Article pubs.acs.org/JPCC
Symmetry-Dependent Optical Properties of Stellated Nanocrystals Alison F. Smith,†,‡ Rebecca G. Weiner,† and Sara E. Skrabalak*,† †
Department of Chemistry, Indiana University, Bloomington, Indiana 47405, United States NAVSEA Crane, Crane, Indiana 47522, United States
‡
S Supporting Information *
ABSTRACT: Stellated metal nanostructures are a class of plasmonic colloids in which large electric field enhancements can occur at their sharp tips, making them excellent candidates for surface-enhanced Raman spectroscopy (SERS) and surface-enhanced infrared spectroscopy (SE-IRS) platforms. Shape-dependent rules for convex polyhedra such as cubes, nanorods, or octahedra exist, which describe far-field scattering and near-field enhancements. However, such rules are lacking for their concave counterparts, which include stellated structures. Here, the optical response of stellated Au nanocrystals with Oh, D4h, D3h, C2v, and Td symmetry were modeled to systematically investigate the role of symmetry, branching, and particle orientation with respect to excitation source using finite difference time domain (FDTD) calculations. Furthermore, these results are compared to experimentally obtained localized surface plasmon bands determined by UV−visible (UV−vis) spectroscopy for ensembles of similarly shaped metallic nanostructures. These UV−vis spectra include that of the first reported all-Au octopodal structure achieved from seed-mediated methods. From these studies, symmetry-dependent rules governing the far-field and near-field optical response are outlined. These rules can be applied to a variety of concave structures to yield the optimized far-field and near-field responses for SERS and SE-IRS platforms.
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to give NCs with high symmetry.6 Thus, the structures selected were the Y-tripod (D3h) and T-tripod (C2v),12,13 pentapod (D3h),14 tetrapod (Td),14 bowtie (D4h),14,15 octopod (Oh),14−17 and hexapod (Oh).18 These structures were modeled based on previously reported nanostructure size and shape. In addition, the experimental LSPR of Au octopods, a newly synthesized structure, is presented for comparison to the FDTD-calculated LSPR. The current rules for convex structures include: (1) the number of resonance bands is determined by the number of ways in which the electron density of a NP can be polarized, with lower symmetry structures displaying more peaks;5,6 (2) the LSPR position can be tuned by altering shape anisotropy;6,19 (3) the far-field scattering intensity will be large when the surface charge is separated by mirror symmetry as long as the mirror plane does not bisect through a NC vertex;5,20 and (4) the near-field enhancement is greatest when the charge accumulation occurs at the smallest number of tips.21−23 For example, the largest LSPR maximum for a cube occurs when excited in the [100] or [110] directions rather than the [111] direction,5 while the maximum near-field enhancement for a cube occurs when the incident light
INTRODUCTION Collective oscillations of conduction electrons, known as localized surface plasmon resonance (LSPR), arise from interactions between nanoscale metallics and electromagnetic radiation.1 Au nanoparticles (NPs) generally exhibit LSPRs in the visible region, but their resonances can be tuned to the infrared (IR) region, enabling applications in surface-enhanced Raman spectroscopy (SERS)1−3 and surface-enhanced infrared spectroscopy (SE-IRS).4 The LSPR wavelength and intensity are largely influenced by nanocrystal (NC) shape because the shape defines the number of possible surface charge distributions and thus the polarizability of the NC.5,6 The LSPR response has been investigated for a myriad of particle shapes, both theoretically and experimentally, producing shape-specific design rules for convex NCs.6 Such rules for concave structures, including stellated NCs, do not exist. Yet, such stellated NPs hold technological promise because they exhibit enhanced electric fields localized at their sharp features, offering enhanced SERS and SE-IRS sensing opportunities.7−11 Here, stellated Au structures were systematically selected to investigate the role of NC symmetry and orientation with respect to the incident light on the LSPR response. This symmetry dependence was determined using finite difference time domain (FDTD) calculations accompanied by comparisons to experimentally determined peak LSPR values. The scope of this study was limited to stellated structures which could reasonably be synthesized building from existing knowledge. That is, branch growth initiates at high energy features of seeds under kinetically controlled growth conditions © XXXX American Chemical Society
Special Issue: Richard P. Van Duyne Festschrift Received: December 15, 2015 Revised: January 25, 2016
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CARY 5000 Bio UV−visible spectrophotometer using a quartz cuvette and a background scan of water. SEM samples were prepared by drop-casting a dispersed particle solution onto a silicon wafer and then washing the wafer with methanol after initial solvent evaporation. Finite Difference Time Domain Calculations. To investigate the roles of NC symmetry and orientation with respect to the propagation direction (k) and polarization direction of incident light on the LSPR, FDTD numerical simulations were performed using Lumerical software. A Au Ytripod, T-tripod, pentapod, and tetrapod with branch lengths of 75 nm and tip widths (TWs) of 10 nm, an octopod and bowtie with face diagonals and transverse face diagonals of 150 nm and TWs of 10 nm with the longitudinal face diagonals of the bowtie of 210 nm, and a hexapod with face-to-face branches of 150 nm and TW of 10 nm were modeled. Scattering spectra (scattering cross-section as a function of wavelength) of the NCs were calculated using FDTD. To calculate the scattering and absorption spectra of the Au octopod obtained experimentally, a Au octopod model was constructed with a face diagonal of 105 nm, a TW of 20 nm, and a branch base width of 55 nm. The dielectric functions for Au were fitted to optical data from Johnson and Christy.27 The refractive index value of the surrounding medium was set to 1.4 to mimic that of PDMS and silica, which are often used in microanalytical platforms.28 The excitation source was a plane wave with a wavelength range of 400−3000 nm, which propagated through a surrounding medium with a refractive index of 1.4. Mesh values were set to (2 nm)3 for scattering and (1 nm)3 for electric field intensity maps. The propagation direction was along various symmetry axes of the NC, and the direction of electric field oscillation with respect to the NC was modeled as depicted in the figures. Electric field intensity maps were calculated with FDTD at the maximum wavelength positions, which were obtained from the scattering spectra. Such intensity maps are often calculated as E2,29 which was selected here to provide direct comparison to existing work. It should be noted that SERS enhancement has an E 4 dependence.29
is polarized such that charge accumulation occurs in the [110] (diagonal) rather than in the [100] direction.23 Here, the theoretical symmetry dependence of concave structures on the number and intensity of far-field LSPR bands and near-field enhancements is presented, including the orientation dependence with respect to incident light direction. The particle orientations with respect to the incident light and polarization directions are not exhaustive; rather, they are comprehensive to systematically develop symmetry-dependent rules governing the optical response of concave structures. For example, our simulations show that modes of anisotropic structures can be selectively turned on or off by changing the polarization direction, similar to that of convex structures.19,24 In addition, electric field (EF) enhancements are maximized when the charge distribution results in the largest effective dipole, just like that of convex structures;21−23 however, we show that this phenomenon does not necessarily occur when charges are accumulated on the least number of tips for concave structures.
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METHODOLOGY Chemicals and Supplies. Chemicals used were L-ascorbic acid (C6H8O6, L-AA, 99%), chloroauric acid (HAuCl4·3H2O, 99.9%), cetyltrimethylammonium bromide (CTAB, 98%, LOT # BCBK3869V), cetyltrimethylammonium chloride (CTAC, 0.78 M), sodium chloride (NaCl, 99.0%), and sodium borohydride (NaBH4, 98.5%), which were purchased from Sigma-Aldrich. Hydrochloric acid (HCl, 1 N) was purchased from Macron. Sodium bromide (NaBr, 99.50%) was purchased from J.T. Baker. Nanopure water (18.2 MΩ·cm) was used in all experiments. Synthesis of Octopodal Au NCs. The octopodal Au NCs were prepared by overgrowth from Au nanocubes. Synthesis of Au Nanocubes. The synthesis of Au nanocubes is adapted from a previous literature protocol.25 Gold seeds were initially prepared. To synthesize seeds, 0.25 mL of HAuCl4·3H2O (10 mM) and 7.5 mL of CTAB (0.1 M) were mixed together. Next, 0.6 mL of freshly prepared NaBH4 (0.01 M) was added, and the solution was mixed by inversion and aged 1 h in an oil bath set to 25 °C. After 1 h, seeds were diluted 10:1. Into a separate vial, 0.2 mL of HAuCl4·3H2O (10 mM), 8 mL of nanopure water, and 1.6 mL of CTAB (0.1 M) were added and mixed by inversion. Next, 0.95 mL of L-AA (0.1 M) was added. Last, 5 μL of seed was added. The reaction vial was capped and allowed to sit undisturbed in a 25 °C oil bath overnight. Particles were collected by centrifugation for 30 min at 3900 rpm and diluted with water to a total volume of 3 mL. Synthesis of Au Octopods. Synthesis of Au octopods was achieved using the seed-mediated method adapted from previous literature protocols.16,26 For branched nanocrystal growth typically, 2 mL of CTAC (0.2 M) solution and 2.5 mL of NaBr (50 mM) were added to a reaction vial. Next, 0.1 mL of HAuCl4· 3H2O (0.1 M) solution was added followed by 1.5 mL of L-AA (0.1 M) solution. Then, 18.9 mL of water was added, followed by 1 mL of cubic Au seed solution. These reaction vials were gently shaken and then capped and allowed to sit undisturbed in a 25 °C oil bath for 2.5 h.
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RESULTS AND DISCUSSION The structures analyzed were selected to systematically investigate the role of NC symmetry and orientation on the LSPR response with respect to the incident light and polarization direction. To investigate the role of symmetry in same-branch systems, a D3h Y-tripod and C2v T-tripod were selected as well as an 8-branched Oh octopod and 8-branched D4h bowtie. In order to investigate the role of branching in systems with the same symmetry, a 3-branched D3h Y-tripod and 5-branched D3h pentapod were selected as well as an Oh 8-branched octopod and Oh 6-branched hexapod. Finally, the Td-symmetric tetrapod was included for completeness as there is no inversion center. Metal NCs with these symmetries have been synthesized previously or reported here for the first time. Although in some cases the branched nanocrystals were achieved with a poor plasmonic metal such as Pt, our simulations were based on Au structures as there is reasonable agreement in terms of the number and positions of resonances between simulated results and previously reported ensemble LSPR measurements for metallic structures of similar shape as described below.12,13,30 The direction of incident light propagation, k, was applied down select Cn rotational axes and is denoted as k-Cn throughout this report. Furthermore, the symmetry operator σv denotes a mirror plane that is parallel to Cn and thus perpendicular to the electric
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CHARACTERIZATION The Au octopods were characterized by scanning electron microscopy and UV−vis spectroscopy. Images of the nanoparticles were taken with an FEI Quanta 600F Environmental Scanning Electron Microscope (SEM) operated at 30 kV and a spot size of 3. SPR measurements were acquired with a Varian B
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The Journal of Physical Chemistry C field E; Pcb denotes a plane that encompasses both the core of the nanoparticle from which the branches emanate and the charge accumulation at the tips of branches. Y-Tripod and T-Tripod. Both Y-tripod and T-tripod metallic nanostructures are synthetically accessible12,13,30 with D3h and C2v symmetry, respectively. The UV−vis spectrum of such Pt tripod structures in water (RI = 1.333) reveal a broad LSPR peak in the near-IR region at approximately 1400 nm.13 The authors attribute this broad LSPR to the heterogeneity of the sample,31 and the optical properties of similarly sized D3h and C2v structures with Au composition were simulated here (Figure 1). A medium
a Pcb. The blue-shift in the k-C2 case relative to the k-C1 case arises from the single branch that lies in σv, the result being elimination of a multipolar band for the k-C2 case and all charges accumulating on the tips opposite the σv (Figure 1). The band present at ca. 850 nm for the Y- and T-tripods is the equivalent of the transverse mode for a nanorod. The far-field scattering spectra (Figure 2a) and electric field (EF) enhancement maps of the Y-tripod demonstrate the ability
Figure 1. Plot of the LSPR spectra exhibited by a T-tripod and Y-tripod Au structure when k is directed along varying symmetry axes for unpolarized E. All branch segments are 75 nm with a 10 nm branch thickness. There is an additional peak for the T-tripod with k along the C1 axis.
with RI = 1.4 was selected to reflect that of PDMS or silica.28 The FDTD-calculated peak LSPR values for these Au structures were ca. 1900 nm, which is expected given the red-shifted LSPR values for Au compared to Pt32 and the larger RI environment33 (Figure 1). Furthermore, the FDTD-calculated LSPR for the Pt Y-tripod is located at 1356 nm compared to the 1380 nm LSPR reported by Maksimuk et al.; the line width of the experimental spectrum is also larger than that of the simulated spectrum (Figure S1).13 Orientation with Respect to the Direction of Incident Light. The optical response of these structures was calculated as a function of the excitation source propagation direction, k, for both unpolarized and polarized sources. For the Y-tripod, there are two scattering bands for k-C2 and k-C3, with the dipolar bands located at 1924 and 1908 nm, respectively (Figure 1). The blueshift in the dipolar band for the k-C3 case compared to the k-C2 case may seem surprising given that both tips on opposite sides of all mirror planes are equidistant for both k-C2 and k-C3 cases; i.e., the restoring force should be equal. However, the plane encompassing the core from which the branches emanate and both tips opposite a mirror plane can be parallel to k (and perpendicular to E) in only the k-C3 case; i.e. there is a σv and Pcb for only the k-C3 case. The core acts as an antenna10 to effectively strengthen the restoring force, resulting in the blue-shift for the kC3 case. This antenna effect has been reported in Au nanostars in which the EF enhancement at the tips of the nanostar is increased compared to similarly sized tips with no central body.10 The Ttripod exhibits three bands for k-C1 and only two bands for k-C2 (Figure 1). The k-C1 and k-C2 cases result in dipole bands located at 1939 and 1908 nm, respectively. Both of these cases have equidistant tips on opposite sides of a σv mirror plane and contain
Figure 2. (a) Plot of the LSPR spectra exhibited by the planar Y-tripod shown in Figure 1 when k is directed along C2 (orange dashed) and C3 (black solid and dashed) axes and the electric field, E, is polarized in the direction indicated. (b−e) The near-field intensity maps of the planar tripod with E polarized along the directions indicated in white. The electric field enhancement (|E|2/|E0|2) is greater for k-C2 than for k-C3. Insets depict the XY view correlating to the intensity maps with the center of the black dot indicating the 0,0 position, and the x and y axes are equivalent for all intensity maps.
to turn modes on or off by polarization direction (Figure 2b,c), similar to that for anisotropic metallic nanostructures such as a spheroid19 or nanocrescent.24 This ability is particularly noticeable for the k-C2 case (Figure 2b,c) in which the polarization parallel to k results in no far-field scattering and no EF enhancement (Figure 2a,c). These EF enhancements are important for surface-enhanced spectroscopies on account of the increase in light intensity compared to the excitation source near the surface of the nanostructure.34 The k-C3 case has the same EF enhancement for both polarization directions. This equivalent enhancement likely arises from the fact that the effective dipoles resulting from both polarizations depicted in Figure 2d,e are equivalent. These maps demonstrate that the largest EF enhancement does not necessarily occur when the charge accumulation is concentrated on the fewest tips (Figure 2d,e). The far-field scattering spectra (Figure 3a) and EF enhancement maps of the T-tripod demonstrate the ability to turn modes on or off by polarization direction (Figure 3a−g). Furthermore, the EF enhancement maps further support the claim that a blueC
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Figure 3. (a) Plot of the LSPR spectra exhibited by the T-tripod shown in Figure 1 when k is directed along C1 (black solid and black dashed) and C2 (orange dashed) axes and the electric field, E, is polarized in the direction indicated on the plot. (b−g) The near-field intensity maps of the T-tripod with E polarized along the directions indicated in white; scale equivalent for b−g. The electric field enhancement (|E|2/|E0|2) is greatest when charge accumulation occurs on the least number of tips. Insets depict the XY view correlating to the intensity maps with the center of the black dot indicating the 0,0 position, and the x and y axes are equivalent for all intensity maps.
shift in the k-C2 case relative to the k-C1 case arises from the single branch that lies in the mirror plane being parallel to k (Figure 3b−g). This is most notable by the ability to completely turn off the dipolar mode for the k-C2 case (Figure 3e). Additionally, the higher-order in-plane LSPR mode is expressed only for the k-C1 case in which the polarization direction is parallel to the branch lying in σv (Figure 3f). Symmetry Dependence: D3h vs C2v. Comparing the k-C3 Ytripod and the k-C1 T-tripod (Figure 1), the dipole band of the Ytripod is blue-shifted compared to that of the T-tripod (1908 vs 1939 nm). This blue-shift can be explained by comparing the distance between the two tips on opposite sides of σv; the distance between these tips of the Y-tripod is less than that of the T-tripod. A shorter distance between charge separations will result in a stronger restoring force and therefore a blue-shifted dipolar resonance. For the case of the k-C2 Y-tripod and the k-C2 T-tripod, the dipolar band of the Y-tripod is red-shifted compared to that of the T-tripod (1924 vs 1908 nm) even though the charge separation remains closer in the Y-tripod case (Figure 1). However, Pcb is parallel to k for the Y-tripod, yet it is perpendicular for the Ttripod. The core acts as an antenna10 to effectively strengthen the restoring force, resulting in the blue-shift for the T-tripod. The lack of an antenna effect also accounts for the large reduction in scattering cross-section intensity seen for the k-C2 Y-tripod; this is the only configuration (Figure 1) in which Pcb is not perpendicular to k. Y-Tripod and Pentapod. Pentapodal metallic NC synthesis by seed-mediated methods has been reported.14 These structures are grown from right bipyramidal seeds, which have two axial vertices from which branches grow in the ⟨111⟩ directions. They also have three equatorial vertices that are intersected by a twin plane from which branches proceed in ⟨112⟩ directions. To investigate the role of branching, the optical properties of a pentapod with D3h symmetry were compared to the Y-tripod (Figures 2 and 4). For the pentapod, the C3 axis lies along the two axial branches. Role of Branching. Like the Y-tripod, there are two scattering bands present for k-C2 and k-C3 (Figure 4). Unlike the Y-tripod, the k-C3 case has a red-shifted dipolar band compared to that of the k-C2 case (1891 vs 1876 nm). Here, Pcb is perpendicular to k for both propagation directions, and these tips are closer for the k-C3 case. However, the k-C2 case has axial tips that are both
Figure 4. Plot of the LSPR spectra of (a) a D3h pentapod with unpolarized E and k along the C3 (gray) and C2 (red) axes and (b) the D3h pentapod with the E-field polarized along the ⟨111⟩ (solid) and the ⟨112⟩ (dashed) directions and (c,d) the near-field intensity maps of the D3h pentapod with the E-field polarized along the ⟨111⟩ and the ⟨112⟩ directions. The scattering intensity reduces more than 2-fold when the core and charge accumulation at the tips on opposite sides of a mirror plane are not in a plane that is perpendicular to k, and the electric field enhancement (|E|2/|E0|2) is also reduced. All branch segments are 75 nm with a 10 nm branch thickness. The inset depicts the XY view correlating to the intensity maps with the center of the black dot indicating the 0,0 position, and the x and y axes are equivalent for all intensity maps.
opposite a mirror plane and directly parallel to the electric field (E). The transverse and longitudinal polarization for the C2 case provides more insight. When the EF is parallel to the axial D
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Figure 5. Plot of (a) experimental absorption (dashed) and FDTD-calculated absorption (black solid) spectra and (b) SEM image of Au octopods. The Au octopodal model for FDTD calculations has a 105 nm face diagonal and 20 nm tip width in accordance with the experimental structure.
Figure 6. Plot of the LSPR spectra of (a) a Au D4h bowtie and an Oh octopod with unpolarized E and k along a C2 and C4 axis for the D4h structures and along a C2, C3, and C4 axis for the Oh structures, (b) the D4h bowtie with the E-field polarized along the transverse (black) and longitudinal (red) axes and P = 45° (black dashed), and (c,d) the near-field intensity maps of the Oh octopod with k along the C4 axis and (e−g) the D4h bowtie with k along the C2 axis with the E-field polarized as indicated with white arrows. The electric field enhancement (|E|2/|E0|2) is greatest when charge accumulation is at the least number of tips for the octopod; scale equivalent for e−f. The modes of the bowtie can be turned on/off by controlling the E direction. The insets depict the XY view correlating to the intensity maps with the center of the black dot indicating the 0,0 position, and the x and y axes are equivalent for all intensity maps. Octopod and bowtie structures with various k-directions are depicted on the right. All branch lengths are 75 nm.
branches (denoted as ⟨111⟩ in Figure 4b), there is a larger farfield intensity as this configuration has Pcb perpendicular to k and also leaves the branches completely parallel to the EF. A transverse polarization has the EF perpendicular to the axial branches, and the far-field intensity reduces. Here, the excited tips are not in a plane with the core that is perpendicular to k, and the EF is not maximally coupled (angled branches). The EFenhancement maps further demonstrate the LSPR modes expressed for ⟨111⟩ and ⟨112⟩ EF polarizations (Figure 4c,d). The charge accumulation in both cases is shared by the same number of tips; however, the effective dipole for the ⟨111⟩ polarization direction is larger than that of the ⟨112⟩ direction, resulting in a greater EF enhancement at the tips. T-Tripod, Y-Tripod, and Pentapod Summary. Coupling the T-tripod and Y-tripod comparison (Figures 1−3) with the Ytripod and pentapod comparison (Figures 3 and 4), it is apparent that the far-field intensity is dependent on P cb being
perpendicular to k. This arrangement will strengthen the restoring force, resulting in a blue-shifted LSPR. While the number of branches did not affect the number of modes, the orientation of branching in which the branches are linearly opposite one another and parallel with the EF will result in a larger far-field intensity and blue-shifted LSPR. Furthermore, EF enhancements depend on the overall effective dipole for the resulting charge distribution rather than on accumulation on more or less tips. Octopod and Bowtie. The octopodal and bowtie nanostructures are synthetically accessible by a seed-mediated coreduction route in which branched growth is directed from cubic and rectangular seeds, respectively.15,16 Here, octopodal Au NCs were achieved for the first time using a seed-mediated synthetic route. The bulk absorption as a function of wavelength for and an SEM image of the resulting Au NCs is depicted in Figure 5. The FDTD-calculated absorption spectrum is also E
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The Journal of Physical Chemistry C shown in Figure 5. There is good agreement for the experimental and calculated maximum absorption wavelengths (607 and 594 nm, respectively). The broad absorption band of the experimental sample is expected on account of size and structural inhomogeneity in the sample.31 The synthesis of the bowtie structure has been previously reported using a seed-mediated coreduction route. The resulting symmetry of the eight-branched octopod is Oh, and the eight-branched bowtie is D4h. From Figure 6, the vastly different optical responses of these two structures is evident. Orientation with Respect to the Direction of Incident Light. The far-field scattering spectra of each particle as a function of propagation direction k was evaluated. For the octopod, there is very little difference in location (808, 813, 813 nm, respectively), number, or intensity of the far-field dipolar bands for k-C4, k-C3, or k-C2 axes, respectively (Figure 6a). However, the near-field calculations for k-C4 show an increased EF enhancement for an EF polarization of 45° compared to that of the transverse or longitudinal EF polarization (Figure 6c,d). These three EF polarizations induce charge separation on opposite sides of a σv. For example, there are four σv operations with respect to the C4 axis, and E can be selected such that charge accumulation occurs at tips opposite these planes (Figure 6c,d). However, the charge density is shared with a total of only 4 tips rather than 8 tips for the 45° polarization. This finding is in accordance with the polarization-dependent near-field distribution observed for convex metallic nanocubes in which the maximum EF enhancement occurs when charges are concentrated at a lower number of corners or tips.21−23 The bowtie exhibits a transverse and longitudinal band similar to that of a spheroid19 or nanorod35 structure for k-C2; however, only the transverse band is present for k-C4 (Figure 6a). The longitudinal and transverse modes of k-C2 can also be selectively turned on or off by polarization of the electric field (Figure 6b), similar to the turning on/off the longitudinal and transverse modes of a spheroid.19 For the bowtie structure, the transverse EF polarization results in a larger EF enhancement at the tips than does the longitudinal or 45° EF polarizations, while all three polarizations result in charges concentrated on a total of eight tips. This is in accordance with EF enhancement at the corners of nanorods.36 Symmetry Dependence: Oh vs D4h. When comparing the bowtie structure to the octopodal structure, a reduction in symmetry leads to an additional dipolar band, with two prominent bands expressed for the bowtie and only one for the octopodal structure (Figure 6a). This finding is in accordance with the convex rule stating that lower symmetry results in a greater number of LSPR bands.6 However, the transverse and longitudinal bands of the bowtie can be completely turned off as shown in Figure 6b, allowing only one band to be expressed without any symmetry reduction; i.e., the symmetry of the particle has not been altered. Therefore, a more universal rule emerges, which is that the possible charge distributions driven by particle symmetry and orientation to k dictate the number of LSPR bands. Octopod and Hexapod. The synthesis of Au hexapods has been reported,18 and the calculated LSPR maxima shown in Figure 7a are within the range of wavelengths reported for the experimental structures.18 To investigate the role of branching, a hexapod with Oh symmetry was compared to the octopod. The branch lengths and tip widths of the hexapods were equivalent to the octopods (see Experimental Section); however, the band
Figure 7. Plot of the LSPR spectra of (a) an Oh hexapod with unpolarized E and k along the C4 (red), C3 (black), and C2 (black dashed) axes and (b) the Oh hexapod with the E-field polarized along the directions depicted with solid and dashed lines and (c,d) the near-field intensity maps of the Oh hexapod with k-C2 and (e) of the Oh octopod with k-C2; the E-field is polarized in the direction indicated in white. The insets depict the XY view correlating to the intensity maps with the center of the black dot indicating the 0,0 position, and the x and y axes are equivalent for all intensity maps. The electric field enhancement (| E|2/|E0|2) is equivalent for the two axial tips and the four equatorial tips of the Oh hexapod. All branch lengths are 75 nm.
intensity and locations with respect to the octopod cannot be directly compared on account of overall volume differences. Role of Branching. Like the octopod, the number, location, and intensity of the far-field dipolar bands for k-C2, k-C3, and k-C4 are similar (Figure 7a). The far-field and EF enhancement at the tips for the k-C2 hexapod are also similar for polarization of incident light, resulting in charge accumulation at two tips (Figure 7a,c) or four tips (Figure 7a,d). This finding is somewhat surprising on account of EF enhancements typically being larger for charges accumulated on the least number of tips23 as demonstrated for the k-C4 octopod structure discussed (Figure 6c,d). Further analysis shows that the EF vectors traveling along the four branches indeed result in an overall field equivalent to that of a linear charge separation (two branches) on account of F
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The Journal of Physical Chemistry C the branches lying flat in a plane, with the branches 45° apart. (see the EF vector map (Figure S2)). This result suggests that the effective dipole rather than the number of tips on which charge is accumulated governs the EF enhancement at the tips of stellated nanostructures. To test this hypothesis, the EF enhancement of the k-C2 octopod with incident light polarized along the four in-plane branches was calculated (Figure 7e). As expected, the EF enhancement was >60, which is a 2-fold increase in the EF enhancement of the k-C4 octopod case in which the incident light is polarized 45° (Figure 6d). Both cases have charge accumulation concentrated at four tips; however, the k-C2 octopod case (Figure 7e) results in a field equivalent to that of linear charge separation as with the k-C2 hexapod. Tetrapod. For completeness, a metallic structure with Td symmetry was included, which has no center of inversion in contrast to the previously discussed structures. Furthermore, the Au tetrapod has been accessed by seed-mediated synthetic routes.14 The far-field scattering of the Au tetrapod is low (40.
largest for the case where charge accumulation is concentrated at the fewest tips (Figure 8b,c). Rather, the EF enhancement is largest for the polarization of incident light that allows for the strongest resulting dipole (Figure 8b−e). For example, the overall horizontal distance between charge accumulation for k-C3 3
with incident light polarized as depicted in Figure 7b is 2 x , where x is the distance between charge accumulation, measured G
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The Journal of Physical Chemistry C field enhancements) for applications in chemical sensing. Moreover, hot spots throughout 2-D and 3-D crystals may be engineered through the use of these branched, plasmonic nanocrystals as building blocks to novel superstructures.
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.5b12280. All-Au octopod spectra and EF vector maps (PDF)
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The optical characterization of NCs and simulations were supported by Indiana University (IU) start-up funds and IU’s Office of the Vice President for Research and the Office of the Vice Provost for Research through the Faculty Research Support Program. Synthesis of NCs was supported by the U.S. National Science Foundation under grant CHE-1306853. SES is a Cottrell Scholar (Research Corporation), Alfred P. Sloan Fellow, and Camille Dreyfus Teacher-Scholar. AFS acknowledges the support from a NSWC Crane PhD Fellowship. RGW acknowledges the support from the Siedle Inorganic Fellowship.
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REFERENCES
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