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

the framework of traditional Mie’s theory. For very small clusters, quantumchemical methods or a jellim model have also been used to calculate thedielectric function from first principles [45–47]. A comprehensive overview ofdifferent theories with references to the original work can be found in Ref. 8.Most of the theories predict the 1/r dependence of the plasmon bandwidth.However, there are discrepancies regarding the size dependence of theplasmon absorption maximum. Some theories predict a red shift, whereasothers predict a blue shift of the plasmon resonance with decreasing particlesize [8]. Certainly, the medium dielectric constant e m has a large effect on theresonance condition, as can be seen from Eq. (3). An increase in e m leads to ared shift of the surface plasmon absorption maximum. Comparison betweentheories and experiments are further complicated by the fact that both red andblue shifts are observed experimentally. Furthermore, it is difficult to preparenearly monodisperse metal nanoparticles over a large range of sizes using thesame capping agent. Because different capping agents have different values ofthe medium dielectric constant e m , it is difficult to distinguish betweencontributions to the plasmon shift due to the particle size and the surroundingmedium.III.DEPHASING OF THE SURFACE PLASMONRESONANCEAlthough the plasmon absorption is well understood in terms of the electromagneticinteraction between the metal particles and light, less is knownabout the decay mechanism of the coherent electron motion. Both thedephasing of the coherent electron motion and the energy relaxation haveto be considered as decay mechanism. The dephasing of the electron motionleads to the loss of coherence, which is usually described by the time constantT 2 . T 2 and the time constant for energy relaxation, T 1 , are related by the puredephasing time T 2* [41]:1¼ C T 2 2h ¼ 1 þ 12T 1 T * ð11Þ2where C is the homogeneous spectral linewidth. The time T 2* can originatefrom collisions that change the plasmon wave vector but not its energy.Relaxation pathways for the plasmon energy decay (T 1 time constant) includethe radiative decay of the plasmon and the nonradiative decay into singleelectron–hole excitation [8,14].For a homogeneously broadened line, the dephasing time T 2 can bedirectly obtained from the absorption spectrum using Eq. (11). Figure 4b/Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.