Letter pubs.acs.org/NanoLett
Systematic Study of Antibonding Modes in Gold Nanorod Dimers and Trimers Kyle D. Osberg,† Nadine Harris,‡ Tuncay Ozel,† Jessie C. Ku,† George C. Schatz,*,‡ and Chad A. Mirkin*,†,‡ †
Department of Materials Science and Engineering, ‡Department of Chemistry, and International Institute for Nanotechnology, Northwestern University, Evanston, Illinois 60208, United States S Supporting Information *
ABSTRACT: Using on-wire lithography to synthesize welldefined nanorod dimers and trimers, we report a systematic study of the plasmon coupling properties of such materials. By comparing the dimer/trimer structures to discrete nanorods of the same overall length, we demonstrate many similarities between antibonding coupled modes in the dimers/trimers and higherorder resonances in the discrete nanorods. These conclusions are validated with a combination of discrete dipole approximation and finite-difference time-domain calculations and lead to the observation of antibonding modes in symmetric structures by measuring their solution-dispersed extinction spectra. Finally, we probe the effects of asymmetry and gap size on the occurrence of these modes and demonstrate that the delocalized nature of the antibonding modes lead to longer-range coupling compared to the stronger bonding modes. KEYWORDS: On-wire lithography, nanoparticle arrays, plasmon coupling, nanorods, plasmonics
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the entire dimer (arrows in Figure 1A). In contrast, this symmetry constraint is lifted in asymmetric rod dimers because a net dipole is induced when the energy levels of the component resonances are separated. Interestingly, when the charge polarizations of these antibonding modes are compared to higher-order resonances in a longer discrete nanorod, important similarities are observed that can lead to a new understanding of their properties and how they can be excited (Figure 1B). For example, the dipole antibonding mode of a symmetric dimer has a very similar charge distribution to the quadrupole resonance (l = 2) of a discrete nanorod of the same overall dimensions (i). Similarly, the antibonding mode of a symmetric trimer and the dipole− quadrupole antibonding mode of an asymmetric dimer can be compared to an octupole resonance (l = 3) of a nanorod of the same total length (ii). Taken together with the fact that the antibonding mode is dark in symmetric structures, which is also true of quadrupole (and other even-order) modes at an angle of incidence normal to the structure,31 we hypothesize that these modes are equivalent and will have very similar properties. Herein, we use on-wire lithography (OWL)32−37 to rationally test this hypothesis by synthesizing 61 ± 6 nm diameter nanorod dimers and trimers (Figure 1C) and measuring their ensemble-averaged optical properties in solution to observe all of their resonance modes. Indeed, we observe these antibonding modes in each of the synthesized structures and
uch of the growth in plasmonics over the past several years can be directly tied to an increase in understanding of how noble metal nanostructures interact across short distances. From surface-enhanced spectroscopies1−5 to plasmonic metamaterials6−9 and Fano resonances,10−14 researchers have become increasingly interested in studying the mechanisms of plasmonic coupling between closely spaced metal nanoparticles for a wealth of important applications.15 In recent years, the study of so-called plasmonic molecules has emerged to help describe and predict how the plasmon resonances of one structure will interact with those in adjacent nanostructures by making a number of analogies to the way atomic orbitals interact to form molecular orbitals through chemical bonding.16−18 The plasmon hybridization model describes how the individual component resonances with given energies interact to form multiple higher and lower energy hybridized states that do not occur in either structure independently.18 When applied to gold nanorod dimers in an end-to-end orientation, the plasmon hybridization model predicts two coupled modes for every existing resonance in the nanorods: a lower energy bonding mode and a higher energy antibonding mode (Figure 1A for longitudinal dipole coupling).19,20 However, several groups have reported observing this antibonding mode, experimentally and theoretically, but only by breaking the symmetry in the dimers (i.e., making one rod longer than the other) or by rotating the angle between the nanorods or the position of the incident light in single-ensemble studies.21−30 While still present, this mode is thought to be dark in symmetric dimers because the component polarizations in each rod cancel each other out and do not induce a net dipole across © XXXX American Chemical Society
Received: August 20, 2014 Revised: November 3, 2014
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averaged data presented herein, the 10% variation in nanorod and gap sizes is averaged out to allow meaningful conclusions based on dimer/trimer geometry and symmetry. To first compare the antibonding mode in symmetric dimers to a quadrupole resonance in a longer discrete nanorod, we synthesized dimers comprising 196 ± 22 nm long nanorods with a 16 ± 3 nm gap and discrete nanorods with the same length as the dimers (406 ± 47 nm) and measured the solution-phase extinction spectra for both structures. Interestingly, for the dimers (blue trace in Figure 2A), three peaks are
Figure 1. (A) Scheme depicting bonding and antibonding states of dipole resonances in a symmetric nanorod dimer. (B) Scheme showing how antibonding modes in ensembles can be thought of as equivalent in terms of charge polarization to quadrupole (i) and octupole (ii) higher-order resonances of discrete nanorods of the same dimensions. Arrows indicate polarization directions. (C) Representative TEM images of symmetric dimers (i), asymmetric dimers (ii), and symmetric trimers (iii) used for this study. Scale bars are equal to 200 nm.
also demonstrate their similarities to higher-order resonances of discrete nanorods of the same overall length in terms of resonance wavelengths, charge polarizations, and electric field profiles. Finally, we study the effects of gap size and gap location to better understand these observations. While researchers have been interested in studying the occurrence of these bonding and antibonding modes in nanorod ensembles, very few synthetic methods are capable of producing the kinds of structures necessary to study these phenomena in a rational way. What is needed is a way to synthesize strongly coupled metal nanorod ensembles with precise control over the number of particles comprising the ensembles and the ability to independently tailor the size and spacing of each particle in order to enable asymmetry. Furthermore, ensemble-averaged studies that ensure the ability to excite all the resonances in the structure can only be achieved when these nanorod ensembles can be dispersed in solution, complicating the problem since most fabrication methods result in nanorod arrays on surfaces. In fact, to our knowledge, none of the previously used synthetic methods to produce these kinds of coupled plasmonic structures can meet all of these requirements, including electron beam lithography, 38−42 solution-phase assembly of discrete nanorods,20,43−46 and, most commonly used, random drying of nanorods from solution for single-particle studies of ensembles that land in the desired orientation.21−23,47,48 In previous publications,34,49,50 we illustrated how OWL overcomes the challenges presented by these other techniques to allow the investigation of the effect of varying gap and rod size on the ensemble-averaged optical properties of gold nanorods, while allowing independent control over the length, number, and placement of each nanorod in the array with sub-5 nm precision based on average gap and rod sizes with ∼10% standard deviation. Because of the nature of the ensemble-
Figure 2. Normalized (A) experimental and (B) DDA-calculated extinction spectra for the symmetric dimer (blue traces) and discrete nanorod (purple traces). Experimental spectra (A) are collected while the rods are dispersed in solution. (B) Orientationally averaged and fixed angle of incidence (normal) are shown as solid and dashed traces, respectively. (C) FDTD-calculated electric field profiles and charge distributions of resonances (i−iv) shown in panel B.
present: the transverse dipole resonance at ∼540 nm that is present in all of our spectra and two lower energy peaks at ∼970 and ∼1400 nm. Using the discrete dipole approximation (DDA), the longitudinal dipole resonance of a discrete 196 nm nanorod was determined to be at 1074 nm (not shown), indicating that the peaks present in the dimer spectrum are likely due to the presence of a higher energy antibonding mode and a lower energy bonding mode, respectively. For the discrete nanorod sample, we can see that, in addition to the transverse mode, there are also two peaks present (purple trace): the quadrupole resonance at ∼970 nm and the longitudinal dipole that is to the red of 1800 nm. Thus, the quadrupole resonance of the discrete nanorod occurs at the same wavelength as the antibonding mode of the dimer, suggesting similarities in their physical properties (Figure 1B). To support these experimental conclusions, we also completed a theoretical comparison of these structures using DDA (Figure 2B), where all of the peaks in both structures are observed in the ensemble-averaged calculations (solid spectra). Importantly, like the quadrupole resonance on the discrete nanorod (iv), the antibonding mode (ii) is not observed if these calculations are run with a fixed angle of incidence normal to the rods and a longitudinal polarization (dashed spectra). This angular B
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selection rule is well-known for quadrupole resonances31 and further supports our hypothesis about the equivalence of these modes. Furthermore, this selection rule also highlights the importance and uniqueness of using OWL to study these structures with ensemble-averaged measurements and helps to explain the difficulty in observing this mode in symmetric structures using surface-based techniques that were employed in the previous studies. As a final comparison based on charge polarization and generated electric field, we also mapped the field intensities around the structures at each resonance using finite-difference time domain (FDTD) simulations (Figure 2C). It is important to note that these field maps were calculated for structures rotated 45° relative to the incident light in order to ensure that all resonances were excited (as has been demonstrated for higher-order modes in single nanorods29). As expected for the dimer, the bonding mode (i) has a strong, localized field in the gap between the nanorods due to the more favorable distribution of charge, whereas the antibonding mode (ii) shows only a small field in the gap due to the symmetrical induced charges on each side of the gap, which creates more delocalized behavior. For the discrete nanorod, the longitudinal dipole (iii) and quadrupole (iv) are confirmed and appear as expected. Importantly, the antibonding mode (ii) and quadrupole (iv) have nearly identical field profiles and charge distributions, helping to explain their other similarities in energy and angle-dependence. In the previous experiments, the dimer was synthesized with a fixed gap size (16 nm), and the resulting antibonding resonance was present at the same wavelength as the quadrupole resonance of the discrete nanorod of the same total length. Using DDA and FDTD simulations, we calculated the extinction spectra and field profiles for nanorod dimers with varying gap size and rod length but constant total length (406 nm, Figure 3a). On the basis of the previous result indicating its similarity to the quadrupole resonance, we hypothesized that the antibonding mode would be independent of gap size. Indeed, we see that the antibonding mode is mostly independent of gap size and does not shift between gap sizes of 4 and 32 nm (Figure 3A). While the bonding mode blueshifts and dampens with increasing gap size, we only see small shifts in the antibonding mode for gap sizes greater than 32 nm. Surprisingly, the antibonding mode has only slightly blueshifted and has not dampened significantly all the way up to a gap size of 72 nm, which is in contrast to the stronger bonding mode that is highly dependent on gap size. This further confirms our comparison to the quadrupole resonance and also indicates the longer range coupled state of the more delocalized antibonding mode. These conclusions are also supported by the FDTD field maps at the antibonding resonance for each structure (Figure 3B). For gap sizes smaller than 32 nm, the overall field profile looks unaffected by increasing gap size; however, for gap sizes larger than 32 nm, the antibonding coupling begins to be affected, leading to the shift in resonance wavelength with no decrease in intensity. Having demonstrated these concepts for quadrupole resonances, we next turned our focus to determining whether these same rules would apply for octupole resonances (Figure 1B (ii)). Similar to the previous example, one way this can be done is by coupling dipole resonances from three rods in a trimer and then comparing the resulting modes to those of a discrete nanorod of the same total length. Like in molecular orbital theory where every new atomic orbital adds another
Figure 3. (A) DDA-calculated, orientationally averaged extinction spectra for symmetric gold nanorod dimers with a fixed total length (406 nm) and varying gap size/rod length (gap sizes ranging from 4 to 72 nm). (B) FDTD-calculated electric field profile maps for all nine spectra. The number at the top left of each image indicates the gap size of the dimer.
molecular orbital, by doing this, three coupled resonance modes are observed experimentally for a trimer with 141 ± 19 nm long nanorods spaced by 12 ± 3 nm gaps (Figure 4A): bonding, antibonding, and nonbonding modes, where the highest energy antibonding mode is the one expected to be comparable to the octupole resonance. Note that this extinction plot is shown differently from the previous ones (energy as a function of extinction) in order to better illustrate the energetics of these bonding phenomena. The black lines are drawn at the DDA-calculated resonance energy values for the component and coupled modes, illustrating a very close match with theory and helping to visualize the effect of coupling the resonances. Again using FDTD to map the field profiles, we can observe the differences in each mode (Figure 4B), where the bonding mode has bonding character between all three rods, the antibonding mode has all antibonding character, and the nonbonding state has adopted a dipole−quadrupole−dipole bonding mode to create a single unfavorable region (“node”) in the center of the ensemble. Interestingly, this is also the arrangement of nodes expected from molecular orbital theory, where the nonbonding mode has a single node in the center and the antibonding mode has one at each of the two gaps. To test our hypothesis about the similarity of the antibonding mode to an octupole resonance, we used FDTD to also simulate the extinction of a discrete nanorod of the same total length as the trimer (444 nm, blue trace in Figure 4C) and found that the octupole does in fact occur at the same wavelength as this antibonding mode (∼720 nm, dashed line in C
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Figure 4. (A) Experimental extinction spectrum of the trimer (red trace) comprising 141 ± 19 nm long nanorods spaced by 12 ± 3 nm gaps plotted as incident light energy as a function of extinction. Black lines indicate the DDA-calculated location of the component and coupled resonance modes. (B) FDTD-calculated electric field profile and charge distribution at each coupled resonance i−iii in panel A. (C) Orientationally averaged (solid) and fixed angle of incidence (dashed) DDA-calculated extinction spectra for the trimer (red trace) and a discrete nanorod of the same total length (444 nm, blue trace). (D) FDTD-calculated electric field profiles for both structures in panel C at ∼720 nm (dashed gray line in C), illustrating the similarity in field distribution and intensity for the two modes. (E−H) The same arrangement and descriptions for panels A−D but for an asymmetric dimer comprising nanorods with lengths of 129 ± 15 and 252 ± 24 nm and a gap size of 8 ± 2 nm. The discrete nanorod was modeled with a length of 388 nm.
Figure 4C). Unlike the quadrupole examples, both modes are also excited when the incident light is fixed normal to the rods and is polarized along the long axis, which is expected for an odd order mode like an octupole.31 As with the dimer, this comparison to the octupole also holds for the charge polarization and field distributions (Figure 4D), which appear nearly identical. As discussed previously, another way to achieve octupole modes in these coupled structures is through an asymmetric dimer where an antibonding mode between a dipole resonance on a shorter rod and a quadrupole resonance on a longer one can be created (Figure 1B (ii)). To test this hypothesis, we synthesized such a dimer with nanorod lengths of 129 ± 15 and 252 ± 24 nm and a gap size of 8 ± 2 nm, where the position of the gap ensures ideal placement for an octupole (one-third of the length of the ensemble). In this case, we again observe three modes (dipole−dipole bonding and quadrupole−dipole bonding and antibonding, Figure 4E,F), where the highest energy antibonding (i) mode is comparable to the octupole resonance. Completing the same calculations as before for a discrete
nanorod of the same total length (389 nm), we again confirm all of the same similarities as the trimer (Figure 4G,H), which strongly supports our hypothesis that each of these modes is equivalent. We did not observe the dipole−dipole antibonding mode in the asymmetric structure (experimentally or theoretically), suggesting that this mode may not occur in these structures with significant asymmetry. This is consistent with the molecular orbital picture in which only states with small energy gaps are able to couple strongly. Indeed, experiment and theory both indicate a transition from the existence of a dipole−dipole antibonding mode to a quadrupole−dipole coupled mode with increasing asymmetry (Supporting Information Figure S1). In conclusion, this work shows how rationally designed, solution-dispersible striped nanowires can be used to probe the similarities between antibonding modes in gold nanorod dimers and trimers to higher order resonances in discrete nanorods of the same total length. The structural control and solutiondispersibility of OWL enabled the systematic study of antibonding modes, which can only be observed when certain D
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geometry and polarization requirements are met, and positions OWL as an extremely powerful technique in the rapidly growing field of plasmonics.
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ASSOCIATED CONTENT
S Supporting Information *
Experimental methods, characteristic TEM images, and additional extinction spectra. This material is available free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Authors
*E-mail:
[email protected]. *E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This material is based upon work supported by the following awards: AFOSR FA9550-09-1-0294; AOARD FA2386-13-14124; and NSF’s MRSEC program (DMR-1121262) at the Materials Research Center of Northwestern University. K.D.O. acknowledges Northwestern University for a Ryan Fellowship and the National Science Foundation for a Graduate Research Fellowship. T.O. acknowledges 3M for a science and technology fellowship, ECS for a summer fellowship, and SPIE for an optics and photonics education scholarship. J.C.K. acknowledges the Department of Defense (DoD) through the National Defense Science and Engineering Graduate Fellowship (NDSEG) Program. Electron microscopy was performed in the EPIC facility of the NUANCE center at Northwestern University.
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