J. Phys. Chem. B 2000, 104, 5053-5055
5053
Coherent Excitation of Acoustic Breathing Modes in Bimetallic Core-Shell Nanoparticles Jose H. Hodak,† Arnim Henglein,‡ and Gregory V. Hartland*,† Department of Chemistry and Biochemistry, and Notre Dame Radiation Laboratory, UniVersity of Notre Dame, Notre Dame, Indiana 46556-5670 ReceiVed: February 14, 2000; In Final Form: April 13, 2000
The low-frequency acoustic breathing modes in Au-Pb core-shell nanoparticles have been studied by timeresolved spectroscopy. The frequency of the breathing mode was determined for a series of samples with a 47 nm diameter Au core and Pb shells of different thickness. The measured frequencies decrease with increasing Pb content, but not to the extent expected from a classical model for a homogeneous sphere. These results show that the acoustic breathing modes of metallic core-shell particles are significantly perturbed when the two metals have different elastic properties.
Introduction The physical and optical properties of metal nanoparticles depend on their size and composition, as well as their environment. This offers the possibility of creating unique materials for catalysis, sensors, or nanoelectronics.1 In particular, there has been significant interest in the optical properties of nanoparticles.2 A large number of studies have focused on the confinement of the electrons in the small metallic volume, and how this affects the relaxation of the electron distribution after ultrafast excitation.3-8 However, the phonon modes of small particles are also affected by size. For example, size-dependent vibrational modes corresponding to expansion and compression of the particles have been observed by both Raman scattering9-13 and time-domain spectroscopic methods.14-19 Detailed studies of Ag and Au particles have shown that the time-resolved experiments yield information about the lowest frequency “breathing” mode of the particles.17,18 This motion is coherently excited by the rapid lattice heating and expansion that occurs following ultrafast laser excitation. In this paper, we report results for the acoustic breathing modes of Au-Pb core-shell particles. To the best of our knowledge, this is the first work on the dynamics of bimetallic nanoparticles. The particles were prepared by growing a shell of Pb around a 47 nm diameter Au core using γ-irradiation.20,21 The frequency of the breathing mode was measured for increasing thickness of the Pb layer. The vibrational frequencies do not show the 1/R size dependence which was previously found for single-component metal particles17,18 and is predicted by the classical theory developed by Lamb.22,23 Experimental Section The ultrafast transient absorption experiments were performed using a pump-probe scheme. The laser system has been described in detail elsewhere.7 The pump laser pulses were centered at 390 nm, and a white light continuum provided the probe pulses. The pump and probe beams were overlapped at the sample, which was a 2 mm optical path length quartz cell. * To whom correspondence should be addressed. E-mail: hartland.1@ nd.edu. † Department of Chemistry and Biochemistry. ‡ Radiation Laboratory.
An overall time resolution of 160-170 fs (full width at halfmaximum, sech2 deconvolution) was determined by optical parametric amplification of the probe. The samples were not allowed to come into contact with air, to prevent oxidative destruction of the Pb layer. The 47 nm diameter Au core particles were prepared by the radiolytic technique described previously.21 The overall concentration of Au was 5.0 × 10-5 M, and the sample had a narrow size distribution with a 7% standard deviation. 60Co γ-irradiation was used for coating the particles with Pb.20 Specifically, the desired amount of Pb(ClO4)2 was added to the deareated Au sol as well as 10-2 M acetone and 0.3 M 2-propanol, and the solution was irradiated until all the Pb was reduced. Particles made by this technique have been characterized in detail by TEM and were shown to consist of a Au core surrounded by a Pb shell.20 Results and Discussion The upper part of Figure 1 shows the absorption spectrum of the 47 nm diameter Au particles. Also shown is the spectrum of pure Pb nanoparticles formed by γ-irradiating a 5.0 × 10-4 M Pb(ClO4)2 solution in the absence of Au. In the lower part of Figure 1, spectra for the particles formed by irradiating the Au colloid/Pb(ClO4)2 solutions are presented. Comparison of the upper and lower portions of Figure 1 reveals that the lower spectra are not a superposition of the pure Au and pure Pb particle spectra. The Au plasmon band is strongly damped and shifts to shorter wavelengths with increasing Pb. These changes in the absorption cross-section show that the Pb is deposited onto the Au particles by γ-irradiation. The diameter of the coated particles was calculated using the relation20
(
D ) Dcore 1 +
[Pb]VPb [Au]VAu
)
1/3
(1)
where VPb and VAu are the molar volumes for Pb and Au, respectively, and [Pb] and [Au] are the concentrations prior to γ-irradiation. The values used here are VPb ) 18.27 cm3/mol and VAu ) 10.33 cm3/mol.20,24 The core diameter was calculated from the frequency of the acoustic signal before adding the Pb layer (see below).18 The number of atomic layers of Pb was
10.1021/jp000578v CCC: $19.00 © 2000 American Chemical Society Published on Web 05/04/2000
5054 J. Phys. Chem. B, Vol. 104, No. 21, 2000
Figure 1. Upper: absorption spectra (for a 0.2 cm path length) of pure Au and Pb nanoparticles in aqueous solution. The overall metal concentration in each case is 5.0 × 10-4 M. Lower: spectra of AuPb core-shell nanoparticles. The molar Au:Pb ratio and the number of atomic layers of Pb are given in the figure.
Letters
Figure 3. Frequency of the acoustic vibrational mode obtained from the data shown in Figure 2 (b). The error bars were determined from the standard deviation of different experimental traces. The solid line is a guide to the eye.
(∼0.05 µJ/pulse).5,7 Time-resolved data (not shown) collected in the first few picoseconds after laser excitation indicates that e-ph coupling in the core-shell particles is similar to pure Au nanoparticles, but with slightly shorter decay times.5,7 Experiments are currently underway to determine whether this is a consequence of the interface, or due to a larger e-ph coupling constant for Pb. The remaining oscillatory signal at longer times arises from the periodic modulation of the electron density in the particles due to the coherently excited breathing motion.17,18 The data in Figure 2 shows that the oscillation frequency decreases with increasing Pb content, i.e., with increasing overall particle diameter. Figure 3 shows a plot of the frequencies obtained by fitting the transient absorption data to the function:
S(t) ) A0e-t/τd cos(2πcνjRt + φ)
Figure 2. Time-resolved data obtained for 47 nm diameter Au nanoparticles (bottom) and Au-Pb core-shell particles with different amounts of Pb. The number of Pb atomic layers is given in the figure. Dotted lines are fits to the data; see text for details. The data has been normalized by the magnitude of the oscillatory signal.
calculated by nPb ) (D - Dcore)/2d, where d is the diameter of a Pb atom, taken as 0.31 nm.20 Figure 2 shows time-resolved data for the Pb-coated Au particles. The experimental traces consist of a fast transient bleach signal, followed by a slower modulated signal. These contributions can be explained in the following way: Excitation with an ultrafast 400 nm laser pulse rapidly increases the electronic temperature of the particles.3,5-8 This broadens the plasmon band, which creates a bleach signal at wavelengths near the band maximum.5,7 Note that this signal appears even for the particles that only have a weak plasmon band (see, for example, the trace corresponding to the particles with nPb ) 38). The bleach recovers as the hot electron gas equilibrates with the lattice by electron-phonon (e-ph) coupling; this occurs in 2-5 ps at the laser powers used in these experiments
(2)
where A0 is the initial amplitude, τd is a damping time, φ is the phase, c is the speed of light, and νjR is the frequency of the oscillation (in cm-1). Previous work has analyzed in detail the excitation and damping mechanisms for the acoustic breathing motion.17,18 Briefly, the energy exchange between the electrons and phonons increases the temperature of the lattice, on a time scale that is shorter than the period of the lowest frequency phonon mode of the particles. The thermal expansion that accompanies the increase in lattice temperature impulsively excites the radial (isotropic) breathing mode.14-19 For a homogeneous elastic sphere with a “free” surface (no stress at the boundary), the breathing mode frequencies are given by 22,23
νjR )
ηcl 2πRc
(3)
In eq 3 cl is the longitudinal speed of sound, R is the radius, and η is an eigenvalue that is given by the roots of the equation η cot η ) 1 - η2/4δ2, where δ ) ct/cl is the ratio of the transverse and longitudinal speeds of sound of the particle.22,23 For Au, η ) 2.93 for the lowest frequency radial “breathing” mode. We have previously shown that this value is in almost perfect agreement with the experimental result for pure Au particles with diameters between 8 and 120 nm.18 The oscillations are damped because of the polydispersity of our samples: different sized particles give different frequencies.
Letters Equation 3 shows that the oscillation frequency should decrease with increasing thickness of the Pb layer for two reasons. First, the overall size of the particles has increased. Second, the deposited Pb layer has a lower speed of sound than the Au corescl(Pb) ) 2160 ms-1 and cl(Au) ) 3240 ms-1.24 However, the reduction in frequency is much smaller than that expected from the change in the particle size. For example, for particles with 20 Pb layers the radius has increased by 25%, whereas the breathing mode frequency has decreased by only 10%. Using an apparent speed of sound in eq 3, that is an average of the speeds of sound for Au and Pb, does not improve the agreement between the calculated and experimental frequencies. At the present, a suitable theory for calculating the vibrational frequencies of core-shell particles (i.e., one that correctly accounts for the difference in the elastic properties of the core and the shell) does not exist. However, insight into how the addition of the Pb shell affects the breathing motion of the particles can be obtained by considering the double spring system shown in Scheme 1. SCHEME 1
There are two vibrational modes in this system: a symmetric mode where both springs either expand or compress in phase, and an antisymmetric mode (one spring expands while the other compresses).25 The symmetric modeswhich corresponds to the one measured in our experimentssis always lower in frequency. If m2 , m1, the amplitude of the oscillation for the symmetric mode is mainly in spring k1. The addition of the second mass/ spring lowers the resonant frequency in a way that is simply like adding extra mass to m1. As m2 increases relative to m1 the amplitude in spring k2 increases, and the frequency of the symmetric mode strongly decreases. Thus, for small Pb layer thickness (m2 , m1) the Pb layer has very little effect on the symmetric breathing mode (the Pb layer “rides” on the vibrational motion of the core). As the amount of Pb increases there is significant expansion/compression in both the core and the shell, producing a stronger decrease in the breathing mode frequency. We stress that this discussion is only qualitative; an accurate description requires that the equations of motion for the particles be solved with the correct boundary conditions. Experiments with bimetallic particles with different combination of metals and geometries (core-shell compared to alloyed) are currently underway. We hope that
J. Phys. Chem. B, Vol. 104, No. 21, 2000 5055 these studies will provide further insight into the physical properties of these unique materials. Acknowledgment. The work described here was supported by the NSF, grant no. CHE98-16164 (G.V.H. and J.H.H.) and by the Office of Basic Energy Sciences of the U.S. Department of Energy through the Notre Dame Radiation Laboratory (A.H.). This is contribution No. 4189 for the Notre Dame Radiation Laboratory. References and Notes (1) Schmid, G. Clusters and Colloids: From Theory to Application; VCH: Weinheim, Germany, 1994. (2) Kriebig, U.; Vollmer, M. Optical Properties of Metal Clusters; Springer: Berlin, 1995. (3) (a) Bigot, J.-Y.; Merle, J.-C.; Cregut, O.; Dannois, A. Phys. ReV. Lett. 1995, 75, 4702. (b) Shahbazyan, T. V.; Perakis, I. E.; Bigot, J. Y. Phys. ReV. Lett. 1998, 81, 3120. (4) (a) Roberti, T. W.; Smith, B. A.; Zhang, J. Z. J. Chem. Phys. 1995, 102, 3860. (b) Smith, B. A.; Zhang, J. Z.; Griebel, U.; Schmid, G. Chem. Phys. Lett. 1997, 270, 139. (5) (a) Ahmadi, T. S.; Logunov, S. L.; El-Sayed, M. A. J. Phys. Chem. 1996, 100, 8053. (b) Logunov, S. L.; Ahmadi, T. S.; El-Sayed, M. A.; Khoury, J. T.; Whetten, R. L. J. Phys. Chem. B 1997, 101, 3713. (c) Link, S.; Burda, C.; Wang, Z. L.; El Sayed, M. A. J. Chem. Phys. 1999, 111, 1255. (6) Perner, M.; Bost, P.; Lemmer, U.; Von Plessen, G.; Feldmann, J.; Becker, U.; Menning, M.; Schmidt, M.; Schmidt, H. Phys. ReV. Lett. 1997, 78, 2192. (7) (a) Hodak, J. H.; Martini, I.; Hartland, G. V. Chem. Phys. Lett. 1998, 284, 135. (b) Hodak, J. H.; Martini, I.; Hartland, G. V. J. Phys. Chem. B 1998, 102, 6958. (c) Hodak, J. H.; Henglein, A.; Hartland, G. V. J. Chem. Phys. 2000, 112, 5942. (8) Del Fatti, N.; Flytzanis, C.; Vallee, F. Appl. Phys. B 1999, 68, 433. (9) Duval, E.; Boukenter, A.; Champagnon, B. Phys. ReV. Lett. 1986, 56, 2052. (10) Fujii, M.; Kanzawa, Y.; Hayashi, S.; Yamamoto, K. Phys. ReV. B 1996, 54, R8373. (11) Tanaka, A.; Onari, S.; Arai, T. Phys. ReV. B 1993, 47, 1237. (12) Krauss, T. D.; Wise, F. W.; Tanner, D. B. Phys. ReV. Lett. 1996, 76, 1376. (13) Ferrrari, M.; Gonella, F.; Montagna, M.; Tosello, C. J. Appl. Phys. 1996, 79, 2055. (14) Nisoli, M.; De Silvestri, S.; Caralleri, A.; Malvezzi, A. M.; Stella, A.; Lanzani, G.; Cheyssac, P.; Kofman, R. Phys. ReV. B 1997, 55, R13424. (15) Krauss, T. D.; Wise, F. W. Phys. ReV. Lett. 1997, 79, 5102. (16) Thoen, E. R.; Steinmeyer, G.; Langlois, P.; Ippen, E. P.; Tudury, G. I.; Brito Cruz, C. H.; Barbosa, L. C.; Cesar, C. L. App. Phys. Lett. 1998, 73, 2149. (17) Del Fatti, N.; Voisin, C.; Chevy, F.; Valle´e, F.; Flytzanis, C. J. Chem. Phys. 1999, 110, 11484. (18) Hodak, J. H.; Henglein, A.; Hartland, G. V. J. Chem. Phys. 1999, 111, 8613. (19) Qian, W.; Lin, L.; Deng, Y. J.; Xia, Z. J.; Zou, Y. H.; Wong, G. K. L. J. App. Phys. 2000, 87, 612. (20) Mulvaney, P.; Giersig, M.; Henglein, A. J. Phys. Chem. 1992, 96, 10419. (21) Henglein, A.; Meisel, D. Langmuir 1998, 14, 7392. (22) Lamb, H. Proc. London Math. Soc. 1882, 13, 189. (23) Dubrovskiy, V. A.; Morochnik, V. S. IzV. Earth Phys. 1981, 17, 494. (24) CRC Handbook of Chemistry and Physics, 80th ed.; CRC Press: Boca Raton, FL, 1999. (25) Norton, M. P. Fundamentals of Noise and Vibration Analysis for Engineers; Cambridge University Press: Cambridge, MA, 1989.
