Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

dation effects also become important, and the plasmon band red shifts withincreasing particle size. At the same time, the plasmon bandwidth increaseswith particle size because the plasmon absorption is the convolution of severalmodes peaking at different wavelengths. This is illustrated by the experimentalspectra in Figs 1a and 4a, which show the plasmon bandwidth as a functionof a particle size.Whereas the plasmon bandwidth increases for the nanoparticles largerthan 20 nm, it also increases for smaller particles (i.e., in the range of sizes forwhich the dipole approximation is applicable). As can be seen from Eq. (3),the extinction coefficient within the dipole approximation does not depend onthe particle dimensions, which implies that the surface plasmon absorption issize independent for particles smaller than f20 nm. However, this conclusioncontradicts experimental observations. Spectroscopic data indicate that theplasmon band is strongly damped for particles smaller than 5 nm in diameterand finally disappears completely for sizes below f2 nm [37–39]. Furthermore,it has been shown experimentally that the plasmon bandwidth isinversely proportional to the particle size for particles smaller than f20 nm[8,12]. It has therefore been argued that for small nanoparticles, the assumptionof the same electronic and optical properties as for bulk materials is nolonger valid. Especially, the use of the bulk dielectric constant, which entersthe Mie equations as the material’s only parameter, is not justified as the particlesize is decreased. Because Mie’s theory has been very successful in describingoptical absorption spectra of metal nanoparticles, most approachesto describing the surface plasmon absorption in the regime of very small sizeshave focused on modifying the dielectric constant (to introduce a sizedependence in it) rather than on changing the Mie model [8,12].In one of the earliest approaches, Kreibig and co-workers [12,13] arguedthat electron-surface scattering is enhanced in small particles as the mean freepath of the conduction-band electrons becomes limited by the physicaldimensions of the nanoparticle. This model will be discussed later in moredetail because it illustrates the concept of introducing size dependence in thedielectric constant; it also allows some physical insight into size-dependentplasmon properties. The mean free path of the electrons in silver and gold ison the order of 40–50 nm [40]. The smaller the particle, the more frequent theelectron-surface collisions are. Each elastic or inelastic electron-surface scatteringevent leads to a loss of coherence in the electron motion. This occurs ona faster timescale for smaller particles because of the enhanced electronsurfacescattering. For a simple two-level system, a faster dephasing leads toan increased line width [41].The size dependence of the dielectric function is introduced in Kreibig’smodel [12,13] by presenting the dielectric constant as a combination of anCopyright 2004 by Marcel Dekker, Inc. All Rights Reserved.