AC Magnetic Nanothermometry: An Investigation of the Influence of Size Distribution of Magnetic Nanoparticles

In this paper, we investigate the influence of the size distribution of magnetic nanoparticles (MNPs) on the magnetic signal and mathematical model of ac magnetic nanothermometry (MNTM). Based on the Taylor expansion of the Langevin function, two novel and real-time temperature estimation models that consider the size distribution of MNPs are proposed. These models use the summation and ratio of odd-harmonic amplitudes of signal induced by MNPs in the differential pick-up coil, respectively. The simulation results show that there is a large difference between the harmonic amplitudes of monosized and multisized MNPs. The experiments are performed under low-frequency (117 Hz) and weak (30 Oe) sinusoidal ac magnetic field. Therefore, the influence of magnetic relaxations and truncation error on MNTM can be ignored. Experimental results show that the maximum temperature estimation error of model I is about 0.63 K with a standard deviation of 0.21 K, whereas that of model II is about 0.60 K with a standard deviation of 0.32 K in the measurement time of 1 s. In addition, the problem of relative temperature sensitivity and noise for these two models are discussed.