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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)]. 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 Pade 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.
Magnetodielectric properties of magnetoactive elastomers comprising micrometer-sized iron particles dispersed in compliant elastomer matrices are experimentally studied in stepwise time-varying dc magnetic fields. It is found that imposition of magnetic field significantly increases both the effective lossless permittivity of these composite materials as well as their effective conductivity. These magnetodielectric effects are more pronounced for larger concentrations of soft-magnetic filler particles and softer elastomer matrices. The largest observed relative change of the effective dielectric constant in the maximum magnetic field of 0.57 T is of the order of 1000%. The largest observed absolute change of the loss tangent is approximately 0.8. The transient response of the magnetodielectric effect to a step magnetic-field excitation can be rather complex. It changes from a simple monotonic growth with time for small magnetic-field steps (<0.1 T) to a non-monotonic behavior with a significant rapidly appearing overshoot for large magnetic-field steps (>0.3 T). The settling time to the magnetic-field step excitation can reach roughly 1000 s and it depends on the applied magnetic field and sample composition. There is also significant hysteresis of the magnetodielectric effect on the externally applied magnetic field. These findings are attributed to the rearrangement of ferromagnetic filler particles in external magnetic fields. The results will be useful for understanding and predicting the transient behavior of magnetoactive elastomers in applications where the control magnetic field is time dependent. (C) 2017 Elsevier Ltd. All rights reserved.
The magnetic properties of a magnetoactive elastomer (MAE) filled with mu m-sized soft-magnetic iron particles have been experimentally studied in the temperature range between 150 K and 310 K. By changing the temperature, the elastic modulus of the elastomer matrix was modified, and it was possible to obtain magnetization curves for an invariable arrangement of particles in the sample and in the case when the particles were able to change their position within the MAE under the influence of magnetic forces. At low (less than 220 K) temperatures, when the matrix becomes rigid, the magnetization of the MAE does not show a hysteresis behavior, and it is characterized by a negative value of the Rayleigh constant. At room temperature, when the polymer matrix is compliant, a magnetic hysteresis exists where the dependence of the differential magnetic susceptibility on the magnetic field exhibits local maxima. The appearance of these maxima is explained by the elastic resistance of the matrix to the displacement of particles under the action of magnetic forces.
Properties of Polydimethylsiloxane and Magnetoactive Polymers with Electroconductive Particles
(2018)
Magnetoactive polymers are intelligent materials whose mechanical and electrical characteristics are reversibly influenced by external magnetic stimuli. They consist of a highly elastic polymer matrix in which magnetically soft and/or hard particles are distributed by means of special fabrication processes. In addition to ferromagnetic particles such as carbonyl iron powder, electrically conductive particles may also be embedded into the polymer matrix. After characterizing a range of compounds, this work focuses on a comparison of the electrical properties and the suitability of various materials for applications, with particular emphasis on integration into 3D and 6D printing processes. 6D printing is based on the selective positioning of particles in a 3D polymer matrix with a further three degrees of freedom for a graduated dispersion of the particles at certain points and in desired directions. The aim is therefore to ensure that the polymers containing electroconductive tracks have the best possible electrical properties, that is, low resistivity but are still capable of being printed. A comparison between the traditionally used compounds containing graphite and carbon black is made for the first time. This latter is found to be greatly superior both in terms of electrical conductivity and applicability to 3D printing and 6D printing.
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)] that uses a realistic representation for the cluster network possessing fractal structure. Two mechanical loading regimes are identified. At small strain amplitudes the exponent beta 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 beta 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.
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 approximate to 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.
The formation of microstructures in magnetoactive polymers (MAPs) is a recently discovered phenomenon found only with very low filler particle concentrations (less than 3 wt %). Due to the degassing process, filler particles collect around an ascending bubble, which dissolves at a certain point leaving particulate rings within the matrix. The formation of toroidal microstructures commences as filler concentration approaches 1 wt %. The development of coherent parallel aligned rings with a compact order continues as particle concentrations increase toward 2 wt %. Between 2 and 3 wt % capillary doublets develop, while mass percentages higher than 3% result in increasing entropy as the random order of particle agglomeration found in higher concentration MAP dominates. Self-structured samples of different filler material and concentrations between 1 and 3 wt % have been investigated using X-ray tomography, where the emerging structures can be observed and visualized. The ring structures resulting from this research represent microinductivities which can be fabricated in a targeted manner, thus enabling new applications in the high-frequency radio field. Furthermore, these anisotropic, but well-organized, structures have magnetic field-dependent implications for optical, thermal, acoustic, and medical applications.