Magnetostriction in elastomers with mixtures of magnetically hard and soft microparticles: effects of non-linear magnetization and matrix rigidity

In this contribution a magnetoactive elastomer (MAE) of mixed content, i.e., a polymer matrix filled with a mixture of magnetically soft and magnetically hard spherical particles, is considered. The object we focus at is an elementary unit of this composite, for which we take a set consisting of a permanent spherical micromagnet surrounded by an elastomer layer filled with magnetically soft microparticles. We present a comparative treatment of this unit from two essentially different viewpoints. The first one is a coarse-grained molecular dynamics simulation model, which presents the composite as a bead-spring assembly and is able to deliver information of all the microstructural changes of the assembly. The second approach is entirely based on the continuum magnetomechanical description of the system, whose direct yield is the macroscopic field-induced response of the MAE to external field, as this model ignores all the microstructural details of the magnetization process. We find that, differing in certain details, both frameworks are coherent in predicting that a unit comprising magnetically soft and hard particles may display a non-trivial re-entrant (prolate/oblate/prolate) axial deformation under variation of the applied field strength. The flexibility of the proposed combination of the two complementary frameworks enables us to look deeper into the manifestation of the magnetic response: with respect to the magnetically soft particles, we compare the linear regime of magnetization to that with saturation, which we describe by the Fr\"{o}hlich-Kennelly approximation; with respect to the polymer matrix, we analyze the dependence of the re-rentrant deformation on its rigidity

Basic magnetic properties of magnetoactive elastomers of mixed content

The results of theoretical and experimental investigations of the polymer composites that belong to a class of magnetoactive elastomers with mixed magnetic content (MAEs-MC) are presented. The fundamental distinction of such composites from ordinary magnetoactive elastomers is that the magnetic filler of MAEs-MC comprises both magnetically soft (MS) particles of size 3–5 µm and magnetically hard (MH) particles whose size is an order of magnitude greater. Since MH particles of the magnetic filler are mixed into a composition in a non-magnetised state, this can ensure preparation of samples with fairly homogeneous distribution of the filler. The 'initiation' process of a synthesised MAE-MC is done by its magnetisation in a strong magnetic field that imparts to the sample unique magnetic and mechanical properties. In this work, it is shown that the presence of MS particles around larger MH particles, firstly, causes an augmentation of magnetic moments, which the MH particles acquire during initiation, and secondly, enhances the magnetic susceptibility and remanent magnetisation of MAEs-MC. These magnetic parameters are evaluated on the basis of the macroscopic magnetostatics from the experimental data of spatial scanning of the field over the space around MAEs-MC made in the shape of a spheroid. A set of samples with a fixed MH and varying MS volume contents that are initiated in two different fields, is used. The developed mesoscopic model of magnetic interactions between the MH and MS phases is able to explain the experimentally observed dependencies of the magnetic parameters on the concentration of the MS phase. The problem is solved numerically under the assumption that the elastic matrix of MAEs-MC is rigid, i.e. the mutual displacements of the particles are negligible. The model helps to elucidate the interaction of the magnetic phases and to establish that the MS phase plays thereby a dual role. On the one hand, the MS phase screens out the field acting inside MH particles, and on the other hand, it forms mesoscopic magnetic bridges between adjoining MH particles, which in turn enhance their field. The combined interplay of these contributions defines the resulting material properties of MAEs-MC on the macroscopic scale

Size-Dependent Properties of Magnetosensitive Polymersomes: Computer Modelling

Magnetosensitive polymersomes, which are amphiphilic polymer capsules whose membranes are filled with magnetic nanoparticles, are prospective objects for drug delivery and manipulations with single cells. A molecular dynamics simulation model that is able to render a detailed account on the structure and shape response of a polymersome to an external magnetic field is used to study a dimensional effect: the dependence of the field-induced deformation on the size of this nanoscale object. It is shown that in the material parameter range that resembles realistic conditions, the strain response of smaller polymersomes, against a priori expectations, exceeds that of larger ones. A qualitative explanation for this behavior is proposed

Magnetorelaxometry in the Presence of a DC Bias Field of Ferromagnetic Nanoparticles Bearing a Viscoelastic Corona

With allowance for orientational Brownian motion, the magnetorelaxometry (MRX) signal, i.e., the decay of magnetization generated by an ensemble of ferromagnet nanoparticles, each of which bears a macromolecular corona (a loose layer of polymer gel) is studied. The rheology of corona is modelled by the Jeffreys scheme. The latter, although comprising only three phenomenological parameters, enables one to describe a wide spectrum of viscoelastic media: from linearly viscous liquids to weakly-fluent gels. The “transverse” configuration of MRX is considered where the system is subjected to a DC (constant bias) field, whereas the probing field is applied perpendicularly to the bias one. The analysis shows that the rate of magnetization decay strongly depends on the state of corona and slows down with enhancement of the corona elasticity. In addition, for the case of “transverse” MRX, we consider the integral time, i.e., the characteristic that is applicable to relaxation processes with an arbitrary number of decay modes. Expressions for the dependence of the integral time on the corona elasticity parameter and temperature are derived

Coarse-Grained Molecular Dynamics Modelling of a Magnetic Polymersome

A coarse-grained molecular dynamics framework is proposed to investigate the equilibrium structure and quasi-static deformational response of a magnetic polymersome, a hollow object whose magnetoactive part is its shell (membrane). In the developed scheme, the shell is modelled as a pair of two concentric interfaces, between which a layer of a linearly viscous fluid filled with magnetic nanoparticles is confined; the thickness of this layer slightly exceeds the nanoparticle diameter. The shell boundaries possess weak bending elasticity, very high surface tension and are impermeable for the nanoparticles. The nanoparticles bear permanent magnetic moments and are translationally and rotationally free inside the layer. The factors favoring the particle aggregation are the magneto-dipole coupling and Zeeman interaction with the external field; the impeding factors are thermal motion and steric restrictions imposed by the boundaries. The volume content of magnetic phase in the shell is sufficiently small (below 11 vol.%) to enable one to clearly observe structure patterns occurring in the basic state and under an applied magnetic field. As shown, both the particle concentration and the level of interparticle interaction strongly affect the extent and type of the aggregation that, in turn, causes overall deformation of the polymersome: stretching along the applied field and shrinking in the transverse plane

Low-Frequency Dynamic Magnetic Susceptibility of Antiferromagnetic Nanoparticles with Superparamagnetic Properties

As is known, the multi-sublattice structure of antiferromagnets (AFMs) entails that, under size diminution to the nanoscale, compensation of the sublattice magnetizations becomes incomplete. Due to that, the nanoparticles acquire small, but finite permanent magnetic moments. An AC field applied to such particles induces their magnetic response, the measurement of which is well within the sensitivity range of the experimental technique. Given the small size of the particles, their magnetodynamics is strongly affected by thermal fluctuations, so that their response bears a considerable superparamagnetic contribution. This specific feature is well-known, but usually is accounted for at the estimation accuracy level. Herein, a kinetic model is proposed to account for the magnetic relaxation of AFM nanoparticles, i.e., the processes that take place in the frequency domain well below the magnetic resonance band. Assuming that the particles possess uniaxial magnetic anisotropy, the expressions for the principal components of the both linear static and dynamic susceptibilities are derived, yielding simple analytical expressions, including those for the case of a random distribution of the particle axes

Low-Frequency Dynamic Magnetic Susceptibility of Antiferromagnetic Nanoparticles with Superparamagnetic Properties

As is known, the multi-sublattice structure of antiferromagnets (AFMs) entails that, under size diminution to the nanoscale, compensation of the sublattice magnetizations becomes incomplete. Due to that, the nanoparticles acquire small, but finite permanent magnetic moments. An AC field applied to such particles induces their magnetic response, the measurement of which is well within the sensitivity range of the experimental technique. Given the small size of the particles, their magnetodynamics is strongly affected by thermal fluctuations, so that their response bears a considerable superparamagnetic contribution. This specific feature is well-known, but usually is accounted for at the estimation accuracy level. Herein, a kinetic model is proposed to account for the magnetic relaxation of AFM nanoparticles, i.e., the processes that take place in the frequency domain well below the magnetic resonance band. Assuming that the particles possess uniaxial magnetic anisotropy, the expressions for the principal components of the both linear static and dynamic susceptibilities are derived, yielding simple analytical expressions, including those for the case of a random distribution of the particle axes

Monte Carlo simulation of the structural and magnetic properties of nanoparticle aggregates

Ce travail est une étude théorique par la méthode de Monte Carlo Metropolis (MCM) de nanoparticules (NPs) ferromagnétiques individuelles ou agrégées, sujettes à un comportement supermagnétique. La méthode MCM est utilisée pour décrire des propriétés à l équilibre, mais la séquence d états par lesquels passe le système dans la simulation avant d atteindre l équilibre ressemble beaucoup aux processus cinétiques réels. Cela s avère être un moyen efficace d étudier des phénomènes hors-équilibre dans les nanosystèmes magnétiques. Après construction de modèles d agrégats multi-particules et rappel de leurs propriétés magnétiques dans l état fondamental, le problème de la relaxation libre du moment magnétique est abordé. La quantification temporelle de la méthode MCM proposée par Nowak et al. est ici modifiée de façon à introduire explicitement l anisotropie magnétique des NPs. La même approche est ensuite utilisée pour décrire la relaxation superparamagnétique d une NP sous un champ bias constant. Finalement la méthode MCM est appliquée à un processus hautement hors-équilibre, l hystérésis magnétique dynamique d une NP sous un fort champ alternatif. Les résultats MCM sont comparés aux solutions exactes de l équation cinétique de Brown. D une part les simulations MCM sont capables de très bien reproduire les dépendances exactes de l aimantation de l ensemble de NPs, d autre part dans le cas de l hystérésis dynamique la simulation MCM obéit à une règle spécifique. Quand on simule un cycle par une série de pas de champs avec un nombre d itérations MCM à chaque pas, chacun de ces deux facteurs peut être choisi arbitrairement tant que leur produit est gardé contantPARIS-BIUSJ-Biologie recherche (751052107) / SudocSudocFranceF

Macroscopic optical effects in low concentration ferronematics

We present a detailed experimental and theoretical study of the optical response of suspensions of ferromagnetic nanoparticles (“ferroparticles”) in nematic liquid crystals (“ferronematics”), concentrating on the magnetic field-induced Frederiks transition. Even extremely low ferroparticle concentrations (at a volume fraction between 2 × 10-5 and 2 × 10-4), induce a significant additional ferronematic linear response at low magnetic field (<100 G) and a decrease in the effective magnetic Frederiks threshold. The experimental results demonstrate that our system has weak ferronematic behavior. The proposed theory takes into account the nematic diamagnetism and assumes that the effective magnetic susceptibility, induced by the nanoparticles, no longer dominates the response. The theory is in good agreement with the experimental data for the lowest concentration suspensions and predicts the main features of the more concentrated ones. The deviations observed in these cases hint at extra effects due to particle aggregation, which we have also observed directly in photograph