# Magnetic Properties of Nanocomposites
## 3 Polymer Nanocomposites
### Polymer Nanocomposites Containing Weakly Interacting Magnetic Nanoparticles
An example of the hysteresis properties of the magnetic NC is shown in Figure 1 (bottom right), where the coercive field (\(H_{c}\)) is reported as a function of temperature (blue symbols). Apparently, the hysteresis disappears at T = 30 K, indicating that all bare magnetite NPs have become magnetically unblocked there, that is, have reached the thermal equilibrium state, in good agreement with the position of the maximum of the corresponding ZFC curve (Figure 1, bottom left). In this material, as well as in almost all systems containing magnetite nanoparticles, the particle magnetization appears to be considerably reduced with respect to the bulk value (in this case, a value around 60 emu/g is measured at room temperature (see Table 1), compared with 92 emu/g of bulk magnetite). This fact has been explained by invoking the presence of a magnetically dead layer at the particle surface [37]; the thickness of such a layer is of the order of 0.5-1 nm. The term \"dead layer\" means a magnetically disordered, extra-hard phase whose contribution to one nanoparticle's net magnetic moment is negligible because of spin compensation; the magnetic field needed to align the frustrated magnetic moments in the dead layer is much higher than the maximum field used in the present measurements. The magnetic disorder of the dead layer arises from competition among magnetic energies (exchange, anisotropies) affected by the symmetry breaking at the boundary of the particle [4]; as a consequence, such a layer is expected to continuously envelop a nanoparticle's core. In the considered NC, the mean interparticle distance (about 25 nm, as deduced from Figure 1, top center) is so large that dipolar interparticle interactions are almost completely negligible (the root mean square (r.m.s.) dipolar energy in this case being as small as \(\langle E_{i}^{2}\rangle^{1/2}\approx 10\frac{\pi^{2}}{r^{3}}\approx 5 \times 10^{-16}\) erg [38]). Therefore, this material can be viewed as containing basically non-interacting, individual NPs of known composition and shape. As a consequence, one should expect that above blocking temperature, the material is in the ideal superparamagnetic (SP) regime. This is not exactly the case, however, because of the small dipolar interactions existing among NPs, as proven by Figure 2, where two scaling laws are compared: the standard SP scaling law, which applies to bona-fide SP systems (top left panel), and the ISP scaling law (top right panel), which applies to systems where the effects of dipolar interactions, although small, are not completely negligible [17; 39]. The abscissa in the top right panel is the ISP scaling parameter, whose expression has been discussed in detail elsewhere [40]; here, \(M_{\rm s}\) is the saturation magnetization, \(k_{B}\) is the Boltzmann's constant, \(N\) is the total number of particles per unit volume, and \(\alpha\) is a constant measuring the dipolar energy. The dipolar temperature T*, a quantity measuring the strength of the dipolar interaction in the ISP model, is very small in this case compared with other NP systems, as shown in Figure 2 (bottom panel, open blue symbols). This magnetic NC is basically in the SP regime (corresponding to T*/T < 1) above 20 K. Instead, the nanopowder has a much higher degree of interaction. Quite interestingly, when the same magnetite NPs are inserted in the same polymeric matrix after being encapsulated into a diamagnetic shell of silica (SiO\({}_{2}\)), the magnetic properties of the NCchange remarkably. Particle coating with silica was done as follows: a dispersion of oleylamine-coated Fe\({}_{3}\)O\({}_{4}\) NPs in cyclohexane was added to cyclohexane and mixed with Igepal CO-520. The pH was adjusted to \(\cong\)10 through the addition of ammonium hydroxide and the formation of a transparent brown microemulsion was ensured with the aid of a sonicator.