Feldheim and Foss
While Eq. (1) pertains to the specific case of a sphere in vacuum, it can be generalized to particles of other shapes embedded in other host media (21,46):
4ab2 em eh a b 3q em eh
In Eq. (5), a and b are the semiaxes of an ellipsoid of revolution, q and are shape factors, and h is the dielectric function of the host medium. Curves 2 and 3 in Fig. 2 are the extinction spectra calculated for a 5-nm Au sphere embedded in hosts with dielectric functions 1.8 and 2.8, respectively. As the host dielectric function is increased, the plasmon resonance condition is shifted to longer wavelengths. Curve 4 is a spectrum calculated for a nonspherical particle (in this case a squat disk with its rotational axis parallel to the propagation vector of the incident light). The plasmon resonance maximum can shift with changes in particle shape. The spectra calculated in Fig. 2 represent the simplest case of isolated particles whose dimensions are very small relative to the incident wavelength. The polarizability expression (Eq. 5) used in these calculations is also the foundation for many theoretical treatments, such as Maxwell-Garnett theory, that attempt to model interacting ensembles of metal nanoparticles (49). Note that Eq. (5) describes only electric dipole induction, not higher-order electric and magnetic induction modes, which become important as the particle dimensions increase relative to the incident wavelength (21,46). Nearly a century ago, Mie developed a theory to address higher multipoles in isolated spheres. However, particles of other shapes are more difficult to treat within the rigorous Mie context, and interparticle interactions for systems that involve anything beyond an electric dipole require very sophisticated treatments. Needless to say, the relevance of such theoretical treatments increases as more complex structures are achieved in experiment.
IV. ELECTRON TRANSPORT IN METAL NANOPARTICLES More recently, the electronic properties of metal particles have been investigated within the context of decreasing electronic device size features to the nanoscopic level (5). Applications of individual particles as computer transistors, electrometers, chemical sensors, and in wireless electronic logic and memory schemes have been described and in some cases demonstrated (50), albeit somewhat crudely at this point. Many of these studies have revealed that electronic devices based on nanoscopic objects (e.g., metal and semiconductor nanoparticles, molecules, carbon nanotubes, etc.) will not function analogously to their macroscopic counter-
Chemistry of metal nanoparticles