Model-Independent Size Distribution Determination of Superparamagnetic Nanoparticles

Superparamagnetic nanoparticles are attracting increasing attention. For most applications, an accurate determination of the superparamagnetic particle size distribution is required. In this work, we report about determination of the core size distribution of superparamagnetic
$\gamma $
-Fe
₂
O
₃
/SiO
₂
core–shell nanoparticle samples. The approach is based on a fit of the experimentally determined
$m$
–
$H$
curves by a superposition of Langevin functions. The scheme used for solving the minimization problem does not use pre-defined model distributions (lognormal or normal). This allows for a larger variability of the obtained distribution, e.g., bi- or multi-modal. We applied our method to determine the core size distributions of five different
$\gamma $
-Fe
₂
O
₃
/SiO
₂
samples. We find that using our approach, we can obtain excellent agreement with the experimental data, and the core size distribution and mean core size values obtained compare well with the results from transmission electron microscopy (TEM) image analysis and X-ray diffraction (XRD) measurements.