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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.

We study via molecular dynamics simulations the self-assembled structures formed by supracolloidal magnetic polymers (SMPs). These are small aggregates of magnetic colloidal particles with polymer-like structures that have been permanently stabilized by means of polymer crosslinking. Here we focus on the fundamental structural and magnetic properties of the self-assembled motifs formed by pairs of identical SMPs under different conditions. We observe that the minimum characteristic density at which the self-assembly of both SMPs into a single aggregate becomes dominant is signaled by a maximum in their net magnetization and radius of gyration.

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., This research was supported by the Russian Science Foundation, Grant No. 19-12-00209. T.S. acknowledges support by the Spanish AEI/MCI/FEDER(UE), Grant No. RTI2018-095441-B-C22, and The Maria de Maeztu R&D Program (Grant No. MDM-2017-0711). Simulations were carried out at the Vienna Scientific Cluster (VSC).

In the present work we study via molecular dynamics simulations filaments of ring and linear shape. Filaments are made of magnetic nanoparticles, possessing a point dipole in their centres. Particles in filaments are crosslinked in a particular way, so that the deviation of the neighbouring dipoles from the head-to-tail orientation is penalised by the bond. We show how the conformation of a single chain and ring filament changes on cooling for different lengths. We also study filament pairs, by fixing filaments at a certain distance and analysing the impact of inter-filament interaction on the equilibrium configurations. Our study opens a perspective to investigate the dispersions of filaments, both theoretically and numerically, by using effective potentials.

In our earlier work (Steinbach et al., 2016 [1] ) we investigated a homogeneous system of magnetically capped colloidal particles that self-assembled via two structural patterns of different symmetry. The particles could form a compact, equilateral triangle with a three-fold rotational symmetry and zero dipole moment and a staggered chain with mirror symmetry with a net magnetisation perpendicular to the chain. The system exhibited a bistability already in clusters of three particles. Based on observations of a real magnetic particles system, analytical calculations and molecular dynamics simulations, it has been shown that the bistability is a result of an anisotropic magnetisation distribution with rotational symmetry inside the particles. The present study is a logical extension of the above research and forms a preparatory stage for the study of a self-assembly of such magnetic particles under the influence of an external magnetic field. Since the magnetic field is only an additive contribution to the total ground state energy, we can study the interparticle interaction energies of candidate ground state structures based on the field-free terms.

Abstract. 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. Graphical abstract

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., J. J. Cerdà, C. Bona, and A. Cerrato acknowledge the financial support of the Spanish Ministry of Economy and Competitiveness (MINECO/AEI/FEDER,UE) through the project Proyecto de I + D (excelencia) DPI2017-86610-P. E. N., E. P., P. S., and S. K. acknowledge the support of the Russian Science Foundation (Grant No. 19-12-00209). Simulations were performed at the IFISC's Nuredduna high-throughput computing clusters, supported by the projects GRID-CSIC.69 T. Sintes also acknowledges support via RTI2018-095441-B-C22, funded by MINECO/AEI/FEDER,UE.

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. © 2019 American Physical Society.

Using Molecular Dynamics computer simulations, we study how an applied magnetic field influences the shape, integrity and internal structure of clusters formed by Stockmayer supracolloidal magnetic polymers (SMPs). We consider SMPs of four different topologies: chain-, Y-, X- and ring-like ones. We find that the highest macroscopic deformation and the strongest monomer rearrangements from a liquid to a local hexatic order is observed for clusters formed by chain-like SMPs. The highest magnetic susceptibility, however, is exhibited by the clusters composed of Y- and X-like SMPs. Clusters formed by ring-like SMPs are basically not affected by the field strengths considered here. It is worth mentioning that those fields are sufficient to cause the dissociation of the clusters formed by other topologies of SMPs.

This article is part of the themed collection: Nanoparticle Assembly: From Fundamentals to Applications, 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., This research has been partially supported by the Austrian Research Fund (FWF): START-Projekt Y 627-N27. Authors are grateful to the Ural Federal University stimulating programme. S. S. K is supported by RFBR mol-a-ved 15-32-20549. E. V. N. acknowledges the support of President RF Grant No. MK-5216.2015.2. The authors are grateful to the Ministry of Education and Science of the Russian Federation (Project 3.12.2014/K) and EU-Project 642774 ETN-Colldense. J. J. C. and T. S. also acknowledge funding from a grant awarded by the Conselleria d'Innovació, Recerca i Turisme del Govern de les Illes Balears and the European Social Fund (ESF).

We investigate the properties of magnetic supracolliodal polymers – magnetic filaments (MFs) – with super-paramagnetic monomers, with and without Van der Waals (VdW) attraction between them. We employ molecular dynamics (MD) simulations to elucidate the impact of crosslinking mechanism on the structural and magnetic response of MFs to an applied external homogeneous magnetic field. We consider two models: plain crosslinking, which results in a flexible backbone; and constrained crosslinking, which provides significant stiffens against bending. We find that for plain crosslinking, even a slight increase of the central attraction leads to collapsed MF conformations. Structures that initially exhibit spherical symmetry evolve into cylindrically symmetric ones, with growing magnetic field strength. Plain crosslinking also allows for conformational bistability. MFs with constrained crosslinking tend to, instead, unravel in field. In both crosslinking scenarios, central attraction is able to hinder low-field magnetic response of MFs, albeit the bistability of plainly crosslinked MFs manifests itself also in the high-field region.

Supracolloidal magnetic polymers (SMPs) are structures made by crosslinking magnetic particles. In this work, using Langevin dynamics simulations, we study the zero-field magnetic properties of clusters formed in suspensions of SMPs with different topologies -- chains, rings, X and Y -- that interact via Stockmayer potential. We find that the presence of central attraction, resulting in the formation of large compact clusters, leads to a dramatic decrease of the suspension initial susceptibility, independently from SMP topology. However, the largest decrease corresponds to chain-like SMPs with strongly interacting particles. This is due to the higher rotational degrees of freedom of SMPs with such topology, which allows the particles to reorganise themselves inside the clusters in such a way that their magnetic moments form energetically advantageous vortex structures with negligible net magnetic moments., Comment: International Conference on Magnetic Fluids - ICMF 2019

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.

We study self-assembly in suspensions of supracolloidal polymer-like structures made of crosslinked magnetic particles. Inspired by self-assembly motifs observed for dipolar hard spheres, we focus on four different topologies of the polymer-like structures: linear chains, rings, Y-shaped and X-shaped polymers. We show how the presence of the crosslinkers, the number of beads in the polymer and the magnetic interparticle interaction affect the structure of the suspension. It turns out that for the same set of parameters, the rings are the least active in assembling larger structures, whereas the system of Y- and especially X-like magnetic polymers tends to form very large loose aggregates. © 2018 Elsevier B.V.

Two different bidisperse approximations of one gamma-distribution were examined in the present manuscript. The bidisperse system was chosen as the first step to allow for polydispersity when studying thermodynamics and microstructure of magnetic fluids. The author used the first-order modified mean-field model for investigating magnetization curves for these approximations and showed that curves are almost identical. Also analyzed was the influence of choosing variant of constructed bidisperse model on the structure factors, which were constructed using the mathematical model, developed in the paper by Novak et al. [J.Chem.Phys. 139 (2013) 224905].

We present a comparative study of the anisometric and anisotropic magnetic colloids at low temperatures. As examples we choose the ellipsoidal and cubic magnetic colloids to illustrate the influence of the shape (particle anisometry) on the ground state structures. To scrutinise the influence of the internal particle anisotropy we address particles with dipoles shifted out from the centre of mass. Of the latter, we distinguish between two types: the first type has a dipole moment pointing radially outwards; the other has a dipole pointing perpendicular to the radius along which it is shifted.

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.

In the present manuscript we develop a theoretical approach to describe the pair correlation function of bidisperse magnetic dipolar hard- and soft-spheres. We choose bidisperse system as the first step to allow for polydispersity when studying thermodynamics of magnetic fluids. Using diagram technique we calculate the virial expansion of the pair correlation function up to the first order in density and fourth order in the dipolar strength. Even though, the radial distribution functions are extremely sensitive to the steric potential, we show that the behaviour of the isotropic centre-centre structure factor is almost indifferent to the type of the short-range repulsion. We extensively compare our theoretical results to the data of molecular dynamics simulations, which helps us to understand the range of validity of the virial expansion both on density and magnetic dipolar strength. We also investigate the influence of the granulometric composition on the height, width, and position of the structure factor first peak in order to clarify whether it is possible to extract structural information from experimentally measured small angle neutron scattering intensities. © 2013 AIP Publishing LLC.

In the present paper, we analyze the influence of the steric potential on the interparticle correlation in magnetic fluids. Using molecular dynamics simulations and diagram technique, we obtain the radial distribution function for a monodisperse system of softdipolar spheres. On the basis of the pair correlation function we compute the pressure associated with the presence of dipolar particles in magnetic fluids. Comparing our findings to the results obtained for dipolar hard spheres it is shown that the steric potential plays a very important role for pressure and should be accurately taken into account.