PURPOSE

The harmonic spectrum of the magnetization of magnetic nanoparticles (MNPs) in the presence of an applied magnetic field can be used to characterize the properties of the microenvironment of the MNPs. The change in temperature and relaxation time has been measured by varying the magnetic field amplitudes or frequency to obtain the harmonic spectrum. However, scaling estimates of temperature or relaxation time are poor if both change simultaneously. In this work, we show that scaling over both the amplitude and frequency of the applied magnetic field allows both the temperature and relaxation to be estimated simultaneously.

METHODS

The scaling methods previously used to measure temperature and relaxation times individually have been expanded to two dimensions allowing both parameters to be estimated simultaneously. Samples with different temperature and relaxation times were measured using a magnetic nanoparticle spectrometer to verify this two-dimensional scaling method. Simulations were also carried out for a range of nanoparticle sizes, and the best particle sizes were estimated for this two-dimensional method.

RESULTS

The two-dimensional scaling method achieved a mean error of 0.83% for relaxation time by considering the temperature variation as well as relaxation time changes. The temperature and viscosity of the MNPs were measured simultaneously with the mean error of 1.03°C and 0.011 mPas. For monodisperse particles with Brownian relaxation, simulation showed that core radius of 16 nm and hydrodynamic radius of 23 nm had best accuracy for the scaling method.

CONCLUSIONS

The two-dimensional scaling method allows both temperature and relaxation time to be estimated simultaneously. The measurement accuracy can be improved by combining information in ratios and phases of the magnetic harmonics of the magnetization and by choosing the optimal particle sizes.