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

Figure 2 Frequency of the acoustic vibrational mode versus the inverse radius ofthe particles: (.) experimental values determined from transient absorption data; (—)calculated values using Eq. (1) and the bulk speeds of sound for Au.that the particles have a normal size distribution and that the average radius Ris much larger than the standard deviation j R , the signal in our experimentcan be expressed as [36]SðtÞ ¼ cos 2p T t þ / e t2 =s 2ð2Þwhere / is the phase of the modulation, T ¼ 2pR =gc l is the period correspondingto pthe average radius of the sample, and the damping time is givenby s ¼ R T =ffiffi2 prR . Fits to the transient absorption data using Eq. (2) are includedin Fig. 1. This analysis yields an average period of T ¼ 15:9 F 0:1 ps,which corresponds to an average radius of R ¼ 24:2 F 0:1 nm for this sample.The damping time is s = 51 F 1 ps, which implies a standard deviationof j R = 1.70 F 0.05 nm. In comparing size distributions, it is common tonormalize the standard deviation by the average radius. For our sample, wefind j R =R ¼ 7:0 F 0:2%, which corresponds to an extremely high-quality,monodisperse sample. In principle, the decay of the modulations could containcontributions from energy relaxation to the environment. Thus, the valueof j R derived from this analysis is strictly an upper limit to the true width ofthe distribution (i.e., j R /R V 7.0%). Note that the number of oscillations inCopyright 2004 by Marcel Dekker, Inc. All Rights Reserved.