interactions caused by the particles' shape anisotropy and their fixed dipole moment. Furthermore, we have analytically identified a specific interplay between energy, and entropy at the microscopic level and found that an unorthodox entropic contribution mediates the organization of particles into the kinked nature of the dipolar chains.

Compressibility of ferrofluids: Towards a better understanding of structural properties.

This paper addresses a computational method aimed at obtaining the isothermal compressibility of ferrofluids by means of molecular dynamics (MD) simulations. We model ferrofluids as a system of dipolar soft spheres and carry out MD simulations in the NPT ensemble. The obtained isothermal compressibility computed via volume fluctuations provides us with a strong evidence that dipolar interactions lead to a higher compressibility of dipolar soft sphere systems: the stronger the dipolar interactions, the bigger is the deviation of the compressibility from the one of a system with no dipoles. Furthermore, we use the isothermal compressibility to calculate the structure factor of ferrofluids at low values of wave vectors, i.e. in the range where it is difficult to predict its behaviour because of a problem with accounting for long-range particle correlations that give the main contribution to the structure factor in this range. Our approach based on the interpolation of the structure factor and the computed isothermal compressibility allows us to obtain the smooth structure factor in the range of low wave vectors and the reliable fractal dimension of the clusters formed in the system.

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.

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.

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.

Revealing the signature of dipolar interactions in dynamic spectra of polydisperse magnetic nanoparticles.

We investigate, via a modified mean field approach, the dynamic magnetic response of a polydisperse dipolar suspension to a weak, linearly polarised, AC field. We introduce an additional term into the Fokker-Planck equation, which takes into account dipole-dipole interaction in the form of the first order perturbation, and allows for particle polydispersity. The analytical expressions, obtained for the real and imaginary dynamic susceptibilities, predict three measurable effects: the increase of the real part low-frequency plateaux; the enhanced growth of the imaginary part in the low-frequency range; and the shift of the imaginary part maximum. Our theoretical predictions find an experimental confirmation and explain the changes in the spectrum.

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

The interweave of competing individual relaxations influenced by the presence of temperature and concentration dependent correlations is an intrinsic feature of superparamagnetic nanoparticle suspensions. This unique combination gives rise to multiple applications of such suspensions in medicine, nanotechnology and microfluidics. Here, using theory and experiment, we investigate dynamic magnetic susceptibility in a broad range of temperatures and frequencies. Our approach allows, for the first time to our knowledge, to separate clearly the effects of superparamagnetic particle polydispersity and interparticle magnetic interactions on the dynamic spectra of these systems. In this way, we not only provide a theoretical model that can predict well the dynamic response of magnetic nanoparticles systems, but also deepen the understanding of the dynamic nanoparticle self-assembly, opening new perspectives in tuning and controlling the magnetic behaviour of such systems in AC fields.

The behavior of a magnetic filament in flow under the influence of an external magnetic field.

We present an extensive numerical study of the behaviour of a filament made of ferromagnetic colloidal particles subjected to the simultaneous action of a fluid flow and a stationary external magnetic field perpendicular to the flow lines. We found that in the presence of a shear flow, the tumbling motion observed at zero field is strongly inhibited when the external magnetic field is applied. The field is able to stabilise the filament with a well defined degree of alignment that depends on the balance between hydrodynamic and magnetic torques. In addition, for a Poiseuille flow, it has been found that the initial position has a long lasting influence on the behaviour of the magnetic filament when the external field is applied.

The effect of links on the interparticle dipolar correlations in supramolecular magnetic filaments.

We present a combined computational and analytical study of supramolecular magnetic filaments, i.e., permanently linked chains of ferromagnetic nanocolloids. We put forward two different models for the interparticle connectivity within the chain. In the first model, the magnetic dipoles of the particles are free to rotate independently from the permanent links. The second model penalises the misalignment of the dipoles by coupling their orientations to the chain backbone. We show that the effect of the long-range magnetic dipolar interactions on the zero field net magnetic moment of the chain becomes less significant in the second case. However, the overall magnetic response in the model of freely rotating dipoles is much weaker.

Nematic phase characterisation of the self-assembling sphere-cylinders based on the theoretically calculated RDFs.

We put forward a theoretical framework to calculate pair distribution functions in the nematic liquid crystals formed by sphere-cylinders that self-assemble in linear chain structures. For a nematically ordered system, one can distinguish between the spatial correlations in the plane perpendicular to the crystalline axis, and in the direction parallel to the latter. Following this separation, we show that the RDFs in the parallel case can be described using a superposition of a chain model and Onsager distribution, whereas the RDFs in the perpendicular case turn out to be that of the soft disks. Based on this concept, we show how the spatial correlations in the system are influenced by the nematic order parameter. We conclude that even if the nematic ordering is high in the system, the imperfection of the crystal is strongly reflected in the pair distributions.

Temperature-induced structural transitions in self-assembling magnetic nanocolloids.

With the help of a unique combination of density functional theory and computer simulations, we discover two possible scenarios, depending on concentration, for the hierarchical self-assembly of magnetic nanoparticles on cooling. We show that typically considered low temperature clusters, i.e. defect-free chains and rings, merge into more complex branched structures through only three types of defects: four-way X junctions, three-way Y junctions and two-way Z junctions. Our accurate calculations reveal the predominance of weakly magnetically responsive rings cross-linked by X defects at the lowest temperatures. We thus provide a strategy to fine-tune magnetic and thermodynamic responses of magnetic nanocolloids to be used in medical and microfluidics applications.

Structure and dynamics in suspensions of magnetic platelets.

In this research, we employ Brownian dynamics simulations, density functional theory, and mean-field theory to explore the profound influence of shape anisotropy of magnetic nanoplatelets on suspension magnetic response. Each platelet is modelled as an oblate cylinder with a longitudinal point dipole, with an emphasis on strong dipolar interactions conducive to self-assembly. We investigate static structural and magnetic properties, characterising the system through pair distribution function, static structure factor, and cluster-size distribution. The findings demonstrate that shape-specific interactions and clustering lead to significant changes in reorientational relaxation times. Under zero field, distinctive modes in the dynamic magnetic susceptibility identify individual particles and particle clusters. In the presence of an applied field, the characteristic relaxation time of clusters increases, while that of single particles decreases. This research provides insights into the intricate interplay between shape anisotropy, clustering, and magnetic response in platelet suspensions, offering valuable perspectives for recent experimental observations.