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

On the Piezomagnetism of Magnetoactive Elastomeric Cylinders in Uniform Magnetic Fields: Height Modulation in the Vicinity of an Operating Point by Time-Harmonic Fields

Soft magnetoactive elastomers (MAEs) are currently considered to be promising materials for actuators in soft robotics. Magnetically controlled actuators often operate in the vicinity of a bias point. Their dynamic properties can be characterized by the piezomagnetic strain coefficient, which is a ratio of the time-harmonic strain amplitude to the corresponding magnetic field strength. Herein, the dynamic strain response of a family of MAE cylinders to the time-harmonic (frequency of 0.1-2.5 Hz) magnetic fields of varying amplitude (12.5 kA/m-62.5 kA/m), superimposed on different bias magnetic fields (25-127 kA/m), is systematically investigated for the first time. Strain measurements are based on optical imaging with sub-pixel resolution. It is found that the dynamic strain response of MAEs is considerably different from that in conventional magnetostrictive polymer composites (MPCs), and it cannot be described by the effective piezomagnetic constant from the quasi-static measurements. The obtained maximum values of the piezomagnetic strain coefficient (∼102 nm/A) are one to two orders of magnitude higher than in conventional MPCs, but there is a significant phase lag (35-60°) in the magnetostrictive response with respect to an alternating magnetic field. The experimental dependencies of the characteristics of the alternating strain on the amplitude of the alternating field, bias field, oscillation frequency, and aspect ratio of cylinders are given for several representative examples. It is hypothesized that the main cause of observed peculiarities is the non-linear viscoelasticity of these composite materials.

Transient Response of Macroscopic Deformation of Magnetoactive Elastomeric Cylinders in Uniform Magnetic Fields

Significant deformations of bodies made from compliant magnetoactive elastomers (MAE) in magnetic fields make these materials promising for applications in magnetically controlled actuators for soft robotics. Reported experimental research in this context was devoted to the behaviour in the quasi-static magnetic field, but the transient dynamics are of great practical importance. This paper presents an experimental study of the transient response of apparent longitudinal and transverse strains of a family of isotropic and anisotropic MAE cylinders with six different aspect ratios in time-varying uniform magnetic fields. The time dependence of the magnetic field has a trapezoidal form, where the rate of both legs is varied between 52 and 757 kA/(s·m) and the maximum magnetic field takes three values between 153 and 505 kA/m. It is proposed to introduce four characteristic times: two for the delay of the transient response during increasing and decreasing magnetic field, as well as two for rise and fall times. To facilitate the comparison between different magnetic field rates, these characteristic times are further normalized on the rise time of the magnetic field ramp. The dependence of the normalized characteristic times on the aspect ratio, the magnetic field slew rate, maximum magnetic field values, initial internal structure (isotropic versus anisotropic specimens) and weight fraction of the soft-magnetic filler are obtained and discussed in detail. The normalized magnetostrictive hysteresis loop is introduced, and used to explain why the normalized delay times vary with changing experimental parameters.

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.

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.

Theory of static magnetization of magnetopolymer composites: The second virial approximation

This paper deals with a theoretical study of the static magnetization of a composite, consisting of nanodisperse single-domain ferromagnetic particles immobilized in a nonmagnetic medium. This situation is typical for magnetopolymer systems-smart materials, which found applications in high industrial and biomedical applications. It is supposed that the composite was polymerized without an external magnetic field; after curing the particles retain the spatial distribution and orientation of their axes of easy magnetization that they had before the host medium polymerization. Our results demonstrate that, in contrast to ferrofluids with a liquid host medium, a magnetic interparticle interaction provokes a decrease of the macroscopic magnetization of the system.

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.

Magnetoelectric Response of Laminated Cantilevers Comprising a Magnetoactive Elastomer and a Piezoelectric Polymer, in Pulsed Uniform Magnetic Fields

The voltage response to pulsed uniform magnetic fields and the accompanying bending deformations of laminated cantilever structures are investigated experimentally in detail. The structures comprise a magnetoactive elastomer (MAE) slab and a commercially available piezoelectric polymer multilayer. The magnetic field is applied vertically and the laminated structures are customarily fixed in the horizontal plane or, alternatively, slightly tilted upwards or downwards. Six different MAE compositions incorporating three concentrations of carbonyl iron particles (70 wt%, 75 wt% and 80 wt%) and two elastomer matrices of different stiffness are used. The dependences of the generated voltage and the cantilever’s deflection on the composition of the MAE layer and its thickness are obtained. The appearance of the voltage between the electrodes of a piezoelectric material upon application of a magnetic field is considered as a manifestation of the direct magnetoelectric (ME) effect in a composite laminated structure. The ME voltage response increases with the increasing total quantity of the soft-magnetic filler in the MAE layer. The relationship between the generated voltage and the cantilever’s deflection is established. The highest observed peak voltage around 5.5 V is about 8.5-fold higher than previously reported values. The quasi-static ME voltage coefficient for this type of ME heterostructures is about 50 V/A in the magnetic field of ≈100 kA/m, obtained for the first time. The results could be useful for the development of magnetic field sensors and energy harvesting devices relying on these novel polymer composites.

Regulating Tissue-Mimetic Mechanical Properties of Bottlebrush Elastomers by Magnetic Field

We report on a new class of magnetoactive elastomers (MAEs) based on bottlebrush polymer networks filled with carbonyl iron microparticles. By synergistically combining solvent-free, yet supersoft polymer matrices, with magnetic microparticles, we enable the design of composites that not only mimic the mechanical behavior of various biological tissues but also permit contactless regulation of this behavior by external magnetic fields. While the bottlebrush architecture allows to finely tune the matrix elastic modulus and strain-stiffening, the magnetically aligned microparticles generate a 3-order increase in shear modulus accompanied by a switch from a viscoelastic to elastic regime as evidenced by a ca. 10-fold drop of the damping factor. The developed method for MAE preparation through solvent-free coinjection of bottlebrush melts and magnetic particles provides additional advantages such as injection molding of various shapes and uniform particle distribution within MAE composites. The synergistic combination of bottlebrush network architecture and magnetically responsive microparticles empowers new opportunities in the design of actuators and active vibration insulation systems.

Magnetorheology: a review

Magnetic Soft Matter is a rapidly evolving discipline with fundamental and practical interest. This is due to the fact that its physical properties can be easily controlled through external magnetic fields. In this review paper, we revisit the most recent progress in the field (since 2010) emphasizing the rheological properties of these fascinating materials. New formulations and flow kinematics are discussed. Also, new members are integrated into the long-lived magnetorheology family and suggestions are provided for future development.

Giant Extensional Strain of Magnetoactive Elastomeric Cylinders in Uniform Magnetic Fields

Elongations of magnetoactive elastomers (MAEs) under ascending-descending uniform magnetic fields were studied experimentally using a laboratory apparatus specifically designed to measure large extensional strains (up to 20%) in compliant MAEs. In the literature, such a phenomenon is usually denoted as giant magnetostriction. The synthesized cylindrical MAE samples were based on polydimethylsiloxane matrices filled with micrometer-sized particles of carbonyl iron. The impact of both the macroscopic shape factor of the samples and their magneto-mechanical characteristics were evaluated. For this purpose, the aspect ratio of the MAE cylindrical samples, the concentration of magnetic particles in MAEs and the effective shear modulus were systematically varied. It was shown that the magnetically induced elongation of MAE cylinders in the maximum magnetic field of about 400 kA/m, applied along the cylinder axis, grew with the increasing aspect ratio. The effect of the sample composition is discussed in terms of magnetic filler rearrangements in magnetic fields and the observed experimental tendencies are rationalized by simple theoretical estimates. The obtained results can be used for the design of new smart materials with magnetic-field-controlled deformation properties, e.g., for soft robotics.

Bio-Inspired Passion Fruit-like Fe3O4@C Nanospheres Enabling High-Stability Magnetorheological Performances

Magnetorheological (MR) fluids have been successfully utilized in versatile fields but are still limited by their relatively inferior long-term dispersion stability. Herein, bio-inspired passion fruit-like Fe₃O₄@C nanospheres were fabricated via a simple hydrothermal and calcination approach to tackle the settling challenge. The unique structures provide sufficient active interfaces for the penetration of carrier mediums, leading to preferable wettability between particles and medium oils. Compared with the bare Fe₃O₄ nanoparticle suspension, the resulting Fe₃O₄@C nanosphere-based MR fluid exhibits desirable stability and relatively low field-off viscosity even at a high particle concentration up to 35 vol %.

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.

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.

Railway Actuator Made of Magnetic Elastomers and Driven by a Magnetic Field

We fabricated a mono-link using bimodal magnetic elastomers that demonstrate drastic changes in the elastic modulus by magnetic fields. The magnetic elastomer is bimodal consisting of large magnetic particles and nonmagnetic fine particles. The storage modulus for bimodal magnetic elastomers was altered from 2.2 × 10⁵ to 1.7 × 10⁶ Pa by a magnetic field of 500 mT. Compression tests up to a strain of 20% also revealed that the on-field stress for the bimodal magnetic elastomer was 1.24 times higher than the off-field stress. The bimodal magnetic elastomer was synthesized for the mono-link and was mounted on the bogie of a railway vehicle. A running test exhibited that the wheel lateral force was reduced by 20% by applying a magnetic field of 390 mT.

Elastic Properties of Magnetorheological Elastomers in a Heterogeneous Uniaxial Magnetic Field

Magnetorheological elastomers (MREs) are stimulus-responsive soft materials that consist of polymeric matrices and magnetic particles. In this study, large-strain response of MREs with 5 vol % of carbonyl iron (CI) particles is experimentally characterized for two different conditions: (1) shear deformation in a uniform magnetic field; and (2), compression in a heterogeneous uniaxial magnetic field. For condition (1), dynamic viscoelastic measurements were performed using a rheometer with a rotor disc and an electric magnet that generated a uniform magnetic field on disc-like material samples. For condition (2), on the other hand, three permanent magnets with different surface flux densities were used to generate a heterogeneous uniaxial magnetic field under cylindrical material samples. The experimental results were mathematically modeled, and the relationship between them was investigated. We also used finite-element method (FEM) software to estimate the uniaxial distributions of the magnetic field in the analyzed MREs for condition (2), and developed mathematical models to describe these phenomena. By using these practicable techniques, we established a simple macroscale model of the elastic properties of MREs under simple compression. We estimated the elastic properties of MREs in the small-strain regime (neo⁻Hookean model) and in the large-strain regime (Mooney⁻Rivlin model). The small-strain model explains the experimental results for strains under 5%. On the other hand, the large-strain model explains the experimental results for strains above 10%.

Magnetically Tunable Vibration Transmissibility for Polyurethane Magnetic Elastomers

The effect of a weak magnetic field on vibration transmissibility was investigated for magnetic elastomers with various volume fractions of magnetic particles. Polyurethane elastomers without magnetic particles exhibited a natural frequency at 53 Hz and were insensitive to a magnetic field of 60 mT. The natural frequency for magnetic elastomers with a volume fraction of 0.23 was 115 Hz at 0 mT, and increased to 134 Hz at 60 mT. The vibration transmissibility was independent of the magnetic field. A linear relation between the natural frequency and (G/m)^1/2 was observed (G: storage modulus, m: mass), indicating that the observed vibration is basically described by a simple harmonic oscillation.

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.