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We propose a theoretical approach for calculating effective electric and magnetic properties of composites, with field dependent restructuring of the filler. The theory combines the effective medium approximation, extended to a field-dependent (variable) percolation threshold, with an approximate treatment of the nonlinearity of material properties. Theoretical results are compared with experiments on magnetorheological elastomers, which in the context of investigated phenomena are often called magnetoactive elastomers (MAEs). In MAEs with soft polymer matrices, the mutual arrangement of inclusions changes in an applied magnetic field. This reorganization of the microstructure leads to unconventionally large changes of electrical and magnetic properties. The obtained theoretical results describe observed phenomena in MAEs well. For the magnetodielectric effect, qualitative agreement between theory and experiment is demonstrated. In the case of magnetic permeability, quantitative agreement is achieved. The theoretical approach presented can be useful for the development of field-controlled smart materials and design of intelligent structures on their basis, because the field dependence of physical properties can be predicted. (C) 2019 Elsevier B.V. All rights reserved.
A randomly inhomogeneous composite consisting of two, ferromagnetic and nonmagnetic (para-or diamagnetic), phases is considered. The dependence of the effective permeability of the composite on the concentration of the ferromagnetic phase and on the applied magnetic field is found for the case of the negligible hysteresis loop. When the hysteresis loop is appreciable, the remanent magnetization as a function of the ferromagnet concentration is calculated.
A randomly inhomogeneous composite consisting of two, ferromagnetic and nonmagnetic (para-or diamagnetic), phases is considered. The dependence of the effective permeability of the composite on the concentration of the ferromagnetic phase and on the applied magnetic field is found for the case of the negligible hysteresis loop. When the hysteresis loop is appreciable, the remanent magnetization as a function of the ferromagnet concentration is calculated.
Various theoretical models (self-consistent field, local linearization, and percolation theory methods and an analytic solution of the linear problem for an ordered medium) for calculating the magnetostatic properties of two-phase composites containing one ferromagnetic phase were considered. The concentration and field dependences of the effective magnetic permeability were found. A method for determining the coercive force and remanent magnetization as functions of the ferromagnetic phase concentration was suggested. Numerical experiments were performed for composites with a periodic distribution of circular inclusions. The results were compared with the analytically calculated effective magnetic permeability.
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.
The magnetization of a magnetoactive elastomer (MAE) with microparticles of soft magnetic carbonyl iron embedded in a highly elastic matrix has been studied. It is shown that at high temperatures its magnetization curve has the form of a specific hysteresis loop. This hysteresis is attributed to the influence of displacement of magnetized particles in the elastically soft elastomer matrix under the effect of magnetic forces, leading to the change of magnetic interaction between the particles. In this case, there is a maximum in the field dependence of the magnetic susceptibility, the occurrence of which has been associated with the competition between rearrangement of particles, when they are displaced in a magnetic field, and saturation of particles' magnetization. When the MAE is cooled below approximately 225 K, both the magnetic hysteresis and the maximum in the field dependence of the magnetic susceptibility disappear. When the MAE material is cooled below the solidification temperature of the elastomer matrix, the displacements of the magnetic particles during magnetization are blocked by the rigid matrix. The magnetization reversal of the MAE is reversible. This means that the shape of subsequent magnetization loops remains constant and the sample returns into the initial non-magnetized state after the magnetic field is turned off.
Magnetoactive elastomers (MAEs) are composite materials comprised of micrometer-sized ferromagnetic particles in a nonmagnetic elastomermatrix. Asingle-particle mechanism ofmagnetostriction in MAEs, assuming the rotation of a soft magnetic, mechanically rigid particle with uniaxial magnetic anisotropy in magnetic fields is identified and considered theoretically within the framework of an alternative model. In this mechanism, the total magnetic anisotropy energy of the filling particles in the matrix is the sum over single particles. Matrix displacements in the vicinity of the particle and the resulting direction of the magnetization vector are calculated. The effect of matrix deformation is pronounced well if the magnetic anisotropy coefficient K is much larger than the shear modulus mu of the elastic matrix. The feasibility of the proposed magnetostriction mechanism in soft magnetoactive elastomers and gels is elucidated. The magnetic-field-induced internal stresses in the matrix lead to effects of magnetodeformation and may increase the elastic moduli of these composite materials.
It is shown that the critical exponent for the effective shear modulus of a composite medium where a compliant polymer matrix is filled with ferromagnetic particles may significantly depend on the external magnetic field. The physical consequence of this dependence is the critical behavior of the relative magnetorheological effect.
Polydimethylsiloxane based magnetoactive elastomers demonstrate above the melting transition range (e.g. at room temperature) an induced uniaxial magnetic anisotropy, which grows with increasing magnetic field. By freezing a material down to 150 K, displaced iron microparticles are immobilized, so that the magnetic anisotropy can be measured. Magnetic anisotropy “constant” is a consequence of particle displacements and a characteristic of the energy of internal deformations in the polymer matrix. The maximum anisotropy constant of the filling is at least one order of magnitude larger than the shear modulus of the pure elastomer (matrix). In a magnetic field, the gain in the rigidity of the composite material is attributed to the magnetomechanical coupling, which is in turn a source of anisotropy. The concept of effective magnetic field felt by the magnetization allows one to explain the magnetization curve at room temperature from low-temperature measurements. The results can be useful for developing vibration absorbers and isolators.