Organization of Metal Nanoparticles for Surface-Enhanced

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Organization of Metal Nanoparticles for Surface Enhanced Spectroscopy: A Difference in Size Matters Reshmi Thomas, and R.S. Swathi J. Phys. Chem. C, Just Accepted Manuscript • Publication Date (Web): 17 Sep 2012 Downloaded from http://pubs.acs.org on September 23, 2012

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The Journal of Physical Chemistry

Organization of Metal Nanoparticles for Surface Enhanced Spectroscopy: A Difference in Size Matters Reshmi Thomas, and R. S. Swathi∗ School of Chemistry, Indian Institute of Science Education and Research-Thiruvananthapuram, Kerala, India - 695016 E-mail: [email protected]

∗ To

whom correspondence should be addressed

1 ACS Paragon Plus Environment


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Abstract We consider the organization of spherical gold nanoparticles from monomers to dimers to trimers and use the finite difference time domain (FDTD) method to explore their utility as substrates in surface enhanced spectroscopy (SES). We investigate homodimers with 20 nm diameter (d) particles as the monomers, and symmetric trimers with a special geometry wherein a d = 40 nm particle is introduced between the two monomeric particles of the homodimer. The optical extinction spectra and the electric field profiles of these assemblies for various separations between the metal particles (s = 3, 6, 9, 12, 15 and 40 nm) are compared with those of the monomers to determine the extent of plasmon coupling. The estimated surface enhanced Raman scattering (SERS) enhancement factors for a typical probe in the vicinity of these nanostructures suggest that the symmetric trimers have two types of hot spots, with the hottest spot giving rise to an enhancement as high as ∼ 1.0 × 107 for s = 3 nm. The symmetric trimers support large electric fields in the vicinity with an interesting gradation within a single trimer and are found to be more efficient than homotrimers. Organized arrays of nanoparticles fabricated from such nanostructures could be interesting substrates for SES experiments than those of uniform size.

Keywords: Localized surface plasmon resonance, plasmon hybridization, surface enhanced spectroscopy, surface enhanced Raman scattering, hot spot, enhancement factor, FDTD method.

Introduction The interaction of metal nanostructures with electromagnetic radiation is very interesting and has been found to give rise to a variety of applications in surface enhanced spectroscopy (SES), 1,2 second harmonic generation, 3 sensors, 4 catalysis, 5 solar cells 6 and photothermal therapy. 7 The origin of these optical effects could be traced to the presence of collective electronic excitations, known as localized surface plasmon resonances (LSPRs) in metal nanostructures. The LSPR excitations in a variety of shapes of metal particles like spheres, 8 rods, 9 triangles, 10 bipyramids, 11 rice, 12 cubes 13 and several others 14 have been studied in the past. Nanomaterials made of metals 2 ACS Paragon Plus Environment

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like Au, 15 Ag, 16 Cu, 17 Pt 18 and Pd 19 are being investigated for various applications in the area of plasmonics. Attempts have been made in the last decade or so to assemble metallic particles of various shapes and obtain well organized nanostructures. When the metal nanoparticles are brought in proximity, the LSPRs on individual particles couple 20 to form new optical modes in these organized structures just as atomic orbitals combine to form molecular orbitals in molecular orbital theory. This is known as plasmon hybridization 21 and is a novel approach that has been used extensively to study optical excitations in nanostructures. Plasmon coupling in organized nanostructured assemblies has been found to give rise to more profound effects than were found in isolated particles. For instance, in surface enhanced Raman scattering (SERS), the enhancement factors (EFs) in Raman signals from molecules in the vicinity of dimers, 22 trimers and oligomers 23 of metal particles are found to be much higher than those at the corresponding monomers. The excitation of LSPRs in these assemblies 24 enhances the incident and the scattered electromagnetic fields in the vicinity, resulting in the enhancement of Raman signals of probes in SERS. In the process of designing organized nanostructured assemblies that could provide enhanced optical signals from probes in SES, attaining a precise control on the gap size between the monomers is a challenging task. However, there have been attempts in the literature to precisely control the nanogap size experimentally and study the enhancement in optical signals of probes as a function of the gap size. 25,26 On the theoretical side, computational techniques such as the finite difference time domain (FDTD) method, 2,27,28 finite element method, 29 discrete dipole approximation 30 and boundary element method 31 have played a significant role in the design of geometries that could be potential substrates in SES experiments. The central theme of theoretical investigations on metal nanostructures is to propose nanoarchitectures that can support strong LSPR excitations with intense electric fields in vicinity so that the spectroscopy of probes at these architectures can be of use in a variety of applications. Nanoassemblies consisting of particles of uniform size are well studied in the literature. 32,33 However, the possibility of a variation in the particle size in a given assembly 34,35 has not received much attention. Synthetic procedures for assembling nanoparticles of various sizes, particularly using DNA



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have recently been reported. 36–38 With the availability of such procedures, study of the optical features of asymmetric nanoparticle oligomers have gained a lot of prominence and have been investigated. 35,39–41 Toroghi and Kik have studied the electric field profiles in small asymmetric silver nanoparticle dimers. 40,41 The plasmonic properties of triangular and L-shaped nanoparticle trimers have been investigated in the last couple of years. 23,42–45 Linear trimers, with a geometry in which there is a gradual decrease in the particle size along the chain have been found to be useful as nanolens for focussing the optical energies to very localized regions. 46,47 There have also been interesting reports of electric field profiles at certain higher order organized assemblies of metal nanoparticles. 47–49 Novel designs of such assemblies consisting of non-uniform particle sizes with a subsequent computational study of the gap size dependence of the plasmon coupling and the electric field profiles can lead to optimal geometries to be used in experiments. 39 Driven by this idea, we consider organizations of spherical gold nanoparticles from monomers to dimers to trimers (see Figure 1) and perform FDTD simulations 50,51 to study the interaction of electromagnetic radiation with these nanostructures. Homodimers with nanoparticles (NPs) of 20 nm diameter (d = 20 nm) as the monomers are first studied. Subsequently, incorporation of a third particle of bigger size (d = 40 nm) in between the two d = 20 nm NPs at equal distances from either NP leads to a special geometry, which we refer to as symmetric trimers. The optical features in homodimers and symmetric trimers are studied for various surface-to-surface separations between the NPs, s = 3, 6, 9, 12, 15 and 40 nm. The simulations are also performed on a homotrimer with d = 20 nm NPs as the monomers, and with a gap size of s = 3 nm, which serves as a model system. Our calculations predict that the geometry of symmetric trimers is a potential system for SES experiments as it gives rise to an interesting gradation of the electric field within a single trimer with strong localization of the fields at the smaller NPs. We first study the optical excitations in gold nanoparticle monomers, dimers and trimers. The electric field intensity distribution patterns around these nanostructures are calculated at two different wavelengths, the extinction maximum (λmax ) corresponding to each structure and 633 nm, the typical laser excitation wavelength that is used in experiments. The SERS EFs for a typical probe


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s d

s

s

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Figure 1: A schematic representation showing the organization of metal nanoparticles from monomers to dimers to trimers, and subsequently to arrays. molecule that could be present in the vicinity of these nanostructures are estimated. A comparative study of the electric field profiles in monomers, dimers and trimers has been found to have important implications in the design of organized arrays of metal nanoparticles, which serve as novel substrates in SES.

Computation Details We use the FDTD method to solve the Maxwell’s equations numerically using discrete grids in both space and time domains. The method makes use of the Yee’s algorithm, in which the derivatives involving space and time variables are replaced by the corresponding finite differences. Evaluations of the electric and the magnetic fields are performed on grids that are interspersed in both space and time intervals. The simulations are performed using the program FDTD Solutions (version 7.5.1), a product of Lumerical Solutions, Inc. Vancouver, Canada. We use the Johnson and Christy dielectric data for modeling the frequency dependence of the dielectric constant of Au. Water, with 5 ACS Paragon Plus Environment


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a refractive index of 1.33 is chosen as the background medium. A total field-scattered field (TFSF) source of light, consisting of plane waves in the wavelength range 400-800 nm is used as the incident beam for the simulations. We use a set of power monitors to calculate the net power flow in certain chosen locations of the simulation region and estimate the absorption and the scattering cross-sections. The extinction cross-section is then evaluated as the sum total of the absorption and the scattering cross-sections. We use perfectly matched layer (PML) and symmetric as well as anti-symmetric boundary conditions wherever the symmetry allowed their use to save the computational time. We use a mesh size of 0.35 nm for all the simulations, after prior convergence testing of the numerical data.

Results and Discussion The optical extinction of the monomeric d = 20 nm and d = 40 nm Au NPs shows that their λmax occur at 527 nm and 535 nm respectively. The simulated extinction spectra and the relative contributions of the absorption and the scattering to the extinction are shown in Figure S1 of Supporting Information. The electric field intensity (I) distribution patterns in the vicinity of the d = 20 nm NP at its λmax as well as at 633 nm are shown in Figure 6 (see Figure S2 of Supporting Information for the field data for d = 40 nm NP). The amplitude of the incident field was chosen to be 1.0 V /m and hence the field intensities actually represent the relative intensities. Note that the incident electromagnetic radiation was polarized along the X-axis. The scale bars in the contours have been kept uniform to the value 20 for a better comparison across the images. However, the actual values of I could be seen from the plots of I vs X that are shown along with the contours. From the data, it is clear that the values of I are large at the λmax in comparison with those at 633 nm for both the particles. However, even at a wavelength of 633 nm, the value of I is at least 10 times the incident I, suggesting that it is possible to observe enhanced optical signals from molecules in the vicinity of these particles by using a laser excitation beam at 633 nm. The intensities and the optical cross-sections are higher for particles of larger size 52 due to the higher


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strengths of the dipolar resonances that are created in the larger NPs (see Figure S1 of Supporting Information). The SERS EF depends on the electric field intensities at the incident as well as the scattered wavelengths. EF ∝ |E(ωinc )|2 |E(ωsca )|2 ' |E(ωinc )|4 when the Raman frequencies are small. This fourth power dependence of the SERS EFs on the incident electric field (E) is well known and has been extensively used by various groups for modeling. 22,29,53 The SERS EFs for a typical probe molecule in the vicinity of the monomeric Au NPs are evaluated using EF ' |E(ωinc )|4 , with λmax as well as 633 nm as the excitation frequencies and by choosing the peak values of I from the calculated field profiles. The values of SERS EF thus obtained for the monomeric Au NPs are tabulated in Table S1 of Supporting Information. In the optical extinction of dimeric Au NPs (with d = 20 nm NPs as the monomers), the response of the electrons to the longitudinal (k) and the transverse (⊥) polarizations of the incident light is different and hence the calculations are performed separately for both the polarizations. The extinction spectra for the dimers as a function of the gap size (s = 3 − 40 nm) for both the polarization states (k and ⊥) of the incident light are presented in Figure 2. We have also included the monomer spectra for comparison. Note that for the monomers, k and ⊥ directions are the same. The values of λmax for various “s” for the k polarization are tabulated in Table 1, while those for the ⊥ polarization are presented in Table S2 of Supporting Information.

A significant red

Table 1: SERS EFs evaluated at λmax and at 633 nm for a typical probe in the vicinity of Au NP dimers for various gap sizes for the k polarization of the incident light. s (nm) λmax (nm) 3 554 6 544 9 539 12 536 15 535 40 530

I(λmax ) 825.3 163.9 80.1 52.6 41.1 26.4

I(633 nm) 203.0 58.9 35.4 26.7 21.5 15.9

EF(λmax ) 6.8 × 105 2.7 × 104 6.4 × 103 2.8 × 103 1.7 × 103 6.9 × 102

EF(633 nm) 4.1 × 104 3.5 × 103 1.3 × 103 7.1 × 102 4.6 × 102 2.5 × 102

shift of λmax for the k polarization and a slight blue shift for the ⊥ polarization with respect to the monomeric band with decreasing “s” can be clearly seen. The shifts arise due to plasmon coupling between the monomeric particles of the dimeric nanostructures, in which the LSPRs on individual


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Figure 3: The relative contributions of the absorption and the scattering to the extinction spectra of homodimer, homotrimer and symmetric trimer for a gap size of s = 3 nm for the k polarization of the incident light. particles couple to give rise to bonding as well as anti-bonding LSPRs in dimers (see Figure S3 of Supporting Information). However, in homodimers, the anti-bonding mode is optically inactive for the k polarization while the bonding mode is inactive for the ⊥ polarization due to a net cancellation of charges for these modes. The excitation of the bonding mode for the k polarization gives rise to a red shift while that of the anti-bonding mode for the ⊥ polarization gives rise to a blue shift. The extents of red and blue shifts depend on the extent of plasmon coupling. The shifts are minimal for the ⊥ polarization as a result of weak plasmon coupling. For the largest value of “s” with s = 40 nm, we almost recover the monomer peak for both the k and the ⊥ polarizations, meaning that the plasmon coupling between the particles is negligible at this separation and beyond. Optical extinction of nanoparticle dimers as a function of the gap size has been studied in the past 54,55 and the trends that we find in the extinction data as a result of plasmon coupling are in agreement with the earlier reports. 56 The λmax values for the dimers when the incident light has k polarization obey the universal plasmon ruler equation proposed by El-Sayed and co-workers. 57 The ratio of the shift in the λmax for the dimers (∆λ ) with respect to the monomer peak, λ0 to that of λ0 follows an exponential dependence on the ratio of the gap size to the particle diameter



(s/d) given by

∆λ λ0

= A e−

s/d τ

+ C, where τ is the decay constant and A and C are some constants.

The simulated extinction data and the corresponding fit to the exponential dependence are shown in Figure S4 of Supporting Information. The values of τ and A are found to be 0.22 and 0.08 respectively, in agreement with the previous reports. 57 The relative contributions of the absorption and the scattering to the total extinction of the homodimers are shown in Figure 3 for the dimer with a gap size of s = 3 nm for the k polarization. The electric field intensity profiles for the dimers for various “s” at their λmax are shown in Figure 4 for the k polarization of the incident light (see Figure 5 for the intensity profiles at 633 nm).

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Figure 4: The electric field intensity distribution profiles in the vicinity of the Au NP dimers and symmetric trimers at their λmax as a function of the gap size for the k polarization of the incident light. (Note: In the plots of I vs X, the scales on the I axis for s = 3 nm are different from those for other values of “s”.) and they decrease with increase in “s” (see Table 1). The regions of enhanced electromagnetic 10 ACS Paragon Plus Environment

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Figure 5: The electric field intensity profiles in the vicinity of the Au NP dimers and symmetric trimers at 633 nm as a function of the gap size for the k polarization of the incident light. (Note: In the plots of I vs X, the scales on the I axis for s = 3 nm are different from those for other values of “s”.)



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Figure 6: The electric field intensity profiles in the vicinity of the Au NP dimers with s = 40 nm for the k as well as the ⊥ polarization of the incident light at their λmax and at 633 nm. The field profiles for the monomeric d = 20 nm Au NPs are also shown.


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fields at the junctions are known as hot spots and could be seen clearly from the field contours. As earlier, the scale bars are kept uniform, at a value of 50 for comparison across various values of “s”. The intensity profiles at λmax as well as at 633 nm for the ⊥ polarization of the incident light can be seen in Figure S5 and Figure S6 of Supporting Information respectively. Note that the intensity profiles for s = 40 nm for both the polarizations are shown separately in Figure 6. It is interesting to note that the intensity values for the dimers with s = 40 nm for both the polarizations (see Table 1 and Table S2) are found to be similar to the corresponding monomeric (d = 20 nm NP) intensities (see Table S1 of Supporting Information), a clear indication for the negligible plasmon coupling. When the monomeric particles of the dimer are separated by large distances, they behave as two isolated monomers rather than as a single dimer and hence both the polarization states of the incident light are the same giving rise to similar extinction maxima and field intensities as that of the monomers. In spite of a number of studies on optical extinction of Au and Ag NP dimers, 54 there are only few investigations in the literature dealing with electric field profiles in the vicinity of the metal dimers. 30 Very recently, Li et al. reported a systematic study of the gap size dependence in Ag NP dimers. 58 However, despite a few reports of the field profiles near Au NP dimers, 22 a systematic investigation on the gap size dependence has not been undertaken. It is interesting to think of defining a gap size for a dimeric system upto which plasmon coupling exists and becomes negligible beyond. We believe that our simulation studies are an important step in this direction and can provide valuable information on the design of universal plasmonic platforms for SES. We then estimate the SERS EFs for the dimers at the hot spots at both the wavelengths for both the polarizations. The values for the k polarization are tabulated in Table 1 (see Table S2 of Supporting Information for the SERS EF values for the ⊥ polarization). The longitudinal plasmon coupling being much stronger in comparison with that of the transverse coupling, the EFs for the k polarization are much larger than those for the ⊥ polarization. Variation in the EF values with gap size is rather strong for the k polarization, while it is minimal for the ⊥ polarization. We now consider the effect of incorporating an additional NP (i) of the same size (d = 20 nm) and (ii) of larger size (d = 40 nm) in between the two monomeric NPs of the homodimer and refer



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Figure 7: A schematic of the plasmon coupling in asymmetric dimers and symmetric trimers of metallic nanoparticles for the k polarization of the incident light. to them as the homotrimer and the symmetric trimer respectively. The optical features of the two above mentioned geometries of trimers are investigated for a gap size of s = 3 nm. The extinction spectra of the homotrimer and the symmetric trimer shown in Figure 2 for the k as well as the ⊥ polarizations of the incident light show that the extinction cross-sections for the symmetric trimer are significantly higher than those for the homotrimer. The optical modes in trimeric nanoparticles can be described using the plasmon hybridization model. Figure S3 of Supporting Information shows the formation of the plasmonic modes of the homotrimer for the k polarization of the incident light. The hybrid modes of the homodimer combine with the monomeric plasmon mode to give rise to four new hybrid modes for the homotrimer. It can be clearly seen from the charge oscillations that two of these modes (second and third in the figure) are equal in energy and therefore the homotrimer has three unique plasmonic modes, all of which are optically active. Similarly, the optical modes of the symmetric trimers can be thought of as being formed when the hybrid modes of the asymmetric dimer combine with the monomeric plasmon mode (see Figure 7). As earlier,


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two of these hybrid modes are degenerate and therefore there are three unique plasmonic modes for the symmetric trimers. However, the simulated extinction spectra for the trimers show only one predominant band, corresponding to the lowest energy plasmonic mode. The other two hybrid modes cannot be found for this gap size of s = 3 nm due to the fact that they possess lower net dipole moments than the lowest energy mode and hence would have low extinction cross-sections. Simulations performed on the symmetric trimer for a gap size of s = 1 nm showed the presence of multiple peaks, arising either due to the higher energy dipolar modes or the multipolar modes (see Figure S7 of Supporting Information). However, at such small gap sizes, quantum effects become important and hence results obtained from classical methods like FDTD have to be interpreted with caution. The relative contributions of the absorption and the scattering to the total extinction of the trimers for a gap size of s = 3 nm are shown in Figure 3 for the k polarization. The calculated electric field intensity profiles for both the structures for the k polarization of the incident light are shown in Figure 8 (see Figure S8 of Supporting Information for the field profiles for the ⊥ polarization). The field intensities for the symmetric trimers are more than twice the values found

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the homotrimers. Thus, we choose the symmetric trimers for the studies on optical excitations and electric field profiles as a function of the gap size. In Figure 2, we show the calculated extinction spectra for the symmetric trimers as a function of the gap size, for the k as well as the ⊥ polarizations of the incident light. In the figure, we have also included the extinction spectra of the d = 40 nm monomeric Au NPs for comparison. For large values of “s”, the plasmon coupling between the monomers in the trimers becomes very weak and hence the resultant extinction spectra will be the sum total of the contributions from the monomeric spectra. Among the d = 20 nm and d = 40 nm NPs, the extinction cross-section for the d = 40 nm NP is much larger in comparison with that of the d = 20 nm NP (see Figure S1 of Supporting Information) and hence the extinction spectra of the symmetric trimers for large “s” will be dominated by the contribution from the d = 40 nm NP. The values of λmax for the symmetric trimers for various “s” for the k polarization are tabulated in Table 2. The corresponding values for Table 2: SERS EFs evaluated at λmax and at 633 nm for a typical probe in the vicinity of Au NP symmetric trimers for various gap sizes for the k polarization of the incident light. Note that the intensities and the EFs are evaluated at two different locations of the symmetric trimers, namely the hottest spots and the hot spots (see Figure 9). ‘*’ refers to the intensities and the EFs evaluated at the hottest spots. s (nm) λmax (nm) 3 573 6 557 9 550 12 547 15 544 40 538

I ∗ (λmax ) 3342.4 604.6 260.5 159.1 114.6 37.9

I ∗ (633 nm) 593.4 149.5 80.0 54.3 43.9 19.8

EF ∗ (λmax ) 1.1 × 107 3.7 × 105 6.8 × 104 2.5 × 104 1.3 × 104 1.4 × 103

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I(λmax ) 2890.5 407.7 156.6 89.0 65.5 38.3

I(633 nm) 509.7 106.5 54.1 35.6 28.9 19.6

EF(λmax ) 8.4 × 106 1.7 × 105 2.5 × 104 7.9 × 103 4.3 × 103 1.5 × 103

EF(633 nm) 2.6 × 105 1.1 × 104 2.9 × 103 1.3 × 103 8.4 × 102 3.8 × 102

the ⊥ polarization can be found in Table S3 of Supporting Information. As earlier, it can be seen that the longitudinal plasmon coupling is much stronger than the transverse plasmon coupling. 16 ACS Paragon Plus Environment

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The electric field intensity profiles for the symmetric trimers as a function of “s” at their λmax are shown in Figure 4 for the k polarization of the incident light (see Figure 5 for the field profiles at 633 nm). Interestingly, from the I vs X graphs of Figure 4, it can be seen that the symmetric trimers support two types of hot spots, near the surfaces of the larger NPs (d = 40 nm) and the surfaces of the smaller NPs (d = 20 nm) at both the junctions. The intensities on the surfaces of the smaller NPs are higher than those on the surfaces of the larger NPs at the two junctions for the k polarization, which we refer to as the hottest spots and the hot spots respectively (see Figure 9). The localization of intense electric fields near smaller particles at the NP junctions

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Figure 9: A schematic representation showing the plasmonic excitations in monomers, dimers and symmetric trimers for various polarization states of the incident light. The green arrows represent the polarization state. The regions of intense electric fields, hot spots and hottest spots are marked in the figure. with an asymmetry in particle size 40,41 occurs because the larger NPs act as antenna to funnel the optical energy towards the smaller NPs. 47–49 In their investigations on nanoantenna made of trimeric plasmonic particles with gradually decreasing sizes and separations, Li et al. 47 and Sburlan et al. 48 reported a gradation in the field intensities across the junctions. The junctions between the smaller nanoparticles were found to support highly enhanced electric fields. This was described as arising due to the multiplicative cascade enhancement of the fields from the larger to the smaller



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nanoparticles. A subsequent study by Sun and co-workers 49 on asymmetric nanoparticle dimers using the coupled dipole model analyzed the field behavior at the junctions in more detail and found that the larger particles act as the antenna, while the smaller particles act as the resonators thereby concentrating the optical energies to very localized regions. Very recent studies by Toroghi and Kik 40,41 focus on the effect of the asymmetry in the geometry of the asymmetric nanoparticle dimer on the field gradation within a single nanoparticle junction. Dimers with large size differences and small interparticle spacings were found to give rise to large field enhancements, giving rise to interesting nonlinear properties. Our studies on symmetric trimers find that the values of the field intensities at the hottest spots are extremely large under resonant excitation conditions, meaning that the probe molecules placed at these locations can show enormous enhancements in optical signals. When the incident light has ⊥ polarization, the hottest spot can be found on the surface of the larger particle, while the hot spot can be found on the surface of the smaller particle in the transverse direction (see Figure S5, Figure S6 and Figure S9 of Supporting Information). This is understandable because the transverse coupling is very weak and the field distribution is dominated by the monomeric field distribution. The monomeric intensities being high for the larger particles, the hottest spots occur at the larger particles. Note that the intensity profiles for s = 40 nm for both the polarizations are shown in Figure S10 of Supporting Information. The calculated SERS EFs for the symmetric trimers at the hottest spots as well as the hot spots for various “s” for the k polarization of the incident light are tabulated in Table 2. The EFs for the ⊥ polarization are smaller in comparison with the corresponding values for the k polarization and are tabulated in Table S3 of Supporting Information. An interesting finding of our study is that the electric field intensities in the vicinity of the symmetric trimers are much higher than those of the homotrimers and the homodimers for the same gap size. A comparison of the field distribution around the homodimer, homotrimer and the symmetric trimer for the gap size, s = 3 nm is shown in Figure 10. It is important to note that our predictions of SERS EFs are based on the calculation of electric field intensities, which govern a lot of other optical processes like absorption and metal enhanced fluorescence, apart


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Figure 10: Electric field intensity distribution in the vicinity of the homodimer, homotrimer and the symmetric trimer for the gap size, s = 3 nm. from SERS and are therefore robust. Symmetric trimers can perform better over homotrimers in any of the SES processes, not just SERS. The rather interesting feature of a gradient in the field intensities at the junctions within a single trimer could have important implications for a number of potential applications. 46 A summary of our investigations on the organization of nanoparticles from monomers to dimers to symmetric trimers with their plasmonic features is shown in Figure 9. To the best of our knowledge, no SES experiments have been reported on symmetric trimers. With the current experimental procedures, 37,38,59 we believe that it should be possible to design the symmetric trimers that we report in this manuscript for SES studies and hope that our study motivates experiments in that direction. Theoretical SERS EFs are often quantified in terms of the maximum values of the electric fields and this gives rise to the fact that the calculated EFs are the upper limits to the experimental EFs. However, a more realistic way of estimating the EF would be by averaging the field over the surface of the NPs. In view of this, we have estimated the SERS EFs for the monomeric d = 20 nm and d = 40 nm Au NPs by averaging the electric fields over a surface area covering a region that is 1 nm away from the surface of the sphere in all cartesian directions (see Figure 11). The average SERS 19 ACS Paragon Plus Environment


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Figure 11: A schematic of the regions chosen for estimating the average SERS EFs. For the dimers and trimers, the contributions from the hot spot regions are separately estimated. EFs of d = 20 nm and d = 40 nm Au NPs at their λmax are found to be 46.5 and 83.9 respectively, while the EFs evaluated at the maximum field values were 5.5 × 102 and 1.3 × 103 respectively. We then consider the homodimer, homotrimer and the symmetric trimer for s = 3 nm and evaluate the average SERS EFs at their λmax in two ways. In the first approach, the averaging is done over a surface area covering a region that is 1 nm away from the surface of the nanostructure in all cartesian directions. In the second approach, we perform an averaging of the electric field over the hot spot region (see Figure 11) alone to estimate the average EF for a probe molecule placed in that region. For the homodimer, we find that the average EFs over the whole surface area and the hot spot region are 1.3 × 103 and 7.6 × 103 , while the EF evaluated with the maximum value of the electric field was found to be 6.8 × 105 . The average EF values for homotrimer are found to be 2.4 × 104 and 1.5 × 105 for the evaluations over the entire surface area and the hot spot region respectively. The SERS EF evaluated with the maximum value of electric field was found to be 1.8 × 106 . In the case of the symmetric trimer, we find that the average values of SERS EFs are 6.4 × 104 and 5.5 × 105 respectively for the evaluations over the entire surface area and the hot spot 20 ACS Paragon Plus Environment

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region, at least two orders of magnitude lower than the value of EF evaluated with the maximum value of the field (1.1 × 107 ). Having found that the symmetric trimers can give rise to enormous local field enhancements, it is now possible to think of further organization of these symmetric trimers into two-dimensional arrays (see Figure 1) in such a way that the junctions consist of particles with a difference in size and explore the utility of the intense electric fields at the hottest spots at these junctions in plasmonics. Experimental realization of similar arrays with nanosized gaps has been achieved 60–62 over the past couple of years. Very recent theoretical studies have also shown that such organized 2D arrays of NPs can lead to better performance over 1D arrays as well as single particles. 63 Our results predict that arrays with particles of non-uniform size can have better performance over arrays made up of particles of uniform size.

Conclusions In conclusion, we have investigated the utility of organized spherical gold nanoparticles, from monomers to dimers to trimers as substrates in SES. A computational study of the optical extinctions and electric field intensity distribution patterns of these nanostructures using the FDTD method has enabled us to arrive at a gap size between the particles (s = 40 nm) beyond which the plasmon coupling becomes negligible. Our studies reveal that the symmetric trimers exhibit an interesting gradation in the electric field intensities at the junctions of a single trimer, and are more efficient in comparison with the homotrimers. Arrays of nanoparticles built from such symmetric trimers could be promising SES substrates.

Acknowledgement The authors thank Prof. K. George Thomas for his valuable suggestions. The authors also acknowledge IISER-TVM for computational facilities. RT thanks CSIR, India for financial support.



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Supporting Information Available Optical spectra, electric field intensity profiles and SERS EFs for monomers, schematic of the plasmon hybridization in homodimers and homotrimers, fit of the extinction data of the dimers to the plasmon ruler equation, field profiles and SERS EFs for the dimers and trimers for the transverse polarization of the incident light are available in the Supporting Information.

This

material is available free of charge via the Internet at http://pubs.acs.org.

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Organization of Metal Nanoparticles for Surface-Enhanced

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