The relation between the number of magnetic particles and the change in storage modulus induced by a magnetic field was investigated for weak hydrogels containing carbonyl iron, iron oxide, and barium ferrite particles with different diameters in primary particles while maintaining the magnetization of magnetic particles. The change in storage modulus exhibited a power dependency against the number of magnetic particles, which was nearly independent of the magnetic particles. The change in storage modulus was successfully scaled by the reduced number of magnetic particles using the diameter of secondary particles. Microphotographs revealed that iron oxide and barium ferrite particles form aggregations while carbonyl iron particles are well dispersed in carrageenan gels. The diameter of secondary particles determined by a relation between the change in storage modulus and the reduced number of magnetic particles showed similar values with those observed in microphotographs.

The magnetorheological response for magnetic elastomers containing carbonyl iron (CI) particles with a diameter of 6.7 μm coated with poly(methyl methacrylate) (PMMA) was investigated to estimate the diameter of secondary particles from the amplitude of magnetorheological response. Fourier-transformed infrared spectroscopy revealed that the CI particles were coated with PMMA, and the thickness of the PMMA layer was determined to be 71 nm by density measurement. The change in the storage modulus for magnetic elastomers decreased by coating and it was scaled by the number density of CI particles as ΔG~N^2.8. The diameter of secondary particle of CI particles coated with PMMA was calculated to be 8.4 μm. SEM images revealed that the CI particles coated with PMMA aggregated in the polyurethane matrix.