Self-Assembled Plasmonic Metamolecules Exhibiting Tunable

Article pubs.acs.org/JPCC

Self-Assembled Plasmonic Metamolecules Exhibiting Tunable Magnetic Response at Optical Frequencies Marc R. Bourgeois,†,∥ Alice T. Liu,‡,∥ Michael B. Ross,†,§ Jacob M. Berlin,*,‡ and George C. Schatz*,† †

Department of Chemistry, Northwestern University, Evanston, Illinois 60208, United States Department of Molecular Medicine, Beckman Research Institute, City of Hope, Duarte, California 91010, United States

‡

S Supporting Information *

ABSTRACT: A bottom-up self-assembly approach is used to synthesize pseudospherical clusters of Au nanoparticles with low size and shape polydispersity. Such plasmonic metamolecules (PMMs) with various diameters are prepared from two different AuNP building block sizes, enabling the investigation of the sizedependent optical properties of these structures. Trends in the UV− vis spectra are reproduced theoretically using generalized multiparticle Mie theory as either the AuNP or PMM diameter are changed. The calculated results indicate that features in the spectra of large PMMs can be associated with magnetic dipole resonances, which strengthen and red-shift with increasing PMM size. Finally, effective medium theory is used to demonstrate that materials composed of these PMMs could exhibit a bulk isotropic magnetic response at optical frequencies.

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diminishes at frequencies higher than several GHz.18,19 However, PMMs offer the possibility to control the magnetic response in the visible and near-infrared, even with plasmonic materials (e.g., Ag or Au), which possess a minimal magnetic response. This control is brought about through their geometric resonances, whereby strong spatial dispersion and circulating displacement currents serve as the source of the magnetic dipole (MD) moment in these structures.20,21 Because the PMM’s optical properties are inherently related to their geometric structure, precise fabrication methods are needed. While top-down methods have been employed successfully to create uniform PMM architectures exhibiting optical magnetism,22,23 they are expensive and limited to twodimensional structures that possess highly anisotropic optical responses. Recently, a hybrid top-down plus self-assembly approach was used to create two-dimensional metamolecules from AuNPs, which exhibited size-dependent MD resonances when excited by s-, but not p-, polarized light.24 Alternatively, bottom-up self-assembly approaches are inexpensive, solutionprocessable, and capable of producing the three-dimensional PMM architectures necessary for an isotropic optical response. The dielectric core−plasmonic satellite motif21 proposed to achieve an isotropic magnetic response has been experimentally demonstrated using Ag and Au NPs self-assembled onto dielectric cores through electrostatic assembly,25,26 Au-thiol chemistry,25 and protein−antibody interactions.27 In each case,

INTRODUCTION Noble metal nanoparticles (NPs) have attracted significant interest due to their strong optical response at visible wavelengths and ability to confine and manipulate light on the nanoscale.1,2 This light−NP interaction arises through the excitation of localized surface plasmon resonances (LSPRs), the coherent oscillation of conduction electrons.2,3 Notably, the frequency, intensity, and line width of the LSPR can be tuned by changing the NP size, shape, and environment.2 Assembling metal nanoparticles and taking advantage of their interparticle interactions can enable greater tunability, unlocking applications in environmental sensing,4−6 biomedicine,7 and materials science.8−10 Improving understanding of how NPs interact in close proximity is therefore essential for the further development of these structures. The strong interactions between metal nanoparticles and visible light have been leveraged by the metamaterial community to create novel materials that possess optical properties not observed in nature, which could enable negative index media,11,12 optical cloaking,13 and imaging below the diffraction limit.14 One class of these materials includes socalled plasmonic metamolecules (PMMs), specially designed subwavelength arrangements of NPs where plasmonic NPs are the fundamental building block. While many methods have been developed that can manipulate the electric field component of light,9,15 creating materials that exhibit optical magnetism, i.e. manipulating their relative permeability μr, remains a challenge.16,17 Although optical magnetism is a prerequisite for realizing negative index media, the magnetic response of virtually all conventional materials rapidly © XXXX American Chemical Society

Received: April 23, 2017 Revised: July 8, 2017

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Figure 1. Synthesis and characterization of Au-based plasmonic metamolecules: (a) Schematic depiction of PMM synthesis using a small molecule cross-linker. TEM micrographs of PMMs composed of (b) 10 nm and (c) 20 nm AuNPs. Scale bars are 500 nm in zoomed-out images and 100 nm in insets. Insets each depict portions of four distinct PMM structures. (d) Experimental extinction spectra for PMMs shown in (b) and (c) (solid traces). Spectra of the free (unassembled) AuNPs are included for reference (dashed lines).

Information. Briefly, a solution of citrate-stabilized AuNPs in water was added dropwise to a prepared solution of cross-linker in ethanol and water, and the reaction solution was shaken on a tabletop shaker at top speed for 2 h. The solution was left on the benchtop for 24 h after shaking and then terminated by the addition of an excess of PEG2000-maleimide and an additional 2 h of shaking. PMMs were then centrifuged to remove excess polymer and resuspended in water for characterization. As has been previously demonstrated, PMMs can be synthesized using AuNPs of varying sizes, and the final PMM size can be tuned by changing the cross-linker concentration.32 Three PMMs of increasing size were thus synthesized using both 10 and 20 nm AuNPs by varying the final concentration of TTMP cross-linker. Although it may be possible to achieve a stronger magnetic response by utilizing larger plasmonic building blocks,33 we observed unreliable aggregation for nanoparticles with diameters >20 nm using TTMP as the cross-linker molecule. Though not addressed in the present work, utilizing larger NPs remains a promising direction warranting further investigation. PMMs with diameters between 50 and 100 nm were synthesized from 10 nm AuNPs, and 20 nm AuNPs yielded 60−200 nm PMMs. Outside of these size ranges, PMMs tended to aggregate, or suffer from large size and shape polydispersity. Extinction spectra of the PMMs were measured using UV−vis absorption spectroscopy. Figure 1d shows that the major peaks in the extinction spectra of the assembled PMMs are significantly red-shifted relative to the free NP LSPRs, which is indicative of strong interparticle coupling and collective optical behavior. PMM size was determined using transmission electron spectroscopy (TEM). The average diameter of each PMM architecture was determined from the TEM images using the ImageJ image processing program (Figure S1). The hydrodynamic diameters of the PMMs were also characterized by dynamic light scattering (DLS). However, since the hydrodynamic diameter includes the polymer and solvent shell around the PMMs, the size reported by DLS will be larger than

the PMMs exhibit spectral features consistent with MD resonances. PMMs consisting of dense clusters of plasmonic NPsthe three-dimensional analogues of the PMMs studied in ref 24are also expected to possess isotropic MD resonances, though they have proven more difficult to realize experimentally as there is no dielectric core to template PMM size. Consequently, previously synthesized dense cluster PMMs28−30 suffered from uncontrolled aggregation leading to broad size and morphology distributions, which precluded useful comparisons between individual and ensemble PMM spectra and limited their utility in creating magnetically responsive metamaterials. Herein, we investigate the optical properties of PMMs synthesized by the self-assembly of AuNP building blocks into relatively uniform, high-volume fraction (>20% Au by volume)31 clusters. Analytic Mie theory calculations are used to rationalize trends in the experimental extinction spectra and to demonstrate that PMM architectures with diameters greater than ∼100 nm exhibit MD resonances. We show that by varying the diameter of either the NP building blocks, or of the assembled PMM structure, the strength and location of the magnetic resonance can be tuned across a broad spectral region in the near-infrared. Furthermore, we calculate magnetic polarizabilities and, using effective medium theory, are able to predict that bulk colloidal solutions of these PMMs are capable of exhibiting an isotropic magnetic response.

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EXPERIMENTAL SECTION PMMs were synthesized by the controlled aggregation of gold nanoparticles (AuNPs) using a small molecule cross-linker, trimethylolpropane tris(3-mercaptopropionate) (TTMP) (Figure 1a). This trivalent thiolated cross-linker allows for the covalent assembly of AuNPs into pseudospherical structures with relatively low polydispersity. The synthesis method has been demonstrated using TTMP as well as other crosslinkers32, and additional details are included in the Supporting B

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The Journal of Physical Chemistry C the actual diameter of the metallic core. Hence, for the purposes of modeling these PMMs, the metallic diameter as determined by TEM was used.

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COMPUTATIONAL DETAILS PMM structures are modeled as 10 or 20 nm spherical NPs arranged into pseudospherical portions of an fcc lattice. The inter-NP spacing, on the unit-cell face, is chosen to be 1.5 nm, which is approximately the end-to-end length of the TTMP cross-linker molecule. The optical response of each PMM is cacluated using generalized multiparticle Mie theory (GMM),34,35 which is an extension of the analytic Mie theory to treat collections of spherical particles. In all calculations, the background refractive index is taken to be 1.33 to mimic an aqueous environment. An analytic fit to the experimental data of Johnson and Christy36 is used for the Au dielectric function with a size-dependent damping factor included to account for surface scattering, which is important for small NPs.3,37 This surface-scattering correction depends on the Fermi velocity of the electrons in the metal, their effective mean free-path length, and a phenomenological constant that scales the magnitude of the damping factor (additional details in Supporting Information). We choose the value of the phenomenological constant so as to match the calculated single NP extinction line width to that measured for a colloidal solution of relatively mono disperse NPs. Electric and magnetic polarizabilities are computed using PMM-centered Mie scattering coefficients, which express the light scattered by the PMM in terms of electric and magnetic multipoles located at the PMM center.38 These coefficients are found using vector translation coefficients39 to re-express the Mie coefficients computed for each NP in a common, PMMcentric coordinate system. Complex effective permittivities and permeabilities for composite materials created by embedding PMMs in a dielectric matrix are calculated as a function of the volume fraction of PMMs within the dielectric matrix (not to be confused with the volume fraction of plasmonic NPs within each PMM) using the Clausius−Mossotti equation.40 This method of computing constitutive parameters is expected to be accurate at low PMM volume fractions,31 typically ∼20% and below, and has been used to obtain effective optical parameters for similar structures.26−29

Figure 2. Effect of PMM size: (a) Experimental (top) and calculated (bottom) extinction spectra for PMMs composed of 10 nm AuNPs. Trace labels denote PMM diameter. (b) Same as (a) but for PMMs composed of 20 nm AuNPs.

representative PMM structures (Figure 2a,b). Overall, there is good agreement between the experimental (top) and calculated (bottom) spectra. Computational constraints, as well as those imposed by our choice of PMM geometry, limited our ability to exactly match PMM diameters used in calculations to those observed experimentally, but trends in the spectral features as a function of PMM size were reproduced despite this limitation. In particular, the calculated spectra for the 10 nm PMMs exhibit a single resonance, while the 20 nm PMM spectra contain a set of peaks that strengthens and red-shifts as the PMM diameter is increased. The theoretical spectra exhibit a set of peaks, whereas the measured spectra show a single broad feature because the calculated spectra are computed for individual PMM geometries, i.e. no structural averaging, and the UV−vis spectra are ensemble measurements, which includes additional broadening due to inhomogeneity of the aggregates’ size, shape, and orientationeven for our low polydispersity samples. It is also worth noting that although we focus on the response of spherical PMMs, we expect our results to remain valid for PMMs that deviate slightly from this ideal shape as previous theoretical studies indicate that orientationaveraged spectra of spherical and ellipsoidal aggregates are remarkably similar.42 Furthermore, in the Supporting Information, we show that there is not a large difference in the MD properties of a prolate spheroidal PMM excited along its longitudinal and transverse axes. Although the identity of the excited modes cannot be directly extracted from extinction spectra, this information is encoded in the spatial distribution of the scattered light. Therefore, to directly quantify the MD character of the electromagnetic response, a multipole decomposition38 is performed on the scattered fields from each simulated PMM.27,28,41 Figure 3a shows the decomposed scattering spectrum of the 134 nm diameter PMM (20 nm NPs) in the spectral region of the broad, red-shifted peak in the experimental spectrum. The

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RESULTS AND DISCUSSION Experimental UV−vis (extinction) spectra for PMMs composed of 10 and 20 nm AuNPs are presented in the top panels of Figure 2a,b, respectively. By changing the TTMP concentration during the PMM synthesis, 50−100 nm and 60−200 nm diameter PMMs with low polydispersity were created from 10 and 20 nm AuNPs, respectively. The extinction spectra of the PMMs composed of 10 nm AuNPs are dominated by a single resonance near 530 nm, which broadens and red-shifts slightly as the PMM diameter is increased. The smallest PMMs composed of 20 nm AuNPs (66 nm, black) exhibit an extinction spectrum similar to the 10 nm AuNP PMMs; however, as the diameter of the PMM is increased, a broad second feature appears from 700 to 800 nm, which redshifts and strengthens with increasing diameter. This behavior is consistent with previous observations of MD resonances from core−satellite PMM structures of different diameters.41 To better understand the measured UV−vis spectra, we employ GMM theory to calculate the extinction spectra of C

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ED moment, lying in the incident plane.17,20,21,27 The field maps also indicate that these PMM structures possess electric field hot spots (regions of large field enhancement) distributed throughout the structure. As the PMM diameter increases, the effective current loops generating the magnetic response become larger, enhancing the strength of the MD. At the same time, more NPs must be added to the cluster to increase its diameter, causing additional coupling between NPs, which shifts the MD resonance toward longer wavelengths. It should be noted that because there are more NPs per PMM in the structures considered in this work relative to the previously reported core−shell structures,25−27 the MD resonances of the current PMMs are further red-shifted than those observed in core−shell structures of identical diameter (Figure S5). Having demonstrated that the isolated PMM structures exhibit both electric and magnetic dipole responses, we now consider their use as a metamaterial building block. Specifically, we consider the bulk optical properties of a metamaterial, which can be described by the effective relative permittivity εeff and permeability μeff. These quantities can be calculated using the Clausius−Mossotti relations, which describe objects embedded in a dielectric matrix (shown schematically in Figure 4a): εeff −1 fα μ − 1 fα = e ; eff = m εeff +2 3V μeff + 2 3V

Figure 3. Multipole decomposition into electric and magnetic components: (a) Calculated scattering spectrum of a PMM (20 nm AuNP; 134 nm diameter) decomposed into electric (ED) and magnetic (MD) dipolar contributions. In this wavelength range, the scattering spectrum computed including up to eight vector spherical harmonics (Total) is accurately reproduced by retaining only the dipolar terms (Sum = ED + MD). (b) Cross-section through the aggregate in the XZ plane when excited near magnetic resonance wavelength (710 nm). Field map reveals strong coupling between adjacent NPs and the circulating electric field vectors characteristic of a magnetic resonance.

where V is the PMM volume, αe and αm are the ED and MD polarizabilities, respectively, found using the PMM-centric scattering coefficients,38 and f is the volume fraction of PMMs within the dielectric. Implicit in this methodology for obtaining the effective constitutive parameters are the assumptions that individual PMMs can be accurately described as radiating dipoles, and that the polarizability tensor is isotropic. The justification for treating PMMs as electric and magnetic dipoles is illustrated in Figure 3a, where the scattering spectrum is almost entirely determined from dipolar contributions, and we can neglect quadrupolar and higher-order multipoles. Additionally, the high degree of symmetry in the pseudospherical PMMs leads to an isotropic optical response, which has been verified using GMM calculations to show that the extinction spectra are independent of the incident light polarization (Figure S6). The real parts of the effective permittivity and permeability for a metamaterial composed of 134 nm PMMs embedded in a dielectric medium with refractive index 1.33 are presented in Figure 4b,c, respectively, as a function of the volume fraction of PMMs within the dielectric material. As the volume fraction of inclusions is increased, the real part of the permittivity becomes elevated with respect to the background dielectric permittivity, while the real effective permeability exhibits a dispersive line shape centered at the MD resonance. Additionally, the strength of the dispersive feature in μeff increases and shifts toward longer wavelengths, indicative of a stronger collective magnetic response. Although this effective medium model does not account for PMM−PMM interactions, its results are expected to be accurate at low volume fractions31 and can be viewed as upper-bound estimates at high volume fractions.26,27 To illustrate the extent to which the bulk magnetic response may be spectrally tuned, Figure 4d presents the real part of the effective permeability for metamaterials composed of 20 nm AuNP PMMs of different diameters with the volume fraction fixed at 30%. Even at these modest and experimentally attainable filling fractions, the bulk permeability is significantly

calculated spectrum in this region is composed of two features: an ED mode near 690 nm and a strong MD mode centered at 710 nm. Repeating this analysis for the other PMMs reveals (Figure S2) that the PMMs composed of 10 nm NPs do not exhibit a strong MD response, whereas those made from 20 nm NPs exhibit a MD resonance that strengthens and red-shifts with increasing PMM diameter. It is also observed that the ratio of light scattered by the MD to the ED (when excited at the MD resonance wavelength) increases with PMM diameter. Although the NP building-block size undoubtedly affects the strength of the MD response, we attribute the absence of MD resonances in the 10 nm PMMs to their relatively small diameters. Indeed, although our synthesis method did not produce PMMs with diameters larger than 100 nm, GMM calculations of larger PMMs constructed from 10 nm NPs exhibit a MD resonance comparable in strength to similarly sized 20 nm AuNP PMMs (Figure S3). The optical properties of AgNP PMMs in this size range were also computed; similar sized structures to the Au PMMs were found to exhibit MDs in the visible, though the intensity of the MD was found to be strongly dependent on the amount of surface scattering included (Figure S4). Interestingly, electric-field map cross-sections (through the center of the PMMs in the incident plane) exhibit circulating electric-field vectors when excited near the MD resonance wavelength; Figure 3b shows such a field map for the 134 nm PMM (at 710 nm). This displacement current is clearly the source of the MD moment, which is oriented perpendicular to D

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CONCLUSIONS We have used theoretical modeling and electrodynamics calculations to describe the optical properties of small molecule cross-linker self-assembled AuNPs, which form colloidally stable PMMs. Using a size-tunable synthetic approach, a diverse group of PMM architectures were assembled and characterized using TEM imaging and UV−vis spectroscopy. GMM calculations were used to investigate the optical responses of individual structures as a function of NP building block and assembled PMM diameters, in each case producing reasonable agreement with experimental spectra. The 20 nm NP PMM architectures with diameters greater than ∼100 nm exhibit a strong, isotropic magnetic dipole resonance that can be tuned by changing the AuNP size and assembled PMM diameter. The high degree of structural tunability and low size and shape polydispersity make these dense cluster PMMs an attractive and flexible platform for creating magnetically responsive metamaterials at optical frequencies. Furthermore, the simultaneous presence of electric-field hot spots and strong MD fields potentially makes these structures ideally suited for applications involving surface-enhanced Raman optical activity,43 surface-enhanced circular dichroism,44,45 and chiral plasmons.46 The biocompatibility of these PMMs,32 coupled with the sensitivity of the MD resonance to PMM structure, could also enable their use as highly sensitive environmental probes in biomedical applications.

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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.7b03817. Additional details on PMM synthesis and characterization; convergence of GMM calculations; multipole decomposition spectra for all PMM structures; GMM spectra for >100 nm diameter 10 nm AuNP PMMs; AgNP PMM extinction and scattering spectra; extinction spectra of PMM structures ranging from core−shell to dense cluster architectures; isotropic PMM response; magnetic response of spheroidal PMM structures (PDF)

Figure 4. Effective optical parameters: (a) Schematic depiction of effective medium showing each inclusion is a single PMM characterized by electric (αe) and magnetic (αm) dipole polarizabilities. (b) and (c) are the real parts of the effective relative permittivity and permeability, respectively, as a function of volume fraction for 134 nm PMMs (20 nm AuNPs). d) Effective relative permeabilities at 30% volume fraction for 20 nm AuNP PMMs. PMM diameters are 105 nm (black), 134 nm (blue), and 165 nm (red).

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different from unity for each metamaterial considered. Although these results are calculated for the ideal case of no size and shape polydispersity, we do not expect a large deviation from the calculated values for samples with relatively low polydispersity (Figure S7). Despite this ability to modulate the effective permeability of these composite materials, the real part of the effective permeability never becomes negative, and the effective permittivity is also positive where the effective permeability shows dispersive behavior. Thus, we have not identified parameter ranges where a negative index material can be created from these PMM structures. Even so, it should also be noted that the bulk magnetic responses of these architectures are stronger than those previously observed in dielectric core−Au satellite PMM structures, even at low volume fractions.26 Furthermore, it is evident that the magnetic response may be tuned across a large spectral region solely by varying PMM diameter. Additional control over NP buildingblock diameter and PMM concentration (volume fraction) increases the flexibility to design magnetically responsive materials.

AUTHOR INFORMATION

Corresponding Authors

*G.C.S.: Phone: 847-491-5657; E-mail: g-schatz@ northwestern.edu *J.M.B.: Phone: 626-256-4673; E-mail: [email protected] ORCID

Marc R. Bourgeois: 0000-0002-9435-9051 Michael B. Ross: 0000-0002-2511-0594 Jacob M. Berlin: 0000-0001-7498-766X George C. Schatz: 0000-0001-5837-4740 Present Address §

M.B.R.: Department of Chemistry, University of California, Berkeley, Berkeley, CA 94720, U.S.A. Author Contributions ∥

M.R.B. and A.T.L. 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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ACKNOWLEDGMENTS This material is based on work supported by NSF Grant CHE1465045. M.B.R. gratefully acknowledges support through the NDSEG graduate fellowship program. A.T.L. gratefully acknowledges support through the H.N. & Frances Berger Foundation Fellowship. A.T.L. also acknowledges Desiree Van Haute for her mentorship and guidance on nanoparticle aggregate synthesis. Marcia Miller, Zhuo Li, and Ricardo Zerda are also appreciated for their assistance with TEM imaging. Research reported in this publication includes work performed in the Electron Microscopy Core at City of Hope supported by the National Cancer Institute of the National Institutes of Health under award number P30CA33572. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health.

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DOI: 10.1021/acs.jpcc.7b03817 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.jpcc.7b03817 J. Phys. Chem. C XXXX, XXX, XXX−XXX