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.

Structural transitions and magnetic response of supramolecular magnetic polymerlike structures with bidisperse monomers.

Supramolecular magnetic polymerlike (SMP) structures are nanoscaled objects that combine the flexibility of polymeric conformations and controllability of magnetic nanoparticles. The advantage provided by the presence of permanent cross-linkers is that even at high temperature, a condition at which entropy dominates over magnetic interactions, the length and the topology of the SMP structures are preserved. On cooling, however, preexistent bonds constrain thermodynamically equilibrium configurations, making a low-temperature regime for SMP structures worth investigating in detail. Moreover, making SMP structures with perfectly monodisperse monomers has been a challenge. Thus, the second open problem in the application of SMP structures is the missing understanding of the polydispersity impact on their structural and magnetic properties. Here extensive Langevin dynamics simulations combined with parallel tempering method are used to investigate SMP structures of four different types, i.e., chainlike, Y-like, X-like, and ringlike, composed of monomers of two different sizes. Our results show that the presence of small particles in SMP structures can qualitatively change the magnetic response at low temperature, making those structures surprisingly more magnetically responsive than their monodisperse counterparts.

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.

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.

Magnetic responsive brushes under flow in strongly confined slits: external field control of brush structure and flowing particle mixture separation.

In the present work magnetic brushes under flow conditions and confined inside narrow slits have been studied using Langevin dynamics simulations. It has been observed that the structural properties of these confined magnetic brushes can be tuned via the application of an external magnetic field, and this control can be exerted with a relatively low content of magnetic colloidal particles in the filaments that form the brushes (20% in the present study). The potential of these brushes to perform a separation process of a size-bidispersed mixture of free non-magnetic colloidal particles flowing through the slit has also been explored. Numerical results show that it is possible to induce a two-fold effect on the bidispersed particle flow: a lateral separation of the two types of flowing colloidal particles and an enhancement of the differences in their velocities. These two features are key elements sought in separation processes and could be very relevant in the design of new chromatographic columns and microfluid separation devices.

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.

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.

Nanoparticle Shape Influences the Magnetic Response of Ferro-Colloids.

The interesting magnetic response of conventional ferro-colloid has proved extremely useful in a wide range of technical applications. Furthermore, the use of nano/micro- sized magnetic particles has proliferated cutting-edge medical research, such as drug targeting and hyperthermia. In order to diversify and improve the application of such systems, new avenues of functionality must be explored. Current efforts focus on incorporating directional interactions that are surplus to the intrinsic magnetic one. This additional directionality can be conveniently introduced by considering systems composed of magnetic particles of different shapes. Here we present a combined analytical and simulation study of permanently magnetized dipolar superball particles; a geometry that closely resembles magnetic cubes synthesized in experiments. We have focused on determining the initial magnetic susceptibility of these particles in dilute suspensions, seeking to quantify the effect of the superball shape parameter on the system response. In turn, we linked the computed susceptibilities to the system microstructure by analyzing cluster composition using a connectivity network analysis. Our study has shown that by increasing the shape parameter of these superball particles, one can alter the outcome of self-assembly processes, leading to the observation of an unanticipated decrease in the initial static magnetic susceptibility.

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.

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.

Supramolecular Magnetic Brushes: The Impact of Dipolar Interactions on the Equilibrium Structure.

The equilibrium structure of supramolecular magnetic filament brushes is analyzed at two different scales. First, we study the density and height distributions for brushes with various grafting densities and chain lengths. We use Langevin dynamics simulations with a bead-spring model that takes into account the cross-links between the surface of the ferromagnetic particles, whose magnetization is characterized by a point dipole. Magnetic filament brushes are shown to be more compact near the substrate than nonmagnetic ones, with a bimodal height distribution for large grafting densities. This latter feature makes them also different from brushes with electric dipoles. Next, in order to explain the observed behavior at the filament scale, we introduce a graph theory analysis to elucidate for the first time the structure of the brush at the scale of individual beads. It turns out that, in contrast to nonmagnetic brushes, in which the internal structure is determined by random density fluctuations, magnetic forces introduce a certain order in the system. Because of their highly directional nature, magnetic dipolar interactions prevent some of the random connections to be formed. On the other hand, they favor a higher connectivity of the chains' free and grafted ends. We show that this complex dipolar brush microstructure has a strong impact on the magnetic response of the brush, as any weak applied field has to compete with the dipole-dipole interactions within the crowded environment.

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.

Behaviour of magnetic Janus-like colloids.

We present a theoretical study of Janus-like magnetic particles at low temperature. To describe the basic features of the Janus-type magnetic colloids, we put forward a simple model of a spherical particle with a dipole moment shifted outwards from the centre and oriented perpendicular to the particle radius. Using direct calculations and molecular dynamics computer simulations, we investigate the ground states of small clusters and the behaviour of bigger systems at low temperature. In both cases the important parameter is the dipolar shift, which leads to different ground states and, as a consequence, to a different microscopic behaviour in the situation when the thermal fluctuations are finite. We show that the head-to-tail orientation of dipoles provides a two-particle energy minima only if the dipoles are not shifted from the particle centres. This is one of the key differences from the system of shifted dipolar particles (sd-particles), in which the dipole was shifted outwards radially, studied earlier (Kantorovich et al 2011 Soft Matter 7 5217-27). For sd-particles the dipole could be shifted out of the centre for almost 40% before the head-to-tail orientation was losing its energetic advantage. This peculiarity manifests itself in the topology of the small clusters in the ground state and in the response of the Janus-like particle systems to an external magnetic field at finite temperatures.