(b) The dependency of changes in the refractive index Δn and polarizability Δα (Å3) of Fe3O4 nanoparticle arrays on the intensity of radiation with wavelengths of 442 nm (rhombus) and 561 nm (square); red dashed lines present the contribution of the thermal effect of cw radiation on the this website change in the refractive index (Equation 3), and blue dashed lines are theoretical approximations based on the approach of free carrier absorption (Equation 4). Because the observed dependence of Δn on the radiation intensity I (Figure 6b)
for Fe3O4 nanoparticle arrays could be considered a linear function, it can be assumed that Δn was caused by the thermal effect of the radiation. We estimated the contribution of this effect to the changes of the composite refractive index using the equation : (3) where c hc was the MMAS heat capacity (0.7 J/g·K), ρ d was the MMAS density (1.3 g/cm3), dn/dT was the MMAS thermo-optic coefficient (−10−5 K−1), and ΔE was the
energy absorbed by the composite per unit volume per second. The thermal effect of cw low-intensity radiation on the change in the refractive index (red Selleck AZD4547 dashed lines in Figure 6b) was relatively small (not more than 20% for blue radiation and 8% for yellow radiation). Generally, the possibility of a nonthermal optical response of the composite due to external optical radiation is associated with the polarization of Fe3O4 nanoparticles in the external field E. Nanoparticle polarization occurs at the spatial separation of positive and negative charges, i.e., at the electron transition Ixazomib concentration to higher allowed energy states (quantum number l ≠ 0). These transitions should be accompanied by the absorption of external radiation. In our case, we observed the absorption of radiation with wavelengths of 380 to 650 nm (Figure 3). This absorption band consisted of three maxima (380, 480, and 650 nm), indicating the broadened quantum-size states for the electrons in Fe3O4 nanoparticles. Because the bandgap of magnetite is rather small (approximately 0.2 eV) [20–22], the conduction and valence bands of the nanoparticles should be coupled due to quantum-size effect . Therefore,
the transitions of Fe3O4 nanoparticle electrons to higher energy states by the action of photons with energies of 2.3 eV (λ = 561 nm) and 2.6 eV (λ = 442 nm) can be considered intraband transitions. In turn, these transitions result in changes in the refractive index of the media as follows [45–47]: (4) where e was the electron 3-Methyladenine order charge, c was the speed of light, ϵ 0 was the electric constant, m e was the electron mass, and N e was the concentration of excited electrons, which depends on the number of photons in the beam or the radiation intensity I. Using Equation 4 to approximate the experimentally observed behavior of Δn(I) (Figure 6b, blue dashed lines), we estimated that the concentration of optically excited electrons in Fe3O4 nanoparticles was approximately 1023 m−3, being the radiation intensity of less than 0.14 kW/cm2.