Article pubs.acs.org/JPCC
Plasmon Evolution in Core−Shell Nanospheroids Quanshui Li† and Zhili Zhang*,‡ †
Department of Physics, School of Mathematics and Physics, University of Science and Technology Beijing, Beijing, 100083, China Department of Mechanical, Aerospace and Biomedical Engineering, University of Tennessee, Knoxville, Tennessee 37996, United States
‡
ABSTRACT: In order to explore the fundamental features of plasmon evolutions in the plasmonic nanostructures along variable geometrical parameters, TiO2−Ag core−shell nanospheroids, which have the distinguishable antibonding and bonding modes, are first used to illustrate the phenomena of plasmon evolutions by simulations. The usual peak-shift behaviors and appearance of the new modes are observed in the far-field extinction spectra. Beneath those phenomena, the unusual mode transformations occur in some modes. In the variable core configuration, when the inner surface of the silver shell is in a close proximity to the outer surface, the dipole antibonding mode evolves to be mixed with the quadrupole mode on the outer surface, while the new emerging mode evolves to the octupole antibonding modes. In the variable shell configuration, when the outer surface approaches the inner surface, the dipole bonding mode tends to evolve to the octupole bonding mode and the new modes emerge and tend to be the triakontadipole-like and octupole-like mode on the outer and inner surfaces. When the polar radius is so large that the outer surface is far away from the inner surface, the dipole antibonding mode evolves to the octupole antibonding mode and the new mode emerges which belongs to the octupole bonding mode. In mode transformation phenomena, one feature is that the evolution is associated with the odd l number (l = 1 for dipole, l = 3 for octupole, and l = 5 for triakontadipole) except for the mixed modes. Another feature is that the antibonding modes can evolve from the octupole to dipole and then octupole modes, in which process the charge distributions for the octupole modes are totally inverse. The retardation effects and the dielectric core effects are also discussed based on the phenomena of the higher order modes. The peak-shift behaviors, the appearance of the new modes, and the mode transformation along variable geometrical parameters have great importance in plasmonic applications due to the tunable resonance wavelength and the local field control.
■
INTRODUCTION Core−shell nanostructures have many useful and promising applications because the core and the shell can be composed of materials with diverse properties. Core−shell spheroids with a dielectric core and a metal shell have been widely used in the enhanced spectra,1−3 sensors,4−7 solar cells,8 and therapeutic application.9,10 Additionally, core−shell spheroids have theoretical significance in the understanding the plasmon coupling effects. The well-accepted hybridization model is first derived with the help of the core−shell spheres11,12 In the hybridization model, plasmon modes of dielectricmetal core−shell spheroids can be understood as the plasmon coupling between the metal solid sphere plasmon mode (charges on the sphere surface) and the metal cavity plasmon mode (charges on the cavity surface). The coupled plasmon modes can be divided into two categories by the charge distribution patterns as illustrated in Figure 1a;11,12 the bonding modes are at the longwave range in the far-field extinction spectra, and the antibonding modes are at the shortwave range. Those plasmon modes evolve along variable geometrical parameters of the core and the shell. The prolate and oblate spheroids with the dielectric core and the metal shell5,13−15 have been theoretically and experimentally investigated for the energy variation of the modes with variable geometrical © 2016 American Chemical Society
parameters such as the size, thickness of the shell, and aspect ratio (the ratio of the major axis to the minor axis). Due to the cancellation of the dipole moments from the charges on the inner and outer surfaces, the net dipole moment of antibonding modes is weak in general, while the special dielectric core, which is TiO216 or ZrO2,17 is found to result in strong antibonding modes in the far-field extinction spectra. For the large particles, the higher- order modes on the surfaces will emerge due to the retardation effects.18 The order of modes can be represented by the l number, which is from the order of spherical harmonics in both the hybridization model11 and the Mie scattering theory.19 The core−shell spheroids with the antibonding and bonding modes have not been investigated in detail for the evolution of the plasmon modes associated with the surface charge distribution patterns with variable geometrical parameters. In the hybridization model, variation of the geometrical parameters results in variable energy of the element plasmon modes of the solid spheroid and cavity. Furthermore, variation of the distance between the inner surface and the outer surface Received: February 23, 2016 Revised: April 5, 2016 Published: April 8, 2016 8891
DOI: 10.1021/acs.jpcc.6b01787 J. Phys. Chem. C 2016, 120, 8891−8899
Article
The Journal of Physical Chemistry C
In this study, the TiO2 core and the silver shell are set as the constant volume (effective radius), respectively. The effective radius (r) of the core is 15 nm, while that (R) of the silver spheroid (if the dielectric core is replaced by silver) is 30 nm. The simulated targets have two configurations. One is that the outer shell is variable and the inner core is fixed. The other is the inner core is variable and the outer shell is fixed. The geometrical variation spans from the prolate to oblate spheroids as illustrated in Figure 2. In this study, the prolate or oblate spheroid is generated by rotating an ellipse around the polar axis (the major axis for the prolate spheroid and the minor axis for the oblate spheroid), which is always along the polarization direction of the electric field. Herein the distances (d) between the inner surface and the outer surface along the polarization direction are defined as R − a in the variable core configuration and a − r for the variable shell configuration.
Figure 1. Schematics of the hybridization model and the charge distribution patterns of the typical modes: (a) hybridization model based on the core−shell sphere and charge distribution pattern of the typical dipole antibonding mode and the typical dipole bonding mode,11,12 (b) quadrupole mode on the surface of the sphere, (c) octupole antibonding mode, (d) octupole bonding mode, and (e) triakontadipole mode on the surface of the sphere. The light polarization direction (E) and the propagation direction (k) are indicated.
changes the interaction of the charges on the two surfaces, such that the antibonding and bonding modes are expected to exhibit the obvious evolution. The evolution is associated with the new mode emerging, peak-shift behavior, and charge distribution variation. The peak-shift behavior means the resonance peak can be tuned to the desired resonance wavelengths. The charge distribution variation in the mode transformation means the local electric field can be changed, which can be useful for enhanced spectra and localized photothermal effects. Additionally, the evolution of the charge distribution with the gradual variation of the geometries can be of fundamental importance for understanding the plasmon phenomena. In this study, TiO2−Ag core−shell nanospheroids with variable geometrical parameters are employed as an example, because the TiO2−Ag core−shell nanosphere has an equal intensity of the dipole antibonding and bonding modes.16 The appearance of the new modes, peak-shift behaviors, and mode transformation are reported. The evolution phenomena associated with the farfield extinction spectra and the charge density distribution are discussed.
Figure 2. Schematic of two configurations. (a−c) Variable core configuration with the evolution from the prolate to oblate spheroids. (b) Core−shell sphere. (d, b, and e) Variable shell configurations with the evolution from the prolate to the oblate spheroids. Here R and r represent the radius of the outer sphere and the inner sphere, respectively. The polar radius (rotation axis) is represented by a, and another arrow represents the equatorial radius. The light polarization direction and the propagation direction are indicated.
■
SIMULATION The plasmonic properties are calculated by FDTD solutions 8.7 (Lumerical solutions, Inc.). The refractive indices of silver20 and TiO221are from the handbooks edited by Palik. TiO2 is a birefringence crystal; however, in simulations the refractive index can be simplified under the average refractive index approximation by assuming the particles are isotropic.16,22,23 In this study the particles are all in the aqueous medium. The refractive index of water used in FDTD software is 1.33. The simulation region is 2 μm × 2 μm × 2 μm. For the variable core configuration, the mesh override region is 145 nm × 145 nm × 145 nm. For the variable shell configuration, this region is set according to the sizes of the prolate shells. For the largest polar radius of 67.5 nm, the mesh override region is 200 nm × 100 nm × 100 nm. The meshing algorithm type in FDTD software is setting as auto nonuniform. The maximum mesh step is set as 0.5 nm in calculating the far-field extinction spectra, while that for calculating the charge density distribution is set as 0.3 nm. The excitation source is total-field scattered-field (TFSF) source. The charge density distribution is calculated from the divergence of the electric field (E) by FDTD software.
Figure 3. Extinction spectra of the core−shell spheroid with variable inner cores. (a) Evolution from the sphere to the oblate spheroid with decreasing polar radius. (b) Evolution from the prolate spheroid to the sphere with decreasing polar radius. The polar radii (a) of the cores are listed in the legend (in nm). Here R = 30 represents the pure silver sphere with a radius of 30 nm, and a = 15 nm represents the core−shell sphere. The polar radii are along the incident polarization of light. 8892
DOI: 10.1021/acs.jpcc.6b01787 J. Phys. Chem. C 2016, 120, 8891−8899
Article
The Journal of Physical Chemistry C
Figure 4. Charge density distribution of the bonding modes in the variable core configuration. The polar radius (a) of the inner core is 25.5 (a), 23.4 (b), 20.0 (c), 17.2 (d), 15.0 (e), 13.2 (f), 11.7 (g), 10.4 (h), 9.3 (i), 8.4 (j), and 6.4 nm (k). The charge density distribution is calculated at each of the resonance wavelengths as labeled. The light polarization direction and the propagation direction are indicated. All color bars are under the same scale.
Figure 5. Charge density distribution of the antibonding modes in the variable core configuration. The polar radius (a) of the inner core is 20.0 (a), 17.2 (b), 15.0 (c), 13.2 (d), 11.7 (e), 10.4 (f), 9.3 (g), 8.4 (h), and 6.4 nm (i). The charge density distribution is calculated at each of the resonance wavelengths as labeled. The light polarization direction and the propagation direction are indicated. All color bars are under the same scale.
■
RESULTS AND DISCUSSION
evolved from the antibonding mode of the core−shell sphere also exhibit the red shift behavior (line 2). When the polar radius of the oblate core decreases toward zero, the antibonding modes converge to the plasmon mode of the pure silver sphere with a radius of 30 nm, while the bonding modes tend to vanish in the infrared range. When the polar radius of the prolate core decreases to 15 nm, the bonding modes evolved are red shifted as indicated by line 3 as shown in Figure 3b, while the antibonding modes also exhibit the red shift behaviors with the
A. Far-Field Extinction Spectra in the Variable Core Configuration. The evolution of far-field extinction spectra in the variable core configuration are shown in Figure 3. When the polar radius of the core keeps decreasing from the radius of the sphere (15 nm), the plasmon modes evolved from the bonding mode of the core−shell sphere exhibit the red shift behavior as indicated by line 1 in Figure 3a. Meanwhile the plasmon modes 8893
DOI: 10.1021/acs.jpcc.6b01787 J. Phys. Chem. C 2016, 120, 8891−8899
Article
The Journal of Physical Chemistry C
Figure 6. Charge density distribution of the antibonding modes when the inner surface approaches the outer surface. The distances between the inner surface and the outer surface are 6.6 (a and c) and 4.5 nm (b and d), which correspond to a polar radius with 23.4 and 25.5 nm, respectively. Resonance wavelengths are shown. The light polarization direction and the propagation direction are indicated. All color bars are under the same scale.
polar radius decreasing (line 4). Furthermore, when the polar radii are large enough, for example, a ≥ 23.4 nm in our cases, which means the distances between the outer surface and inner surface are less than 6.6 nm (d = R − a ≤ 6.6 nm), one new mode emerges in the antibonding band. The peak-shift behaviors of the dielectric-metal core−shell spheroids have been calculated with the variable cores and the fixed aspect ratios of the outer shell as 1.5 and 4.575.5,13 If the light polarization is perpendicular to the major axis of the prolate or oblate core, the antibonding modes are red shifted with increasing aspect ratio,5,13 which corresponds to line 2 in Figure 3. When the light polarization is along the major axis of the prolate or oblate core, the bonding modes show the red shift behavior with decreasing aspect ratio of the core,5,13 which is partly like the phenomena indicated by line 3 in Figure 3. The above phenomena can be qualitatively understood by the hybridization model and the simple harmonic oscillator model.13 The plasmon modes of the core−shell spheroid are from the hybridization of the mode of the solid spheroid and that of the cavity in the infinite metal medium as shown in Figure 1a. For the solid spheroid and the spheroidal cavity, opposite charges distribute on the hemispherical surfaces along the polarization direction. In the simple harmonic oscillator model, the resonance frequency for the solid spheroid depends on the restoring force which arises from the coulomb attraction of the surface charges on the opposite ends.13 For the solid prolate spheroid, the distance of the opposite charges increases with increasing polar radius, and then the restoring force keeps decreasing, so the resonance frequency decreases, that is, the resonance wavelength is red shifted. Then for the solid oblate spheroid with decreasing polar radius, the distance between the opposite charges decreases and the restoring force is enhanced, so the resonance wavelength is blue shifted. The cavity mode is in reverse,13 that is, the oblate and prolate cavity with decreasing polar radius will exhibit the red shift behavior of the resonance wavelengths. If the energy (frequency) of the cavity mode is higher than that of the solid spheroid mode, the antibonding mode is cavitylike and the bonding mode is solid-particle-like, which is the usual effect for the plasmon modes of the core−shell sphere. Herein cavity-like means the plasmon mode is dominated by the
Figure 7. Extinction spectra of the core−shell spheroid with the stretched polar axis (a) of the outer spheroid. Extinction spectra are normalized by the intensity of the bonding mode of the core−shell sphere. Tick labels on the left side represent the maximum of the resonance peak in the left part of the spectra. Tick labels on the right side represent the maximum of the resonance peaks in the right part of the spectra. Polar radii are along the incident polarization of light.
cavity mode arising from the charges on the inner surface. Solid-particle-like means the plasmon mode is dominated by the solid-particle mode arising from the charges on the outer surface. If the energy of the cavity mode is lower than that of the solid sphere mode, the antibonding mode is solid-particle-like and the bonding mode is cavity-like.13 For the situation of the oblate core in our cases, the energy of the cavity mode can be lower than the constant energy of the sphere modes,5,13 so the antibonding modes are solid-particle-like and tend to be the mode of the pure silver solid sphere when the core is going to vanish. Meanwhile the bonding modes are cavity-like and exhibit the red shift behavior with decreasing polar radius, phenomena which are different from the blue shift behaviors reported in the results.5,13 We believe it is reasonable that the bonding modes tend to be lower energy (red shift) and vanish when the core flattens and disappears. For the situation of the prolate core, the energy (frequency) of the cavity mode keeps decreasing with decreasing polar radius, 8894
DOI: 10.1021/acs.jpcc.6b01787 J. Phys. Chem. C 2016, 120, 8891−8899
Article
The Journal of Physical Chemistry C
C. Far-Field Extinction Spectra in the Variable Shell Configuration. For the variable shell configuration as shown in Figure 7, the evolved modes associated with the bonding mode of the core−shell sphere exhibit the red shift behavior with the increasing polar radius a crossing over the oblate to the prolate shells as indicated by line 5 if the distances between the inner surface and the outer surface are not too small. However, when the inner surface and outer surface are very close such that a ≤ 20.8 nm or d = a − r ≤ 5.8 nm, there are two modes in the bonding band. For the modes associated with the antibonding mode of the core−shell sphere, all modes are red shifted with increasing polar radius as indicated by line 6. When the distance between the inner surface and the outer surface is large enough such as d ≥ 36 nm, the new mode emerges. The new modes are still red shifted with increasing polar radius as indicated by line 7. From the oblate to the prolate shells, the energy of the solid spheroid modes decreases with increasing polar radius. This phenomenon can be found in the longitudinal modes of the solid spheroids25 and the nanorods26,27 with increasing aspect ratios. Because of this reason the bonding modes are red shifted. D. Charge Density Distribution Patterns in the Variable Shell Configuration. When the distance of the outer surface and the inner surface is not very close (d > 8.4 nm or a > 23.4 nm), the charge density distribution patterns of the dipole bonding modes are shown in Figure 8b−k. With a distance of 8.4 nm as shown in Figure 8a, the charge distribution on the outer surface exhibits the early sign of the octupole component. When the distance decreases to 5.8 nm, a new bonding mode emerges. For the modes at the longwave side which is evolved from the dipole bonding modes, they tend to be the octupole-like bonding mode. The features of the charge distribution of the octupole bonding mode are sketched in Figure 1d. The new mode at the shortwave side tends to exhibit the triakontadipole-like and octupole-like mode on the outer and inner surfaces as shown in Figure 9. Herein, the
which results in the antibonding modes being red shifted. When the inner surface and the outer surface are close enough (such as d ≤ 6.6 nm), the strong interaction of the charges on them results in the new modes. The charge distribution patterns of the new modes are shown in Figure 6. B. Charge Density Distribution Patterns in the Variable Core Configuration. To explore the plasmon evolution behaviors, the plasmon modes should be identified. The charge density distributions of the modes labeled as line 1 and line 3 are shown in Figure 4, which belong to the typical charge distribution pattern of the dipole bonding mode. The charge density distributions of the modes labeled as line 2 and line 4 are shown in Figure 5. When the polar axis is smaller than 17.2 nm (Figure 5b−i), the modes belong to the typical dipole antibonding modes. When the polar axis is 20.0 nm, the charges on the outer surface exhibit unapparent quadrupole distribution as shown in Figure 5a. The features of the charge distribution of the quadrupole mode are shown in Figure 1b. With the polar radius increasing the inner surface will approach the outer surface. If their distance is small enough, such as 6.6 and 4.5 nm, the dipole antibonding mode is found to be mixed with the quadrupole charge distribution on the outer surface as shown in Figure 6a and 6b. Meanwhile, the new antibonding modes are observed, and they have different evolution phenomena as shown in Figure 6c and 6d. For a distance of 6.6 nm, the outer surface first emerges with the octupole mode while the inner surface still keeps the dipole mode. The features of the charge distribution of the octupole mode have been reported in the hollow nanosphere18 and the nanoring.24 Herein, those of the octupole antibonding mode are sketched in Figure 1c. As the distance decreases to 4.5 nm, the outer surface emerges with the very unapparent quadruple mode component and the inner surface emerges with the octupole mode. In this situation the charges on the inner and outer surface form an octupole antibonding mode.
Figure 8. Charge density distribution patterns of the bonding modes in the variable shell configuration. The polar radius (a) of the outer spheroid is 23.4 (a), 26.4 (b), 30 (c), 34.4 (d), 39.9 (e), 46.9 (f), 51 (g), 53.3 (h), 55.8 (i), 61.2 (j), and 67.5 nm (k). The charge density distribution is calculated at each of the resonance wavelengths as labeled. The light polarization direction and the propagation direction are indicated. All color bars are under the same scale. 8895
DOI: 10.1021/acs.jpcc.6b01787 J. Phys. Chem. C 2016, 120, 8891−8899
Article
The Journal of Physical Chemistry C features of the charge distribution of the triakontadipole bonding mode are shown in Figure 1e. It must be noted that
the octupole or triakontadipole charge distribution is not complete because the charge distributions on the far-end surface related to the light propagation do not turn to these types from the dipole or octupole modes. This effect can be due to the retardation effect which causes the asymmetry in the plasmon mode along the direction of propagation of the incident light.28 When the inner surface and outer surface are close, such as a distance of 3.7 nm, the outer surface and the inner surface exhibit the octupole antibonding mode as shown in Figure 10a. With the polar radius or the distance increasing, the modes on the inner surface transform to the dipole modes and then with the polar radius further increasing, the modes on the outer surface also transform to the dipole modes as shown in Figure 10b−e. For the prolate outer spheroids, the octupole modes start to exhibit on the outer surface, and with the polar radius of the prolate increasing, such as to 51.0 nm, the core also exhibits the octupole modes. In this time the octupole antibonding modes emerge again. The electric field direction is indicated in Figure 10, which means the surface charge distribution of the first and last octupole antibonding modes is totally inverse by the evolution. Though they are all octupole antibonding modes, different positive and negative charge distributions along the electric field generate the different modes and the different energy (resonant frequency/wavelength).
Figure 9. Charge density distribution patterns of the bonding modes in the variable shell configuration. The polar radius (a) of the outer spheroid is 20.8 (a and c) and 18.7 nm (b and d). The charge distribution patterns are calculated at each of the resonance wavelengths as labeled. The light polarization direction and the propagation direction are indicated. All color bars are under the same scale.
Figure 10. Charge density distribution patterns of the antibonding modes as labeled as line 6 in Figure 4. The polar radius (a) of the outer spheroid is 18.7 (a), 20.8 (b), 23.4 (c), 26.4 (d), 30 (e), 34.4 (f), 39.9 (g), 46.9 (h), 51 (i), 53.3 (j), 55.8 (k), and 61.2 nm (l). The charge distribution patterns are calculated at each of the resonance wavelengths as labeled. The light polarization direction and the propagation direction are indicated. All color bars are under the same scale. 8896
DOI: 10.1021/acs.jpcc.6b01787 J. Phys. Chem. C 2016, 120, 8891−8899
Article
The Journal of Physical Chemistry C
E. Discussion. From the evolution in two configurations, the antibonding and bonding modes are evolved with the odd l number, such as dipole (l = 1), octupole (l = 3), and triakontadipole (l = 5) except for the mixed modes. In the mixed modes, the quadruple (l = 2) mode mixes with the modes with the odd l. The higher order (octupole and triakontadipole) modes on the inner or outer surfaces of the core−shell spheres are observed on the facing surfaces of the gap in the dimer configuration.29 The higher order modes on one monomer are closely associated with the asymmetrical influence of the surface charges on the other monomer along the polarization direction of light. For the single ellipsoids in our cases, there is no asymmetrical influence along the polarization direction. One of the reasons for the higher order modes can be attributed to the retardation effects. Here we pay attention to the modes of the nanoshells with the empty cavity which excludes the effects of the dielectric core. The extinction spectra are shown in Figure 12a. For the large prolate shell with the spherical cavity, there is the octuple antibonding mode on the outer surface as shown in Figure 12b. This mode arises from the retardation effects of the large sizes along the polarization direction. For the oblate shell as shown in Figure 12c, the mode at 394 nm tends to the octupole bonding mode, while this mode is also not complete due to the retardation effects along the propagation direction of light. The mode at 365 nm (as shown in Figure 12d) also exhibits the octupole bonding mode, while the charge distribution of this mode is opposite to that of the mode at 394 nm. For the modes of the oblate shells, the formation of the higher modes should not be due to the retardation effects. The charges on the close surfaces are believed to be more important.
The new bonding modes emerge when the polar radius increases to 51.0 nm as shown in Figure 11. Those modes are all octupole bonding modes.
Figure 11. Charge density distribution patterns of the modes evolved from the antibonding bands labeled as line 7 in Figure 4. The polar radius (a) of the outer spheroid is 51 (a), 53.3 (b), 55.8 (c), 61.2 (d), and 67.5 nm (e). The charge distribution patterns are calculated at each of the resonance wavelengths as labeled. The light polarization direction and the propagation direction are indicated. All color bars are under the same scale.
Figure 12. Extinction spectra of the nanoshells with the empty cavity and the charge density distribution patterns of the selected modes. (A) Extinction spectra. The polar radius (a) of the outer spheroid is 67.5 (b), 18.7 (c), and 18.7 nm (d). For the inner core it is 25.5 nm (e). Charge distribution patterns are calculated at each of the resonance wavelengths as labeled. The light polarization direction and the propagation direction are indicated. All color bars are under the same scale. 8897
DOI: 10.1021/acs.jpcc.6b01787 J. Phys. Chem. C 2016, 120, 8891−8899
The Journal of Physical Chemistry C
■
Besides the retardation effects, the dielectric core effects are also very important to the formation of the higher order modes. As shown in Figure 12e, there are no higher order modes on the surfaces and the mode at 449 nm is the bonding mode. Compared with Figure 6b and 6d, the TiO2 core generates the antibonding modes and brings the dipole and higher order modes. As shown in Figure 11, the octupole bonding modes are also generated by the dielectric cores and they do not emerge on the surfaces of the nanoshell with the empty cavity. For the specific structures with the appropriate dielectric core there may be different charge density distribution patterns, which are corresponding to different energy. The energy of the antibonding mode is higher than that of the bonding modes at the same order of the modes.11,12,30 Those usual phenomena also exist in the evolution of the core−shell nanospheroids. By the simple TiO2−Ag core−shell spheroids with the variable geometrical parameters, the appearance of new higher order modes and the mode evolution of the antibonding and bonding modes are illustrated. Those new observations can be added to the fundamental features of the plasmons and helpful to further understand the mechanisms of them.
REFERENCES
(1) Jackson, J. B.; Westcott, S. L.; Hirsch, L. R.; West, J. L.; Halas, N. J. Controlling the surface enhanced Raman effect via the nanoshell geometry. Appl. Phys. Lett. 2003, 82, 257−259. (2) Oldenburg, S. J.; Westcott, S. L.; Averitt, R. D.; Halas, N. J. Surface enhanced Raman scattering in the near infrared using metal nanoshell substrates. J. Chem. Phys. 1999, 111, 4729−35. (3) Tanabe, K. Field Enhancement around Metal Nanoparticles and Nanoshells: A Systematic Investigation. J. Phys. Chem. C 2008, 112, 15721−15728. (4) Kalele, S. A.; Ashtaputre, S. S.; Hebalkar, N. Y.; Gosavi, S. W.; Deobagkar, D. N.; Deobagkar, D. D.; Kulkarni, S. K. Optical detection of antibody using silica−silver core−shell particles. Chem. Phys. Lett. 2005, 404, 136−141. (5) Wang, H.; Brandl, D. W.; Le, F.; Nordlander, P.; Halas, N. J. Nanorice: A hybrid plasmonic nanostructure. Nano Lett. 2006, 6, 827− 832. (6) Jian, Z.; Xing-chun, D.; Jian-jun, L.; Jun-wu, Z. Tuning the number of plasmon band in silver ellipsoidal nanoshell: Refractive index sensing based on plasmon blending and splitting. J. Nanopart. Res. 2011, 13, 953−958. (7) Chaffin, E. A.; Bhana, S.; O’Connor, R. T.; Huang, X.; Wang, Y. Impact of core dielectric properties on the localized surface plasmonic spectra of gold-coated magnetic core shell nanoparticles. J. Phys. Chem. B 2014, 118, 14076−14084. (8) Ding, B.; Lee, B. J.; Yang, M.; Jung, H. S.; Lee, J.-K. Surfaceplasmon assisted energy conversion in dye-sensitized solar cells. Adv. Energy. Mater. 2011, 1, 415−421. (9) Hirsch, L. R.; Jackson, J. B.; Lee, A.; Halas, N. J.; West, J. L. A Whole blood immunoassay using gold nanoshells. Anal. Chem. 2003, 75, 2377−2381. (10) Loo, C.; Lin, A.; Hirsch, L.; Lee, M. H.; Barton, J.; Halas, N. J.; West, J.; Drezek, R. Nanoshell-enabled photonics-based imaging and therapy of cancer. Technol. Cancer Res. Treat. 2004, 3, 33−40. (11) Prodan, E.; Radloff, C.; Halas, N. J.; Nordlander, P. A Hybridization model for the plasmon response of complex nanostructures. Science 2003, 302, 419−422. (12) Prodan, E.; Nordlander, P. Plasmon hybridization in spherical nanoparticles. J. Chem. Phys. 2004, 120, 5444−5454. (13) Brandl, D. W.; Nordlander, P. Plasmon modes of curvilinear metallic core/shell particles. J. Chem. Phys. 2007, 126, 144708. (14) Chung, H. Y.; Leung, P. T.; Tsai, D. P. Dynamic modifications of polarizability for large metallic spheroidal nanoshells. J. Chem. Phys. 2009, 131, 124122. (15) Hooshmand, N.; Jain, P. K.; El-Sayed, M. A. Plasmonic spheroidal metal nanoshells showing larger tunability and stronger near fields than their spherical counterparts: An effect of enhanced plasmon coupling. J. Phys. Chem. Lett. 2011, 2, 374−378. (16) Li, Q. S.; Zhang, Z. L. Broadband tunable and double dipole surface plasmon resonance by TiO2 Core/Ag shell nanoparticles. Plasmonics 2011, 6, 779−784. (17) Laaksonen, K.; Suomela, S.; Puisto, S. R.; Rostedt, N. K. J.; AlaNissila, T.; Nieminen, R. M. Influence of high-refractive-index oxide cores on optical properties of metal nanoshells. J. Opt. Soc. Am. B 2014, 31, 494−502. (18) Yin, J.; Zang, Y.; Xu, B.; Li, S.; Kang, J.; Fang, Y.; Wu, Z.; Li, J. Multipole plasmon resonances in self-assembled metal hollownanospheres. Nanoscale 2014, 6, 3934−3940. (19) Uwe Kreibig, M. V. Optical properties of metal clusters; SpringerVerlag: Berlin, Heidelberg, 1995; p 29. (20) Lynch, D. W.; Hunter, W. R. Comments on the optical constants of metals and an introduction to the data for several metals. In Handbook of optical constants of solids; Palik, E. D., Ed.; Academic Press: San Diego, 1985; Vol. 1, pp 350−357. (21) Ribarsky, M. W. Titanium dioxide(TiO2) (Rutile). In Handbook of optical constants of solids, Palik, E. D., Eds.; Academic Press: San Diego, 1985; Vol. 1, pp 795−804. (22) Thiele, E. S.; French, R. H. Computation of light scattering by anisotropic spheres of rutile titania. Adv. Mater. 1998, 10, 1271−1276.
■
CONCLUSIONS The plasmon evolution of the TiO2−Ag core−shell spheroids is investigated by the far-field extinction spectra and charge density distribution patterns. In the variable core configuration, the antibonding and bonding modes are in general red shifted with decreasing polar radius. If the polar radius is so large that the inner surface of the metal shell is in close proximity to the outer surface, the new antibonding modes emerge. The antibonding modes are the dipole antibonding modes mixed with quadrupole modes on the outer surface and octupole modes. In the variable shell configuration, the antibonding and bonding modes are red shifted with increasing polar radius in general. If the polar radius is so small that the outer surface closely approaches the inner surface, the new bonding modes emerge. The dipole modes evolve to the octupole-like mode, and the new modes tend to be the triakontadipole-like and octupole-like modes on the outer and inner surfaces. If the polar radius is so large that the outer surface is far away from the inner surface, the dipole antibonding modes evolve to the octupole antibonding mode and a new mode emerges which is the octupole bonding mode. We found the evolutions are all associated with the odd l number (l = 1 for dipole, l = 3 for octupole, l = 5 for triakontadipole) except for the mixed modes. In the variable shell configuration, the antibonding modes evolve from octupole to dipole then octupole modes; however, two types of octupole modes have the opposite charge distribution. For the higher modes, the retardation effects and the dielectric core effects are discussed.
■
Article
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
■
ACKNOWLEDGMENTS This work was supported by Fundamental Research Funds for the Central Universities (grant no. FRF-TP-14-072A2), the Beijing Higher Education Young Elite Teacher Project (no. YETP0391). 8898
DOI: 10.1021/acs.jpcc.6b01787 J. Phys. Chem. C 2016, 120, 8891−8899
Article
The Journal of Physical Chemistry C (23) McNeil, L. E.; Hanuska, A. R.; French, R. H. Orientation dependence in near-field scattering from TiO2 particles. Appl. Opt. 2001, 40, 3726−3736. (24) Fu, Y. H.; Zhang, J. B.; Yu, Y. F.; Luk’yanchuk, B. Generating and manipulating higher order fano resonances in dual-disk ring plasmonic nanostructures. ACS Nano 2012, 6, 5130−5137. (25) Norton, S. J.; Vo-Dinh, T. Spectral bounds on plasmon resonances for Ag and Au prolate and oblate nanospheroids. J. Nanophotonics 2008, 2, 029501. (26) Yu; Chang, S.-S.; Lee, C.-L.; Wang, C. R. C. Gold nanorods: Electrochemical synthesis and optical properties. J. Phys. Chem. B 1997, 101, 6661−6664. (27) Link, S.; Mohamed, M. B.; El-Sayed, M. A. Simulation of the optical absorption spectra of gold nanorods as a function of their aspect ratio and the effect of the medium dielectric constant. J. Phys. Chem. B 1999, 103, 3073−3077. (28) Grady, N. K.; Halas, N. J.; Nordlander, P. Influence of dielectric function properties on the optical response of plasmon resonant metallic nanoparticles. Chem. Phys. Lett. 2004, 399, 167−171. (29) Li, Q.; Zhang, Z. Bonding and anti-bonding modes of plasmon coupling effects in TiO2-Ag core-shell dimers. Sci. Rep. 2016, 6, 19433. (30) Park, T.-H.; Nordlander, P. On the nature of the bonding and antibonding metallic film and nanoshell plasmons. Chem. Phys. Lett. 2009, 472, 228−231.
8899
DOI: 10.1021/acs.jpcc.6b01787 J. Phys. Chem. C 2016, 120, 8891−8899
