Abstract :
[en] Superparamagnetic Iron Oxide Nanoparticles (SPION) are nanosize crystals of magnetite or maghemite. Their peculiar magnetic properties makes them particularly suited for a variety of biomedical applications, ranging from cellular imaging to cancer treatment by hyperthermia [1]. The usual theory used to describe their magnetic behaviour is that de- veloped by Paul Langevin [2], which only applies to idealized (isotropic, monodisperse in size and non-interacting) nanoparticles at high temperatures. Reality however always deviates from that theoretical framework: real samples exhibit polydispersity in sizes, particles usually have at least one anisotropy axis, and, particulary in biological media, they tend to aggregate, leading to locally high particle volumic fractions and therefore interaction between their magnetic moments [3]. All those phenomena impact the mag- netization of particle ensembles in a non-trivial way and are impossible to model simul- taneously theoretically. In this work, these deviations from the Langevin law are studied numerically, at thermo- dynamic equilibrium and at 300K, using a Metropolis algorithm, and compared with ex- perimental data obtained using a Vibrating Sample Magnetometer for real SPION, whose size distribution was evaluated by transmission electron microscopy. Thorough tests are led on the simulations to ensure convergence of the magnetization. The effect of each parameter on the field-dependent magnetization curves is then studied. Figure 1 shows an example of the impact of one of those parameters: inhibiting rota- tion of the particles (i.e. the Brown relaxation process). As can be seen, it leads to a slower saturation of the magnetization in samples with a high size dispersion parameter (σL = 0.5). Likewise, the presence of dipolar interaction between particles also leads to slower saturation in such samples, as does drying samples under a magnetic field perpen- dicular to the measurement field (as opposed to drying them under a field parallel to the measurement field, which yields the opposite effect). These various modifications of the curves result in erroneous size dispersion parameters when fitting them to an integrated Langevin equation. The simulations compare well with experimental results, as can be seen on figure 2. In future work, the simulations could be improved by changing the anisotropy model from uniaxial to a more realistic cubic anisotropy.
