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

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

Effect of Piezoelectric BaTiO3 Filler on Mechanical and Magnetoelectric Properties of Zn0.25Co0.75Fe2O4/PVDF-TrFE Composites

Polymer-based multiferroics, combining magnetic and piezoelectric properties, are studied experimentally—from synthesis to multi-parameter characterization—in view of their prospects for fabricating biocompatible scaffolds. The main advantage of these systems is facile generation of mechanical deformations and electric signals in response to external magnetic fields. Herein, we address the composites based on PVDF-TrFE polymer matrices filled with a combination of piezoelectric (BaTiO3, BTO) and/or ferrimagnetic (Zn0.25Co0.75Fe2O4, ZCFO) particles. It is shown that the presence of BTO micron-size particles favors stripe-type structuring of the ZCFO filler and enhances the magnetoelectric response of the sample up to 18.6 mV/(cm∙Oe). Besides that, the admixing of BTO particles is crucial because the mechanical properties of the composite filled with only ZCFO is much less efficient in transforming magnetic excitations into the mechanical and electric responses. Attention is focused on the local surfacial mechanical properties since those, to a great extent, determine the fate of stem cells cultivated on these surfaces. The nano-indentation tests are accomplished with the aid of scanning probe microscopy technique. With their proven suitable mechanical properties, a high level of magnetoelectric conversion and also biocompatibility, the composites of the considered type are enticing as the materials for multiferroic-based polymer scaffolds

Multiferroic Coupling of Ferromagnetic and Ferroelectric Particles through Elastic Polymers

Multiferroics are materials that electrically polarize when subjected to a magnetic field and magnetize under the action of an electric field. In composites, the multiferroic effect is achieved by mixing of ferromagnetic (FM) and ferroelectric (FE) particles. The FM particles are prone to magnetostriction (field-induced deformation), whereas the FE particles display piezoelectricity (electrically polarize under mechanical stress). In solid composites, where the FM and FE grains are in tight contact, the combination of these effects directly leads to multiferroic behavior. In the present work, we considered the FM/FE composites with soft polymer bases, where the particles of alternative kinds are remote from one another. In these systems, the multiferroic coupling is different and more complicated in comparison with the solid ones as it is essentially mediated by an electromagnetically neutral matrix. When either of the fields, magnetic or electric, acts on the ‘akin’ particles (FM or FE) it causes their displacement and by that perturbs the particle elastic environments. The induced mechanical stresses spread over the matrix and inevitably affect the particles of an alternative kind. Therefore, magnetization causes an electric response (due to the piezoeffect in FE) whereas electric polarization might entail a magnetic response (due to the magnetostriction effect in FM). A numerical model accounting for the multiferroic behavior of a polymer composite of the above-described type is proposed and confirmed experimentally on a polymer-based dispersion of iron and lead zirconate micron-size particles

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