## 2 Special Features of Nanoparticles  
### Particle size dependent properties of inorganic nanoparticles  
Ensembles of isolated nanoparticles with particle sizes below around 20 nm exhibit physical properties that may differ from their bulk counterparts. The effects are sometimes crucial, as they will strongly influence the desired or expected property of the nanocomposite. A significant influence of particle size is observed as well as on magnetic, dielectric, electronic, optical, thermodynamic, and thermomechanical, and on structural properties. The following explanations rely on general features, found in metallic, ceramic and semiconducting nanoparticles. Size-dependent magnetic properties have been studied for around two decades. [PERSON] _et al._[13, 14] reported an increasing saturation magnetization in the particle size range from 7.5 nm to 25 nm. In this size regime, the authors also observed a decrease of the transition temperature. [PERSON] _et al._ described similar behavior for Co-containing ferrite nanoparticles [15]. The size dependence of saturation magnetization is depicted exemplarily in Figure 2 (left). These dependencies can be stated as general rules as nanoparticles are typically covered by a 0.5 to 1 nm thin, nonmagnetic surface layer. As the amount of surface increases with decreasing particle size, the ratio of nonmagnetic surface layer to magnetic material also increases. Size-dependent refractive indices were reported for narrow band-gap semiconducting nanoparticles such as PbS by [PERSON] _et al._[16]. Above 25 nm particle size the refractive index of PbS at different wavelengths was more or less independent of the particle size, and near the bulk values, respectively. For PbS particles with diameters below 25 nm the refractive indices decreased significantly with size. Similar observations were made from these authors featuring the absorption coefficient. In Si-nanoclusters a significant luminescence peak blue-shift was calculated for decreasing  
Figure 2: Examples for typical particle size-dependent physical properties. Left: Saturation magnetization as a function of particle size. Data taken from [15]. Right: Band gap energy for SnO\({}_{2}\) as a function of particle size. Data taken from [19]. particle size. In parallel, the spectra became broader with decreasing particle size. These effects were described in the size regime from 2 to 6 nm [17]. Theoretical considerations predicted size-dependent energy band gap and dielectric constants for semiconducting nanoparticles [18]. [PERSON] _et al._[19] studied the size dependence of band gap energies in SnO\({}_{2}\) quantum dots. Figure 2 (right) shows the significant increasing band gap energy with decreasing particle size. [PERSON] _et al._[20] and [PERSON] _et al._[21] observed a blue shift of the plasmon losses with decreasing particle size in SnO\({}_{2}\). Concerning thermodynamic properties such as phase transitions or phase stabilities, interesting observations were made for materials existing in several polymorphs. The physical properties such as optoelectronic, photochemical or catalytic properties may be influenced by phase as well as by size. This is the case for ZrO\({}_{2}\) and TiO\({}_{2}\), both existing in different phases, and very interesting as nanofillers in composites. [PERSON] _et al._[22] described an inverse relationship between transformation temperature and particle size in ZrO\({}_{2}\), and deduced a grain size dependent phase diagram. [PERSON] _et al._[23] made energetic considerations and calculated decreasing transition temperatures with decreasing particle sizes for nanoscaled ZrO\({}_{2}\). [PERSON] and [PERSON] [24] analyzed the phase stability of nanocrystalline TiO\({}_{2}\). They found anatase to be more stable than rutile when the particle size decreased below around 14 nm. Phase stabilities of TiO\({}_{2}\) and ZrO\({}_{2}\) were also investigated by [PERSON] _et al._[25, 26].