Surface relief of magnetoactive elastomeric films in a homogeneous magnetic field: molecular dynamics simulations

Effects of Filler Anisometry on the Mechanical Response of a Magnetoactive Elastomer Cell: A Single-Inclusion Modeling Approach

A finite-element model of the mechanical response of a magnetoactive elastomer (MAE) volume element is presented. Unit cells containing a single ferromagnetic inclusion with geometric and magnetic anisotropy are considered. The equilibrium state of the cell is calculated using the finite-element method and cell energy minimization. The response of the cell to three different excitation modes is studied: inclusion rotation, inclusion translation, and uniaxial cell stress. The influence of the magnetic properties of the filler particles on the equilibrium state of the MAE cell is considered. The dependence of the mechanical response of the cell on the filler concentration and inclusion anisometry is calculated and analyzed. Optimal filler shapes for maximizing the magnetic response of the MAE are discussed.

An integrated immunochromatographic device for C-reactive protein detection using hierarchical dendritic gold nanostructure films

Immunochromatographic test strips typically consist of sample pad, conjugate pad, nitrocellulose membrane, and absorbent pad. Even minute variations in the assembly of these components can lead to inconsistent sample-reagent interactions, thereby reducing reproducibility. In addition, the nitrocellulose membrane is susceptible to damage during assembly and handling. To address this issue, we propose to replace the sample pad, conjugate pad, and nitrocellulose membrane with hierarchical dendritic gold nanostructure (HD-nanoAu) films to develop a compact integrated immunochromatographic strip. The strip uses quantum dots as a background fluorescence signal and employs fluorescence quenching to detect C-reactive protein (CRP) in human serum. A 5.9 μm thick HD-nanoAu film was electrodeposited on an ITO conductive glass by the constant potential method. The wicking kinetics of the HD-nanoAu film was thoroughly investigated, and the results indicated that the film exhibited favorable wicking properties, with a wicking coefficient of 0.72 μm ms^-0.5. The immunochromatographic device was fabricated by etching three interconnected rings on HD-nanoAu/ITO to designate sample/conjugate (S/C), test (T), and control (C) regions. The S/C region was immobilized with mouse anti-human CRP antibody (Ab1) labeled with gold nanoparticles (AuNPs), while the T region was preloaded with polystyrene microspheres decorated with CdSe@ZnS quantum dots (QDs) as background fluorescent material, followed by mouse anti-human CRP antibody (Ab2). The C region was immobilized with goat anti-mouse IgG antibody. After the samples were added to the S/C region, the excellent wicking properties of the HD-nanoAu film facilitated the lateral flow of the CRP-containing sample toward the T and C regions after binding to AuNPs labeled with CRP Ab1. In the T region, CRP-AuNPs-Ab1 formed sandwich immunocomplexes with Ab2, and the fluorescence of QDs was quenched by AuNPs. The ratio of fluorescence intensity in the T region to that in the C region was used to quantify CRP. The T/C fluorescence intensity ratio was negatively correlated with the CRP concentration in the range of 26.67-853.33 ng mL^-1 (corresponding to 300-fold diluted human serum), with a correlation coefficient (R²) of 0.98. The limit of detection was 15.0 ng mL^-1 (corresponding to 300-fold diluted human serum), and the range of relative standard deviation: 4.48-5.31%, with a recovery rate of 98.22-108.33%. Common interfering substances did not cause significant interference, and the range of relative standard deviation: 1.96-5.51%. This device integrates multiple components of conventional immunochromatographic strips onto a single HD-nanoAu film, resulting in a more compact structure that improves the reproducibility and robustness of detection, making it promising for point-of-care testing applications.

Dynamically tunable lamellar surface structures from magnetoactive elastomers driven by a uniform magnetic field

Stimuli responsive materials are key ingredients for any application that requires dynamically tunable or on-demand responses. In this work we report experimental and theoretical investigation of magnetic-field driven modifications of soft-magnetic elastomers whose surface was processed by laser ablation into lamellar microstructures that can be manipulated by a uniform magnetic field. We present a minimal hybrid model that elucidates the associated deflection process of the lamellae and explains the lamellar structure frustration in terms of dipolar magnetic forces arising from the neighbouring lamellae. We experimentally determine the magnitude of the deflection as a function of magnetic flux density and explore the dynamic response of lamellae to fast changes in a magnetic field. A relationship between the deflection of lamellae and modifications of the optical reflectance of the lamellar structures is resolved.

Switching-field and first-order-reversal-curve distribution measurements in magnetic elastomers by molecular dynamics simulations: Accounting for polydispersity

In this work we employ molecular dynamics simulations to investigate the first-order-reversal-curve distribution 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.

Microstructured Magnetoactive Elastomers for Switchable Wettability

We demonstrate the control of wettability of non-structured and microstructured magnetoactive elastomers (MAEs) by magnetic field. The synthesized composite materials have a concentration of carbonyl iron particles of 75 wt.% (≈27 vol.%) and three different stiffnesses of the elastomer matrix. A new method of fabrication of MAE coatings on plastic substrates is presented, which allows one to enhance the response of the apparent contact angle to the magnetic field by exposing the particle-enriched side of MAEs to water. A magnetic field is not applied during crosslinking. The highest variation of the contact angle from (113 ± 1)° in zero field up to (156 ± 2)° at about 400 mT is achieved in the MAE sample with the softest matrix. Several lamellar and pillared MAE structures are fabricated by laser micromachining. The lateral dimension of surface structures is about 50 µm and the depth varies between 3 µm and 60 µm. A systematic investigation of the effects of parameters of laser processing (laser power and the number of passages of the laser beam) on the wetting behavior of these structures in the absence and presence of a magnetic field is performed. In particular, strong anisotropy of the wetting behavior of lamellar structures is observed. The results are qualitatively discussed in the framework of the Wenzel and Cassie–Baxter models. Finally, directions of further research on magnetically controlled wettability of microstructured MAE surfaces are outlined. The obtained results may be useful for the development of magnetically controlled smart surfaces for droplet-based microfluidics.

Magneto-elastic coupling as a key to microstructural response of magnetic elastomers with flake-like particles

Using the combination of experiment and molecular dynamics simulations, we investigate structural transformations in magnetic elastomers with NdFeB flake-like particles, caused by applied moderate magnetic fields. We explain why and how those transformations depend on whether or not the samples are initially cured by a short-time exposure to a strong field. We find that in a cured sample, a moderate magnetic field leads mainly to in-place flake rotations that are fully reversed once the applied field is switched off. In contrast, in an initially non-cured sample the flakes perform both translation and rotations under the influence of a moderate applied field that lead to the formation of chain-like structures that remain such even if the field is switched off.

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.

Reconfigurable Surface Micropatterns Based on the Magnetic Field-Induced Shape Memory Effect in Magnetoactive Elastomers

A surface relief grating with a period of 30 µm is embossed onto the surface of magnetoactive elastomer (MAE) samples in the presence of a moderate magnetic field of about 180 mT. The grating, which is represented as a set of parallel stripes with two different amplitude reflectivity coefficients, is detected via diffraction of a laser beam in the reflection configuration. Due to the magnetic-field-induced plasticity effect, the grating persists on the MAE surface for at least 90 h if the magnetic field remains present. When the magnetic field is removed, the diffraction efficiency vanishes in a few minutes. The described effect is much more pronounced in MAE samples with larger content of iron filler (80 wt%) than in the samples with lower content of iron filler (70 wt%). A simple theoretical model is proposed to describe the observed dependence of the diffraction efficiency on the applied magnetic field. Possible applications of MAEs as magnetically reconfigurable diffractive optical elements are discussed. It is proposed that the described experimental method can be used as a convenient tool for investigations of the dynamics of magnetically induced plasticity of MAEs on the micrometer scale.

A Cascading Mean-Field Approach to the Calculation of Magnetization Fields in Magnetoactive Elastomers

We consider magnetoactive elastomer samples based on the elastic matrix and magnetizable particle inclusions. The application of an external magnetic field to such composite samples causes the magnetization of particles, which start to interact with each other. This interaction is determined by the magnetization field, generated not only by the external magnetic field but also by the magnetic fields arising in the surroundings of interacting particles. Due to the scale invariance of magnetic interactions (O(r−3) in d=3 dimensions), a comprehensive description of the local as well as of the global effects requires a knowledge about the magnetization fields within individual particles and in mesoscopic portions of the composite material. Accordingly, any precise calculation becomes technically infeasible for a specimen comprising billions of particles arranged within macroscopic sample boundaries. Here, we show a way out of this problem by presenting a greatly simplified, but accurate approximation approach for the computation of magnetization fields in the composite samples. Based on the dipole model to magnetic interactions, we introduce the cascading mean-field description of the magnetization field by separating it into three contributions on the micro-, meso-, and macroscale. It is revealed that the contributions are nested into each other, as in the Matryoshka’s toy. Such a description accompanied by an appropriate linearization scheme allows for an efficient and transparent analysis of magnetoactive elastomers under rather general conditions.

Magneto-Mechanical Coupling in Magneto-Active Elastomers

In the present work, the magneto-mechanical coupling in magneto-active elastomers is investigated from two different modeling perspectives: a micro-continuum and a particle–interaction approach. Since both strategies differ significantly in their basic assumptions and the resolution of the problem under investigation, they are introduced in a concise manner and their capabilities are illustrated by means of representative examples. To motivate the application of these strategies within a hybrid multiscale framework for magneto-active elastomers, their interchangeability is then examined in a systematic comparison of the model predictions with regard to the magneto-deformation of chain-like helical structures in an elastomer surrounding. The presented results show a remarkable agreement of both modeling approaches and help to provide an improved understanding of the interactions in magneto-active elastomers with chain-like microstructures.

Magnetostriction in elastomers with mixtures of magnetically hard and soft microparticles: effects of nonlinear 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 on 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 nontrivial reentrant (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 Fröhlich–Kennelly approximation; with respect to the polymer matrix, we analyze the dependence of the reentrant deformation on its rigidity.

Magnetic-field-induced stress in confined magnetoactive elastomers

We present a theoretical approach for calculating the state of stress induced by a uniform magnetic field in confined magnetoactive elastomers of arbitrary shape. The theory explicitly includes the magnetic field generated by magnetizable spherical inclusions in the sample interior assuming a non-linear magnetization behavior. The initial spatial distribution of particles and its change in an external magnetic field are considered. This is achieved by the introduction of an effective demagnetizing factor where both the sample shape and the material microstructure are taken into account. Theoretical predictions are fitted to the stress data measured using a specifically designed experimental setup. It is shown that the theory enables the quantification of the effect of material microstructure upon introducing a specific microstructural factor and its derivative with respect to the extensional strain in the undeformed state. The experimentally observed differences between isotropic and anisotropic samples, compliant and stiff elastomer matrices are explained.

Characterisation of the magnetic response of nanoscale magnetic filaments in applied fields

Incorporating magnetic nanoparticles (MNPs) within permanently crosslinked polymer-like structures opens up the possibility for synthesis of complex, highly magneto-responsive systems. Among such structures are chains of prealigned magnetic (ferro- or super-paramagnetic) monomers, permanently crosslinked by means of macromolecules, which we refer to as magnetic filaments (MFs). In this paper, using molecular dynamics simulations, we encompass filament synthesis scenarios, with a compact set of easily tuneable computational models, where we consider two distinct crosslinking approaches, for both ferromagnetic and super-paramagnetic monomers. We characterise the equilibrium structure, correlations and magnetic properties of MFs in static magnetic fields. Calculations show that MFs with ferromagnetic MNPs in crosslinking scenarios where the dipole moment orientations are decoupled from the filament backbone, have similar properties to MFs with super-paramagnetic monomers. At the same time, magnetic properties of MFs with ferromagnetic MNPs are more dependent on the crosslinking approach than they are for ones with super-paramagnetic monomers. Our results show that, in a strong applied field, MFs with super-paramagnetic MNPs have similar magnetic properties to ferromagnetic ones, while exhibiting higher susceptibility in low fields. We find that MFs with super-paramagnetic MNPs have a tendency to bend the backbone locally rather than to fully stretch along the field. We explain this behaviour by supplementing Flory theory with an explicit dipole-dipole interaction potential, with which we can take in to account folded filament configurations. It turns out that the entropy gain obtained through bending compensates an insignificant loss in dipolar energy for the filament lengths considered in the manuscript.

Field-induced surface deformation of magnetoactive elastomers with anisometric fillers: a single-particle model

Surface relief of magnetoactive elastomers (MAEs) based on soft polymer matrices filled with anisometric magnetically hard fillers is studied theoretically in magnetic fields applied perpendicular to the MAE surface. A single-particle 2D cell model describing the rotation of one individual elliptical particle in a near-surface MAE layer is developed. The equilibrium rotation angle of particles is defined by a balance between Zeeman, magnetic anisotropy and elastic (generated in the polymer matrix) energy increments. The Stoner-Wohlfarth model is used to describe magnetic properties of the filler particles while the elastic energy as a function of the particle rotation angle is evaluated numerically using FEM simulations. A representative surface MAE system is constructed via superposition of single-particle cells with field-driven magnetic particles, and surface relief characteristics are derived for various sets of geometric and statistical parameters. Limitations of the proposed approach have been discussed.

Static magnetization of immobilized, weakly interacting, superparamagnetic nanoparticles

The magnetization curve and initial susceptibility of immobilized superparamagnetic nanoparticles are studied using statistical-mechanical theory and Monte Carlo computer simulations. The nanoparticles are considered to be distributed randomly within an implicit solid matrix, but with the easy axes distributed according to particular textures: these are aligned parallel or perpendicular to an external magnetic field, or randomly distributed. The magnetic properties are calculated as functions of the magnetic crystallographic anisotropy barrier (measured with respect to the thermal energy by a parameter σ), and the Langevin susceptibility (related to the dipolar coupling constant and the volume fraction). It is shown that the initial susceptibility χ is independent of σ in the random case, an increasing function of σ in the parallel case, and a decreasing function of σ in the perpendicular case. Including particle-particle interactions enhances χ, and especially so in the parallel case. A first-order modified mean-field (MMF1) theory is accurate as compared to the simulation results, except in the parallel case with a large value of σ. These observations can be explained in terms of the range and strength of the (effective) interactions and correlations between particles, and the effects of the orientational degrees of freedom. The full magnetization curves show that a parallel texture enhances the magnetization, while a perpendicular texture suppresses it, with the effects growing with increasing σ. In the random case, while the initial response is independent of σ, the high-field magnetization decreases with increasing σ. These trends can be explained by the energy required to rotate the magnetic moments with respect to the easy axes.

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.

The loss of mechanical stability and the critical magnetization of a ferromagnetic particle in an elastomer

The rotation of a spherical magnetically soft ferromagnetic particle with uniaxial magnetic anisotropy and located in an elastomer through a certain angle under the action of a magnetic field has been studied theoretically. It was found that if the particle loses its mechanical stability, its rotation angle becomes critically dependent on the magnetic field magnitude. The magnetically induced critical rotation of the particle in the elastomer has a magneto-elastic origin and is accompanied by a critical change in the magnetization of the particle multidomain state, as occurs in the case of second-order magnetic phase transitions. The transition of a particle in a soft-elastic elastomer from the multidomain state into a uniformly magnetized one was shown to be independent of the magnitude of the particle magnetic anisotropy field. The particle rotation was found to result in the appearance of a maximum in the field dependence of the magnetic susceptibility.

Effect of Material Composition on Tunable Surface Roughness of Magnetoactive Elastomers

We investigated magnetic-field-induced modifications of the surface roughness of magnetoactive elastomers (MAEs) with four material compositions incorporating two concentrations of ferromagnetic microparticles (70 wt% and 80 wt%) and exhibiting two shear storage moduli of the resulting composite material (about 10 kPa and 30 kPa). The analysis was primarily based on spread optical reflection measurements. The surfaces of all four materials were found to be very smooth in the absence of magnetic field (RMS roughness below 50 nm). A maximal field-induced roughness modification (approximately 1 μm/T) was observed for the softer material with the lower filler concentration, and a minimal modification (less than 50 nm/T) was observed for the harder material with the higher filler concentration. All four materials showed a significant decrease in the total optical reflectivity with an increasing magnetic field as well. This effect is attributed to the existence of a distinct surface layer that is depleted of microparticles in the absence of a magnetic field but becomes filled with particles in the presence of the field. We analyzed the temporal response of the reflective properties to the switching on and off of the magnetic field and found switching-on response times of around 0.1 s and switching-off response times in the range of 0.3–0.6 s. These observations provide new insight into the magnetic-field-induced surface restructuring of MAEs and may be useful for the development of magnetically reconfigurable elastomeric optical surfaces.

Simulation of Magnetodielectric Effect in Magnetorheological Elastomers

We present the results of numerical simulation of magnetodielectric effect (MDE) in magnetorheological elastomers (MRE)—the change of effective permittivity of elastomer placed under the external magnetic field. The computer model of effect is based on an assumption about the displacement of magnetic particles inside the elastic matrix under the external magnetic field and the formation of chain-like structures. Such displacement of metallic particles between the planes of capacitor leads to the change of capacity, which can be considered as a change of effective permittivity of elastomer caused by magnetic field (magnetodielectric effect). In the literature, mainly the 2D approach is used to model similar effects. In this paper, we present a new approach of magnetorheological elastomers simulation—a 3D-model of the magnetodielectric effect with ability to simulate systems of 105 particles. Within the framework of the model, three types of particle size distributions were simulated, which gives an advantage over previously reported approaches. Lognormal size distribution was shown to give better qualitative match of the modeling and experimental results than monosized type. The developed model resulted in a good qualitative agreement with all experimental data obtained earlier for Fe-based elastomers. The proposed model is useful to study these novel functional materials, analyze the features of magnetodielectric effect and predict the optimal composition of magnetorheological elastomers for further profound experimental study.