Nanoparticles electronic energy levels

Although no quantum confinement should occur in the electronic energy level structure of lanthanides in nanoparticles because of the localized 4f electronic states, the optical spectrum and luminescence dynamics of an impurity ion in dielectric nanoparticles can be significantly modified through electron-phonon interaction. Confinement effects on electron-phonon interaction are primarily due to the effect that the phonon density of states (PDOS) in a nanocrystal is discrete and therefore the low-energy acoustic phonon modes are cut off. As a consequence of the PDOS modification, luminescence dynamics of optical centers in nanoparticles, particularly, the nonradiative relaxation of ions from the electronically excited states, are expected to behave differently from that in bulk materials. 

Colloid properties are intrinsic and extrinsic, the first being e.g. chemical behavior, ionization potential or crystallographic structure, the second collective phenomena such as electron gas and lattice resonance. The scheme of electron-energy-levels highly dependent on cluster size and cluster shape is often cited as based on a quantum-size effect. Still most of the behavior of isolated and assembled metal nanoparticles could be deduced from the classic electromagnetic theory without any use of quantum behavior or statistic (Figure 5). Only ultra-small or semi-conductor clusters are not readily described by collective phenomena due a the well-defined assembly of atoms in nano-crystals or due the low number of electrons respectively. 

Hyun et al. [345] prepared PbS Q-dots in a suspension and tethered them to Ti02 nanoparticles with a bifunctional thiol-carboxyl linker molecule. Strong size dependence due to quantum confinement was inferred from cyclic voltammetry measurements, for the electron affinity and ionization potential of the attached Q-dots. On the basis of the measured energy levels, the authors claimed that pho-toexcited electrons should transfer efficiently from PbS into T1O2 only for dot diameters below 4.3 nm. Continuous-wave fluorescence spectra and fluorescence transients of the PbS/Ti02 assembly were consistent with electron transfer from small Q-dots. The measured charge transfer time was surprisingly slow ( 100 ns). Implications of this fact for future photovoltaics were discussed, while initial results from as-fabricated sensitized solar cells were presented. 

Figure 10.9. (a) Schematic structure of a silicon quantum dot crystal and (b) its calculated electronic structure as a function of interparticle distance H. The size of the nanoparticles is L = 6.5 nm. At small H, a splitting of the quantized energy levels of single dots results in the formation of three-dimensional minibands. Reproduced from Ref. 64, Copyright 2001, with permission from the American Institute of Physics. 

Fig. 1 The effect of size on metals. Whereas bulk metal and metal nanoparticles have a continuous band of energy levels, the limited number of atoms in metal clusters results in discrete energy levels, allowing interaction with light by electronic transitions between energy levels. Metal clusters bridge the gap between single atoms and nanoparticles. Even though in the figure the energy levels are denoted as singlets, we must remark that the spin state of the silver clusters is not yet firmly established...

The fuzzy frontier between the molecular and the nanometric level can be elucidated from an electronic point of view. Molecules and small clusters can be described as systems in which the metal atoms form well-defined bonding and antibonding orbitals. Large clusters or small nanoparticles (quantum dots) with dimensions of a few nanometers are intermediate between the size of molecules and bulk material, presenting discrete energy levels with a small band gap owing to quantum-mechanical rules. Finally, larger particles tend to lose this trend and display a typical band structure similar to that of the bulk material. 

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