LETTER pubs.acs.org/JPCL
Plasmonic Spheroidal Metal Nanoshells Showing Larger Tunability and Stronger Near Fields Than Their Spherical Counterparts: An Effect of Enhanced Plasmon Coupling Nasrin Hooshmand,† Prashant K. Jain,*,‡ and Mostafa A. El-Sayed*,§ †
Department of Chemistry and Chemical Engineering, Marvdasht Branch, Islamic Azad University, Marvdasht, Iran Department of Chemistry and Miller Institute for Basic Research in Science, University of California, Berkeley, California 94720, United States § Laser Dynamics Laboratory, School of Chemistry and Biochemistry, Georgia Institute of Technology, Atlanta, Georgia 30332-0400, United States ‡
bS Supporting Information ABSTRACT: Two of the most tunable nanostructure geometries for nanoplas monics include the metal nanoshell structure and the spheroidal geometry. We systematically investigate the effect of combining both geometries within the same nanostructure. Localized surface plasmon resonances (LSPRs) of spheroidal gold nanoshells are simulated as a function of their aspect ratio. The longaxis LSPR mode of a spheroidal nanoshell red shifts with decreasing shell thickness, similar to a spherical nanoshell. A higher aspect ratio spheroidal nanoshell shows a larger fractional LSPR red shift for the same thickness normalized by core dimensions. This is because coupling between the inner and outer surface plasmons of the nanoshell is stronger for the elongated spheroidal geometry as compared to that for the spherical case, increasing in strength with increasing aspect ratio. It is the result of this enhanced plasmon coupling that spheroidal nanoshells of aspect ratio 4 are over two times more tunable than spherical nanoshells. Also, the plasmonic field enhancement is an order of magnitude larger for the spheroidal nanoshells of aspect ratio 4 as compared to spherical nanoshells. These effects observed in the spheroidal nanoshell are analogous to those in a dimer of spheroidal nanopaticles. SECTION: Nanoparticles and Nanostructures
T
he research on plasmonic (gold and silver) nanostructures has increased remarkably in the past decade due to their interesting properties resulting from their localized surface plasmon resonances (LSPRs).1-4 LSPRs results in a strong enhancement in the optical absorption, scattering, and near-field intensities of noble metal nanoparticles, allowing their use in numerous applications such as biological imaging, selective photothermal therapy, surface-enhanced Raman scattering (SERS), optical wave guiding, and biochemical sensing.5-11 The LSPR also shows strong tunability. The LSPR frequency depends not only on the size, the metal type, and the dielectric constant of the surrounding medium but also on the geometry of the nanostructure.12-17 Nanoparticles of elongated spheroidal geometry (e.g., gold nanorods) are a canonical example of such tunability, in which case the frequency of the LSPR oscillation along the long axis is strongly dependent on the spheroid aspect ratio.18-20 In addition, the near-field enhancement at the tips of nanorods is many-fold higher than that on the surface of a nanosphere, also known as the lightning rod effect.6,21-23 At the same time, the effect of interparticle coupling on the LSPR is also very important and has received a lot of attention in recent research.24-30 As two nanoparticles come closer to each r 2011 American Chemical Society
other, there is a strong red shift of the LSPR (polarized along the interaction direction) due to favorable coupling between LSPR modes of the individual nanoparticles.25,26,31 The strength of this plasmon coupling decays as a function of interparticle gap scaled by the nanoparticle size with a trend that is universal irrespective of nanoparticle size, shape, metal type, and surrounding media.26,32 Interestingly, it has also been found that the metal nanoshell structure shows a plasmon coupling behavior quite analogous to that of the two-particle system.33 The dipolar LSPR mode of a metal nanoshell is a hybrid mode resulting from coupling between the surface plasmon modes on the inner and outer boundary of the metal shell.16 With decreasing metal shell thickness, a red shift of the LSPR is observed due to increasing strength of coupling between the inner and outer surface plasmons.16,33,34 The fractional LSPR shift due to this coupling also decays as per a universal scaling law, in this case as a function of the shell thickness normalized by the core dimensions.33 In addition to LSPR tunability, coupling in the nanoshell structure Received: January 8, 2011 Accepted: January 24, 2011 Published: February 02, 2011 374
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Figure 2. Fractional red shift (Δλ/λ0) of the long-axis LSPR mode as a function of the ratio of the thickness to core dimension along the long axis.
different core dimensions. Similar calculations are shown for two other aspect ratios, that is, R = 2 and 3 in the Supporting Information (Figures S3 and S4). All spectra show that the spheroidal nanoshells have red-shifted LSPRs for both transverse and longitudinal modes compared to a solid gold spheroid of the same outer dimensions. Similar to the case of spherical nanoshells, there is an increasing LSPR red shift as the shell becomes thinner.16,33,34 Note that the shifts are much stronger for the long-axis mode compared to those for the short-axis mode. Henceforth, we focus only on the long-axis mode because it exhibits greater tunability. To reliably deduce the effect of aspect ratio on the LSPR tunability of the spheroidal nanoshell, it is most instructive to plot the LSPR red shift (normalized by the LSPR wavelength maximum of a solid spheroid of the same dimensions) as a function of the shell thickness (normalized by the core dimension) for different aspect ratios (Figure 2). Spheroidal nanoshells with a higher aspect ratio show a larger fractional LSPR red shift for the same normalized thickness. For aspect ratio R = 4, the fractional shift is ∼2.5 times larger than that in the spherical (R = 1) nanoshell at the smallest thickness to core dimension ratio. Thus, the spheroidal nanoshells (R = 4) offer over twice the tunability of that of their spherical counterparts. The LSPR mode of a nanoshell is a hybrid mode resulting from the coupling of plasmon oscillations on the inner and outer surface of the shell.34 The LSPR red shift is a measure of the strength of this coupling. In the case of a spheroidal nanoshell, the surface plasmons (both inner and outer) polarized along the long axis have a much higher polarizability compared to the case of the spherical geometry due to the higher curvature along the long axis.28 As a result, the strength of coupling, which is directly proportional to the polarizabilities of the interacting modes,28 is much stronger between the inner and outer surface plasmon modes of the spheroidal nanoshell as compared to those in a spherical one (for the same normalized thickness). This is manifested as larger fractional LSPR red shifts for higher aspect ratios of the spheroidal nanoshell. This is analogous to the observation that plasmon coupling in nanoparticle dimers is stronger when the interacting particles have a higher aspect ratio and/or end curvature along the direction of the coupling.32 A closely related phenomenon is the larger field enhancement seen at the junction between two elongated/spheroidal nanoparticles.32,46 The field enhancement at the junction of the dimer increases with increasing aspect ratio of the nanoparticles. In the present study, we find this trend to be valid for the nanoshell geometry. The spheroidal nanoshells support much stronger
Figure 1. DDA-calculated extinction efficiency spectra of spheroidal silica core-gold nanoshells with different shell thicknesses. Calculations are performed for fixed outer long-axis dimension Lo = 80 nm, aspect ratio R = 4, and incident light polarization along the (a) long axis and (b) short axis. The core dimension along the long axis, Li, is varied as 28, 32, 40, and 48 nm. The medium is water.
has been shown to result in enhanced electric field enhancements and improved medium sensitivities.35-40 We combine two of the most tunable plasmonic geometries, that is, the nanoshell structure and the spheroidal shape, and theoretically investigate the optical properties of the resulting structure, that is, a spheroidal nanoshell. While the LSPRs of spherical nanoshells are well-studied,41-44 spheroidal nanoshells have received less attention. Experimentally, the Halas group has synthesized spheroidal particles consisting of a dielectric Fe3O4 core and a gold shell, a nanostructure known as the nanorice.45 It has been demonstrated that this geometry has greater tunability, larger local field enhancement, and greater LSPR sensitivity than other dielectric-metal nanostructures.45 In this study, we show that these enhanced optical properties originate from increased plasmon coupling between the inner and outer surface plasmon in the spheroidal nanoshell structure. We provide a systematic dependence of plasmon coupling in the spheroidal nanoshell on its aspect ratio and quantify the enhancement in tunability and near-field intensity resulting from the enhanced coupling. We calculated LSPR spectra of spheroidal silica core-gold nanoshells as a function of their aspect ratio and shell thickness using the discrete dipole approximation (DDA) method. Figure 1 shows extinction spectra for aspect ratio R = 4 spheroidal nanoshells with an outer long-axis dimension Lo of 80 nm and 375
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Scheme 1. Geometry of Silica Core-Gold Shell Spheroids Analyzed in This Worka
a
The inner and outer dimensions along the long axis are specified by Li and Lo, respectively, such that the thickness along the long axis is given by Lo - Li. The spheroid aspect ratio (R) is given by the ratio of the outer dimension along the long axis (Lo) to that along the short axis (So). The aspect ratio of the core is constrained to be the same as that of the outer spheroid.
plasmonic fields as compared to their spherical counterparts. The near-field intensity at the surface of a spherical (R = 1) nanoshell of 40 nm diameter and a 7 nm thick shell is enhanced ∼25-fold relative to that of the ambient field. When the aspect ratio of the nanoshell is increased to R = 3, the field enhancement at the surface increases to almost 200. For spheroidal nanoshells of aspect ratio R = 4, the field is enhanced over 400-fold. Thus, the maximum field enhancement increases rapidly with increasing aspect ratio.47 In summary, the plasmon coupling in the spheroidal nanoshell structure is much stronger as compared to the spherical nanoshell, increasing in strength with increasing aspect ratio of the spheroid. As a result, spheroidal nanoshells manifest few-fold higher LSPR tunability and order-of-magnitude larger near-field enhancements. Thus, we quantitatively demonstrate that spheroidal nanoshells are better suited than their currently popular spherical counterparts for tunable nanoplasmonics and applications in field-enhanced spectroscopy and refractive index sensing.45
’ CALCULATION METHODS The discrete dipole approximation (DDA) method was used for the calculation of the LSPR spectra of spheroidal gold nanoshells as a function of the metal shell thickness and the spheroidal aspect ratio (Scheme 1). The advantage of DDA over other methods is that it includes multipolar effects and finite size effects which become quite important for particles approaching the wavelength of light. Details of this method have been described before.6,17,48 Briefly, the spheroidal target is represented as a cubic array of N dipoles located on a cubic lattice. The total volume of the target is defined by the effective radius reff, the radius of an equal volume sphere. The inner dimensions and outer dimensions along the long axis are specified by Li and Lo, respectively, such that the thickness is given by Lo - Li. In the case of the spheroidal nanoshell, another variable is the aspect ratio (R), which is the ratio of the outer long-axis dimension of the spheroid (Lo) to the short-axis dimension (So). The calculations were carried out for fixed So = 20 nm and aspect ratio R varying as 1, 2, 3, and 4 and reff = 10.0, 12.6, 14.4, and 15.9 nm, respectively. We used an interdipole spacing of 1 nm. The thickness of the metal shell along the long axis was systematically varied. The complex refractive index of gold was assumed to be the same as that of the bulk metal.49 The refractive index of the surrounding medium was considered to be 1.33 for water, and
Figure 3. Near-field enhancement in the vicinity of a spheroidal silica core-gold nanoshell as a function of the spheroidal aspect ratio. A twodimensional spatial profile of the near-field intensity enhancement (mapped to a RGB color scale) over a plane passing through the longitudinal cross section of the spheroid is shown for (a) a nanoshell of aspect ratio R = 1 with an outer diameter of 40 nm and shell thickness of 7 nm, (b) a spheroidal nanoshell of aspect ratio R = 3 with an outer dimension of 60 nm and shell thickness of 12 nm along the long axis, and (c) a spheroidal nanoshell of aspect ratio R = 4 with an outer dimension of 80 nm and shell thickness of 16 nm along the long axis. (d) Line profile of the field enhancement along the long axis of the spheroid for all three aspect ratios. Calculations were performed using the finite difference time domain method employing a plane wave with incident light polarization along the long axis of the spheroid and a wavelength selected to be around the near-field intensity maximum for each nanostructure, that is, 590, 720, and 850 nm for (a), (b), and (c) respectively.
the core refractive index was taken to be 1.44 for silica at all wavelengths. For this calculation, we used the DDSCAT 6.1 376
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code. Plasmon resonance spectra were calculated for two polarization directions, parallel to the long axis of the spheroid and perpendicular to it. The accuracy of DDA calculations has been questioned for nanoshells, especially for coarse grids, that is, when the shell thickness becomes comparable to the interdipole spacing.50 Therefore, we validated our DDA simulations by comparison with Mie theory calculations for spherical metal nanoshells. We found that the DDA prediction for a 10 nm radius gold nanosphere with over 30000 discrete dipoles is very similar to the analytic Mie theory result, showing the reliability of DDA for nanospheres (Supporting Information Figure S1). For spherical silica core-gold nanoshells of 40 nm diameter but varying shell thickness (5, 7, 10, and 14 nm), we found good agreement of the LSPR maxima (to within 3 nm) between Mie theory and DDA calculations with a 1 nm interdipole spacing (Supporting Information, Figure S2). However, the DDA-calculated extinction efficiency and line width do not show perfect agreement with those calculated by Mie theory. Nevertheless, the DDA results achieved with a 1 nm interdipole spacing are perfectly valid for our analyses, which rely on LSPR maxima alone. The finite difference time domain method (full three-dimensional simulations using EM Explorer 2.0 with 1 nm mesh, plane wave excitation, and default analytic boundary conditions) was used to calculate the near-field in the vicinity of nanoshells of different aspect ratios (R = 1, 3, and 4) but similar thickness to long axis dimension ratios (Figure 3).
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’ ASSOCIATED CONTENT
bS
Supporting Information. Validation of DDA-simulated spectra of spherical nanoshells by comparison with those calculated by Mie theory and DDA calculations of the long-axis and short-axis LSPR spectra of spheroidal nanoshells of aspect ratios 2 and R = 3. This material is available free of charge via the Internet at http://pubs.acs.org.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected] (P.K.J.); melsayed@gatech. edu (M.A.E.-S).
’ ACKNOWLEDGMENT This work was supported by the Division of Materials Research of the National Science Foundation (No. 0906822). P.J. thanks the Miller Institute for their fellowship. N.H. thanks the Research Council of the Islamic Azad University of Marvdasht for support. ’ REFERENCES (1) Mie, G. Beitrage Zur Optik Truber Medien, Speziell Kolloidaler Metallosungen. Ann. Phys. 1908, 25, 377–445. (2) Mulvaney, P. Surface Plasmon Spectroscopy of Nanosized Metal Particles. Langmuir 1996, 12, 788–800. (3) Henglein, A. Physicochemical Properties of Small Metal Particles in Solution: “Microelectrode” Reactions, Chemisorption, Composite Metal Particles, and the Atom-to-Metal Transition. J. Phys. Chem. 1993, 97, 5457–5471. (4) Bohren, C. F.; Huffman, D. R. In Absorption and Scattering of Light by Small Particles; Wiley: New York, 1983. 377
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