Single-particle mechanism of magnetostriction in magnetoactive elastomers

Abstract

Magnetoactive elastomers (MAEs) are composite materials comprised of micrometer-sized ferromagnetic particles in a nonmagnetic elastomer matrix. A single-particle mechanism of magnetostriction 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 µ 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.

Effect of single-particle magnetostriction on the shear modulus of compliant magnetoactive elastomers

“…Magnetic energy of the particle and elastic energy of the surrounding matrix taking into account rotation of the particle in a magnetic field [18] can be written as the following sum:…”

“…Fig 1) and M ϕ is the angle determining the direction of the magnetic moment (M = |M|) of the inclusion. The first term in (1) describes the energy of the magnetic anisotropy, the second term stands for the Zeeman energy and the third term represents the elastic energy of the matrix taking into account an additional rotation of the particle due to the influence of the magnetic field [18]. If all particles are identical and have the same orientation of the anisotropy axis, in the case of low concentration, when the mutual influence of the elastic fields of MAE particles can be neglected, the volume density of single-particle energy in a magnetic field can be written as:…”

“…From (18) it follows that in the saturation limit the magnetic-field contribution to the effective modulus depends on the concentration of the particles and the elasticity of the matrix.…”

“…In conventional ferromagnetic materials, MS is a consequence of the occurrence of magnetoelastic stresses upon magnetization [13 -17]. In MAEs, the inherent MS of magnetic inclusions can be neglected, because the MS of these composite materials is much larger than the MS of individual inclusions [18]. MS in MAEs is caused by the action of the magnetized particles on the nonmagnetic matrix.…”

“…The peculiarity of description of mechanical deformations in MAEs, as compared to conventional elastomers, is that the magnetic inclusion has additional degrees of freedom, which must be taken into account when calculating the effective characteristics of MAE in an external magnetic field. As shown in [18], these degrees of freedom are the directions of the magnetic moment vectors of filler particles and the orientations of the easy magnetization axes of magnetic inclusions. Crucial effect of the magnetic anisotropy of filler particles on the equilibrium structure and magnetization of ferrogels has been recently investigated in [54] by coarse-grained molecular dynamics simulations.…”