Magnetic elastomers, consisting of magnetic particles embedded in a polymer matrix, exhibit complex macroscopic responses due to the interplay of magnetic interactions, particle anisotropy, and matrix elasticity. Using coarse-grained molecular dynamics simulations, we investigate the zero-field dynamic magnetic response of two model systems: in the first S1 model the matrix exerts elastic constraints on particle translations only, while in the second model S2, both translation and rotation of particles cause elastic penalty. We systematically vary particle magnetic moment, internal anisotropy, and spring rigidity to assess their impact on dynamical susceptibility and particle orientation distributions. Our results reveal that in S1, the magnetic response is primarily governed by dipolar interactions and anisotropy, with matrix rigidity playing a minor role. In contrast, the S2 model exhibits a pronounced dependence on spring stiffness, particularly at high anisotropy, where mechanical constraints strongly modulate magnetic relaxation. The findings demonstrate that the combination of dipolar interactions, magnetic anisotropy, and mechanical constraints produces a rich spectrum of relaxation behaviors, highlighting the crucial role of particle-matrix coupling in tuning the dynamic properties of magnetic elastomers.

Magnetic active particles offer a versatile route to externally controlled microscale transport by combining self-propulsion with field-tunable orientation, as realized in both synthetic and living magnetic microswimmers. Here, we develop a theoretical framework for three-dimensional active Brownian motion in a uniform magnetic field, incorporating coupled translational and rotational dynamics and providing analytical approximations for low-order displacement moments. At long times, the system dynamics reduces to a combination of enhanced diffusion and permanent drift absent in regular active Brownian particles. The field acts as an external controller, channeling activity toward one of these two types of motion. At intermediate time scales, the interplay between rotational noise, self-propulsion, and magnetic alignment results in pronounced non-Gaussian displacement statistics. First-passage properties exhibit strong field sensitivity, highlighting the potential of magnetic guidance to optimize search processes and targeted delivery in active matter systems. Theoretical predictions are validated by numerical simulations.

We study binary ferrofluids composed of multicore "nanoflowers" of magnetically hard CoFe2O4 and magnetically soft MnFe2O4, as a way to optimise heat dissipation while suppressing aggregation-properties essential for biomedical applications. Bulk magnetometry and molecular dynamics simulations were combined to elucidate their behaviour. Experiments show wasp-waisted hysteresis, composition-dependent coercivity, and strong protocol dependence (field cooling). Simulations reproduce these trends and reveal the underlying structure-property coupling: (i) in an applied magnetic field, CoFe2O4 forms chains that dominate collective switching; (ii) adding MnFe2O4 "poisons" these chains-shortening and de-branching clusters-thereby lowering coercivity and loop area relative to a weighted superposition of the individual component responses without interactions; (iii) dipolar coupling reciprocally hardens the magnetically soft phase and softens the magnetically hard phase even without large-scale aggregation; and (iv) at higher total volume fraction (ϕ = 0.1) magnetically soft particles still suppress chain growth, reducing mean cluster size by up to an order of magnitude while keeping heating-relevant hysteresis close to Stoner-Wohlfarth expectations. These results establish composition-controlled microstructure as a means to decouple thermal output from aggregation: CoFe2O4 : MnFe2O4 mixtures can be tuned to enhance loss mechanisms while mitigating aggregation, offering a route to binary ferrofluids optimized for magnetic hyperthermia and drug delivery.

Magnetic nanogels (MNGs)─deformable colloidal particles composed of cross-linked polymers with embedded magnetic nanoparticles (MNPs)─facilitate remote manipulation of their rheology and internal structure through biocompatible magnetic fields. This property renders MNGs particularly promising for applications in drug delivery and hyperthermia, although the rheological characteristics of these systems are not yet fully understood. In this research, we create an in silico planar rheometer by combining the solutions of Lattice-Boltzmann-based Navier-Stokes equations with molecular dynamics-tracked MNGs trajectories. Conducting steady shear experiments allows us to measure the viscosity of MNG suspensions by evaluating the effects of uniform external magnetic fields (H⃗) (in terms of strength and direction), concentration, and dipolar coupling interactions among MNPs within the MNGs. The application of H⃗ hinders colloid rotation and increases viscosity, while rotating H⃗ fields generate shear flow in otherwise stationary MNG suspensions. Differences in the rheological behavior between deformable and rigid colloids are highlighted.

We report direct numerical simulations of elastic turbulence in shear-driven flow of a dilute polymer solution within a three-dimensional straight channel. Most existing approaches in the literature employ the Oldroyd-B model or its advanced version, the finite extensible nonlinear elastic model introduced by Peterlin (FENE-P model), for simulation of polymer hydrodynamics, with their limitations of being continuum models. To overcome such restriction, we explicitly model the dilute polymer solution utilizing a classical bead-spring representation for each polymer chain and, therefore, also accounting for spatial variations in polymer concentration. We show that the viscoelastic instability forms in elastic waves and eventually chaotic flow, which persists above the transition with increasing Weissenberg number further into viscoelastic turbulence.

This study examines the magnetic properties of multicore magnetic nanoparticles (MMNPs) using Brownian dynamics simulations in conjunction with the Landau-Lifshitz-Gilbert equation. We demonstrate that the magnetic responses of MMNPs, both static and dynamic, are governed by a complex interplay between the cores magnetic anisotropy and the strength of intercore magnetic interactions. We show that for a single multicore in a liquid carrier, the distribution of the anisotropy axes inside does not impact its initial magnetic response. These insights are crucial for refining the design of multicore magnetic particles in various applications, including magnetic hyperthermia, data storage, and targeted drug delivery, where accurate control over magnetic characteristics is vital.

We present the thermal Stoner-Wohlfarth (tSW) model and apply it in the context of molecular dynamics simulations. The model is validated against an ensemble of immobilized, randomly oriented uniaxial particles (solid superparamagnet) and a classical dilute ferrofluid for different combinations of anisotropy strength and magnetic field/moment coupling, at a fixed temperature. We compare analytical and simulation results to quantify the viability of the tSW model in reproducing the equilibrium properties (with and without dipole-dipole interactions) and dynamic properties (without dipole-dipole interactions) of magnetic soft matter systems. We show that if the anisotropy of a particle is more than five times higher than the thermal fluctuations, the tSW model is applicable and efficient. This approach allows one to consider the interplay between N & eacute;el and Brownian relaxation, often neglected in the fixed point-dipole representation-based magnetic soft matter theoretical investigations.

The properties of suspensions of magnetic platelets are studied using Brownian dynamics simulations. Each platelet is shaped like an oblate cylinder with a longitudinal point dipole at its centre. The...

Magnetic nanogels (MNGs) are highly attractive for biomedical applications because of their potential for remote control of the rheology and internal structure of these soft colloids with biocompatible magnetic fields. In this contribution, using molecular dynamics simulations, we investigate the impact of the cross-linker distribution in the body of a MNG on the shape and magnetic response to constant and AC magnetic fields and relate those properties to the behaviour of non-magnetic tracers placed in the MNGs and left to escape. We find that if no AC magnetic field is applied, although the escape times of the tracer particles barely depend on morphology, the highest degree of subdiffusion is observed for the gels with a non-uniform cross-linkerer distribution. We also find how the eigen frequency at which particles relax locally in the polymer matrix affects the dynamic magnetic response of the gel. We show that a magnetic field-induced wobbling can facilitate drug release from gels.

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.

In this work we employ molecular dynamics simulations to investigate the first-order-reversal-curve distribu-tion and switching-field distribution of magnetic elastomers. We model magnetic elastomers in a bead-spring approximation with permanently magnetized spherical particles of two different sizes. We find that a different fractional composition of particles affects the magnetic properties of elastomers obtained as a result. We prove that the hysteresis of the elastomer can be attributed to the broad energy landscape with multiple shallow minima and caused by dipolar interactions.

Nowadays, magnetoresponsive soft materials, based not simply on magnetic nanoparticles but rather on multiple components with distinct sizes and magnetic properties in both liquid and polymeric carriers, are becoming more and more widespread due to their unique and versatile macroscopic response to an applied magnetic field. The variability of the latter is related to a complex interplay of the magnetic interactions in a highly nonuniform internal field caused by spatial inhomogeneity in multicomponent systems. In this work, we present a combined analytical and simulation study of binary superparamagnetic systems containing nanoclusters and dispersed single-domain nanoparticles in both liquid and solid carrier matrices. We investigate the equilibrium magnetic response of these systems for wide ranges of concentrations and interaction energies. It turns out that, while the magnetization of a binary solid can be both above and below that of an ideal superparamagnetic gas, depending on the concentration of the dispersed phase and the interparticle interactions, the system in a liquid carrier is highly magnetically responsive. In liquid, a spatial redistribution of the initially homogeneously dispersed phase in the vicinity of the nanocluster is observed, an effect that is reminiscent of the so-called haloing effect previously observed experimentally on micro- and milliscales.

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, the magnetized beads form a transient network that coarsens in time into compact clusters. Here we investigate how an increased volume fraction ϕ of the granulate accelerates the coarsening, whereas a homogeneous magnetic field B⊥ oriented in vertical direction impedes the emergence and growth of the networks. We explore the coarsening dynamics in the (ϕ,B)-control parameter space, and observe that low filling fractions are more susceptible to an increase of B⊥ than high ones.

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

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)], 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.

In recent years, there has been an increasing interest in magnetic nanoparticles with non-spherical shapes. This is largely due to their broad span of tuneable properties, which allow for tailoring of the colloidal properties by altering the magnetic anisometry or shape anisotropy of the nanoparticle. Although extensive research has gone into novel synthesis methods, the theoretical and analytical treatment of magnetic colloidal suspensions still predominantly focuses on spherical particles. This paper explores the microstructure and initial static magnetic susceptibility of systems of anisometric dipolar magnetic nanoplatelets in order to understand the applicability of dipolar sphere-based theories and models for such systems. We find that the microstructure as characterized by the particle distribution and magnetic clustering of platelets diverges significantly from that of spheres both quantitatively and qualitatively. We find lower initial static magnetic susceptibilities in nanoplatelet systems than in comparable suspensions of dipolar spheres. At lower values of the magnetic coupling constant, this can be accounted for by applying corrections to the volume fraction. However, this approach is less accurate for systems with stronger magnetic interactions. By providing predictions of and explanations for the observed effects, we aim to facilitate the use of magnetic nanoplatelet suspensions in the broad range of applications.

The idea of creating magnetically controllable colloids whose rheological properties can be finely tuned on the nano-or micro-scale has caused a lot of experimental and theoretical effort. The latter resulted in systems whose building blocks are ranging between single magnetic nanoparticles to complexes of such nanoparticles bound together by various mechanisms. The binding can be either chemical or physical, reversible or not. One way to create a system that is physically bound is to let the precrosslinked supracolloidal magnetic polymers (SMPs) to cluster due to both magnetic and Van-der-Waals-type forces. The topology of the SMPs in this case can be used to tune both magnetic and rheological properties of the resulting clusters as we show in this work. We employ Molecular Dynamics computer simulations coupled with explicit solvent modelled by Lattice-Boltzmann method in order to model the behaviour of the clusters formed by chains, rings, X-and Y-shaped SMPs in a shear flow with externally applied magnetic field. We find that the shear stabilises the shape of the clusters not letting them extend in the direction of the field and disintegrate. The clusters that show the highest response to an applied field and higher shape stability are those made of Y-and X-like SMPs.

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.

In complex colloidal systems, interparticle interactions strongly affect the dynamics of the constituting particles. A study of the dynamical response also provides invaluable information on the character of those interactions. Here we demonstrate how tuning the electrostatic interactions by an ionic surfactant in dispersions of magnetic nanoplatelets leads to developing new dynamic modes in magnetic response spectra. The collective modes can be induced or suppressed by either varying the concentration ratio of the magnetic nanoplatelets (MP) to the surfactant or increasing the MP concentration reflecting the nanoscale characteristics of this fluid magnet.

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, the magnetized beads form a transient network that coarsens in time into compact clusters. Here we investigate how an increased volume fraction 𝜙 of the granulate accelerates the coarsening, whereas a homogeneous magnetic field 𝐵 oriented in vertical direction impedes the emergence and growth of the networks. We explore the coarsening dynamics in the (𝜙,𝐵)-control parameter space, and observe that low filling fractions are more susceptible to an increase of 𝐵 than high ones.