Optical Extinction Properties of Aggregated Ultrafine Silver

Dec 27, 2010 - Optical extinction properties of ultrafine silver nanoparticles assembled on silica nanospheres are numerically studied using the discr...
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Optical Extinction Properties of Aggregated Ultrafine Silver Nanoparticles on Silica Nanospheres Qi Lin and Zhijun Sun* Department of Physics, Xiamen University, Xiamen, Fujian 361005, People's Republic of China ABSTRACT: Optical extinction properties of ultrafine silver nanoparticles assembled on silica nanospheres are numerically studied using the discrete dipole approximation method. As silver nanoparticles are arranged on such a closed spherical substrate and are coupled in optical interactions, plasmon resonance modes for various possible polarizations and incidence directions are present in their extinction spectra. The main features of the spectra are shown to be related to three proposed plasmon resonance modes, e.g., coupled monomer mode, coupled septamer mode, and closed-loop plasmon resonance mode. The three types of modes successively come into play and appear to dominate with an increase of the number of silver nanoparticles. Coupling and collective plasmon resonances are shown to be effective only when the silver nanoparticles are closely packed such that their interspacings are within a few nanometers. For shells formed by coalesced silver nanoparticles, only the collective plasmon resonance mode in the continuous layer of metal shell is effective; the effect of surface morphology or roughness is minor.

1. INTRODUCTION Interaction of light with plasmonic metal nanoparticles (NPs) can result in strongly enhanced local fields and leave signatures in their optical extinction spectra sensitively,1 which is promising for their application in sensing,2-4 imaging,5,6 biotechnology,7 and nonlinear optics.8 To optimize and have better control of the NPs' optical properties, in recent years, researchers have also been actively studying NPs of various shapes9-11 and novel complex structures, such like core/shell NPs12-14 and artificially assembled NPs.15-17 In this work, we numerically study the optical extinction properties of ultrafine silver nanoparticles (diameter d < 10 nm) that are assembled on silica nanospheres (diameter D = 101-2 nm). The background is partly that, in real situations, synthesis of dielectric/metal core/shell NPs usually involves gradual deposition of ultrafine metal nanoparticles onto the surface of dielectric cores.18-21 Evolution of their optical properties during growth of the shell was experimentally observed. Previous theoretical explanations were mostly based on ideal core/shell structures with continuous, smooth, and uniformly thick metal shells. Recently, there has also been a great deal of research interest in the study of optical properties of closely spaced metal NP arrays; and ultrafine NPs are concerned in some reports,16,22-26 in which the metal NPs were all in planar arrays. In this work, the ultrafine metal NPs are assembled on spherical substrates of comparatively much larger dielectric nanospheres, such that the metal NPs are in forms of closed cages or shells. In the numerical calculations, the discrete dipole approximation (DDA) method is used with the code DDSCAT 7.0 r 2010 American Chemical Society

developed by Draine and Flatau,27 and the extinction spectra (i.e., extinction efficiency, Qext) are calculated for the structures of ultrafine silver NPs on silica nanospheres. All of the NP systems are surrounded by water. The refractive indices of water and silica, as plotted in Figure 1(a), are fitted from data in refs 28 and 29. Figure 1(b) shows size-corrected real and imaginary parts of the permittivities of silver NPs of various sizes (d = 3, 5, 8, and 10 nm in diameter), compared with those of bulk silver.29 The size-corrections are performed with the equation and parameters used in ref 23. In the DDA calculations, we choose the dipole grid of 1/3 nm. Thus convergence for accuracy of the calculations is fulfilled according to the criteria in ref 30. Meanwhile, shapes of the nanostructures are also well-defined using the grid size, e.g., there are 382, 1767, 7238, and 14138 dipoles in each NP of size d = 3, 5, 8, and 10 nm, respectively. For simplicity in modeling, both the Ag NPs and silica nanospheres are considered spherical, and the Ag NPs are uniformly and symmetrically distributed on the surface of silica nanospheres. In this situation, the calculated extinction spectra are almost independent of polarization or propagation directions of the incidence light; but various local modes that are polarization-dependent may leave characteristic features in the spectra, as short-range plasmon resonances play important roles in some conditions. Note that the spectra are all plotted with respect to the vacuum wavelength. Received: August 18, 2010 Revised: December 8, 2010 Published: December 27, 2010 1474

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Figure 1. (a) Refractive indices of water and silica, fitted to the data from refs 28 (water) and 29 (silica). (b) Size-corrected real (solid lines) and imaginary (dash lines) parts of the permittivity of Ag nanoparticles (d = 3, 5, 8, 10 nm) compared with those of bulk silver (fitted to the data from ref 29).

2. NUMERICAL RESULTS AND DISCUSSIONS 2.1. Effects of Coverage of Ag NPs on Silica Nanospheres and Interparticle Couplings. In Figure 2, the extinction spec-

tra of different numbers of Ag NPs (d = 5 nm) on silica nanospheres (D = 50 nm) were calculated. As the number N = 168, the Ag NPs are closest-packed on the silica nanosphere, i.e., NPs just touch their neighbors. And for N = 672, the neighboring Ag NPs are merged into each other with their nominal centerto-center distance equal to d/2. Note that, although a closed shell is formed for N = 672, there still exist unfilled vacancies underneath the NPs in the model. Generally, optical interaction with isolated individuals of such ultrafine metal NPs is in the quasistatic regime, their optical extinction is mainly due to absorption. Therefore, the position of the extinction peak is almost independent of the NP's size.1 For multiple ultrafine metal NPs, optical couplings between them are effective only for interspacings within just a few nanometers.22,23,26 This is different from that of a system with much larger metal particles (∼102 nm in size), in which plasmons undergo higher-order oscillations. Scatterings from large-size particles can modify local fields in their neighboring ones and also interfere in the far field, thus the effect of interparticle coupling is prominent even for interspacings of hundreds of nanometers.15,31 Here the NPs are extremely fine and in an aggregated form on the silica nanosphere. For smaller numbers of NPs (N = 24, 48, and 72), since the Ag NPs are sparsely distributed on the silica nanospheres (e.g., an interparticle gap ≈ 8 nm for N = 72), positions of their main extinction peaks are almost unchanged locating at the wavelength of 420 nm, as observed in Figure 2. It suggests that interactions between the Ag NPs are not effective and almost not dependent on their interspacings. For reference, it was calculated that, for a single Ag NP of 5 nm in diameter hosted in water, the extinction peak locates at 400-nm-wavelength,25 and peak Qext ≈ 1.2. In comparison, a red-shift of the peak position and decrease of the

Figure 2. Extinction spectra of N silver nanoparticles (d = 5 nm) assembled on silica nanosphere (D = 50 nm). Inset schematics of (a) show closest-packing (N = 168) and merging (N = 672) of neighboring Ag NPs. For N = 672, the extinction value is reduced with a factor of 0.2 in display. Part (b) is a local magnification of (a). Part (c) is a 2D schematic illustration of the nanostructure. (d) Illustration of the coupled monomer (CM) mode and coupled septamer (CS) mode. (e1, e2, e3) defines local coordinates on the surface of silica nanosphere. (e) indicates three submodes of the CM mode, which are related to the polarization direction of the incidence field with respect to quasi-planar arrangement of the monomer Ag NP and its neighbors.

extinction efficiency for the Ag NPs on silica nanosphere are attributed to an increase in the effective refractive index around the NPs for the presence of the silica nanosphere.32 It is also obvious that, with an increase of the number of Ag NPs, the peak extinction efficiency increases, but the increase rate is lower than that of the number of Ag NPs. This implies that the extinction is not simply a superposition of the extinction of uncoupled individual ones, but there is a limiting factor due to interaction between them. Interestingly, even with such small numbers of Ag NPs, due to their cage-like form around the silica nanospheres, secondary extinction peaks appear in the long wavelength range (850-900 nm), which are more clearly shown in Figure 2(b); and the Qext value grows with increase of the number of NPs. But there is no such peak in the spectrum of a single Ag NP mentioned above. This is another evidence of the role of interparticle couplings for the sparsely distributed Ag NPs on the silica nanosphere. The situation may be considered as the initial transition stage for shell formation, and the secondary extinction peak will evolve into the main extinction peak of a closed core/shell structure. 1475

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The Journal of Physical Chemistry C When there are more Ag NPs on the silica nanosphere, interspacings between the NPs are reduced, thus interparticle couplings will come to play an important role on the plasmon resonances. Recall that, for two closely spaced Ag NPs, their coupling can be in a longitudinal mode (or attraction mode) and/or a transverse mode (or repulsion mode) dependent on polarization states of the incidence light.16,25 The interparticle coupling modifies plasmon resonances in each one of the NPs, and usually results in a small shift of the main extinction peak. In the case that the NPs are in separation, free charges of the plasmons are still confined within individual ones. But when the NPs are in touch or coalesced such that there can be exchange of free charges between them, new resonance peaks will appear on the longer-wavelength side of the spectrum due to collective plasmon resonances along the long-axis of the dimer system in the longitudinal coupling mode mentioned above.25 In the system of our work, we have to consider couplings between more NPs. In that d , D and the Ag NPs are closely packed on the surface of a silica nanosphere, locally the Ag NPs can be considered to be in a quasi-planar hexagonal arrangement. Thus, each Ag NP on the silica nanosphere is primarily coupled with six nearest neighboring ones. On the basis of this approximation, we can first study the plasmon resonances in a supercell of Ag NPs forming a septamer system. Similar to the dimer case, there can be two types of modes depending on whether confinement of the plasmon resonances is mainly within the individual Ag NPs or the whole septamer system. Here we name them as “coupled monomer (CM) mode” and “coupled septamer (CS) mode”, as schematically illustrated in Figure 2(d). It is known that plasmons are oscillating free charges (electrons) associated with electromagnetic (EM) fields at optical frequency; plasmonic coupling between adjacent Ag NPs can be via EM field interactions or additionally via exchange of charges. The former (EM interaction) is relatively a weak coupling process especially when interspacing between the NPs is large, and is typical for the CM mode here; while the latter (charge exchange) is a strong coupling process, usually taking place when the NPs are in touch or coalesced, and is typical for the CS mode. Actually, for the cases of N = 24, 48, and 72, only weak EM interactions exist for the CM mode between neighboring Ag NPs due to large interspacings of the NPs. But when the Ag NPs are extremely close-packed, e.g., for N = 168, plasmon resonances of both the CM and CS modes can be prominent. In the following, we give further explanations on their manifestation in the extinction spectrum. For a septamer of Ag NPs, orthogonally there are six illumination states dependent on the polarization and propagation directions of incidence light with respect to the arrangement of the septamer NPs. They are schematically shown in Figure 2(e), where (e1, e2, e3) defines local coordinates on the silica nanosphere, EF and kF are the electric field and wave vector of the incidence light, respectively. As studied in ref 25, due to coupling between the Ag NPs, the main extinction peak of the septamer has a blue or red shift from that of a single Ag NP; and the shift is dependent only on the polarization of the incidence field, not on the incidence direction. Therefore, the CM mode in a septamer of Ag NPs has three submodes, corresponding to EF//e1, EF// e2 and EF//e3, respectively. In the whole system, such septamer supercells are distributed all around the silica nanosphere. For the incidence of arbitrarily polarized light propagating in any direction, Ag NP septamers at different locations on the silica nanosphere surface will be illuminated in various polarization

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states relative to local arrangement of the Ag NPs. In the local coordinates, the incidence field (EF) can be projected to the orthogonal directions (e1, e2, e3). Thus, all three submodes of the CM mode will play roles. Even after integration of their effects in all the septamers around the nanosphere, the submodes may still be distinct in the extinction spectrum, provided that they are not too dispersive for a moderate D/d ratio. Here, in Figure 2(a) for N = 168, we do observe three subpeaks, at 350, 400 and 440 nm, in the wide extinction band corresponding to the CM mode. Referring to regularities on the peak shift for different polarization modes obtained in ref 25, we here attribute the CM mode subpeak at 350 nm to the coupling with surrounding neighbors under polarization projection perpendicular to the local surface of the silica nanosphere (i.e., EF//e3), the subpeak at 400 nm to coupling under polarization projection in e1-direction (EF//e1), and the subpeak at 440 nm to coupling under polarization projection in e2-direction (EF//e2). Besides plasmon resonances in the coupled monomer Ag NPs, collective plasmon resonances can exist in a larger scale, e.g., within the supercell of septamer Ag NP aggregates for the “coupled septamer (CS) mode”. Collective plasmon resonances in the Ag NP septamers are supposed to appear at longer wavelengths. Although optical properties of septamer metal NPs have been theoretically studied,25,33 detailed mechanisms still need more elucidation. It was explicitly pointed out that some features in the extinction spectrum of a septamer are related to subradiant and superradiant mode Fano-type resonances.17,33 Phenomenally, referring to the analysis in refs 25 and 33, we may attribute the extinction peaks at both 550 and 650 nm in Figure 2 (N = 168) to submodes of the CS mode. The small peaks at even longer wavelengths are supposedly due to collective plasmon resonances in an even larger scale, e.g., within scope of the next nearest neighboring NPs. A closed-loop resonance of collective plasmons around the whole silica nanosphere will be the startup of shelllike plasmon resonances. But for the case of closest-packed NPs (N = 168) on the silica nanosphere with moderate D/d ratio, only the nearest interparticle couplings are effective. Collective plasmon resonances in a much larger scale are suppressed by high resistivity in the layer of Ag NPs for transfer of free charges, as the charges are subjected to strong scattering from the NPs' boundaries. As such, closed-loop plasmon resonance is still weak for N = 168, and may relate to the small extinction peak at 820 nm. For the case of coalesced Ag NPs on the silica nanosphere in Figure 2 (N = 672), a full Ag shell is formed; the main extinction peak appears at the wavelength of 760 nm with a highly increased extinction efficiency of ∼3.5. This extinction peak is believed to be due to the dipolar plasmon resonance in the full Ag shell, and is an extension of the above-mentioned closed-loop plasmon resonance. In this case, the free charges can transport in the continuous shell with low resistivity; while the short-range plasmon resonances (e.g., CM and CS modes) are highly suppressed, as plasmons cannot be effectively confined in the local tangential plane without boundaries of the Ag NPs. Thus the extinction becomes dominated by optical scattering of the dipolar plasmon resonance mode in the continuous Ag shell. Additionally, it is noticed that there appears to be another distinct extinction peak at the wavelength of 330 nm. This is believed to be due to quasistatic plasmon resonance in the direction of the shell thickness (i.e., e3-direction), and is intrinsically of the same type as the resonance mode at 350 nm for N = 168. From these numerical simulations, it is observed that an Ag nanoshell structure has a much stronger optical extinction than that of Ag NPs, and the 1476

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Figure 3. Extinction spectra of silica-core/shell structures with the shells being a uniform silver layer [(a) and (b)] or a closely packed silver nanoparticles layer [(c) and (d)], and their dependence on the silica core diameter (D) and shell thickness (ts) or diameter of the silver nanoparticles (d). Insets are 2D schematic illustrations of the corresponding structures.

main extinction peak appears in the near-infrared range, which is of one's interest in many applications. 2.2. Effects of Structure Dimensions and Shell Morphology. As a reference, we present in Figure 3, parts (a) and (b), the extinction spectra of ideal silica/silver core/shell nanostructures for various dimensions of the core diameter (D) and shell thickness (ts). Optical properties of such core/shell structures have been theoretically well studied, particularly for shells of metal Au.34-37 Generally, the main extinction peak of such an ideal core/shell structure is attributed to dipolar plasmon resonance in the complete shell; besides, there is a shoulder on the shorter wavelength side of the main peak due to quadruple plasmon resonances. It is also shown here that, for the fixed core diameter of 50 nm, the main extinction peak blueshifts with increase of the shell thickness; and for the fixed shell thickness of 5 nm, the main extinction peak redshifts with an increase of the core diameter. In both cases, there is a small peak at 330 nm that does not obviously shift, which is ascribed to plasmon resonance across the shell thickness. In a quasi-static limit, the position of the resonance peak is not sensitive to the shell thickness. Note that this peak is usually not observed for such core/shell nanostructures with a metal of Au, as it is above the interband transition energy. We then show, in Figure 3, parts (c) and (d), the extinction spectra of the closest-packed Ag NPs on silica nanospheres for various sizes of the Ag NPs and silica nanospheres. It is observed that, for this type of structure, the extinction is mainly affected by the nearest interparticle couplings and short-range collective plasmon resonances, instead of closed-loop collective plasmon resonances. For the fixed core diameter of 50 nm in Figure 3(c), the efficiency in the main extinction band (CM mode) increases prominently with an increase of the Ag NPs' size. It happens to be the same for single metal NPs,1 and is certainly to be reflected in the coupled mode. It is also shown that specific features of the CM-mode extinction band (e.g., exact position and relative efficiency values of the subpeaks) vary with change of the Ag NPs' size, and do so for other extinction peaks at longer wavelengths as well. It suggests that resonance positions of the

Figure 4. Extinction spectra of closest-packed silver nanoparticles of various sizes on silica nanospheres with their inner halves merged in a continuous surrounding silver layer of thickness t (solid lines). The dashed lines are for structures with uniform shell thickness (ts), same as those in Figure 3(a).

coupled modes are dependent on the size of the Ag NPs. In comparison, for fixed sizes of the Ag NPs (d = 5 nm) in Figure 3(d), the shapes and positions of the main extinction peaks have only small changes. The changes may be only due to different numbers of the Ag NPs on the silica nanospheres of different sizes. Here we should be aware that the concerned CM and CS modes exist only within the scope of quasi-planar nearest neighboring Ag NPs; for the case of closest-packed Ag NPs, what determines the spectrum is the sizes and statistic weights of various modes, instead of long-range plasmon couplings between the Ag NPs. For the structures in Figure 3, parts (c) and (d), there are actually no continuous metallic shells formed surrounding the silica cores. Now, suppose that the vacancies between the Ag NPs and the silica cores are filled with Ag due to a coalescing of metal NPs, as schematically shown in the inset of Figure 4, the structure can be considered as a continuously closed Ag shell of thickness t (= d/2) on the silica core with regular Ag protrudings. We may then use it to model the experimentally synthesized core/shell nanostructures with rough surface morphologies. Figure 4 shows the calculated extinction spectra of such core/shell structures with various t (or d), in which we also compare the two spectra 1477

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size. When we compare them with Figures 2 and 3, we can expect that, with such core/shell nanostructures composed of multilayer ultrafine metal NPs instead of continuous metal shells, the main extinction peak can be shifted into an even longer-wavelength near-infrared range.

Figure 5. Extinction spectra of multilayer silver nanoparticles closely packed on the silica nanospheres. Diameters of the shell silver nanoparticles are 3 nm in (a) and 5 nm in (b). Inset of (a) is a local magnification of the spectra. “#L” refers to number of layers.

for t = 3 and 5 nm with those of the ideal core/shell structures with ts = 3 and 5 nm. It is observed that the modeled roughness has little impact on the extinction spectra. They have similar spectrum profiles, close peak positions, and same regularities on shift of the peak positions with respect to variation of the shell thickness. Thus, only the continuous metal layer is effective for the closed-loop plasmon resonances. As usual, small nanoscale protrusions contribute to local modes, but they will not be dominant once a larger-scale mode is involved. 2.3. Multilayer Ag NPs on Silica Nanospheres. Considering that closely packed discrete metal NPs without coalescence may also be experimentally assembled on dielectric cores with novel techniques, e.g., using chemically or biologically surfacemodified metal NPs and dielectric nanospheres, we also calculated the optical extinction spectra of closely packed multilayer Ag NPs on silica nanospheres, shown in Figure 5. Keeping the core diameter fixed at D = 50 nm, diameters of the Ag NPs are varied, d = 3 nm in Figure 5(a) and 5 nm in Figure 5 (b). For spectra of both cases, the Qext value of the extinction band at around 330-400 nm almost proportionally increases with an increase of the stacking layers. It suggests that the coupled monomer (CM) mode is still effective in layered structures, that an increase of the Qext value is related to increased numbers of the Ag NPs. Particularly, for d = 3 nm in Figure 5(a), the extinction band for the CM mode appears to be more prominent for the increased number of layers. The major difference between the extinction spectra for multilayer Ag NPs in Figure 5, parts (a) and (b), is that the extinction for short-range collective plasmon resonances (e.g., at 510 and 620 nm) is dominant for d = 5 nm in Figure 5(b), whereas the extinction for long-range collective plasmon resonances is dominant for d = 3 nm in Figure 5(a). This suggests that the multilayer of larger NPs behave more like discrete particles in their optical extinction spectra; and that of finer NPs behave more like shells in their optical extinction spectra, as the occupancy ratio for NPs in the effective layer of shell is higher for finer NPs. It is interesting that characteristics of their extinction spectra are so sensitively dependent on the NP

3. CONCLUSIONS We studied the optical extinction properties of ultrafine Ag NPs (a few nanometers in diameter) assembled on silica nanospheres (tens of nanometers in diameter). Due to the particular arrangement of the Ag NPs on such spherical substrates, their extinction properties are shown to be different from those of aggregates with only a few Ag NPs and those that are assembled in planar arrays, although there are similarities and relevance. We proposed and interpreted the existence of the coupled monomer (CM) mode, coupled septamer (CS) mode, and closed-loop plasmon resonance mode, and their roles in optical interaction with the structures of various configurations. The work may be illuminate understanding of the evolution of optical extinction properties of dielectric/metal core/shell nanostructures during their initial stage of shell growth in experimental synthesis. Also, the conclusion on the effects of surface morphology can be a reference for experimental study on the modification of surface texture or symmetry breaking to tune the optical properties of core/shell nanoparticles.38-41 The work also suggests that multifarious three-dimensional assembly of noncoalesced metal nanoparticles offers a new measure to produce and control novel optical properties of metallic nanostructures. ’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ ACKNOWLEDGMENT This work has been financially supported by NSFC (No. 60707012), RFDP (No. 20070384022), and the NCET Program (No. 08-0469) of the People's Republic of China. We also acknowledge support from the China-Australia Joint Laboratory for Functional Nanomaterials at Xiamen University. ’ REFERENCES (1) Kreibig, U.; Vollmer, M. Optical Properties of Metal Clusters; Springer-Verlag: Berlin Heidelberg, 1995. (2) Storhoff, J. J.; Elghanian, R.; Mucic, R. C.; Mirkin, C. A.; Letsinger, R. L. J. Am. Chem. Soc. 1998, 120, 1959–1964. (3) Lal, S.; Grady, N. K.; Kundu, J.; Levin, C. S.; Lassiter, J. B.; Halas, N. J. Chem. Soc. Rev. 2008, 37, 898–911. (4) Kahl, M.; Voges, E.; Kostrewa, S.; Viets, C.; Hill, W. Sens. Actuators, B 1998, 51, 285–291. (5) Pugh, V. J.; Szmacinski, H.; Moore, W. E. Appl. Spectrosc. 2003, 57, 1592–1598. (6) Reiss, G.; H€utten, A. Nat. Mater. 2005, 4, 725–726. (7) Sarikaya, M.; Tamerler, C.; Jen, A. K. Y.; Schulten, K.; Baneyx, F. Nat. Mater. 2003, 2, 577–585. (8) Hamanaka, Y.; Fukuta, K.; Nakamura, A.; Liz-Marzan; Mulvaney, P. Appl. Phys. Lett. 2004, 84, 4938–4940. (9) Fuchs, R. Phys. Rev. B 1975, 11, 1732–1740. (10) Kelly, K. L.; Coronado, E.; Zhao, L. L.; Schatz, G. C. J. Phys. Chem. B 2002, 107, 668–677. (11) Cobley, C. M.; Skrabalak, S. E.; Campbell, D. J.; Xia, Y. Plasmonics 2009, 4, 171–179. 1478

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