Modeling the properties of ferrogels in uniform magnetic fields

Pair correlations of the easy magnetisation axes of superparamagnetic nanoparticles in a ferrofluid/ferrocomposite

The widespread use of magnetic nanoparticles in modern technologies and medical applications highlights the need for reliable theoretical models that can predict their physical properties. The pair correlation function of two randomly selected superparamagnetic nanoparticles in a ferrofluid/ferrocomposite is studied to depict the joint probability density of the easy magnetisation axes across the planes of parameters of major importance; these are the interaction of ferroparticles with an external magnetic field, the energy of magnetic anisotropy inside the superparamagnetic nanoparticle, and the interparticle magnetic dipole-dipole interaction. Assuming the rotational symmetry of the system, we come to the conclusion that the pair correlations of interest are dependent only on the polar angles, determining the inclinations of the ferroparticle easy axes from the direction of an external magnetic field. The dimer configuration, where two ferroparticles are in close contact along a magnetic field with their easy magnetisation axes aligned, is the most probable. This configuration becomes more pronounced with increasing anisotropy energy, dipolar coupling constant, and external magnetic field.

Molecular dynamics simulations of microscopic structural transition and macroscopic mechanical properties of magnetic gels

Magnetic gels with embedded micro-/nano-sized magnetic particles in cross-linked polymer networks can be actuated by external magnetic fields, with changes in their internal microscopic structures and macroscopic mechanical properties. We investigate the responses of such magnetic gels to an external magnetic field, by means of coarse-grained molecular dynamics simulations. We find that the dynamics of magnetic particles are determined by the interplay of magnetic dipole-dipole interactions, polymer elasticity, and thermal fluctuations. The corresponding microscopic structures formed by the magnetic particles, such as elongated chains, can be controlled by the external magnetic field. Furthermore, the magnetic gels can exhibit reinforced macroscopic mechanical properties, where the elastic modulus increases algebraically with the magnetic moments of the particles in the form of ∝(m-mc)2 when magnetic chains are formed. This simulation work can not only serve as a tool for studying the microscopic and the macroscopic responses of the magnetic gels, but also facilitate future fabrications and practical controls of magnetic composites with desired physical properties.

Density functional approach to elastic properties of three-dimensional dipole-spring models for magnetic gels

Magnetic gels are composite materials consisting of a polymer matrix and embedded magnetic particles. Those are mechanically coupled to each other, giving rise to the magnetostrictive effects as well as to a controllable overall elasticity responsive to external magnetic fields. Due to their inherent composite and thereby multiscale nature, a theoretical framework bridging different levels of description is indispensable for understanding the magnetomechanical properties of magnetic gels. In this study, we extend a recently developed density functional approach from two spatial dimensions to more realistic three-dimensional systems. Along these lines, we connect a mesoscopic characterization resolving the discrete structure of the magnetic particles to macroscopic continuum parameters of magnetic gels. In particular, we incorporate the long-range nature of the magnetic dipole-dipole interaction and consider the approximate incompressibility of the embedding media and relative rotations with respect to an external magnetic field breaking rotational symmetry. We then probe the shape of the model system in its reference state, confirming the dependence of magnetostrictive effects on the configuration of the magnetic particles and on the shape of the considered sample. Moreover, calculating the elastic and rotational coefficients on the basis of our mesoscopic approach, we examine how the macroscopic types of behavior are related to the mesoscopic properties. Implications for real systems of random particle configurations are also discussed.

Elastically-mediated collective organisation of magnetic microparticles

Gels are soft elastic materials made of a three-dimensional cross-linked polymer network and featuring both elastic and dissipative responses under external mechanical stimuli. Here we investigate how such gels mediate the organization of embedded magnetic microparticles when driven by an external field. By constructing a continuum theory, we demonstrate that the collective dynamics of the embedded particles result from the delicate balance between magnetic dipole-dipole interactions, thermal fluctuations and elasticity of the polymer network, verified by our experiments. The proposed model could be extended to other soft magnetic composites in order to predict how the elastic interactions mediate the aggregation of the embedded elements, fostering technological implications for multifunctional hydrogel materials.

Review on the advancements of magnetic gels: towards multifunctional magnetic liposome-hydrogel composites for biomedical applications

Magnetic gels have been gaining great attention in nanomedicine, as they combine features of hydrogels and magnetic nanoparticles into a single system. The incorporation of liposomes in magnetic gels further leads to a more robust multifunctional system enabling more functions and spatiotemporal control required for biomedical applications, which includes on-demand drug release. In this review, magnetic gels components are initially introduced, as well as an overview of advancements on the development, tuneability, manipulation and application of these materials. After a discussion of the advantages of combining hydrogels with liposomes, the properties, fabrication strategies and applications of magnetic liposome-hydrogel composites (magnetic lipogels or magnetolipogels) are reviewed. Overall, the progress of magnetic gels towards smart multifunctional materials are emphasized, considering the contributions for future developments.

Modeling and theoretical description of magnetic hybrid materials—bridging from meso- to macro-scales

Magnetic gels and elastomers consist of magnetic or magnetizable colloidal particles embedded in an elastic polymeric matrix. Outstanding properties of these materials comprise reversible changes in their mechanical stiffness or magnetostrictive distortions under the influence of external magnetic fields. To understand such types of overall material behavior from a theoretical point of view, it is essential to characterize the substances starting from the discrete colloidal particle level. It turns out that the macroscopic material response depends sensitively on the mesoscopic particle arrangement. We have utilized and developed several theoretical approaches to this end, allowing us both to reproduce experimental observations and to make theoretical predictions. Our hope is that both these paths help to further stimulate the interest in these fascinating materials.

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.

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.

Classical density functional theory for a two-dimensional isotropic ferrogel model with labeled particles

In this study, we formulate a density functional theory (DFT) for systems of labeled particles, considering a two-dimensional bead-spring lattice with a magnetic dipole on every bead as a model for ferrogels. On the one hand, DFT has been widely studied to investigate fluidlike states of materials, in which constituent particles are not labeled as they can exchange their positions without energy cost. On the other hand, in ferrogels consisting of magnetic particles embedded in elastic polymer matrices, the particles are labeled by their positions as their neighbors do not change over time. We resolve such an issue of particle labeling, introducing a mapping of the elastic interaction mediated by springs onto a pairwise additive interaction (pseudosprings) between unlabeled particles. We further investigate magnetostriction and changes in the elastic constants under altered magnetic interactions employing the pseudospring potential. It is revealed that there are two different response scenarios in the mechanical properties of the dipole-spring systems: While systems at low packing fractions are hardened as the magnetic moments increase in magnitude, at high packing fractions softening due to diminishing effects from the steric force, associated with increases in the volume, is observed. The validity of the theory is also verified by Monte Carlo simulations with both real springs and pseudosprings. We expect that our DFT approach may promote our understanding of materials with particle inclusions.

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.

Reversible magnetomechanical collapse: virtual touching and detachment of rigid inclusions in a soft elastic matrix

Soft elastic composite materials containing particulate rigid inclusions in a soft elastic matrix are candidates for developing soft actuators or tunable damping devices. The possibility to reversibly drive the rigid inclusions within such a composite together to a close-to-touching state by an external stimulus would offer important benefits. Then, a significant tuning of the mechanical properties could be achieved due to the resulting mechanical hardening. For a long time, it has been argued whether a virtual touching of the embedded magnetic particles with subsequent detachment can actually be observed in real materials, and if so, whether the process is reversible. Here, we present experimental results that demonstrate this phenomenon in reality. Our system consists of two paramagnetic nickel particles embedded at finite initial distance in a soft elastic polymeric gel matrix. Magnetization in an external magnetic field tunes the magnetic attraction between the particles and drives the process. We quantify our experimental results by different theoretical tools, i.e., explicit analytical calculations in the framework of linear elasticity theory, a projection onto simplified dipole-spring models, as well as detailed finite-element simulations. From these different approaches, we conclude that in our case the cycle of virtual touching and detachment shows hysteretic behavior due to the mutual magnetization between the paramagnetic particles. Our results are important for the design and construction of reversibly tunable mechanical damping devices. Moreover, our projection on dipole-spring models allows the formal connection of our description to various related systems, e.g., magnetosome filaments in magnetotactic bacteria.

Tunable dynamic moduli of magnetic elastomers: from characterization by x-ray micro-computed tomography to mesoscopic modeling

Ferrogels and magnetorheological elastomers are composite materials obtained by embedding magnetic particles of mesoscopic size in a crosslinked polymeric matrix. They combine the reversible elastic deformability of polymeric materials with the high responsivity of ferrofluids to external magnetic fields. These materials stand out, for example, for significant magnetostriction as well as a pronounced increase of the elastic moduli in the presence of external magnetic fields. By means of x-ray micro-computed tomography, the position and size of each magnetic particle can be measured with a high degree of accuracy. We here use data extracted from real magnetoelastic samples as input for coarse-grained dipole-spring modeling and calculations to investigate internal restructuring, stiffening, and changes in the normal modes spectrum. More precisely, we assign to each particle a dipole moment proportional to its volume and set a randomized network of springs between them that mimics the behavior of the polymeric elastic matrix. Extending our previously developed methods, we compute the resulting structural changes in the systems as well as the frequency-dependent elastic moduli when magnetic interactions are turned on. Particularly, with increasing magnetization, we observe the formation of chain-like aggregates. Interestingly, the static elastic moduli can first show a slight decrease with growing amplitude of the magnetic interactions, before a pronounced increase appears upon the chain formation. The change of the dynamic moduli with increasing magnetization depends on the frequency and can even feature nonmonotonic behavior. Overall, we demonstrate how theory and experiments can complement each other to learn more about the dynamic behavior of this interesting class of materials.

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.

Polymer architecture of magnetic gels: a review

In this review article, we provide an introduction to ferrogels, i.e. polymeric gels with embedded magnetic particles. Due to the interplay between magnetic and elastic properties of these materials, they are promising candidates for engineering and biomedical applications such as actuation and controlled drug release. Particular emphasis will be put on the polymer architecture of magnetic gels since it controls the degrees of freedom of the magnetic particles in the gel, and it is important for the particle-polymer coupling determining the mechanisms available for the gel deformation in magnetic fields. We report on the different polymer architectures that have been realized so far, and provide an overview of synthesis strategies and experimental techniques for the characterization of these materials. We further focus on theoretical and simulational studies carried out on magnetic gels, and highlight their contributions towards understanding the influence of the gels' polymer architecture.

Dynamics in a one-dimensional ferrogel model: relaxation, pairing, shock-wave propagation

Based on theory and simulations, we elucidate the relaxation dynamics of a one-dimensional ferrogel model and provide classification scenarios.

Shear elasticity of isotropic magnetic gels

The paper deals with a theoretical study of the effective shear modulus of a magnetic gel, consisting of magnetizable particles randomly and isotropically distributed in an elastic matrix. The effect of an external magnetic field on the composite modulus is the focus of our consideration. We take into account that magnetic interaction between the particles can induce their spatial rearrangement and lead to internal anisotropy of the system. Our results show that, if this magnetically induced anisotropy is insignificant, the applied field reduces the total shear modulus of the composite. Strong anisotropy can qualitatively change the magnetomechanic effect and induce an increase of this modulus with the field.

Magnetorheological response of highly filled magnetoactive elastomers from perspective of mechanical energy density: Fractal aggregates above the nanometer scale?

The dynamic shear modulus of magnetoactive elastomers containing 70 and 80 mass % of carbonyl iron microparticles is measured as a function of strain amplitude via dynamic torsion oscillations in various magnetic fields. The results are presented in terms of the mechanical energy density and considered in the framework of the conventional Kraus model. The form exponent of the Kraus model is further related to a physical model of Huber et al. [Huber et al., J. Phys.: Condens. Matter 8, 409 (1996)10.1088/0953-8984/8/29/003] that uses a realistic representation for the cluster network possessing fractal structure. Two mechanical loading regimes are identified. At small strain amplitudes the exponent β of the Kraus model changes in an externally applied magnetic field due to rearrangement of ferromagnetic-filler particles, while at large strain amplitudes, the exponent β seems to be independent of the magnetic field. The critical mechanical energy characterizing the transition between these two regimes grows with the increasing magnetic field. Similarities between agglomeration and deagglomeration of magnetic filler under simultaneously applied magnetic field and mechanical shear and the concept of jamming transition are discussed. It is proposed that the magnetic field should be considered as an additional parameter to the jamming phase diagram of rubbers filled with magnetic particles.

Force-induced elastic matrix-mediated interactions in the presence of a rigid wall

We consider a soft elastic matrix that contains particulate inclusions and is bounded by a rigid wall, e.g., the substrate. Such a situation arises in elastic composite materials. They may serve as soft actuators when forces are imposed on or induced between the embedded particles. We investigate how the presence of the rigid wall affects the interactions between the inclusions. First, for no-slip boundary conditions, we transfer Blake's derivation of a corresponding Green's function from low-Reynolds-number hydrodynamics to the linearly elastic case. Then, we list the general expressions to describe the situation for point-like particles in the presence of no-slip and free-slip surface conditions. To compare the effect of the different surface conditions to each other and to the bulk behavior, we address the example situation of pairwise interactions between two embedded particles. The axis through both particle centers is either aligned parallel or perpendicular to the surface. Our results suggest that walls with free-slip surface conditions are preferred when they serve as substrates for soft actuators made from elastic composite materials. As we further demonstrate, the presence of a rigid wall can qualitatively change the interactions between the inclusions. In effect, it can switch attractive interactions into repulsive ones (and vice versa). It should be straightforward to observe the effects in future experiments and to combine our results, e.g., with the modeling of biological cells and tissue on rigid surfaces.

Effect of single-particle magnetostriction on the shear modulus of compliant magnetoactive elastomers

The influence of an external magnetic field on the static shear strain and the effective shear modulus of a magnetoactive elastomer (MAE) is studied theoretically in the framework of a recently introduced approach to the single-particle magnetostriction mechanism [V. M. Kalita et al., Phys. Rev. E 93, 062503 (2016)10.1103/PhysRevE.93.062503]. The planar problem of magnetostriction in an MAE with magnetically soft inclusions in the form of a thin disk (platelet) having the magnetic anisotropy in the plane of this disk is solved analytically. An external magnetic field acts with torques on magnetic filler particles, creates mechanical stresses in the vicinity of inclusions, induces shear strain, and increases the effective shear modulus of these composite materials. It is shown that the largest effect of the magnetic field on the effective shear modulus should be expected in MAEs with soft elastomer matrices, where the shear modulus of the matrix is less than the magnetic anisotropy constant of inclusions. It is derived that the effective shear modulus is nonlinearly dependent on the external magnetic field and approaches the saturation value in magnetic fields exceeding the field of particle anisotropy. It is shown that model calculations of the effective shear modulus correspond to a phenomenological definition of effective elastic moduli and magnetoelastic coupling constants. The obtained theoretical results compare well with known experimental data. Determination of effective elastic coefficients in MAEs and their dependence on magnetic field is discussed. The concentration dependence of the effective shear modulus at higher filler concentrations has been estimated using the method of Padé approximants, which predicts that both the absolute and relative changes of the magnetic-field-dependent effective shear modulus will significantly increase with the growing concentration of filler particles.

Thermophoretically induced large-scale deformations around microscopic heat centers

Selectively heating a microscopic colloidal particle embedded in a soft elastic matrix is a situation of high practical relevance. For instance, during hyperthermic cancer treatment, cell tissue surrounding heated magnetic colloidal particles is destroyed. Experiments on soft elastic polymeric matrices suggest a very long-ranged, non-decaying radial component of the thermophoretically induced displacement fields around the microscopic heat centers. We theoretically confirm this conjecture using a macroscopic hydrodynamic two-fluid description. Both thermophoretic and elastic effects are included in this theory. Indeed, we find that the elasticity of the environment can cause the experimentally observed large-scale radial displacements in the embedding matrix. Additional experiments confirm the central role of elasticity. Finally, a linearly decaying radial component of the displacement field in the experiments is attributed to the finite size of the experimental sample. Similar results are obtained from our theoretical analysis under modified boundary conditions.

Elongated micro-structures in magneto-sensitive elastomers: a dipolar mean field model

Based on a dipole model for the mutual magnetic interactions among the magnetizable micro-particles in magneto-sensitive elastomers we develop a mean field approach to describe the arrangement of these particles into elongated micro-structures. If these micro-structures are oriented parallel to an external magnetic field the present approach provides an efficient calculation of the behavior of such samples, which is a result of the interplay between micro-structure and shape effects. Accordingly, we are able to draw comprehensive phase diagrams for the resultant deformation and predict for very oblate samples a discontinuous shape change in the presence of a homogeneous external field.

Anisotropic magnetoresistivity in structured elastomer composites: modelling and experiments

A constitutive model for the anisotropic magnetoresistivity in structured elastomer composites (SECs) is proposed. The SECs considered here are oriented pseudo-chains of conductive-magnetic inorganic materials inside an elastomer organic matrix. The pseudo-chains are formed by fillers which are simultaneously conductive and magnetic dispersed in the polymer before curing or solvent evaporation. The SEC is then prepared in the presence of a uniform magnetic field, referred to as Hcuring. This procedure generates the pseudo-chains, which are preferentially aligned in the direction of Hcuring. Electrical conduction is present in that direction only. The constitutive model for the magnetoresistance considers the magnetic pressure, Pmag, induced on the pseudo-chains by an external magnetic field, H, applied in the direction of the pseudo-chains. The relative changes in conductivity as a function of H are calculated by evaluating the relative increase of the electron tunnelling probability with Pmag, a magneto-elastic coupling which produces an increase of conductivity with magnetization. The model is used to adjust experimental results of magnetoresistance in a specific SEC where the polymer is polydimethylsiloxane, PDMS, and fillers are microparticles of magnetite-silver (referred to as Fe3O4[Ag]). Simulations of the expected response for other materials in both superparamagnetic and blocked magnetic states are presented, showing the influence of the Young's modulus of the matrix and filler's saturation magnetization.

Single-particle mechanism of magnetostriction in magnetoactive elastomers

Magnetoactive elastomers (MAEs) are composite materials comprised of micrometer-sized ferromagnetic particles in a nonmagnetic elastomer matrix. A single-particle mechanism of magnetostriction in MAEs, assuming the rotation of a soft magnetic, mechanically rigid particle with uniaxial magnetic anisotropy in magnetic fields is identified and considered theoretically within the framework of an alternative model. In this mechanism, the total magnetic anisotropy energy of the filling particles in the matrix is the sum over single particles. Matrix displacements in the vicinity of the particle and the resulting direction of the magnetization vector are calculated. The effect of matrix deformation is pronounced well if the magnetic anisotropy coefficient K is much larger than the shear modulus µ of the elastic matrix. The feasibility of the proposed magnetostriction mechanism in soft magnetoactive elastomers and gels is elucidated. The magnetic-field-induced internal stresses in the matrix lead to effects of magnetodeformation and may increase the elastic moduli of these composite materials.

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.

Ferrogels cross-linked by magnetic particles: Field-driven deformation and elasticity studied using computer simulations

Ferrogels, i.e., swollen polymer networks into which magnetic particles are immersed, can be considered as "smart materials" since their shape and elasticity can be controlled by an external magnetic field. Using molecular dynamics simulations on the coarse-grained level, we study a ferrogel in which the magnetic particles act as the cross-linkers of the polymer network. In a homogeneous external magnetic field, the direct coupling between the orientation of the magnetic moments and the polymers by means of covalent bonds gives rise to a deformation of the gel, independent of the interparticle dipole-dipole interaction. In this paper, we quantify this deformation, and, in particular, we investigate the gel's elastic moduli and its magnetic response for two different connectivities of the network nodes. Our results demonstrate that these properties depend significantly on the topology of the polymer network.

Buckling of paramagnetic chains in soft gels

We study the magneto-elastic coupling behavior of paramagnetic chains in soft polymer gels exposed to external magnetic fields. To this end, a laser scanning confocal microscope is used to observe the morphology of the paramagnetic chains together with the deformation field of the surrounding gel network. The paramagnetic chains in soft polymer gels show rich morphological shape changes under oblique magnetic fields, in particular a pronounced buckling deformation. The details of the resulting morphological shapes depend on the length of the chain, the strength of the external magnetic field, and the modulus of the gel. Based on the observation that the magnetic chains are strongly coupled to the surrounding polymer network, a simplified model is developed to describe their buckling behavior. A coarse-grained molecular dynamics simulation model featuring an increased matrix stiffness on the surfaces of the particles leads to morphologies in agreement with the experimentally observed buckling effects.

Superelastic stress–strain behavior in ferrogels with different types of magneto-elastic coupling

Anisotropic ferrogels and magnetorheological elastomers allow for reversible tunability of their markedly nonlinear stress–strain properties.

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.

Tunable dynamic response of magnetic gels: impact of structural properties and magnetic fields

Ferrogels and magnetic elastomers feature mechanical properties that can be reversibly tuned from outside through magnetic fields. Here we concentrate on the question of how their dynamic response can be adjusted. The influence of three factors on the dynamic behavior is demonstrated using appropriate minimal models: first, the orientational memory imprinted into one class of the materials during their synthesis; second, the structural arrangement of the magnetic particles in the materials; and third, the strength of an external magnetic field. To illustrate the latter point, structural data are extracted from a real experimental sample and analyzed. Understanding how internal structural properties and external influences impact the dominant dynamical properties helps to design materials that optimize the requested behavior.

Reconfigurable and actuating structures from soft materials

The recent interest in reconfigurable soft materials may lead to the next paradigm in the development of adaptive and actuating materials and structures. Actuating soft materials eventually can be precisely designed to show stimuli-sensing, multi-length scale actuation, tunable transport, programmed shape control and multifunctional orthogonal responses. Herein, we discuss the various advances in the emerging field of reconfigurable soft materials with a focus on the various parameters that can be modulated to control a complex system behavior. In particular, we detail approaches that use either long-range fields (i.e. electrical, magnetic) or changes in local thermodynamic parameters (e.g., solvent quality) in order to elicit a precise dimensional and controlled response. The theoretical underpinnings and practical considerations for different approaches are briefly presented alongside several illustrative examples from the recent studies. In the end, we summarize recent accomplishments, critical issues to consider, and give perspectives on the developments of this exciting research field.

Theory and simulation of anisotropic pair correlations in ferrofluids in magnetic fields

Anisotropic pair correlations in ferrofluids exposed to magnetic fields are studied using a combination of statistical-mechanical theory and computer simulations. A simple dipolar hard-sphere model of the magnetic colloidal particles is studied in detail. A virial-expansion theory is constructed for the pair distribution function (PDF) which depends not only on the length of the pair separation vector, but also on its orientation with respect to the field. A detailed comparison is made between the theoretical predictions and accurate simulation data, and it is found that the theory works well for realistic values of the dipolar coupling constant (λ = 1), volume fraction (φ ≤ 0.1), and magnetic field strength. The structure factor is computed for wavevectors either parallel or perpendicular to the field. The comparison between theory and simulation is generally very good with realistic ferrofluid parameters. For both the PDF and the structure factor, there are some deviations between theory and simulation at uncommonly high dipolar coupling constants, and with very strong magnetic fields. In particular, the theory is less successful at predicting the behavior of the structure factors at very low wavevectors, and perpendicular Gaussian density fluctuations arising from strongly correlated pairs of magnetic particles. Overall, though, the theory provides reliable predictions for the nature and degree of pair correlations in ferrofluids in magnetic fields, and hence should be of use in the design of functional magnetic materials.

Nonmonotonic field-dependent magnetic permeability of a paramagnetic ferrofluid emulsion

The ferrofluid emulsion, made of kerosene-based ferrofluid droplets suspended in nonmiscible aviation oil, demonstrates experimentally the nonmonotonic dependence of the effective magnetic permeability as a function of the uniform static magnetic field. In weak fields the emulsion permeability rapidly grows; it reaches its maximum at fields on the order of 1 kA/m; after that, it decays to zero. The theoretical explanation of the effect, as we show here, could be based on the following idea: In a weak magnetic field the growth of the induced droplet magnetic moment is faster than the linear one due to the droplet elongation accompanied by the reduction of the demagnetizing field. Further increase of the external magnetic field strength cannot lead to a significant decrease of the demagnetizing field, as the droplets are already highly elongated. On the other hand, the magnetic susceptibility of the ferrofluid reduces with the field strength. Thus, the effective magnetic permeability of the ferrofluid suspension starts decreasing. The developed theoretical model describes well the experimental observations.

A Highly Tunable Silicone-Based Magnetic Elastomer with Nanoscale Homogeneity

Magnetic elastomers have been widely pursued for sensing and actuation applications. Silicone-based magnetic elastomers have a number of advantages over other materials such as hydrogels, but aggregation of magnetic nanoparticles within silicones is difficult to prevent. Aggregation inherently limits the minimum size of fabricated structures and leads to non-uniform response from structure to structure. We have developed a novel material which is a complex of a silicone polymer (polydimethylsiloxane-co-aminopropylmethylsiloxane) adsorbed onto the surface of magnetite (γ-Fe(2)0(3)) nanoparticles 7-10 nm in diameter. The material is homogenous at very small length scales (< 100 nm) and can be crosslinked to form a flexible, magnetic material which is ideally suited for the fabrication of micro- to nanoscale magnetic actuators. The loading fraction of magnetic nanoparticles in the composite can be varied smoothly from 0 - 50% wt. without loss of homogeneity, providing a simple mechanism for tuning actuator response. We evaluate the material properties of the composite across a range of nanoparticle loading, and demonstrate a magnetic-field-induced increase in compressive modulus as high as 300%. Furthermore, we implement a strategy for predicting the optimal nanoparticle loading for magnetic actuation applications, and show that our predictions correlate well with experimental findings.