Measurement of Brownian Relaxation of Magnetic Nanoparticle by a Multi-Tone Mixing-Frequency Method

A detection scheme for hydrodynamic size distribution of magnetic nanoparticles (MNPs) is demonstrated by a mixing-frequency method in this paper. MNPs are driven into the saturation region by a low frequency sinusoidal magnetic field. A multi-tone high frequency sinusoidal magnetic field is then applied to generate mixing-frequency signals that are highly specific to the Brownian relaxation of MNPs. These highly sensitive mixing-frequency signals from MNPs are picked up by a pair of balanced built-in detection coils. The relation between MNPs' hydrodynamic size distribution and phase delays of the mixing-frequency signals behind the applied field are derived, and are experimentally verified. Iron oxide MNPs with the core diameter of 30 nm are used for the measurement of Brownian relaxation. The results are fitted well with Debye model. This study provides a volume-based magnetic sensing scheme for the real-time measurement of MNPs hydrodynamic size distribution.