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Imaging and dispersion relations of surface plasmon modes in silver nanorods by near-field spectroscopy
Chemical Physics Letters 412 (2005) 41–45 www.elsevier.com/locate/cplett
Imaging and dispersion relations of surface plasmon modes in silver nanorods by near-field spectroscopy Jong Kuk Lim a,b, Kohei Imura a,c, Tetsuhiko Nagahara a, Seong Keun Kim b,*, Hiromi Okamoto a,c,* a
Department of Molecular Structure, Institute for Molecular Science, 38 Nishigonaka, Myodaiji, Okazaki, Aichi 444-8585, Japan b School of Chemistry, Seoul National University, Seoul 151-747, Korea c The Graduate University for Advanced Studies, Myodaiji, Okazaki, Aichi 444-8585, Japan Received 5 May 2005; in final form 22 June 2005 Available online 14 July 2005
Abstract Surface plasmons of silver nanorods were investigated by using scanning near-field optical microscopy. Near-field transmission images showed spatially oscillatory patterns in nanorods. The oscillatory features of images are attributable to plasmon-mode wavefunctions. From the near-field images and spectra, dispersion relations of surface plasmon modes for various silver nanorods are obtained. It is found that dispersion relation of a nanorod is dependent on its diameter. The spectral features obtained are compared with those for gold nanorods. 2005 Elsevier B.V. All rights reserved.
1. Introduction Collective oscillations of electrons on surfaces of metals, known as surface plasmons (SPs), are extensively studied not only for the fundamental interests, but also for possible applications to sensor technology to characterize molecules on the interface between metals and dielectric media [1], to extremely sensitive surface enhanced Raman scattering (SERS) [2–5], to plasmonic devices [6–8], and so on. With plasmonic devices, it is also expected that a very small channel for transporting photons is possible. Recently, non-diffraction limited transport of SPs was in fact demonstrated [9,10] and there has been continuing intensive interests in the properties of SPs in laterally confined metal structures.
* Corresponding authors. Fax: +82 889 5719 (S.K. Kim); +81 564 55 4639 (H. Okamoto). E-mail addresses: [email protected] (S.K. Kim), [email protected] (H. Okamoto).
0009-2614/$ - see front matter 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2005.06.094
One of the fundamental properties which characterizes SPs is dispersion relation. The dispersion relations of SPs in noble metal nanowires fabricated by electron beam lithography were obtained by using far-field optical extinction spectroscopy [11,12]. In case of several silver (Ag) nanowires having an identical cross-section, it was reported that all the measured points follow a single dispersion regardless of the length, and that the nanowire shows larger wave vectors than those for a flat metal/glass interface at a given frequency. These observations indicate that the plasmon propagation is slower in a silver nanowire than in a flat silver/glass interface. It was also found that the upper limit of the frequency for SPs is smaller on a silver nanowire than on a flat metal/ glass interface. Recently, Imura et al. [13–15] reported that near-field images of gold (Au) nanorods show spatially oscillating patterns along the rod axis, and were attributed to spatial characteristics of plasmon-mode wavefunctions. They demonstrated that direct measurements of both wave vectors and resonance energies of SPs are possible by near-field measurements, and the
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results were utilized to obtain the dispersion relation. Similar oscillating images for nanowires fabricated by electron beam lithography were recently reported by Hohenau et al. [16] using a collection-mode near-field microscopy. In this Letter, we report near-field imaging of SP modes in single Ag nanorods. We used the results to obtain dispersion relations of SPs in Ag nanorods, and the dispersion curves were compared with those in the previous studies [11,15]. We will also discuss difference between the results for Ag and Au on the basis of macroscopic dielectric functions.
2. Experiment The Ag nanorod sample was chemically synthesized. The procedure for the synthesis is basically the same as that reported by Hu et al. [17]. We used silver nitrate (AgNO3) and tri-sodium citrate (Na3C6H5O7) as a starting material and a reducing agent, respectively, and sodium dodecylsulfonate (C12H25SO3Na, SDSN) as a surfactant for rod growth. Typically, 25 cm3 of 4 · 10 4 mol dm 3 water solution of silver nitrate, 2–3 cm3 of 1 · 10 2 mol dm 3 tri-sodium citrate, and 25 cm3 of 2 · 10 3 mol dm 3 SDSN were mixed. Then the mixture was stirred, and boiled at 100 C for 60–90 min to obtain a turbid yellow-green solution. The lengths of the nanorods were controlled by changing the concentration of the reducing agent (tri-sodium citrate) from 4 · 10 4 mol dm 3 (giving short rods) to 6 · 10 4 mol dm 3 (long rods). Other surfactants such as sodium dodecylbenzene sulfonate (C12H25C6H4SO3Na, SDBS) and sodium dodecylsulfate (C12H25OSO3Na, SDS) were also examined to obtain nanorods in high density. Of the three surfactants tried, SDSN gave the highest yield of nanorods. To separate Ag nanorods from other nanoparticles (spheres and other shapes), the mixture after reaction was diluted with ultra pure water (18 MX cm 1) to
100 cm 3 in volume and then centrifuged at 6000 rpm for 30 min. After centrifugation, the supernatant was removed and the sediment was diluted by ultra pure water again. This procedure was repeated, until the color of the supernatant becomes vanished. The synthesized Ag nanorods were investigated by using scanning electron microscope (SEM) (Hitachi, S-900) to verify its density and morphology. Far-field extinction spectra were taken in water solutions. The sample for the near-field optical experiment was prepared by spin coating the solution on a cover slip. Figs. 1 and 2 show, respectively, SEM images and far-field extinction spectra in water solution of the synthesized nanorods. A 500-W Xenon discharge lamp (Ushio, UXL500SX) illuminated the sample through an aperture of a tapered Au-coated near-field fiber probe tip (JASCO) by using a home-made scanning near-field optical microscope (SNOM) [18]. The aperture diameters of the fiber tips were measured to be 50–100 nm by SEM. The transmitted light was collected by an objective lens (Nikon, NA 0.85) and detected by a CCD array detector (Andor,
Fig. 2. Far-field extinction spectra of silver nanorods solutions synthesized in SDSN (a) and SDBS (b).
Fig. 1. SEM images of silver nanorods synthesized in sodium dodecyl sulfonate (SDSN), (a), and in sodium dodecylbenzene sulfonate (SDBS), (b). Images were taken on cleaned silicon wafers.
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DV401-FI) equipped with a polychromator. A sheet polarizer was used to characterize the polarization of the SP modes. The typical scan step size was 12.5 nm for an area of 1 lm · 1 lm. The distance between the sample and the tip was maintained at about 10–15 nm by a shear force feedback mechanism.
3. Results and discussion 3.1. Features of nanorods prepared For the samples in Fig. 1a,b, SDSN and SDBS were used as surfactants, respectively. From Fig. 1 it is found that use of SDSN gives higher density of nanorods than SDBS. The nanorods have various lengths and diameters, and quite a few particles appear to be nanosphere-like, under the magnification scales of Fig. 1. The number density of nanorods was 30% in Fig. 1a. In the far-field extinction spectra in aqueous solution in Fig. 2, the curves (a) and (b) indicate, respectively, the samples prepared by using SDSN and SDBS. Extinction peaks at 440 and 420 nm for respective curves are contributed mainly from the SP resonances for Ag nanospheres [17,19]. Compared with the spectrum for the solution prepared with SDBS, that with SDSN shows a peak at a longer wavelength (20 nm). In addition to difference in the peak positions, the relatively enhanced extinction in the longer wavelength region is observed. Such a difference between the two solutions should be due to the difference in the number density of the nanorods. In the nanorods, the resonance energy of SPs polarized along the longitudinal axis becomes low with increasing the aspect ratio (or the length). Because the number density of the nanorods is higher in the solution prepared with SDSN than that prepared with SDBS, relative extinction in the longer wavelength region is enhanced for the sample prepared with SDSN. The difference in the peak position can also be explained in a similar way. 3.2. Near-field images and dispersion relations We investigated a number of near-field images and spectra for nanorods. Representative images and spectra are shown in Fig. 3. The topographic image is broadened due to the probe tip shape, and the actual dimension of the rod (shown by solid lines) estimated by deconvolution is (20 ± 4) nm (diameter) · (530 ± 25) nm (length). Fig. 3b–d are near-field transmission images probed at 806, 920, and 1008 nm, respectively. Dark spots indicate reduction of the transmitted light. In these figures, the number of the dark spots is decreasing from 5 to 3 on going from Fig. 3b to d. The spatial dependence of transition probability in the nanorod is approximately given by square modulus of the wave
Fig. 3. Representative images a nanorod and the near-field spectrum. (a) Topography of the silver nanorod, (20 ± 4) nm in diameter and (530 ± 25) nm in length. (b)–(d) Near-field transmission images probed with an unpolarized light at 806, 920, and 1008 nm, respectively. (e) Near-field spectrum taken at the position marked ÔXÕ in the near-field transmission (b).
functions of the SP modes [13–15,20]. Therefore, the wavelengths of the SP modes, ksp, can be directly determined from the near-field transmission images. The absolute value of wave vector, ksp, is given by ksp = 2p/ksp. The wave vectors for SP modes determined from the near-field images are 26.9, 21.1, and 18.3 lm 1 for Fig. 3b–d, respectively. Fig. 3e shows the near-field spectrum measured at the position ÔXÕ indicated in Fig. 3b. In this spectrum, the relative extinction is calculated by [I(substrate) I(X)]/I(substrate) where I(substrate) and I(X) denote the transmitted light intensity measured at the substrate and at the position ÔXÕ, respectively. Two resonant peaks are clearly seen at 806 and 920 nm, and another resonance possibly present at 1000 nm. These wavelengths are the ones at which the images of Fig. 3b–d were obtained.
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Fig. 4. Dispersion relations of SPs of the nanorods obtained in this study and those reported in [11]. The experimental uncertainty is typically ±4 nm for the diameter while that for the length is typically ±25 nm. The dotted curve indicates the approximate position of the dispersion curve obtained for gold nanorods (diameter 20 nm) in [15].
Other nanorods were investigated in the same way. From the obtained wave vectors and resonance energies, dispersion curves for Ag nanorods can be obtained (Fig. 4). In Fig. 4, the dispersion relation for Ag nanowires (85 nm · 75 nm cross-section) reported in [11] is also plotted (crossed symbols). The dispersion relations presently obtained for two nanorods with diameters around 20 nm (with different lengths) are represented by open circles and squares in Fig. 4. The two nanorods of ca. 20-nm diameters give nearly identical dispersion curves, regardless of their lengths. This result agrees with [11] and our previous study for Au nanorods [15]. The dispersion curve for nanorods with larger diameters around 35 nm is located close to those of nanowires in [11], but in slightly lower resonance-energies side. It is evident from Fig. 4 that the dispersion relation is strongly dependent on the diameter of the rod or the wire: as the diameter increases, the resonance frequencies also increase. The slope of dispersion curve (dEres/ dksp, where Eres denotes the resonance energy), which gives the group velocity of the SPs, also seems to increase with increasing the diameter, if compared at a fixed resonance energy. Under the dipolar approximation of spheroidal metal particles, the resonance energy is dependent on the aspect ratio of the particle [21]. The resonance energy is lowered with increasing the aspect ratio. The observed diameter dependence on the dispersion curve is qualitatively consistent with the theoretical expectation for the spheroid model. 3.3. Comparison between Ag and Au nanorods In our previous study, a dispersion curve for Au nanorods of around 20 nm in diameter was experimentally obtained [15]. Dispersion relation for the Ag nanorods of 20 nm in diameter (open symbols in Fig. 4) is
located in the position close to that for the 20 nm Au nanorods [15], but in slightly higher energy side. Under the theoretical model based on the dipolar oscillation in spheroidal metal particles [21], as well as that based on a flat metal surface [22], the wave vector of SP depends only on the real part of dielectric function of the metal. The absolute value of the real part of the dielectric function (negative value) for Ag is a little larger than that for Au in the region from visible to near-infrared. In this case the resonance energy for a Ag nanorod should be higher than that for a Au nanorod of the same diameter, if compared at the same wave vector. The observed results agree qualitatively with the theoretical expectation. From a quantitative point of view, however, the difference between the observed dispersion curves of the Ag and Au nanorods are smaller than expected from the dielectric functions for these materials (for example, real part of the dielectric function, er, at 704 nm is 23.4 and 16.8 for Ag and Au, respectively [23]). Although the origin of this discrepancy between the observation and the expectation is not clear yet, it may be due to uncertainty or systematic errors in estimation of the rod diameters. If the crystal morphology [24] of the Ag nanorods synthesized here is different from that of Au, the effective cross-sections are possibly different between Ag and Au even if apparent diameters estimated from the topographic measurements are the same. Chemical and physical environments around the nanorods, such as trace adsorbates, surface electric charges, etc., may be also different for Ag and Au, which may cause apparent differences in diameter. The spectral widths of SP bands of Ag and Au nanorods are also compared. The spectral width is estimated by half width at half maximum in the longer wavelength side of each resonant peak. The width estimated in this way from Fig. 3e for Ag is, on average, ca. 220 cm 1. In a similar way, the width for Au is estimated from [15] to be ca. 300 cm 1. Although the uncertainties for the estimated widths may be quite large, we can recognize a tendency that the peak width for the Ag nanorod is sharper than that for the Au nanorod. According to the theoretical model for spheroidal-shaped metal nanoparticles [21], the spectral width is expected to be inversely proportional to the slope of the real part of the dielectric function against frequency, (der/dx) 1, while it is linearly proportional to the imaginary part of the dielectric function (ei). The slope of the real part is approximately the same for Au and Ag [23]. Consequently, the difference in the spectral widths originates principally in the imaginary parts of the dielectric functions of metals, which predicts a narrower spectral width for Ag than for Au by a factor of 2 or 3 (ei = 0.39 and 1.07, respectively, for Ag and Au at 704 nm [23]). However, experimentally observed difference of spectral width for Ag and Au nanorods (ca. 220 and 300 cm 1) is smaller than expected. One of potential reasons would be resulted
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from distorted shapes and/or irregularities of Ag nanorods. Such distortions and irregularities were found sometimes for Ag nanorods, and the spectral width tends to be broad in those rods.
4. Conclusion We have shown wavefunction images and near-field spectra in Ag nanorods. From the near-field images and spectra, we obtained experimental dispersion relations for SPs of Ag nanorods. Nanorods with the same diameters give a single dispersion curve regardless of their length, and the resonance energy becomes higher as the diameter increases. Differences in spectral features for Ag and Au are qualitatively explainable by the difference in dielectric functions of the metals.
Acknowledgements The authors thank Prof. Dongho Kim (Yonsei Univ.) for his kind guidance to J.K.L. and valuable discussion. This work was supported in part by Grants-in-Aid for Scientific Research (16350015, 16750017, and 17655011) to H.O. and K.I. from JSPS and from MEXT, and by the Grant (R02-2003-000-10073-0) to S.K.K. from the Basic Research Program of the Korea Science and Engineering Foundation. Support by the International Collaboration Program of the Institute for Molecular Science is also acknowledged.
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[2] K. Kneipp, H. Kneipp, I. Itzkan, R.R. Dasari, M.S. Feld, Chem. Rev. 99 (1999) 2957. [3] S. Nie, S.R. Emory, Science 275 (1997) 1102. [4] R.M. Sto¨ckle, Y.D. Suh, V. Deckert, R. Zenobi, Chem. Phys. Lett. 318 (2000) 131. [5] N. Hayazawa, Y. Inouye, Z. Sekkat, S. Kawata, Chem. Phys. Lett. 335 (2001) 369. [6] W.L. Barnes, A. Dereux, T.W. Ebbesen, Nature 424 (2003) 824. [7] H. Ditlbacher, J.R. Krenn, G. Schider, A. Leitner, F.R. Aussenegg, Appl. Phys. Lett. 81 (2002) 1762. [8] S.I. Bozhevolnyi, F.A. Pudonin, Phys. Rev. Lett. 78 (1997) 2823. [9] J.R. Krenn, B. Lamprecht, H. Ditlbacher, G. Schider, M. Salerno, A. Leitner, F.R. Aussenegg, Europhys. Lett. 60 (2002) 663. [10] S.A. Maier, P.G. Kik, H.A. Atwater, S. Meltzer, E. Harel, B.E. Koel, A.A.G. Requicha, Nat. Mater. 2 (2003) 229. [11] G. Schider, J.R. Krenn, A. Hohenau, H. Ditlbacher, A. Leitner, F.R. Aussenegg, W.L. Schaich, I. Puscasu, B. Monacelli, G. Boreman, Phys. Rev. B 68 (2003) 155427. [12] J.R. Krenn, G. Schider, W. Rechberger, B. Lamprecht, A. Leitner, F.R. Aussenegg, J.C. Weeber, Appl. Phys. Lett. 77 (2000) 3379. [13] K. Imura, T. Nagahara, H. Okamoto, J. Am. Chem. Soc. 126 (2004) 12730. [14] K. Imura, T. Nagahara, H. Okamoto, J. Phys. Chem. B 108 (2004) 16344. [15] K. Imura, T. Nagahara, H. Okamoto, J. Chem. Phys. 122 (2005) 154701. [16] A. Hohenau, J.R. Krenn, G. Schider, H. Ditlbacher, A. Leitner, F.R. Aussenegg, W.L. Schaich, Europhys. Lett. 69 (2005) 538. [17] J.-Q. Hu, Q. Chen, Z.-X. Xie, G.-B. Han, R.-H. Wang, B. Ren, Y. Zhang, Z.-L. Yang, Z.-Q. Tian, Adv. Funct. Mater. 14 (2004) 183. [18] K. Imura, T. Nagahara, H. Okamoto, Chem. Phys. Lett. 400 (2004) 500. [19] Y. Sun, B. Gates, B. Mayers, Y. Xia, Nano Lett. 2 (2002) 165. [20] K. Matsuda, T. Saiki, S. Nomura, M. Mihara, Y. Aoyagi, S. Nair, T. Takagahara, Phys. Rev. Lett. 91 (2003) 177401. [21] U. Kreibig, M. Volmer, Optical Properties of Metal Clusters, Springer, Berlin, 1995. [22] H. Raether, Surface Plasmons, Springer, 1988. [23] P.B. Johnson, R.W. Christy, Phys. Rev. B 6 (1972) 4370. [24] C.J. Johnson, E. Dujardin, S.A. Davis, C.J. Murphy, S. Mann, J. Mater. Chem. 12 (2002) 1765.
Imaging and dispersion relations of surface plasmon modes in silver nanorods by near-field spectroscopy Jong Kuk Lim a,b, Kohei Imura a,c, Tetsuhiko Nagahara a, Seong Keun Kim b,*, Hiromi Okamoto a,c,* a
Department of Molecular Structure, Institute for Molecular Science, 38 Nishigonaka, Myodaiji, Okazaki, Aichi 444-8585, Japan b School of Chemistry, Seoul National University, Seoul 151-747, Korea c The Graduate University for Advanced Studies, Myodaiji, Okazaki, Aichi 444-8585, Japan Received 5 May 2005; in final form 22 June 2005 Available online 14 July 2005
Abstract Surface plasmons of silver nanorods were investigated by using scanning near-field optical microscopy. Near-field transmission images showed spatially oscillatory patterns in nanorods. The oscillatory features of images are attributable to plasmon-mode wavefunctions. From the near-field images and spectra, dispersion relations of surface plasmon modes for various silver nanorods are obtained. It is found that dispersion relation of a nanorod is dependent on its diameter. The spectral features obtained are compared with those for gold nanorods. 2005 Elsevier B.V. All rights reserved.
1. Introduction Collective oscillations of electrons on surfaces of metals, known as surface plasmons (SPs), are extensively studied not only for the fundamental interests, but also for possible applications to sensor technology to characterize molecules on the interface between metals and dielectric media [1], to extremely sensitive surface enhanced Raman scattering (SERS) [2–5], to plasmonic devices [6–8], and so on. With plasmonic devices, it is also expected that a very small channel for transporting photons is possible. Recently, non-diffraction limited transport of SPs was in fact demonstrated [9,10] and there has been continuing intensive interests in the properties of SPs in laterally confined metal structures.
* Corresponding authors. Fax: +82 889 5719 (S.K. Kim); +81 564 55 4639 (H. Okamoto). E-mail addresses: [email protected] (S.K. Kim), [email protected] (H. Okamoto).
0009-2614/$ - see front matter 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2005.06.094
One of the fundamental properties which characterizes SPs is dispersion relation. The dispersion relations of SPs in noble metal nanowires fabricated by electron beam lithography were obtained by using far-field optical extinction spectroscopy [11,12]. In case of several silver (Ag) nanowires having an identical cross-section, it was reported that all the measured points follow a single dispersion regardless of the length, and that the nanowire shows larger wave vectors than those for a flat metal/glass interface at a given frequency. These observations indicate that the plasmon propagation is slower in a silver nanowire than in a flat silver/glass interface. It was also found that the upper limit of the frequency for SPs is smaller on a silver nanowire than on a flat metal/ glass interface. Recently, Imura et al. [13–15] reported that near-field images of gold (Au) nanorods show spatially oscillating patterns along the rod axis, and were attributed to spatial characteristics of plasmon-mode wavefunctions. They demonstrated that direct measurements of both wave vectors and resonance energies of SPs are possible by near-field measurements, and the
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results were utilized to obtain the dispersion relation. Similar oscillating images for nanowires fabricated by electron beam lithography were recently reported by Hohenau et al. [16] using a collection-mode near-field microscopy. In this Letter, we report near-field imaging of SP modes in single Ag nanorods. We used the results to obtain dispersion relations of SPs in Ag nanorods, and the dispersion curves were compared with those in the previous studies [11,15]. We will also discuss difference between the results for Ag and Au on the basis of macroscopic dielectric functions.
2. Experiment The Ag nanorod sample was chemically synthesized. The procedure for the synthesis is basically the same as that reported by Hu et al. [17]. We used silver nitrate (AgNO3) and tri-sodium citrate (Na3C6H5O7) as a starting material and a reducing agent, respectively, and sodium dodecylsulfonate (C12H25SO3Na, SDSN) as a surfactant for rod growth. Typically, 25 cm3 of 4 · 10 4 mol dm 3 water solution of silver nitrate, 2–3 cm3 of 1 · 10 2 mol dm 3 tri-sodium citrate, and 25 cm3 of 2 · 10 3 mol dm 3 SDSN were mixed. Then the mixture was stirred, and boiled at 100 C for 60–90 min to obtain a turbid yellow-green solution. The lengths of the nanorods were controlled by changing the concentration of the reducing agent (tri-sodium citrate) from 4 · 10 4 mol dm 3 (giving short rods) to 6 · 10 4 mol dm 3 (long rods). Other surfactants such as sodium dodecylbenzene sulfonate (C12H25C6H4SO3Na, SDBS) and sodium dodecylsulfate (C12H25OSO3Na, SDS) were also examined to obtain nanorods in high density. Of the three surfactants tried, SDSN gave the highest yield of nanorods. To separate Ag nanorods from other nanoparticles (spheres and other shapes), the mixture after reaction was diluted with ultra pure water (18 MX cm 1) to
100 cm 3 in volume and then centrifuged at 6000 rpm for 30 min. After centrifugation, the supernatant was removed and the sediment was diluted by ultra pure water again. This procedure was repeated, until the color of the supernatant becomes vanished. The synthesized Ag nanorods were investigated by using scanning electron microscope (SEM) (Hitachi, S-900) to verify its density and morphology. Far-field extinction spectra were taken in water solutions. The sample for the near-field optical experiment was prepared by spin coating the solution on a cover slip. Figs. 1 and 2 show, respectively, SEM images and far-field extinction spectra in water solution of the synthesized nanorods. A 500-W Xenon discharge lamp (Ushio, UXL500SX) illuminated the sample through an aperture of a tapered Au-coated near-field fiber probe tip (JASCO) by using a home-made scanning near-field optical microscope (SNOM) [18]. The aperture diameters of the fiber tips were measured to be 50–100 nm by SEM. The transmitted light was collected by an objective lens (Nikon, NA 0.85) and detected by a CCD array detector (Andor,
Fig. 2. Far-field extinction spectra of silver nanorods solutions synthesized in SDSN (a) and SDBS (b).
Fig. 1. SEM images of silver nanorods synthesized in sodium dodecyl sulfonate (SDSN), (a), and in sodium dodecylbenzene sulfonate (SDBS), (b). Images were taken on cleaned silicon wafers.
J.K. Lim et al. / Chemical Physics Letters 412 (2005) 41–45
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DV401-FI) equipped with a polychromator. A sheet polarizer was used to characterize the polarization of the SP modes. The typical scan step size was 12.5 nm for an area of 1 lm · 1 lm. The distance between the sample and the tip was maintained at about 10–15 nm by a shear force feedback mechanism.
3. Results and discussion 3.1. Features of nanorods prepared For the samples in Fig. 1a,b, SDSN and SDBS were used as surfactants, respectively. From Fig. 1 it is found that use of SDSN gives higher density of nanorods than SDBS. The nanorods have various lengths and diameters, and quite a few particles appear to be nanosphere-like, under the magnification scales of Fig. 1. The number density of nanorods was 30% in Fig. 1a. In the far-field extinction spectra in aqueous solution in Fig. 2, the curves (a) and (b) indicate, respectively, the samples prepared by using SDSN and SDBS. Extinction peaks at 440 and 420 nm for respective curves are contributed mainly from the SP resonances for Ag nanospheres [17,19]. Compared with the spectrum for the solution prepared with SDBS, that with SDSN shows a peak at a longer wavelength (20 nm). In addition to difference in the peak positions, the relatively enhanced extinction in the longer wavelength region is observed. Such a difference between the two solutions should be due to the difference in the number density of the nanorods. In the nanorods, the resonance energy of SPs polarized along the longitudinal axis becomes low with increasing the aspect ratio (or the length). Because the number density of the nanorods is higher in the solution prepared with SDSN than that prepared with SDBS, relative extinction in the longer wavelength region is enhanced for the sample prepared with SDSN. The difference in the peak position can also be explained in a similar way. 3.2. Near-field images and dispersion relations We investigated a number of near-field images and spectra for nanorods. Representative images and spectra are shown in Fig. 3. The topographic image is broadened due to the probe tip shape, and the actual dimension of the rod (shown by solid lines) estimated by deconvolution is (20 ± 4) nm (diameter) · (530 ± 25) nm (length). Fig. 3b–d are near-field transmission images probed at 806, 920, and 1008 nm, respectively. Dark spots indicate reduction of the transmitted light. In these figures, the number of the dark spots is decreasing from 5 to 3 on going from Fig. 3b to d. The spatial dependence of transition probability in the nanorod is approximately given by square modulus of the wave
Fig. 3. Representative images a nanorod and the near-field spectrum. (a) Topography of the silver nanorod, (20 ± 4) nm in diameter and (530 ± 25) nm in length. (b)–(d) Near-field transmission images probed with an unpolarized light at 806, 920, and 1008 nm, respectively. (e) Near-field spectrum taken at the position marked ÔXÕ in the near-field transmission (b).
functions of the SP modes [13–15,20]. Therefore, the wavelengths of the SP modes, ksp, can be directly determined from the near-field transmission images. The absolute value of wave vector, ksp, is given by ksp = 2p/ksp. The wave vectors for SP modes determined from the near-field images are 26.9, 21.1, and 18.3 lm 1 for Fig. 3b–d, respectively. Fig. 3e shows the near-field spectrum measured at the position ÔXÕ indicated in Fig. 3b. In this spectrum, the relative extinction is calculated by [I(substrate) I(X)]/I(substrate) where I(substrate) and I(X) denote the transmitted light intensity measured at the substrate and at the position ÔXÕ, respectively. Two resonant peaks are clearly seen at 806 and 920 nm, and another resonance possibly present at 1000 nm. These wavelengths are the ones at which the images of Fig. 3b–d were obtained.
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Fig. 4. Dispersion relations of SPs of the nanorods obtained in this study and those reported in [11]. The experimental uncertainty is typically ±4 nm for the diameter while that for the length is typically ±25 nm. The dotted curve indicates the approximate position of the dispersion curve obtained for gold nanorods (diameter 20 nm) in [15].
Other nanorods were investigated in the same way. From the obtained wave vectors and resonance energies, dispersion curves for Ag nanorods can be obtained (Fig. 4). In Fig. 4, the dispersion relation for Ag nanowires (85 nm · 75 nm cross-section) reported in [11] is also plotted (crossed symbols). The dispersion relations presently obtained for two nanorods with diameters around 20 nm (with different lengths) are represented by open circles and squares in Fig. 4. The two nanorods of ca. 20-nm diameters give nearly identical dispersion curves, regardless of their lengths. This result agrees with [11] and our previous study for Au nanorods [15]. The dispersion curve for nanorods with larger diameters around 35 nm is located close to those of nanowires in [11], but in slightly lower resonance-energies side. It is evident from Fig. 4 that the dispersion relation is strongly dependent on the diameter of the rod or the wire: as the diameter increases, the resonance frequencies also increase. The slope of dispersion curve (dEres/ dksp, where Eres denotes the resonance energy), which gives the group velocity of the SPs, also seems to increase with increasing the diameter, if compared at a fixed resonance energy. Under the dipolar approximation of spheroidal metal particles, the resonance energy is dependent on the aspect ratio of the particle [21]. The resonance energy is lowered with increasing the aspect ratio. The observed diameter dependence on the dispersion curve is qualitatively consistent with the theoretical expectation for the spheroid model. 3.3. Comparison between Ag and Au nanorods In our previous study, a dispersion curve for Au nanorods of around 20 nm in diameter was experimentally obtained [15]. Dispersion relation for the Ag nanorods of 20 nm in diameter (open symbols in Fig. 4) is
located in the position close to that for the 20 nm Au nanorods [15], but in slightly higher energy side. Under the theoretical model based on the dipolar oscillation in spheroidal metal particles [21], as well as that based on a flat metal surface [22], the wave vector of SP depends only on the real part of dielectric function of the metal. The absolute value of the real part of the dielectric function (negative value) for Ag is a little larger than that for Au in the region from visible to near-infrared. In this case the resonance energy for a Ag nanorod should be higher than that for a Au nanorod of the same diameter, if compared at the same wave vector. The observed results agree qualitatively with the theoretical expectation. From a quantitative point of view, however, the difference between the observed dispersion curves of the Ag and Au nanorods are smaller than expected from the dielectric functions for these materials (for example, real part of the dielectric function, er, at 704 nm is 23.4 and 16.8 for Ag and Au, respectively [23]). Although the origin of this discrepancy between the observation and the expectation is not clear yet, it may be due to uncertainty or systematic errors in estimation of the rod diameters. If the crystal morphology [24] of the Ag nanorods synthesized here is different from that of Au, the effective cross-sections are possibly different between Ag and Au even if apparent diameters estimated from the topographic measurements are the same. Chemical and physical environments around the nanorods, such as trace adsorbates, surface electric charges, etc., may be also different for Ag and Au, which may cause apparent differences in diameter. The spectral widths of SP bands of Ag and Au nanorods are also compared. The spectral width is estimated by half width at half maximum in the longer wavelength side of each resonant peak. The width estimated in this way from Fig. 3e for Ag is, on average, ca. 220 cm 1. In a similar way, the width for Au is estimated from [15] to be ca. 300 cm 1. Although the uncertainties for the estimated widths may be quite large, we can recognize a tendency that the peak width for the Ag nanorod is sharper than that for the Au nanorod. According to the theoretical model for spheroidal-shaped metal nanoparticles [21], the spectral width is expected to be inversely proportional to the slope of the real part of the dielectric function against frequency, (der/dx) 1, while it is linearly proportional to the imaginary part of the dielectric function (ei). The slope of the real part is approximately the same for Au and Ag [23]. Consequently, the difference in the spectral widths originates principally in the imaginary parts of the dielectric functions of metals, which predicts a narrower spectral width for Ag than for Au by a factor of 2 or 3 (ei = 0.39 and 1.07, respectively, for Ag and Au at 704 nm [23]). However, experimentally observed difference of spectral width for Ag and Au nanorods (ca. 220 and 300 cm 1) is smaller than expected. One of potential reasons would be resulted
J.K. Lim et al. / Chemical Physics Letters 412 (2005) 41–45
from distorted shapes and/or irregularities of Ag nanorods. Such distortions and irregularities were found sometimes for Ag nanorods, and the spectral width tends to be broad in those rods.
4. Conclusion We have shown wavefunction images and near-field spectra in Ag nanorods. From the near-field images and spectra, we obtained experimental dispersion relations for SPs of Ag nanorods. Nanorods with the same diameters give a single dispersion curve regardless of their length, and the resonance energy becomes higher as the diameter increases. Differences in spectral features for Ag and Au are qualitatively explainable by the difference in dielectric functions of the metals.
Acknowledgements The authors thank Prof. Dongho Kim (Yonsei Univ.) for his kind guidance to J.K.L. and valuable discussion. This work was supported in part by Grants-in-Aid for Scientific Research (16350015, 16750017, and 17655011) to H.O. and K.I. from JSPS and from MEXT, and by the Grant (R02-2003-000-10073-0) to S.K.K. from the Basic Research Program of the Korea Science and Engineering Foundation. Support by the International Collaboration Program of the Institute for Molecular Science is also acknowledged.
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