# Magnetic Behaviour of Iron Oxide/Dextran Nanoparticles in a Keratin Matrix
## 4 Discussion  
According to the ESEM and AFM data, the MNPs can be individuated only within the clusters. Single MNPs, if present, are not detectable in the regions with high reflectivity where keratin is predominant if not exclusively present. Starting from the manufacturer datasheet, an estimation of the number of MNPs dispersed in the films can be attempted. The density of the purchased solution is equal to 4 \(\times\) 10\({}^{12}\) MNPs/uL. The number of MNPs in the pristine solution is further reduced when added to the water solution with keratin, depending on the percentage chosen. The percentage in the final solution was selected to be in the range between 2.5 and 20%, the maximum limit before precipitation occurs. As previously described, the films were deposited by spin coating on square-cut silicon wafer pieces with an area of 2 \(\times\) 2 cm\({}^{2}\). The quantity of solution placed on them was about 100 uL. For a sample with a 10% concentration, the volume of MNPs in the solution is roughly 10 uL, and the number of MNPs is thus about 4 \(\times\) 10\({}^{13}\). If all MNPs are deposited, one can calculate the number of MNPs per unit area, i.e., 10\({}^{5}\) MNPs/u\({}^{2}\). This is  
Figure 8: NanoMOKE M vs. H cycles of a 20% sample at (**a**) 300 and (**b**) 15 K. Some cycles recorded on different spots are reported: one of a cluster, two spots of the bright regions, and one of a pure keratin sample. a relatively large number and, if one evaporates a drop of the final solution, the color of the residual is brown indeed. However, the quantity of solution that remains on the substrate dramatically reduces when spinning starts and a 200 nm film of keratin plus MNPs forms. The color of the thin films is still relatively transparent. Therefore, MNP density cannot be precisely calculated, though it can be reasonably estimated to within a few hundred per um2. From the AFM analysis, the number and size of clusters is in reasonable agreement with the estimation made for the 10% sample. The detection of a low density of single MNPs always presents a sensitivity problem, even for Magnetic Force Microscopy (MFM) or Electrostatic AFM (EFM). It is also difficult to select a microscopy technique sensitive to subsurface features (like Ultrasonic Force Microscopy (UFM) or Peak Force AFM) that is capable of clearly detecting MNPs, especially if they are placed at different depths. The weak signal obtained with NanoMOKE is therefore indicative of the presence of MNPs, although a quantitative analysis cannot be conducted yet. The PPMS-VSM data suggest that the MNPs, designed to be used in a liquid environment [22], are not isolated and interact with each other when they are mixed with keratin in a solid sample. In fact, the ideal magnetic behavior of a sample of non-interacting MNPs would show a monotonic increase in FC magnetization with decreasing T [18]. As observed in Figure 2, the magnetization of the FC curve first increases at high T values and then approaches a constant value at lower T values. As reported in Figure 9b, the T\({}_{\text{B}}\) distribution can be extracted from the first derivative of the difference between the ZFC and FC curves, as described by [PERSON] et al. [18,25]. From this graph, a broad peak at 118 K can be noticed as well as a smaller one at 201 K. A possible explanation of the presence of two peaks in the T\({}_{\text{B}}\) distribution is that the MNPs have a bimodal size distribution [26]. According to the information provided by the producer, the MNPs used have a monomodal size distribution peaked at 8 nm. Thus, the behavior shown in Figure 9b needs a different interpretation. From the literature, one can advance further hypotheses such as the presence of clusters mixed to non-interacting nanoparticles [27, 28, 29, 30] or an anisotropic effect appearing at low temperature [31], such as spin-freezing [32].