Acoustic Oscillations and Elastic Moduli of Single Gold Nanorods

NANO LETTERS

Acoustic Oscillations and Elastic Moduli of Single Gold Nanorods

2008 Vol. 8, No. 10 3493-3497

Peter Zijlstra,† Anna L. Tchebotareva,‡ James W. M. Chon,*,† Min Gu,† and Michel Orrit*,‡ Centre for Micro-Photonics, Faculty of Engineering and Industrial Sciences, Swinburne UniVersity of Technology, P.O. Box 218, Hawthorn, 3122, VIC Australia, and MoNOS Huygens Laboratorium, UniVersiteit Leiden, 2300 RA Leiden, The Netherlands Received August 13, 2008; Revised Manuscript Received September 2, 2008

ABSTRACT We present the first acoustic vibration measurements of single gold nanorods with well-characterized dimensions and crystal structure. The nanorods have an average size of 90 nm × 30 nm and display two vibration modes, the breathing mode and the extensional mode. Correlation between the dimensions obtained from electron microscope images and the vibrational frequencies of the same particle allows us to determine the elastic moduli for each individual nanorod. Contrary to previous reports on ensembles of gold nanorods, we find that the single particle elastic moduli agree well with bulk values.

Metal nanowires and nanorods open attractive avenues in photonics1 and quantum electronics.2 Understanding their structure and elastic properties is crucial for many of their future uses. In contrast to a polycrystalline bulk metal, nanoparticles often are single crystals or are composed of very few single crystals. Defects are rare or absent because they easily anneal at nearby surfaces. As size decreases, the surface-to-volume ratio increases and surface effects (such as surface tension or melting) become significant. At small enough scales, the mechanical properties are expected to differ from those of bulk materials. Electronic confinement and atomic discreteness may also affect elastic moduli. The elasticity of gold and silver nanoparticles has been studied on ensembles through laser-induced acoustic oscillations.3-5 It appears that vibrational modes depend in unique ways on the size, shape,3 crystal structure,5,6 and local environment7,8 of a nanoparticle. In ensemble measurements, however, differences from bulk elastic properties are likely to be screened by the differences between the individual particles. Recent ultrafast spectroscopic measurements on single gold nanospheres7 and single silver nanocubes8 demonstrated how to remove this heterogeneity. They revealed differences in the local environment, but they did not directly yield the mechanical properties. This can only be achieved when the precise morphology and dimensions of each individual particle are known, which requires electron microscopy and ultrafast spectroscopy of the same single * Corresponding authors. E-mail: [email protected]. E-mail: [email protected]. † Swinburne University of Technology. ‡ Universiteit Leiden. 10.1021/nl802480q CCC: $40.75 Published on Web 09/23/2008

 2008 American Chemical Society

nanoparticle.9 Here, we measure the acoustic responses and electron micrographs of the same single gold nanorods, from which we derive their elastic constants. Contrary to previous reports5,10 on ensembles of gold nanorods, we find the elastic moduli of single nanorods to agree well with bulk values, confirming theoretical estimates.11,12 The gold nanorods used in this study were prepared by silver-assisted seed-mediated growth.13 This yielded nanoparticles with an average length of 92 ( 9 nm and an average width of 33 ( 3 nm. After preparation, the remaining solutes were diluted by 4 orders of magnitude through centrifugation. This dilution ensured a minimum of surfactant remaining on the surface of the rod without inducing any noticeable aggregation. After this, the nanorod solution was spin-coated on a clean fused silica glass coverslip. The coverslip was marked by femtosecond laser writing to help locate the same nanorods for spectroscopy and electron microscopy. The sample surface was imaged by both scanning electron microscopy (SEM) and single-particle white-light scattering.9,14,15 Measuring the plasmon energy and line width facilitates the identification of isolated rods. For singleparticle white-light microscopy,14 the reflected light from a high-power Xenon lamp was collected by the focusing objective and directed to an avalanche photodiode (APD). The spot was raster-scanned over the sample surface. To increase the visibility of the rods, the reflected light was bandpass-filtered (638 ( 45 nm) before detection. Some nanorods appear dimmer because part of their scattering spectrum falls outside the filter band. The unfiltered scattering

Figure 1. Single gold nanorods (a) Scanning electron micrograph showing three gold nanorods (bar length 1 µm). (b) White-light scattering scan showing isolated rods. The box encloses the area of part a (bar length 1 µm). (c) Scattering spectrum of two individual gold nanorods in unpolarized white light. Solid lines are Lorentzian fits. (inset) Polarized scattering versus angle, with dipolar cosine fits (solid lines).

spectrum of each individual nanorod was dispersed by a spectrograph on a cooled CCD. Figure 1a shows an SEM image of a small area, from which we identify single nanorods and extract their accurate dimensions. Figure 1b shows white-light scattering in the same area, where diffraction-limited spots correlate well with the single rods in SEM. We measured the white-light scattering spectra of more than 30 individual particles (see Figure 1c and Supporting Information Figure S1). The plasmon energies are distributed between pΩLSP ) 1.8 - 2 eV (λ ∼ 690-620 nm). The intrinsic line width is Γintr ) 112 ( 15 meV, in good agreement with earlier reports.16 These Lorentzian lines help us select individual nanorods and optimize the probe wavelength for each rod. In all cases, the polarized scattered intensity followed the expected dipolar angle dependence. Plasmons, the collective free electron excitations created by a pump pulse, decay through radiative and nonradiative channels.15 Nonradiative decay releases thermal energy and excites mechanical vibrations of the particle by two distinct mechanisms.17,18 First, the sudden surge in electron temperature applies additional pressure on the particle surface. Second, as the electronic energy is transferred to the lattice, equilibrium interatomic distances increase because of anharmonicity. Electron-lattice relaxation being fast (1-3 ps) compared to acoustic oscillations (provided the particle is not too small), the particle is suddenly brought out of mechanical equilibrium and coherent oscillations are launched. The pump-probe measurements were conducted in the same home-built microscope as used for the white-light scattering measurements. The ultrafast spectroscopy study was performed in transmission and probed the extinction by the particle. Acoustic oscillations of the nanoparticles were 3494

excited with the pulsed output (∼300 fs pump pulses) of a Ti:sapphire laser (λpump ) 800 nm), modulated by an acoustooptic modulator. The relative transmission change was probed with the frequency-doubled signal beam of an optical parametric oscillator (OPO), tunable between 520 and 700 nm. For all particles, the probe wavelength was tuned to the longitudinal plasmon absorption band. The pump-probe delay time was scanned by a delay line. In all measurements, the pump and probe pulse energies at the back aperture of the objective were 2 pJ and ∼0.1 pJ (average powers 160 and 8 µW), respectively. These very low laser pulse energies did not induce any shape changes in the nanorods (see Supporting Information Figure S2). Except for polarization measurements, both the pump and the probe pulses were circularly polarized. Figure 2a shows the vibrational trace of the bottom right rod in Figure 1a obtained by pump-probe spectroscopy. The particle dimensions are 90 nm × 29 nm and pΩLSP ∼ 1.94 eV (∼643 nm). For this particle, we tuned the probe laser frequency to pω ) 1.86 eV (670 nm). The power spectrum of the Fourier transform of the trace is shown in Figure 2b. We found two distinct Lorentzian resonances for all the rods. A rod’s (nontorsional) vibrational modes are labeled by two integers, n, the radial number, and l, the angular momentum number.19,3 Spherical particles only show the radially symmetric breathing mode (n,l) ) (0,0).7,3 As the spherical symmetry is broken in nanorods, they additionally display the fundamental extensional (n,l) ) (0,2) mode. Following the work of Hu et al.,4 we attribute the lower peak in the optical response to this extensional mode and the higher peak to the fundamental breathing mode. The inset of Figure 2a shows the early part of the vibration trace fitted with a sum of damped oscillating terms: δu(t) ) A exp(-t ⁄ τcool) +

∑

δuk(0)

k)(ext,br)

exp(-t ⁄ τk) cos(2πνkt - φk) (1)

where δu is the relative transmission change ∆T/T. The initial electronic response was omitted. The first term represents the cooling of the particle, where A characterizes the change of optical response due to the initial lattice heating, and τcool is a characteristic cooling time. In the second oscillating term, k )(ext,br) refers to the (n,l) ) (0,2) extensional and (n,l) ) (0,0) breathing modes. δuk(0) is the initial amplitude of the vibrational modes in the optical response, and νk, τk, and φk are their respective frequency, damping time, and phase. Fitting eq 1 to the vibrational trace of Figure 2 gives the extensional frequency νext ) 9.78 ( 0.01 GHz and damping time τext ) 1 ( 0.06 ns. The breathing mode has a frequency of νbr ) 80.6 ( 0.1 GHz, and the damping time is τbr ) 122 ( 8 ps. Figure 2c shows the probe laser polarization dependence of δuk(0). For both the breathing mode and the extensional mode, δuk(0) follows the expected dipolar dependence, which arises from that of the optical response. The quality factors of the modes, Qk ) 2πνkτk/2, for about 20 measured particles are Qext ) 28 ( 9 for the extensional mode and Qbr ) 37 ( 6 for the breathing mode (the errors are the standard deviations). These values are significantly higher than those of ensembles4 and agree well with those Nano Lett., Vol. 8, No. 10, 2008

Figure 2. Single nanorod vibrations. (a) Vibrational trace of a single gold rod. (inset) Zoom on the highlighted part, fitted with eq 1. (b) Power spectral density of the trace in part a after Fourier transform. (inset) Zoom on the high-frequency peak. (c) Polarization dependence of the optical response δuk(0) for the breathing mode (squares) and the extensional mode (circles), with cosine fits (solid lines).

Figure 3. Probe photon energy dependence. (a) Vibrational traces of a single gold nanorod for three different probe photon energies. The nanorod has dimensions 86 nm × 30 nm and pω ) 1.92 eV (648 nm). (b) Probe photon energy dependence of δuk(0). The lines represent the difference between two Lorentzian line shapes with a different frequency, line width, and intensity. The surface plasmon energy is indicated by the vertical line.

of breathing modes of single gold nanospheres7 and single silver nanocubes.8 In Figure 3a, we show vibrational traces of a single gold nanorod for three different probe photon energies. The mechanical oscillations induce a periodic modulation of the energy, line width, and intensity of the surface plasmon band, ISP, giving rise to a strong dependence of the optical response on the probe photon energy with respect to the surface plasmon band. In Figure 3b, we show δuk(0) (obtained from fits with eq 1) as a function of probe photon energy. The measured δuk(0) is very well represented by the difference between two Lorentzian line shapes with a slightly different frequency, line width, and intensity. From the Lorentzian fits, we find that the breathing mode vibration mainly modulates the intensity and energy of the surface plasmon (∆ISP ) 0.01%, ∆pΩLSP/∆Γ ∼ 12), whereas the extensional mode vibration induces a line broadening comparable to the shift in energy (∆ISP ) 0.01%, ∆pΩLSP/∆Γ ∼ 1). Hu et al.4 calculated the vibration frequencies of a polycrystalline free rod in a simple classical model and compared the results with a finite element method. They found a breathing frequency which scales with the bulk longitudinal speed of sound cl and the inverse particle width. The bulk longitudinal speed of sound can be expressed as a function of the bulk (K) and shear (µ) moduli of the Nano Lett., Vol. 8, No. 10, 2008

nanorods20 (cl ) [(K + 4/3µ)/F]1/2, where F is the density of bulk gold). The extensional frequency scaled with the inverse length and the square root of the Young’s modulus. Although the obtained analytical relations4 strictly hold only in the limit of infinite aspect ratio, Hu et al. found an excellent agreement with finite element calculations down to aspect ratios as small as ∼2.5,4 with an error smaller than 1%. Because our rods are single-crystalline, the Young’s modulus probed by the extensional mode Elong depends on their growth direction.5 We determined the growth direction of our nanorods by high resolution transmission electron microscopy (TEM). The TEM image in Figure 4 shows that the particles are perfect single crystals without any defects. From the crystal plane spacing and orientation, we deduce the growth direction, [100], and the relevant Young’s modulus for the extensional mode, Elong ) E[100] ) 42 GPa.5 The effect of the crystallinity on the breathing frequency of the rods is expected to be small because cl is mainly determined by the bulk modulus of gold independently of the growth direction (see the Supporting Information). Figure 4b shows the correlation between breathing frequency νbr and the rod diameter (width). The dotted line represents the analytical approximation to νbr from ref 4. We find good agreement between the theoretical and experimental breathing frequencies, indicating that the bulk and shear 3495

Figure 4. Elastic moduli. (a) High resolution TEM image showing the single crystalline structure of the gold nanorods with a [100] growth direction (bars are 5 nm long). (b) Correlation between diameter (width) and breathing frequency νbr. The dotted line is the calculated νbr for a free rod. The error in measured frequency is smaller than the symbol size. (c) Correlation between the measured aspect ratio and the frequency ratio (νbr/νext)/AR. The dotted line indicates the calculated ratio of 3.24 for a free rod with the [100] Young’s modulus in the longitudinal direction. The green solid data points indicate the particles that have a Young’s modulus close to the value of bulk gold; the open square symbols indicate the nanorods which display a large deviation from the bulk Young’s modulus. (d) Correlation between the frequency and damping rate for the breathing mode. (e) Correlation between the frequency and damping rate for the extensional mode. The colors of the data points are as described in part c.

moduli of the nanorods are close to the values for bulk gold. As reported by Hu et al.,4 the ratio between the breathing and extensional mode frequency only depends on the aspect ratio, AR ) length/diameter, of the rod. More specifically, when the crystal structure of the rod is taken into account for the extensional mode, (νbr/νext)/AR ) 3.24 (see the Supporting Information). In Figure 4c, we plot this frequency ratio as a function of the measured aspect ratio. For a subpopulation of the rods, we find a frequency ratio close to the theoretically expected ratio. Therefore, the Young’s modulus of these rods is close to the bulk value for a macroscopic cylinder with axis in [100] direction. Our finding agrees with nanoindentation experiments on micrometer sized silver21 and gold nanowires,22 reporting Young’s moduli close to bulk values. Hence, we conclude that surface and size effects on elastic properties are still negligible here. Indeed, theoretical arguments suggest that size effects are insignificant for widths larger than 5 nm.11,12 Previous pump-probe studies on ensembles of gold nanorods5,10 have reported elastic moduli which were ≈25-40% lower than the bulk values. As suggested by the authors, the discrepancy may have resulted from a population bias by the optical signal strength.5 For a larger portion of the rods, we find a frequency ratio which is 15-25% lower than expected. The corresponding Young’s modulus is ∼60 GPa, 50% higher than the expected [100] value. We propose that the apparent stiffening is caused by coupling to the substrate (also see Supporting Information Figure S3). Van der Waals interactions23 favor contact of the nanorods to the substrate with their {001} or {110} long facets5 for a majority of rods. Coupling to the substrate 3496

increases the restoring force and, thereby, the extensional frequency. We propose that some of the nanorods do not rigidly adhere to the surface, due to local adsorbates such as residual surfactant. These uncoupled nanorods would show an extensional frequency close to that of free rods. This hypothesis is supported by the significant phase delay we found for the extension mode of rods interacting with the substrate, from φext ) -0.3 ( 0.1 rad for the “free” rods to φext ) -0.1 ( 0.1 rad for the “sticking” rods (see Supporting Information Figure S4). We found φbr ) 0.65 ( 0.15 rad for the breathing mode of all rods, with no difference between the two above-mentioned subpopulations. This was expected for this mode, which does not involve large shear displacements with respect to the substrate. In Figure 4d and e, we show the scatter plots of the measured damping rates vs the corresponding vibrational frequencies. A simple model for the damping of the acoustic vibrations of a sphere in a homogeneous medium predicts that both the period and the damping time should be proportional to the size of the particle.24 Measurements on a larger number of particles are needed to explore a possible correlation between the coupling of the rods to the substrate and the damping rates of extensional mode. However, the absence of a clear correlation between the damping rates and the oscillation frequencies indicates that there is a significant heterogeneity in the microenvironment of the nanorods. For the first time, we have determined the elastic moduli of individual gold nanorods from their vibration modes and precise dimensions. Contrary to earlier reports, we find that continuum elasticity theory is compatible with the measured Nano Lett., Vol. 8, No. 10, 2008

vibrations of large free nanorods and with bulk gold’s elastic moduli. Deviations in frequencies νext or νbr can be attributed to effects of the local mechanical environment. The sensitivity of the extensional frequency to interaction with the substrate could be exploited to probe the contact of the nanoparticle with its local environment and its elastic properties. Our results are the first step toward experimentally exploring the scale on which the elastic moduli of a nanoparticle start to differ from bulk values. Acknowledgment. The authors would like to thank Joel van Embden and Christian Po´tzner for their help with the high resolution transmission microscope imaging. P.Z., J.W.M.C., M.G., and M.O. acknowledge the support from the Australian Research Council. A.L.T. and M.O. acknowledge the support from the Foundation for Fundamental Research on Matter (FOM) and the Dutch Organization for Scientific Research (NWO). Supporting Information Available: Information on white light scattering measurements, heating of the nanorods, the estimated particle temperature after excitation, analytical expressions for the vibrational frequencies, effect of the local environment, and a more detailed analysis of the measured phase of the vibrations. This material is available free of charge via the Internet at http://pubs.acs.org. References (1) Maier, S. A.; Brongersma, M. L.; Kik, P. G.; Meltzer, S.; Requicha, A. A. G.; Atwater, H. A. AdV. Mater. 2001, 13, 1501–1505. (2) Chang, E.; Sørensen, A. S.; Demler, E. A.; Lukin, M. D. Nat. Phys. 2007, 3, 807–812. (3) Hartland, G. V. Annu. ReV. Phys. Chem. 2006, 57, 403–430. (4) Hu, M.; Wang, X.; Hartland, G. V.; Mulvaney, P.; Pe´rez-Juste, J.;

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Sader, J. E. J. Am. Chem. Soc. 2003, 125, 14925–14933. (5) Petrova, H.; Pe´rez-Juste, J.; Zhang, Z. Y.; Zhang, J.; Kosel, T.; Hartland, G. V. J. Mater. Chem. 2006, 16, 3957–3963. (6) Tang, Y.; Ouyang, M. Nat. Mater. 2007, 6, 754–759. (7) van Dijk, M. A.; Lippitz, M.; Orrit, M. Phys. ReV. Lett. 2005, 95, 267406. (8) Staleva, H.; Hartland, G. V. J. Phys. Chem. C 2008, 112, 7535–7539. (9) Tchebotareva, A. L.; Van Dijk, M. A.; Ruijgrok, P. V.; Fokkema, V.; Hesselberth, M. H. S.; Lippitz, M.; Orrit, M. ChemPhysChem, published online Aug 7, http://dx.doi.org/10.1002/cphc.200800289 (10) Hu, M.; Hillyard, P.; Hartland, G. V.; Kosel, T.; Pe´rez-Juste, J.; Mulvaney, P. Nano Lett. 2004, 4, 2493–2497. (11) Diao, J. K.; Gall, K.; Dunn, M. L. J. Mech. Phys. Sol. 2004, 52, 1935– 1962. (12) Liang, H. Y.; Upmanyu, M.; Huang, H. C. Phys. ReV. B 2005, 71, 241403. (13) Nikoobakht, B.; El-Sayed, M. A. Chem. Mater. 2003, 15, 1957–1962. (14) Lindfors, K.; Kalkbrenner, T.; Stoller, P.; Sandoghdar, V. Phys. ReV. Lett. 2004, 93, 037401. (15) So¨nnichsen, C.; Franzl, T.; Wilk, T.; von Plessen, G.; Feldmann, J.; Wilson, O.; Mulvaney, P. Phys. ReV. Lett. 2002, 88, 077402. (16) Novo, C.; Gomez, D.; Pe´rez-Juste, J.; Zhang, Z. Y.; Petrova, H.; Reismann, M.; Mulvaney, P.; Hartland, G. V. Phys. Chem. Chem. Phys. 2006, 8, 3540–3546. (17) Hartland, G. V. J. Chem. Phys. 2002, 116, 8048–8055. (18) Perner, M.; Gresillon, S.; Marz, J.; von Plessen, G.; Feldmann, J.; Porstendorfer, J.; Berg, K. J.; Berg, G. Phys. ReV. Lett. 2000, 85, 792– 795. (19) Love, A. E. H. A Treatise on the mathematical theory of elasticity; Dover: New York, 1927. (20) Landau, L. D.; Lifshitz, E. M. Theory of elasticity; Pergamon: London, UK, 1959. (21) Li, X. D.; Hao, H. S.; Murphy, C. J.; Caswell, K. K. Nano Lett. 2003, 3, 1495–1498. (22) Wu, B.; Heidelberg, A.; Boland, J. J. Nat. Mater. 2005, 4, 525–529. (23) Van Oss, C. J.; Chaudhury, M. K.; Good, R. J. Chem. ReV. 1988, 88, 927–941. (24) Voisin, C.; Del Fatti, N.; Christofilos, D.; Valle´e, F. Appl. Surf. Sci. 2000, 164, 131–139.

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