Spectroscopy of Homo- and Heterodimers of Silver and Gold

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The Spectroscopy of Homo and Heterodimers of Silver and Gold Nanocubes as a Function of Separation: a DDA Simulation Nasrin Hooshmand, Daniel O'Neil, Abdullah M. Asiri, and Mostafa A. El-Sayed J. Phys. Chem. A, Just Accepted Manuscript • Publication Date (Web): 16 Jun 2014 Downloaded from http://pubs.acs.org on June 18, 2014

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The Journal of Physical Chemistry

The Spectroscopy of Homo and Heterodimers of Silver and Gold Nanocubes as a Function of Separation: a DDA Simulation Nasrin Hooshmand*, Daniel O’Neil*, Abdullah M. Asiri† and Mostafa El-Sayed*, ** *Laser Dyanmics Laboratory, School of Chemistry and Biochemistry, Georgia Institute of Technology, Atlanta, Georgia 30332-0400 E-mail: [email protected] ** Adjunct Professor, Department of Chemistry, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia

† Department of Chemistry, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia

Abstract: The plasmonic fields of silver and gold nanocubes are known to be among the strongest of any plasmonic metallic nanoparticles. Aggregation dominates their use in imaging and sensing applications due to the resulting enhancement of the plasmonic field in between the nanoparticles (hot spots). The first step in the aggregation process is dimerization. In the present work, we used the discrete dipole approximation (DDA) to calculate the interdimer separation dependence of the absorption and scattering components of the localized surface plasmon resonance (LSPR) extinction of homo and heterodimers of Ag and Au nanocubes when excited parallel to their interparticle axis. We also examined the changes in the nanocube surface plasmonic field distributions as the dimer separation was varied. The results from the homodimers were as expected: as the cubes were brought together, there was a red-shift in the primary plasmon band in accordance with the universal scaling law. Additionally, as the particles moved together, scattering contributed more to the overall extinction. By examining the E-field distributions, we found that the hot spot geometry changes abruptly at small separations. At very short distances, the hot spot is located in between the adjacent faces and away from the corners of these faces. At larger separations it moves towards the adjacent corners. We observed apparently anomalous behavior for the heterodimer. First, the E-field resulting from excitation of the Ag dominated plasmon resonance was significantly weaker than expected. Second, the red-shift of the gold dominated plasmon resonance did not follow the universal scaling law. The most likely explanation for these observations is that the silver plasmon mixes strongly with the energetically resonant, but nonplasmonic, gold interband transition to form a hybrid resonance that produces weaker overall field intensity on the two nanocubes at short separation.

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Keywords: plasmonic, nanoparticles, hybridization, computational

INTRODUCTION The field of plasmonic metal nanoparticles has been the subject of intense research recently for their interesting optical and photothermal properties arising from their localized surface plasmon resonance (LSPR). A plasmon is the collective oscillatory motion of electrons resulting from the coherent excitation of the “free” electrons in the conduction band. This leads to an in-phase strong electromagnetic oscillation.1-4 This LSPR is tunable and strongly dependent on the shape, size, composition, and relative dielectric function of the nanostructure.5-7 The oscillation of the electrons results in a strong enhancement in the optical absorption, scattering and near-field intensities of noble metal nanoparticles allowing for their use in numerous applications such as biological imaging, selective photothermal therapy, surface enhanced Raman scattering (SERS), optical wave guiding, and biochemical sensing.8 The effect of coupling between the surface plasmons of adjacent particles, such as in nanoparticle aggregates, is very important and has received a great deal of attention in recent years. Coupling typically results in a shift in the LSPR wavelength and a great enhancement of the plasmonic E-field.9,10 This is important in optical technologies in chemical and biological imaging,11,12 sensing,13-15 and therapeutics.16-19 This interparticle plasmon coupling forms the basis of the intense enhancement of spectroscopic signals (e.g., SERS) from molecules adsorbed at nanoparticle junctions, providing the capability for single-molecule sensing and detection.20,21 The overall strength of coupling depends on the polarization direction of the exciting field and the distance between nanoparticles. It has been observed that the LSPR shift due to coupling decreases exponentially with increasing interparticle distance.10,22 When normalized to particle size, the relationship holds for many nanoparticles with different sizes, shapes, metals, and media; this has been termed the universal scaling law.9,23

Silver and gold nanocubes with sharp corners are known to have very strong plasmonic fields concentrated at their corners. The study of the coupling between a pair of silver nanocubes and the effect of rounding the cube corners on their coupling strength has recently been carried out.24 In the present paper, we used the discrete dipole approximation (DDA) method to study the distance dependence of the plasmonic field coupling between homodimers (Ag-Ag or Au-Au)


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and heterodimers (Ag-Au) of nanocubes with sharp corners. We examined the dependence of the interaction with light on interparticle separation. We looked at the effect on the LSPR extinction wavelength and the relative importance of the contribution of the absorption and scattering to the total extinction peak intensity. Finally, we studied the field intensity distribution and the hot spot formation between adjacent nanoparticles at small interparticle separations. 2. METHOD OF CALCULATION There are several methods to simulate the optical properties of the metallic nanoparticles. DDA is one of the most powerful theoretical method for simulating extinction, absorption, and scattering spectra of plasmonic nanoparticles as well as plsmonic field distribution.25-27 The advantage of this method is that it includes multipolar and finite size effects which are quite important for particles of size close to the wavelength of light. Details of this method have been described before.25-31 Briefly, the nanoparticles are described as a cubic array of several thousand dipoles located on a cubic lattice. In our study we looked at cubes and pairs of cubes with a side length of 42 nm. Each dipole occupied 1 nm3 leading to 74088 dipoles for calculations with a single cube and 148176 dipoles for the dimers. The interparticle separation between the pairs was varied. The refractive index of gold or silver was assumed to be the same as that of the bulk metal.32 The refractive index of the surrounding medium was set to equal 1.33 (that of water) at all wavelengths. Plasmon resonance spectra were calculated for light propagated parallel to the interparticle axis. The plasmonic field intensification factor (in log scale of ‫ ׀‬E‫׀‬2/‫ ׀‬E0‫׀‬2) located on the surface of a pair of cubes and calculated with the DDA technique at different excitation wavelengths. For these calculations, we used the DDSCAT 6.1 code developed by Draine and Flatau.25 3. RESULTS Previous experimental studies have examined the effect of changing the interparticle distance and the incident polarization on the spectra of the dimers of gold and silver nanospheres.22,33 In the present work we compare the theoretical results of the plasmonic coupling between homoand heterodimers of silver and gold nanocubes with sharp corners on their extinction, absorption and scattering and plasmonic field intensity.

3.A. Gold-gold nanocube dimer



As two plasmonic nanoparticles are brought close together, hybridization occurs between the plasmon modes of the particles.22,34,35 These hybrid modes tend to be red-shifted but depending on the polarization of light, may be blue-shifted. Figure 1 shows the calculated extinction, absorption and scattering spectra for a pair of Au nanocubes with 42 nm edges in water as a function of the interparticle separation. Figure 1 shows that as the cubes are moved together, the extinction peak red shifts. It is clear from Figure 2b that these cubes follow the typical scaling law seen for other particles. The total extinction increases from 5 a.u. for a single particle (or a large separation) to 18 a.u. for 2 nm separation. The percentage of scattering increases from less than 1% for a single nanocube to 5% for 2 nm separation. Upon decreasing the separation, the extinction band maximum red-shifts from 585 nm to 641 nm. These results are expected. Larger particles tend to have a larger scattering-to-absorption ratio and a redder extinction peak than small particles. As the interparticle separation of the dimer is decreased, it behaves more like a single large particle than two small particles.

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Figure 1. Interparticle separation dependence of the DDA simulated extinction (black), absorption (red) and scattering (green) spectra resulting from excitation parallel to the interparticles axis for a pair of sharp-cornered Au nanocubes in water. The separation distance is indicated by d.


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Figure 2. (a) DDA simulation results of the dependence of the extinction spectra on the separation distance of a pair of Au nanocubes with 42 nm edges in water; (b) the dependence of the extinction band maximum shift (scaled by the wavelength of the plasmon band maximum of the monomer) as a function of the interparticle separation (weighted by the length of the nanoparticle.) This exponential dependence suggests that the extinction spectra of gold nanocube pairs follows the universal scaling law; (c) the exponential dependence of the intensity of the band maxima of the extinction peaks on the interparticle separation.

To better understand the hybridization process between the two approaching nanocubes, the Efield plasmonic enhancement was calculated for a single gold nanoparticle and dimers with various separations. For these calculations, a single wavelength at the peak of the plasmon band of interest was used to excite the particle or dimer. Figure 3 shows the E-field enhancement around a single gold nanocube (excited at 585 nm), a dimer with 2 nm of separation (641 nm excitation), and a dimer with 10 nm separation (613 nm excitation). The field around the single nanocube shows the characteristic pattern of field concentration at the corners. The 10 nm separated dimer shows a similar pattern with a slight strengthening of the field near the adjacent corners. When the separation is reduced to 2 nm the field strength moves away from the adjacent corners and to in between facing facets of the dimer.



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Figure 3. Relative E-field intensities, or the plasmonic enhancement ratio distribution ‫׀‬E‫׀‬2 /‫ ׀‬E0‫׀‬2 for (a) single Au cube (excited at 585 nm) and two pairs of Au-Au dimers with (b) 2 nm of separation (excited at 641 nm) and (c) 10 nm of separation (excited at 613 nm). At 10 nm, each cube in the dimer has an E-field distribution which looks similar to the isolated cube. However, at 2 nm, the strongest field is located at the center of the adjacent faces.

3.B Silver-silver dimer: DDA calculations were repeated for pairs of silver nanocubes. Figure 4 shows that the extinction spectrum of a widely separated pair is nearly identical to that of the monomer. They both have four bands: two strong bands at long wavelengths (probably dipolar) and two weak higher order bands at short wavelengths. As the separation decreases, all the bands shift to longer wavelengths, but the shorter wavelength bands seem to shift further than the longer wavelength bands. While a strong doublet is observed for 60 nm of separation, one band of the doublet becomes weaker but broader in the 20 nm separation spectrum. It is possible that the higher order bands become stronger and the higher energy dipolar band is submerged under the strong higher order band. Figure 4 shows the results of the decomposition of the extinction band into absorption and scattering. While the absorption is more intense than scattering for the single Ag cube (and for the pair at 200 nm), they become comparable in intensity at 60 nm separation and the scattering becomes stronger at shorter distances.


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Figure 5 shows that with increasing the interparticle gap separation, the magnitude of the redshift of the plasmon band decreases and the results indicate that the universal scaling law is valid for silver-silver nanocube dimers.

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Figure 4. Interparticle separation dependence of the DDA simulated extinction (black), absorption (red) and scattering (blue) spectra resulting from excitation parallel to the interparticle axis for a pair of sharp-cornered Ag nanocubes with 42 nm sides in water. The large increase in scattering as the particles are moved close together is responsible for the frequent use of aggregated Ag nanoparticles in SERS studies.



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Figure 5. Testing the universal scaling law for the silver nanocube dimers: (a) extinction spectra for 42 nm silver cube dimers at varying separations; (b) the fractional shift of the extinction band peak wavelength as a function of the interparticle separation (weighted by the size of the nanoparticle); (c) the exponential decrease of the intensity of the strongest extinction peak as the interparticle separation increases.

The E-fields of silver dimers and an isolated silver cube were calculated in a similar manner as was used for the gold particles. Due to the presence of multiple distinguishable plasmonic modes for a single silver particle, only the peak wavelength for the main resonance at 481 nm was excited. As seen in Figure 6, this produced an E-field distribution that is similar to the single gold nanocube. The hybridized dimer modes were examined as well yielding similar results as to those for the Au-Au nanocube dimer. At 10 nm of separation, the field strength is strongest at the corners. At 2 nm of separation, the strongest field moves to the center of the adjacent faces. In all cases, the fields are stronger than for the equivalent gold nanocube systems, as expected.


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Figure 6. Relative electric-field intensities, ‫׀‬E‫׀‬2 / ‫ ׀‬E0‫׀‬2 for (a) a single silver nanocube (excited at 481 nm) and Ag-Ag nanocube dimers each one has 42 nm edge lengths with (b) 2 nm inter-particle separation (excited at 553 nm) and (c) 10 nm interparticle separation (excited at 517 nm). Again at small separation, the hot spots are formed between the faces facing one another and away from their corners. As the cubes move away from one another, the corner’s focusing effect of the plasmon electrons takes over causing more enhancement of the field at the corners of the faces facing one another. 3.C.A Mixed modes in silver-gold heterodimers The results from the heterodimers yield more exciting conclusions. We expect that the plasmonic modes of gold and silver will mix to form hybrid modes. Naively, we might think that the two hybrid modes would be (ΨAu + ΨAg) and (ΨAu – ΨAg), where ΨAu and ΨAg are the dipolar modes for gold and silver respectively. However, since the energies of the uncoupled modes are so different (gold at 585 nm and silver at 481 nm) the hybrid modes will not have equal contributions from gold and silver. Additionally, as was discussed by Sheikholeslami et al. in their work on silver-gold nanosphere heterodimers33, because the interband transition of gold strongly overlaps energetically with the silver nanocube's natural LSPR resonance, the LSPR resonance of the Ag nanocube may strongly couple to it. As Figure 7 shows, at large separations there is no coupling between the silver and gold cubes. The spectrum is nearly identical to the summation of the spectra for a single gold cube and a single silver cube. As the Au cube gets closer to the Ag cube, mixing occurs between the wavefunctions of two particles. The band around 600 nm, which is predominantly gold-like in character (as discussed later), red-shifts with decreasing separation (although it does not follow the universal scaling law like the



homodimers). The higher energy bands of silver below 500 nm decrease in intensity as the cubes move closer to one another.


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Figure 7. DDA simulation of extinction spectra for sharp-cornered Ag-Au heterodimers each with 42 nm edges in water as a function of the interparticle separation when the incident radiation is polarized parallel to the interparticle axis. As the separation is reduced, the lower energy resonance (the gold type) increases in intensity. The high energy bands (the silver type) weaken in intensity as the plasmonic silver wavefunctions mix with the “dark” nonplasmonic gold interband transition. 3.C.B. E-Field visualizations reveal contributions in the mixed modes

E-fields were calculated at different excitation wavelengths to unravel the interplay between the gold and silver nanocube electronic systems. Although the hybrid bands contain both gold and silver components, most of the bands will be predominantly composed of either gold (at the low energy region in Figure 7) or silver (at the high energy region in Figure 7). It is expected that the band near 600 nm is mostly gold-like in character because the spectra in Figure 7 show it


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forming from the gold based resonance of the 200 nm separation spectrum. This is borne out in Figure 8, which shows the fields resulting from exciting a 2 nm separated dimer with 615 nm light and a 10 nm dimer with 597 nm light. With 10 nm of separation the field is located primarily upon the corners of the gold cube (on the right). At 2 nm of separation, the field strength increases on the silver cube due to increased mixing-in of silver’s dipolar wavefunction, however, it is still weaker than the field around the gold cube. This hybrid mode can be represented as Ψ = aΨAu + bΨAg where a > b. Just as with the homodimers, the E-field is strongest at the corners and between the adjacent faces.

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Figure 8. The calculated E-field enhancement for an Ag-Au heterodimer of nanocubes excited in the Au dominated spectral band. a) Exciting the cubes that are separated by 10 nm at 597 nm produces a field located almost entirely on the gold nanocube. b) When the particles are separated by only 2 nm and excited at 615 nm, the field is still strongest around the corners of the gold cube but is also present in between the adjacent faces and the corners of the silver nanocube. This suggests that although band around 600 nm is mostly gold-like in character, it still has a component of the silver plasmon mode.

Exciting at a shorter wavelength stimulates hybrid modes that have more silver character. Figure 9 shows the result of probing 2 nm and 10 nm dimers at 487 nm. In both cases we see essentially no field strength around the gold cubes’ corners. This supports the claim that this hybrid mode contains little gold dipole character. Interestingly, as the distance is reduced from 10 nm to 2 nm, the overall field strength is reduced contrary to what was seen with all other dimer pairs and excitation wavelengths. This is because silver’s dipole mode hybridizes with the



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gold interband transition. Exciting the interband transition produces an incoherent excitation and little net E-field and so a hybrid mode containing significant interband transition-character will produce a weaker overall E-field. We would also expect that there would be little to no E-field located on the gold nanocube, which is observed. We surmise that the wavefunction of this mode has the form Ψ = aΨAg + bΨAu + cΨIB, where ΨIB is the interband excited state wavefunction, with a > c and b ≈ 0. This wavefunction explains the absence of E-field around the gold nanoparticle.

Figure 10 shows a schematic overview of the proposed mixing scheme for gold and silver nanocubes. There are, of course, other modes present in the spectra. These high energy resonances are likely comprised mostly of silver’s higher order modes. a k ⊗

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Figure 9. The calculated E-field enhancement for an Ag-Au heterodimer of nanocubes. a) When the particles are separated by 2 nm and excited at 487 nm, the field is strongest around the corners of the silver cube. b) Separating the cubes by 10 nm and exciting at 487 nm yields a similar pattern. Most interestingly, reducing the separation weakens the field. Typically, increasing coupling, strengthens the field. In this instance, the silver plasmon mode mixes with gold’s interband transition. Since the interband transition is not plasmonic, this reduces the overall enhancement.


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Figure 10. An overview of the proposed coupling model for the gold and silver nanocubes. (a) The extinction spectrum of a silver and gold nanocube separated by 2 nm. At this distance, there is significant mixing of the plasmonic modes of the two particles to form hybrid resonances. The two strongest bands are labeled 1 and 2. (b) A schematic representation of which modes mix to form the two strongest hybrid modes. Due to the similarity in energy, gold’s interband transition wavefunction can mix with silver’s dipolar plasmonic wavefunction to produce the mixed wavefunction corresponding to the extinction band labeled 1.



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Conclusions Exciting homodimers of gold and silver nanocubes parallel to the interparticle axis gave results consistent with expectations. Decreasing the distance between the cubes strengthened the E-field around the particles and red-shifted the extinction in agreement with the universal scaling law and gave an exponential dependence of the dimer extinction intensity on their separation. At 2 nm of separation the strongest region of the plasmonic field moved away from the corners of the cubes to the center of the adjacent faces. Different behavior is observed for the heterodimer. As the gold and silver cubes moved closer together, their plasmon modes mixed to form hybrid modes. Gold’s dipolar mode weakly mixed with silver’s higher energy dipolar mode. As a result, this hybrid mode enhanced the E-field primarily around the gold nanocube. Due to their similar energies, silver’s dipolar mode mixed with the nonplasmonic interband transition of gold. Since the interband transition results from an incoherent excitation, it yields no E-field and this hybrid mode had a weaker enhancement than the unhybridized silver mode.

Acknowledgements: We acknowledge the support of the NSF (DMR-1206637).


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Spectroscopy of Homo- and Heterodimers of Silver and Gold

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