J. Phys. Chem. B 2006, 110, 19923-19928
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Optical Properties of Au-Ag Nanoboxes Studied by Single Nanoparticle Spectroscopy† Min Hu,§,∇ Hristina Petrova,‡ Andrew R. Sekkinen,§ Jingyi Chen,§ Joseph M. McLellan,§ Zhi-Yuan Li,# Manuel Marquez,| Xingde Li,⊥ Younan Xia,*,§ and Gregory V. Hartland*,‡ Department of Chemistry, UniVersity of Washington, Seattle, Washington 98195-1700, INEST Group, Research Center, Philip Morris USA, Inc., Richmond, Virginia 23234, Department of Chemistry and Biochemistry, UniVersity of Notre Dame, Notre Dame, Indiana 46556-5670, Institute of Physics, Chinese Academy of Sciences, P.O. Box 603, Beijing 100080, P. R. China, NCTCN Center, Physical and Chemical Properties DiVision, NIST, Gaithersburg, Maryland 20899, and Department of Bioengineering, UniVersity of Washington, Seattle, Washington 98195 ReceiVed: April 5, 2006; In Final Form: June 2, 2006
The optical properties of two Au-Ag nanobox samples with average edge lengths of 44 and 58 nm and wall thicknesses of 6 and 8 nm, respectively, have been studied by single particle spectroscopy. The measurements gave an average line width of Γ h ) 306 ( 7 meV with a standard deviation of σ ) 30 meV for the 44-nm boxes, and Γ h ) 350 ( 9 meV with σ ) 35 meV for the 58-nm boxes. These line widths are much broader than those of gold nanorods with comparable resonance energies. The increased broadening is attributed to a combination of surface scattering of electrons, as well as increased radiation damping for the nanoboxes. Discrete dipole approximation calculations have been performed with and without surface scattering of electrons to compare with the experimental spectra. The calculations confirm that both electron-surface scattering and radiation damping are important effects in this system.
1. Introduction The optical properties of metal nanoparticles are very different from the bulk material because of the collective oscillation of free electrons in the conduction band, which is known as surface plasmon resonance (SPR).1 The SPR peak may vary from the visible to the near-IR range, depending on the size, shape, material, and structure of the particles. Most of the research on the optical properties of metal nanoparticles has been done on ensembles in solution, where a distribution of sizes and shapes is involved. This makes it very difficult to correlate the optical properties to the structure of the particles. Single nanoparticle spectroscopy provides a solution to this problem. The scattered light from single metal nanoparticles can be easily detected by a standard laboratory spectrometer using an optical microscope in conjunction with either total internal reflection2 or dark-field illumination.3 Most of the research on single-nanoparticle spectroscopy has focused on correlating the resonance energy with the size and shape of the nanoparticles.4,5 Only a few studies have addressed the width of the plasmon resonance,6,7 although this is a very important property, not only for fundamental issues, but also in optical applications such as surface-enhanced Raman scattering (SERS) spectroscopy8 and sensing.9,10 Recently, plasmon damping in spherical gold nanoparticles and gold nanorods was investigated by the Feldmann group.6,7 They found that the width of the peak becomes broader for larger spherical nanoparticles †
Part of the special issue “Charles B. Harris Festschrift”. * Corresponding author. E-mail:
[email protected] (G.V.H.);
[email protected] (Y.X.). § Department of Chemistry, University of Washington. ∇ Philip Morris USA, Inc. (INEST ) Interdisciplinary Network of Emerging Science and Technologies: Philip Morris USA Postgraduate Research Program). ‡ University of Notre Dame. # Chinese Academy of Sciences. | NIST. ⊥ Department of Bioengineering, University of Washington.
because of radiation damping, while the nanorods examined in their experiments yielded narrower line widths because of a significant reduction in the nonradiative plasmon decay.6,7 The experimental results were compared to calculated spectra using Mie theory for the spheres, and a quasi-static approximation for the rods.6,7 The results indicate that there is no contribution from the surface scattering of electrons in these experiments. Heterogeneous core-shell and alloyed structures of metal nanoparticles have also been examined. For example, GuyotSionnest and co-workers studied core-shell Au-Ag nanorods.11 They found increased broadening in the spectra when adding a Ag shell onto the Au nanorod surface, which they attributed to electron scattering at the silver and gold interface. Very little effect from the particle-solution interface was detected.11 We recently reported results from spherical core-shell Au-Ag nanoparticles and their alloyed structures.12 Spectral broadening was also observed for these bimetallic particles, but it was attributed to the wavelength dependence of the dielectric constants of the nanoparticles, that is, interfacial scattering was not a major effect. Lounis and co-workers studied single gold particles with sizes down to ∼5 nm using an absorption-based technique.13 They observed significant broadening at small sizes due to surface scattering of electrons. Finally, we have recently examined single gold nanorods with different widths via light scattering.14 The results show that the line width for the nanorods is controlled by a competition between surface scattering of electrons and radiation damping, and that the relative magnitudes of these two effects are in good agreement with the results reported in refs 6 and 13. This last set of experiments is somewhat unusual: the line width of the longitudinal plasmon resonance (electron oscillation along the major axis of the rod) is controlled by the width of the rod.14 In this paper, we present single-nanoparticle spectroscopy studies of nanoboxes consisting of a Au-Ag alloy. The nanoboxes are hollow cubes recently developed in our group.15,16 The line widths observed in the scattering spectra of these
10.1021/jp0621068 CCC: $33.50 © 2006 American Chemical Society Published on Web 07/12/2006
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particles are less broad than those of the Au spheres measured by the Feldmann group for a similar resonance energy,7 but are much broader than those of either the pure Au nanorods6 or the Au-Ag core-shell nanorods.11 The experimental spectra are compared with spectra calculated using the discrete dipole approximation (DDA) method (both with and without surface scattering of electrons).17,18 The results of this study indicate that both surface scattering of electrons at the particle-solution interface and radiation damping have significant effects on the spectra of the nanoboxes. 2. Experimental Section Preparation of Au-Ag Nanoboxes. Monodispersed silver nanocubes were first prepared using a slightly modified version of the polyol synthesis described in ref 19. Briefly, 5 mL of ethylene glycol (EG; J. T. Baker) was added to a disposable 6-dram glass scintillation vial (VWR Internantional) and heated in an oil bath at 145 °C for 1 h. Then, 0.5 mL of a 3 mM solution of HCl (J. T. Baker) in EG was added. After 10 min, solutions of AgNO3 (1.5 mL of a 94 mM solution in EG; Aldrich) and poly(vinyl pyrrolidone) (PVP; 1.5 mL of a 147 mM solution in EG in terms of the repeating unit, MW ≈ 55 000; Aldrich) were injected at a rate of 22.5 mL/h using a dual channel syringe pump (KDS-200, Stoelting, Wood Dale, IL). Following injection, the vial was loosely capped. Upon injection of the AgNO3 and PVP, the color of the solution became milky white, took a pinkish hue, and then turned clear over a period of about 6-7 h. The solution was left in this state for another 20 h until the vial was sealed. After sealing, the solution remained clear for an additional 1-2 h, then it gradually turned yellow. The color intensified over the next hour, going from dark yellow to reddish-brown and finally thick greenishgray. The total reaction time was 22-24 h. Magnetic stirring at 350 rpm was applied throughout the synthesis. The final product was washed and collected by centrifugation for 30 min at 3,900 rpm, first with acetone to remove EG, then at least twice with water to remove excess PVP. Cubes were the primary product in this synthesis (>95%). They formed stable suspensions in water without any additional stabilizers and were used as templates for the synthesis of Au-Ag alloy boxes in the next step. In a typical procedure for synthesizing nanoboxes, a 75-µL aliquot of the as-obtained dispersion of Ag nanocubes was added to a solution of 5 mg of PVP (MW ≈ 55 000) in 5 mL of deionized water. This solution was then refluxed for 2 min. A specific amount of a 0.2 mM HAuCl4 aqueous solution was added dropwise into the reaction system. Vigorous magnetic stirring was maintained during the entire process until the color of the solution became stable. The solution was cooled to room temperature, and the white AgCl precipitate was removed by dissolving with a saturated NaCl solution. The solution was then centrifuged at 10 000 rpm for 15 min, and the supernatant containing the dissolved AgCl was removed using a pipet. The solid was rinsed with water, centrifuged three more times, and finally redispersed in water for further characterization and usage. Characterization of Au-Ag Nanoboxes. The samples for scanning electron microscopy (SEM) and transmission electron microscopy (TEM) studies were prepared by placing small drops of the dispersions of metal nanostructures on silicon substrates (Silicon Valley Microelectronics, San Jose, CA) or copper grids coated with amorphous carbon (Ted Pella, Redding, CA), respectively. The samples were allowed to dry at room temperature in a fume hood. The SEM images were obtained using
Figure 1. SEM images of Au-Ag nanoboxes synthesized via galvanic replacement reaction. The average size was measured from the TEM images as (A) 44.4 ( 4.1 nm and (B) 58.2 ( 5.5 nm. The errors indicate standard deviations. The wall thicknesses for the nanoboxes are 5.7 ( 0.9 nm and 7.6 ( 1.2 nm, respectively. The upper insets in panels A and B are the corresponding TEM images, and the lower inset in panel A is the true color image recorded by a dark-field microscope; the red dots correspond to the 44 nm nanoboxes.
a field-emission microscope (Sirion XL, FEI, Hillsboro, OR) operated at 15 kV. The TEM images were taken using a Philips 420 electron transmission microscope operated at 120 kV. The percentages of gold and silver in the nanostructures were analyzed using an atomic emission spectrophotometer (Thermo Jarrell Ash Corp., Franklin, MA) equipped with a Jarrell Ash 955 inductively coupled plasma system. The emission lines at 328.0 and 242.8 nm were used to measure the contents of silver and gold, respectively. Single-Nanoparticle Spectroscopy. An Olympus IX-71 inverted optical microscope was used for dark-field microscopy. The illumination light comes from the output of a 100 W halogen lamp with a dark-field oil-immersion condenser (Olympus U-DCW). The nanobox samples were diluted into lower concentrations from the as-synthesized solution, and a drop of the solution was air-dried on a glass microscope slide. Before taking spectra, a drop of immersion oil (refractive index ) 1.516) was applied to the sample area, and a cover slip was then placed on the top of the oil. The Rayleigh scattering light from a single nanoparticle was collected with a 60× objective and directed to an imaging monochromator (Acton Research MicroSpec 2150i). The dispersed light was imaged onto a Roper Scientific 100 × 1340 B liquid N2-cooled charge-coupled device (CCD) camera. Normalized Rayleigh scattering spectra from individual particles were obtained by subtracting and dividing by a background taken from a nearby area of the CCD detector. The acquisition times for the spectra were 10-20 s. 3. Results and Discussion Spectroscopic and Structural Analysis. Figure 1 shows representative SEM and TEM images of two different sized nanoboxes. The galvanic replacement reaction between Ag and
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Figure 3. Experimental line widths (full-width-at-half-maximum) versus resonance energy for the 44-nm and 58-nm Au-Ag nanoboxes and the Au nanorods.
Figure 2. Rayleigh scattering spectra recorded using dark-field illumination for (A) 44-nm and (B) 58-nm Au-Ag nanoboxes. Two different particles are shown in each panel. The blue curve in panel A shows the scattering spectrum taken from a gold nanorod in a sample with a mean width of 14 ( 2 nm and a mean aspect ratio of 3.6 ( 0.8. The distortion in the peak shape for the red-shifted spectra in panels A and B arises from a cutoff in our instrument response function.
Au produces well-defined hollow boxes, with good control of both the size and the shape of the particles. The uniform thin walls of the boxes can be clearly seen in the TEM images in the insets of Figure 1. The average edge length of the two nanobox samples (measured by counting over 100 particles) was 44 ( 4 nm and 58 ( 5 nm, and the wall thickness was measured as 6 ( 1 nm and 8 ( 1 nm (about 1/7 of the edge length), respectively. The errors indicate the standard deviation in the dimension. The nanoboxes actually consist of an alloy of Au and Ag. Analysis using atomic emission spectroscopy shows that the Au/Ag atomic ratio was 2.5:1 for the 44-nm nanoboxes and 2:1 for the 58-nm nanoboxes. We have shown elsewhere that the extinction spectra of the Au-Ag nanoboxes can be tuned from the visible to the near-IR region, depending on how far the galvanic replacement reaction is allowed to proceed.16,20 For these two specific nanoboxes, the SPR occurs around 750 nm. In Figure 1A, the insert also shows a dark-field microscopy image of the nanoboxes. The majority of the particles are “red”, indicating that they are Au-Ag nanoboxes. The “blue” dots can be assigned to Ag nanocubes that have not reacted; these particles are expected to have their plasmon resonance in the 450 nm region or the spectrum.21 Figure 2 shows representative single nanoparticle Rayleigh scattering spectra for the two different sized Au-Ag nanobox samples (two spectra are shown for each sample). There are several features to note about the experimental spectra. First, the difference in resonance peak positions for different nanoboxes in the same sample is due to the distribution of sizes. The plasmon position is determined by both the edge length and the wall thickness,16,20 and the experimental samples exhibit a range of different values for these dimensions. Furthermore, the resonance of the nanoparticles also depends on the refractive index of the surrounding environment.1 The local refractive
index may vary for different particles, thus causing differences in the resonance frequency.4,9,10 Also shown in Figure 2A is the Rayleigh scattering spectrum from a gold nanorod. Compared with the Au-Ag nanoboxes, the Au nanorods have much narrower spectra.6,14 The line widths measured for the nanorods are consistent with the results reported by the Feldmann group.6 Note that the particles with red-shifted spectra in Figure 2 have asymmetric peak shapes. This is attributed to a cutoff in our light source/detector system. Because of this distortion, it is difficult to fit the spectra to a Lorentzian function.6,7 Thus, the resonance energies and line widths were measured directly from the spectra: the line widths Γ were obtained from the halfwidth-at-half-maximum using only the blue portion of the spectrum. This is shown schematically in Figure 2B. Figure 3 shows the line widths plotted against the resonance energies for the 44-nm and 58-nm nanoboxes, and the Au nanorods. The Au-Ag nanoboxes have resonance energies in the 1.55-1.75 eV range, which is consistent with the SPR peak in the ensemble solution. As discussed above, the variation in resonance energy is due to differences in the particle dimensions within the samples and variations in their environment. The line widths vary from 270 to 380 meV for the 44-nm nanoboxes, and from 310 to 420 meV for the 58-nm nanoboxes. The line widths are much broader than those of the Au nanorods. As will be shown below, the variation in line width can be understood as arising from differences in both the wall thickness and the volume of different nanoboxes. There does not appear to be any correlation between the line width and the resonance energy, implying that the edge length and wall thickness are random variables. The average line width from the data in Figure 3 is Γ h ) 306 ( 7 meV (standard deviation σ ) 30 meV) for the 44-nm boxes, and Γ h ) 350 ( 9 meV (σ ) 35 meV) for the 58-nm boxes (the errors given for Γ h are the standard error, σ/xN.) Note that the average line width for the 58-nm boxes is significantly broader than that for the 44-nm boxes, even though the 44-nm boxes have thinner walls and, therefore, should show a stronger electron-surface scattering effect. DDA Calculations. The light-scattering spectra of the nanoboxes were modeled using the DDA method.17,20 These calculations require information about the dielectric constants of the particles and the environment. The environment was treated as oil (refractive index ) 1.516). Reliable dielectric constant data for Au-Ag alloys are available for the visible region of the spectrum,22-24 but not for the near-IR region where the plasmon resonance occurs for the nanoboxes. Thus, the dielectric constant of the particles was taken as an average of the dielectric constants of Ag and Au: alloy ) RAu + (1 -
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R)Ag, where R is the mole fraction of Au in the particle. The values for Au and Ag were taken from ref 25. This averaging procedure is probably not accurate for the visible region, where the interband transitions of Au and Ag make a significant contribution to the dielectric function,25 but should be appropriate for the near-IR region, which is dominated by the freeelectron contributions.26 The thin walls of the nanoboxes mean that the modification of the dielectric function of the particles by electron-surface scattering must be included. Surface scattering is accounted for in the calculations in the following way: First, the dielectric constant is split into interband and intraband (or free-electron) contributions:1,27,28
(ω) ) ib(ω) + f(ω)
(1)
The free-electron component can be calculated using the Drude model, and is given by1,29
1f(ω) ) 1 - ωp2/(ω2 + γ2)
(2a)
2f(ω) ) ωp2γ/ω(ω2 + γ2)
(2b)
where 1f and 2f are the real and imaginary components of the dielectric constant, respectively, ωp is the plasma frequency, and γ is the damping constant for the electrons. Surface scattering is included by writing1,27,28
γ ) γbulk + AνF/Leff
(3)
where A is a constant, νF is the Fermi velocity of the electrons, and Leff is the effective mean free path length of the electrons. This last quantity is the key parameter for describing electronsurface scattering. Coronado and Schatz recently derived a general expression for the effective path length for convex particles of Leff ) 4V/S,30 where V is the volume and S is the surface area of the particle. We have recently shown that this expression gives a consistent description of electron-surface scattering for gold nanorods and nanospheres.13,14 However, it is not clear whether this expression is appropriate for the hollow structures considered in this work. To make progress (and provide some context for our results), we approximate the particles as a thin, flat plate and write Leff ) 2w, where w is the wall width. This expression should be correct for particles where the edge lengths are much greater than the wall thicknesses (the particles in the present study are close to this approximation). In the spectral region of interest for the nanoboxes ω . γ, which means that the modified dielectric constants can be simply written as
1(ω) ≈ 1bulk(ω)
(4a)
2(ω) ≈ 2bulk(ω) + ωp2/ω3 × AνF/Leff
(4b)
where 1bulk(ω) and 2bulk(ω) are the dielectric constants of the bulk metal. Thus, surface scattering of electrons simply adds an extra term to the imaginary component of the dielectric constant of the metal. In the absence of radiation damping (see below), the line width of the plasmon resonance is given by Γ ) 22/|∂1/∂ω|.1 Using eq 4b for 2 and eq 2a for 1 yields an expression for the line width that is analogous to eq 3: Γ ) Γbulk + AνF/Leff. Thus, for a free-electron metal, electron-surface scattering increases the line width by an amount AνF/Leff. Results for the two different sized boxes with and without surface scattering are presented in Figure 4. The spectra
Figure 4. The scattering spectra calculated using the DDA method for (A) 44-nm and (B) 58-nm Au-Ag nanoboxes. The surrounding medium is oil with a refractive index of 1.516. In both panels, the red curve represents the spectra calculated without surface scattering, and the green curve represents the spectra calculated with surface scattering.
calculated without surface scattering are shown as the red lines. The green lines show the results of the DDA calculations including surface scattering via eq 4b. The surface-scattering parameter used in these calculations was A ) 1. The line widths obtained from fitting of the DDA spectra to a Lorentzian function are 163 meV for the 44-nm nanoboxes with surface scattering, and 101 meV without surface scattering. The line widths for the 58-nm nanoboxes are 180 and 134 meV with and without surface scattering, respectively. Thus, in these calculations, surface scattering of electrons increases the line width by 61 meV for the 44-nm nanoboxes, compared to 46 meV for the 58-nm nanoboxes. The effect is stronger in the 44 nm nanoboxes because they have thinner walls. The calculated spectra also show that electron-surface scattering significantly reduces the peak amplitude of the scattering efficiency. Note that the increase in the line width due to electron-surface scattering in the calculated spectra is slightly less than AνF/Leff. This is because the values of 1 used in the calculations are slightly different from the Drude model values (eq 2a), that is, ∂1bulk/∂ω * 2ωp2/ω3 (see eq 4b and the discussion below this equation). Effectively, this modifies the surface scattering term by a factor of (2ωp2/ω3)/|∂1bulk/∂ω|, which is approximately 0.8 in the spectral region of interest. Consistent with the experimental spectra, the calculated spectra for the 58-nm nanoboxes are broader than those for the 44-nm nanoboxes, even though surface scattering is stronger for the 44-nm nanoboxes. This is due to radiation damping, that is, energy loss for the plasmon oscillation due to emission of radiation.1,6,7,8 The DDA calculations include the contribution from the induced dipole of the particle in the local electric field, which means that they include the radiation damping effect.17,18,31 The magnitude of radiation damping is proportional to the volume of the particles and is, therefore, larger for the 58-nm nanoboxes.6,7,8 It is important to note that the calculated
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line widths are significantly narrower than the experimental line widths: this can be easily seen by visually comparing the experimental and calculated spectra in Figures 2 and 4, respectively. Analysis of Plasmon Damping. To understand the differences between the two samples, and the difference between the calculated and experimental line widths, we need to consider the different sources of broadening for the plasmon resonance. In general, the line width can be decomposed into contributions from the bulk dielectric constants, surface scattering, and radiation damping:1
Γ ) Γbulk + Γsurf + Γrad
(5)
The bulk contribution is given by Γbulk ) 22bulk/|∂1bulk/∂ω|,1,32 and is calculated to be 70 meV from the data in ref 25 for both the 44-nm and 58-nm nanoboxes. The surface scattering term is given by Γsurf ) AνF/Leff (see above), and the radiation damping effect is proportional to the particle volume.6,7,8 Following Sonnischen et al., we write Γrad ) hκV/π.6 Thus, for a given sample (specific values of V and Leff), the relative contributions from surface scattering and radiation damping to the line width are determined by A and κ. The magnitude of the radiation damping effect in the DDA calculations can be directly obtained from the spectra calculated without electron-surface scattering. In this case, the line width is simply given by Γ ) Γbulk + hκV/π, which means that the difference between the 44-nm and 58-nm boxes is given by ∆Γ ) hκ∆V/π. For ∆Γ ) 33 meV and ∆V ) 68.6 × 103 nm3, this yields κ ) 3.6 × 10-7 fs-1 nm-3, which is consistent with the value of κ ) (5.5 ( 1.5) × 10-7 fs-1 nm-1 determined from recent single-particle spectral measurements for gold rods and spheres.6,14 To determine the values of A and κ from the experimental data, we write eq 6 as Γ h - Γbulk ) AνF/L h eff + hκV h /π, where we h are the average values for the explicitly note that Γ h, L h eff and V experimental line width, effective path length, and volume, respectively. For the 44-nm boxes, Γ h ) 306 ( 7 meV, L h eff ) 12 ( 2 nm, and V h ) (52 ( 18) × 103 nm3, while, for the 58h ) (121 nm boxes, Γ h ) 350 ( 9 meV, L h eff ) 16 ( 2 nm, and V ( 36) × 103 nm3. Using Γ h bulk ) 70 meV and solving the two equations for the two unknowns yields A ) 2 ( 1 and κ ) (9 ( 5) × 10-7 fs-1 nm-1. The errors are mainly due to the uncertainty in V and Leff. Note that both the surface scattering parameter and the coefficient for radiation damping are significantly larger than the values recently determined for solid gold particles.6,13,14 In particular, the value of A is much larger than expected. The results presented above show that the broadening in the nanobox spectra arises from both radiation damping and electron-surface scattering. This is somewhat unusual. Typically, large particles show radiation damping effects, and small particles show surface scattering. Thus, these two effects occur in different size ranges and are usually seen in separate experiments.6,13 In our recent single-particle study of gold nanorods, the electron-surface scattering effect was observed for samples of thin rods (widths less than 15 nm), and radiation damping was observed for thick rods (widths greater than 20 nm).14 The nanoboxes are unique because they have relatively large volumes (they are 7 times larger than 15 nm wide rods with a similar resonance energy), but they have thinner walls. Thus, they are subjected to both radiation damping (due to their large volume) and surface scattering of electrons (from the thin walls). It is important to note that the magnitudes of these two effects are similar for the two nanoboxes studied in this paper.
h and the values of A and Using the average values of L h eff and V κ determined from the experiments, we calculate Γsurf ) 170 meV and Γrad ) 65 meV for the 44-nm boxes, and Γsurf ) 128 meV and Γrad ) 151 meV for the 58-nm boxes. The broader line widths for the 58-nm boxes can thus be seen as a consequence of the greater radiation damping in this system. For applications such as SERS, it is desirable to have narrow resonances (high quality factors). For nanoboxes with an edge length-to-wall thickness ratio of 1:7 (the system studied here), we calculate that the line width should be minimized for an edge length of 40 nm. Boxes smaller than this will show increased broadening due to surface scattering, and boxes larger than this will show increased broadening due to radiation damping. The last point addressed here is the value of the surface scattering parameter of A ) 2 ( 1 determined from our experiments. This is much larger than the typical value of A < 1 found in the literature.1,13,14,27,28 There are several possible reasons for this difference: (i) The walls of the boxes in our samples may not be perfectly flat and parallel. For example, imperfections such as thinning in the centers would not appear in the TEM images, but would have a significant effect on Leff, leading to an increased contribution from surface scattering. (ii) A more likely explanation for the unrealistically large value of A is that the expression Leff ) 2w is not appropriate for the nanoboxes. It would be useful to have a rigorous treatment of electron-surface scattering for particles such as nanoboxes and nanoshells, especially considering the importance of these materials in biophysical applications.33 (iii) Finally, the estimate of the electron-surface scattering contribution was made using Γbulk ) 70 meV. As noted above, the dielectric constants for Au-Ag alloys are not well-known in the near-IR region. It is possible that Γbulk could be significantly larger than 70 meV and, therefore, that the values of A and κ determined from the analysis of our experiments are too large. If more accurate dielectric constant data becomes available, then the line width measurement from these experiments could be reanalyzed to yield more accurate values of A and κ. 4. Summary and Conclusions The optical properties of Au nanoboxes have been investigated by single nanoparticle spectroscopy. Two samples were examined: boxes with an edge length of 44 ( 4 nm and wall thickness of 6 ( 1 nm, and boxes with an edge length of 58 ( 5 nm and wall thickness of 8 ( 1 nm. The resonances observed in the single-particle spectra occur in the 1.55-1.75 eV energy range, and the average line widths are Γ h ) 306 ( 7 meV (σ ) 30 meV) for the 44-nm boxes and Γ h ) 350 ( 9 meV (σ ) 35 meV) for the 58-nm boxes. The line width contains contributions from both radiation damping (which is proportional to the volume) and surface scattering of electrons (which is inversely proportional to the wall thickness). Analysis of the average line widths, using the dimensions of the particles determined by TEM, and comparison to DDA calculated spectra shows that the broader line width for the larger 58-nm boxes is a consequence of the greater radiation damping in this system. Acknowledgment. This work has been supported in part by a grant from the NSF (DMR-0451788) and a fellowship from the David and Lucile Packard Foundation. Y.X. is a Camille Dreyfus Teacher Scholar. Z.-Y.L. was supported by the National Natural Science Foundation of China (No. 10525419). X.L. acknowledges the support from the NSF (Career Award). Part of the research was performed at the Nanotech User Facility (NUTF), a member of the National Nanotechnology Infrastruc-
19928 J. Phys. Chem. B, Vol. 110, No. 40, 2006 ture Network (NNIN) supported by the NSF. G.V.H. acknowledges the support of the Petroleum Research Fund administered by the American Chemical Society, and the NSF. We thank Yujie Xiong for his assistance with TEM. References and Notes (1) Kreibig, U.; Vollmer, M. Optical Properties of Metal Clusters; Springer: Berlin, 1995. (2) Sonnichsen, C.; Geier, S.; Hecker, N. E.; von Plessen, G.; Feldmann, J.; Ditlbacher, H.; Lamprecht, B.; Krenn, J. R.; Aussenegg, F. R.; Chan, V. Z. H.; Spatz, J. P.; Moller, M. Appl. Phys. Lett. 2000, 77, 2949. (3) Schultz, S.; Smith, D. R.; Mock, J. J.; Schultz, D. A. Proc. Natl. Acad. Sci. U.S.A. 2000, 97, 996. (4) Mock, J. J.; Barbic, M.; Smith, D. R.; Schultz, D. A.; Schultz, S. J. Chem. Phys. 2002, 116, 6755. (5) Kuwata, H.; Tamaru, H.; Esumi, K.; Miyano, K. Appl. Phys. Lett. 2003, 83, 4625. (6) Sonnichsen, C.; Franzl, T.; Wilk, T.; von Plessen, G.; Feldmann, J.; Wilson, O.; Mulvaney, P. Phys. ReV. Lett. 2002, 88, 077402. (7) Sonnichsen, C.; Franzl, T.; Wilk, T.; von Plessen, G.; Feldmann, J. New J. Phys. 2002, 4, 93. (8) Wokaun, A.; Gordon, J. P.; Liao, P. F. Phys. ReV. Lett. 1982, 48, 957. (9) Haes, A. J.; Van Duyne, R. P. Anal. Bioanal. Chem. 2004, 379, 920. (10) Miller, M. M.; Lazarides, A. A. J. Phys. Chem. B 2005, 109, 21556. (11) Liu, M. Z.; Guyot-Sionnest, P. J. Phys. Chem. B 2004, 108, 5882. (12) Wang, X.; Zhang, Z. Y.; Hartland, G. V. J. Phys. Chem. B 2005, 109, 20324. (13) Berciaud, S.; Cognet, L.; Tamarat, P.; Lounis, B. Nano Lett. 2005, 5, 515.
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