Letter pubs.acs.org/NanoLett
Uniform Circular Disks With Synthetically Tailorable Diameters: TwoDimensional Nanoparticles for Plasmonics Matthew N. O’Brien,†,§ Matthew R. Jones,‡,§ Kevin L. Kohlstedt,† George C. Schatz,† and Chad A. Mirkin*,†,‡ †
Department of Chemistry and International Institute for Nanotechnology and ‡Department of Materials Science and Engineering, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208 United States S Supporting Information *
ABSTRACT: Herein, we report the synthesis of structurally uniform gold circular disks as two-dimensional plasmonic nanostructures that complement the well-established onedimensional rod and three-dimensional shell structures. We show that a Au conproportionation reaction can be used to etch a collection of nonuniform triangular prisms into a uniform circular disk product with thickness and diameter varying 40% smaller (0.23 eV at 799 nm for disks versus 0.39 eV at 780 nm for triangular prisms) and is comparable to the most uniform rods reported to date from Murray and co-workers (0.23 eV at 799 nm for disks versus 0.23 eV at ∼750 nm for rods).24 The significant improvement observed from triangular prism to circular disk can be attributed to several mechanisms: (1) The circular disk samples are more structurally uniform, as discussed above. (2) The triangular prism particle can support two distinct in-plane dipolar modes (one corresponding to tip-to-tip oscillations and the other corresponding to oscillations from the center of one edge to the opposite tip), whereas the circular disk can only support one in-plane dipolar mode due to higher symmetry. This increased degeneracy of the in-plane plasmon modes in the circular disks allows more of the excitation energy to be pumped into a single mode, which results in a stronger oscillator strength and a narrower linewidth. (3) The presence of sharp tips on the triangular prisms is responsible for considerable radiative damping, which is mitigated significantly when they are etched to produce circular disks.12,41 The narrow FWHM observed here thus indicates both the quality of the circular disk nanoparticles and points toward their potential utility in plasmonics. To better understand how the spectral features of the circular disks change as a function of disk diameter, we simulated disk extinction spectra with a discrete dipole approximation (DDA) model.43−45 These simulations confirm the observed trends in both LSPR position, which redshifts with an increase in diameter, and in plasmon bandwidth, which decreases for disk diameters changing from 33 to 90 nm but then increases for disk diameters larger than 90 nm (Figure 2B, Table 1). The plasmon bandwidth increases at short wavelengths and small particle sizes due to the spectral proximity of the LSPR position to the gold interband transitions and surface scattering effects, and it increases at long wavelengths due to radiative damping effects (Supporting Information Figure S5). We have additionally included simulated extinction coefficients for a range of circular disk sizes in order to enable their use in applications in which knowledge of precise particle concentrations is necessary (Supporting Information Figure S6).
Table 1 are approximately half of the edge length of the initial triangular prisms. This observation is what one would expect if the synthesized disk were inscribed within the original triangular prism and thus supports the claims that the conproportionation reaction proceeds in a self-limiting fashion. To characterize the variation in nanoparticle dimensions at each stage in this process, and thus quantify to what extent the conproportionation reaction improves nanoparticle uniformity, we measured the area and perimeter of a statistically significant number of nanoparticles from TEM images (see Experimental Details in Supporting Information). We then determined an average edge length or diameter for triangular prisms and circular disks, respectively, from both the area and perimeter measurements, and determined a coefficient of variation (CV) for each measurement. This method provides a less biased and more reproducible accounting of nanoparticle dimensions than a single measurement of edge length per nanoparticle and allows us to capture the variation in both size and crosssectional shape. Applying this analysis to the precursor and product nanoparticles for a range of sizes shows that the uniformity of the nanoparticles improves significantly from triangular prism to circular disk, with a final dispersity in disk diameter of less than 10% for multiple different sizes (Table 1). This improvement in uniformity is in stark contrast to analogous systems that utilized a fast conproportionation rate36 and thus, emphasizes the importance of the self-limiting, tip-selective approach used here. More broadly, the CVs for the circular disk nanoparticles reported here are comparable to those for the one- and three-dimensional structures discussed above. In many cases, it is also important to know and compare the spectral bandwidth of the LSPR between different nanoparticles, as this metric is closely tied to the strength and lifetime of a plasmon oscillation.39,40 Spectral broadening in an ensemble measurement can come from properties inherent to the material (such as the nanoparticle composition, shape, and size)12,41,42 as well as sample uniformity, both of which limit the utility of a collection of particles. To assess spectral bandwidth, we have fit the in-plane dipole plasmon resonance from UV− vis measurements of circular disk nanoparticles to a Lorentzian function and determined the FWHM. Importantly, when C
DOI: 10.1021/nl5038566 Nano Lett. XXXX, XXX, XXX−XXX
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interband transitions would both dephase the transverse mode of the disk and make it more difficult to observe. To evaluate the effect of surface scattering, we simulated the extinction spectra of gold disks with a constant diameter (D = 46.5 nm) and systematically varied their thickness (Figure 3B, C). For small thicknesses, electron scattering at the particle boundaries becomes increasingly important, as the electron mean free path is larger than the physical dimension of the nanoparticle.39,41 As the thickness doubles from 7.5 to 15 nm, T/L increases by a factor of 7.35 (from 0.00165 to 0.0121), and when doubled again from 15 to 30 nm, T/L increases by an additional factor of 20.2 (from 0.0121 to 0.245). If the absolute extinction of the transverse mode is examined rather than the relative extinction, an increase from 0.3 to 2.8 is observed as the thickness increases from 7.5 to 30 nm (Figure 3C). Maps of the electric field polarization across the circular disks confirm that the observed extinction originates from a transverse dipole mode (Figure 3D, E). It is important to note that this strong damping of the transverse mode is only significant for the thin structures synthesized in this work and would not occur to the same extent for two-dimensional structures of greater thickness that have been reported elsewhere.32,33 To investigate the effect of the interband transitions, simulations identical to those described above were repeated for silver circular disks (Figure 3B). The interband transitions of silver are significantly blueshifted relative to those of gold and, more importantly, the imaginary part of the dielectric function (associated with losses due to the interband transitions) is roughly an order of magnitude smaller at the position of the transverse mode. Consequently, one would expect that if the interband transitions were a dominant effect that inhibits observation of a transverse dipole mode in gold disks, then these modes would be more easily observed in the case of silver. For gold and silver disks of the same diameter and a thickness of 7.5 nm, T/L is ∼14 times greater for silver, in support of our hypothesis. An increased T/L for silver as compared to gold is also observed for other thicknesses, but to a lesser extent. Although the above simulations confirm that surface scattering and gold interband transitions are indeed important factors that decrease the extinction of the transverse mode in gold circular disks, both of these effects are also present for gold rods with similar dimensions and yet a transverse mode is still experimentally observed.46 This result suggests that particle shape must also be an important effect that dictates the extent to which an anisotropic gold particle supports a transverse mode. To confirm this, simulations similar to those described above were repeated for rods with a constant 46.5 nm length and systematically varied thickness (more commonly referred to as the diameter), illuminated and polarized in an analogous fashion (Figure 3A, B). A comparison of the T/L values for gold rods and disks with a thickness of 7.5 nm indeed demonstrates that rods are ∼43 times greater. While a detailed analysis of this shape effect is beyond the scope of this work, we hypothesize that it originates from the difference in particle symmetry. The rotational symmetry of the rod (about its long axis) increases the number of degenerate transverse modes it can support and, therefore, increases the total transverse oscillator strength. The circular disk, on the other hand, has a single transverse mode due to its lack of symmetry in this dimension (i.e., rotations about an axis parallel to the plane of the disk), which results in a smaller oscillator strength. The reverse is true for the longitudinal mode, where the rotational symmetry of the circular faces increases the number of
In contrast to many other highly anisotropic nanoparticle structures, we do not observe any high energy plasmon modes normally attributed to oscillations perpendicular to the major axis of the structure (i.e., transverse). The modes we do observe match well with simulations as in-plane (longitudinal) dipolar oscillations (Figure 2B). These results suggest that the circular disks synthesized here may be described as “effectively twodimensional” plasmonic structures because the observable plasmon modes are confined to the two-dimensional plane of the nanoparticle. In order to understand the plasmonic origins of this observation, we employed DDA methods to simulate the extent to which circular disks of a particular size and composition can support a transverse plasmon mode (Figure 3). Particle extinction spectra were modeled with illumination
Figure 3. DDA simulations of transverse and longitudinal plasmon modes in circular disk and rod-shaped particles. (A) Longitudinal and transverse plasmon modes can be excited in gold disks (green) and rods (red) depending on the electric field polarization (E) and the wave vector (k) of the incident light. (B) The extinction ratio between the transverse and longitudinal modes (T/L) is plotted versus particle thickness for gold and silver disks with D = 46.5 nm (green and blue, respectively) and for gold rods with a length = 46.5 nm (red). (C) Simulated extinction spectra of 46.5 nm diameter disks polarized in the transverse orientation with a range of thicknesses (listed in the legend). Only the longitudinal mode (L) for the synthetically achievable 7.5 nm thick disk is shown for comparison. Electric field plots of the transverse mode are shown for (D) 7.5 nm thick gold disks and (E) 20 nm thick gold disks.
in an edge-on orientation with the electric field polarized perpendicular to the disk and separately with illumination in a face-on orientation with the electric field polarized in the plane of the disk to attempt to maximally excite the transverse (T) and longitudinal modes (L), respectively (Figure 3A). The ratio of the maximum extinction efficiency of the transverse and the longitudinal peaks (T/L) provides a quantitative metric for the relative oscillator strength of the two modes and thus the likelihood that each would be observed in an ensemble measurement (Figure 3B). We hypothesized that surface scattering for thin structures and the spectral proximity of the transverse mode to the gold D
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ACKNOWLEDGMENTS This material is based upon work supported by the AFOSR under Award Nos. FA9550-11-1-0275 and FA9550-12-1-0280. This work was supported by the National Science Foundation’s MRSEC program (DMR-1121262) at the Materials Research Center of Northwestern University. This work made use of the EPIC facility (NUANCE CenterNorthwestern University), which has received support from the MRSEC program (NSF DMR-1121262) at the Materials Research Center, and the Nanoscale Science and Engineering Center (EEC-0118025/ 003), both programs of the National Science Foundation; the State of Illinois; and Northwestern University. M.N.O. and M.R.J. gratefully acknowledge support through a NSF Graduate Research Fellowship. M.R.J. would like to thank Dr. Mario Hentschel for useful discussion.
degenerate longitudinal modes it can support compared to the rod, which has a single longitudinal mode. This symmetryrelated shape effect has additional implications for orientationally averaged measurements, such as an ensemble UV−vis measurement, as there are a different number of polarizations that can be used to excite each mode in the requisite particle geometry. The transverse mode for rods can be excited when the particle is illuminated in a tip-on fashion with perpendicularly polarized light and also in a side-on fashion with light polarized perpendicular to the length of the rod (Figure 3A). In the case of the disk, however, symmetry demands that the transverse mode only be excited with a single orientation and polarization of light. The reverse of this argument is again true for the longitudinal mode. These effects collectively act to increase both the absolute and the relative extinction of the transverse mode for rods as compared to disks in both single particle experiments with polarized light and in orientationally averaged experiments (Supporting Information Figure S7). In summary, this methodology provides access to a structurally uniform and tailorable class of two-dimensional circular disk nanostructures with spectrally narrow and broadly tunable plasmon resonances. The approach used here, based upon differences in chemical reactivity of surface atoms on different facets of anisotropic nanostructures, could likely be extended to other shapes and compositions as a generalizable method for improving colloidal uniformity. Beyond expanding the toolkit of well-defined nanoparticles available to researchers, access to these structures will be beneficial to a variety of plasmonic investigations that would otherwise be extremely challenging using the conventional anisotropic nanoparticles available to the field. In particular, the “effectively twodimensional” nature of the plasmon mode in this structure might provide access to unusual types of plasmon coupling that would be difficult to replicate with other structures. One can also envision using these building blocks in the assembly of one-, two-, and three-dimensional optically active materials,34,47−50 as the well-defined surface chemistry of gold allows these nanoparticles to be functionalized with a wide array of surface ligands,51−55 and the two-dimensional shape allows access to assemblies with unique symmetries.50,53,56 Such materials may be useful for studies of fundamental coupling phenomena, the engineering of Fano resonances, and the design of chiral optical metamaterials.
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* Supporting Information S
Experimental details and additional data. This material is available free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
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[email protected]. Author Contributions §
These authors contributed equally. The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes
The authors declare no competing financial interest. E
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NOTE ADDED AFTER ASAP PUBLICATION This article was published ASAP on January 6, 2015. Values were changed for T/L in the second paragraph on page D. The correct version was published on January 7, 2015.
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