Dynamic moduli of magneto-sensitive elastomers: a coarse-grained network model

The viscoelastic properties of magneto-sensitive elastomers (MSEs) in a low-frequency regime are studied using a coarse-grained network model. The proposed model takes into account the mechanical coupling between magnetic particles included in a whole network structure and magnetic interactions between them. We show that the application of a constant uniform magnetic field leads to the splitting of the relaxation spectrum into two branches for the motions of the particles parallel and perpendicular to the field. The shear dynamic moduli G' and G'' of MSEs are calculated as a function of frequency. The values of G' and G'' are shown to depend on the direction of the shear deformation with respect to the magnetic field. For instance, both G' and G'' decrease if the magnetic field is applied parallel to the shear velocity (D-geometry) and increase if it is applied along the shear gradient (G-geometry). The latter prediction is in a qualitative agreement with existing experimental data. The theory allows us to analyse experimental data and to extract the structural characteristics of MSEs.