Dipolar interactions among magnetite nanoparticles for magnetic hyperthermia: a rate-equation approach

Rate equations are used to study the dynamic magnetic properties of interacting magnetite nanoparticles viewed as double well systems (DWS) subjected to a driving field in the radio-frequency range. Dipole-dipole interaction among particles is modeled by inserting an ad-hoc term in the energy barrier to simulate the dependence of the interaction on both the interparticle distance and degree of dipole collinearity. The effective magnetic power released by an assembly of interacting nanoparticles dispersed in a diamagnetic host is shown to be a complex function of nanoparticle diameter, mean particle interdistance and frequency. Dipolar interaction markedly modifies the way a host material is heated by an assembly of embedded nanoparticles in magnetic hyperthermia treatments. Nanoparticle fraction and strength of the interaction can dramatically influence the amplitude and shape of the heating curves of the host material; the heating ability of interacting nanoparticles is shown to be either improved or reduced by their concentration in the host material. A frequency-dependent cut-off length of dipolar interactions is determined and explained. Particle polydispersity entailing a distribution of particle sizes brings about non-trivial effects on the heating curves depending on the strength of dipolar interaction.