Dipolar interactions among magnetic dipoles of iron oxide particles dispersed in mili-size hydrogel beads
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The recently published Mean Field Interacting Superparamagnet Model (MFISP model), which introduces the effective demagnetizing factor NE, is tested in specimens having a random-like spatial distribution of magnetic nanoparticles, where different hierarchies of clustering are present. These specimens are ferrogel PVA/iron oxide beads synthesized by a one-pot route, having spheroidal shapes and sizes of about 1 mm, and chain and disk-like arrays (superstructures) of beads. Raman analyses indicated that magnetic nanoparticles are composed by a mixture of magnetite and maghemite. Beads swell 208% by hydration in about 40 min. The increase of the ac susceptibility as a function of hydration time closely reflects the effect of bead swelling, in agreement with the expected diminution of dipole–dipole interactions. Measured susceptibility is analyzed in terms of the susceptibility ? of non-interacting particles and the effective demagnetizing factor NE of the specimen, which depends on swelling. The Specific Absorption Rate of electromagnetic power by the beads grows with the hydration time in agreement with ac susceptibility behavior. For long hydration times susceptibility and high field magnetization decrease. This is explained by the occurrence of oxidation of magnetite/maghemite to hematite. Isothermal magnetization experiments are performed on each superstructure in two perpendicular principal directions each. Results are consistently described with the MFISP model by considering two hierarchies of clustering: beads themselves and clusters within the beads. From the whole set of experiments, it is possible to estimate values for the volume fractions of particles in clusters and clusters in beads, given by xpc=0.46(15) and xcb=0.16(5). The susceptibility of non-interacting particles, ?=13(4), is also obtained, which results about five times larger than the measured (apparent) one. The MFISP model proves to be a convenient and efficient tool for the analysis of magnetization studies of complex 3d dispersions of magnetic nanoparticles, allowing an experimental determination of relevant physical information, otherwise not accessible by magnetic measurements. © 2020 Elsevier B.V.