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Coupling of Plasmon Resonances in Tunable Layered Arrays of Gold Nanoparticles Alastair Cunningham,†,§ Stefan M€uhlig,‡ Carsten Rockstuhl,‡ and Thomas B€urgi§,*,† † ‡
Physikalisch-Chemisches Institut, Ruprecht-Karls-Universit€at Heidelberg, Im Neuenheimer Feld 253, D-69120 Heidelberg, Germany Institute of Condensed Matter Theory and Solid State Optics, Abbe Center of Photonics, Friedrich-Schiller-Universit€at Jena, 07743 Jena, Germany ABSTRACT: Using bottom-up and self-assembly processes, large scale layered arrays of strongly coupled gold nanoparticles with controllable dimensions were fabricated. By carefully adjusting the distance between adjacent gold nanoparticle arrays, it is possible to control the coupling of the localized surface plasmon polariton resonance as sustained by individual gold nanoparticles. A greater interaction is observed at smaller separations, leading to a well pronounced shift in the spectral position of resonances that can be adjusted with high precision. Simulations showed good agreement with experimental observations in an in-depth investigation of such structures, suggesting minimal separations of only one nanometer are achieved.
’ INTRODUCTION The coupling of metallic nanoparticles can be described both qualitatively and quantitatively by plasmon hybridization,1 an analogous model to that used in molecular orbital theory, which describes the mixing and splitting of the dipolar localized surface plasmon polariton resonances (LSPR) exhibited by metallic nanoparticles. The model is both a useful means of explaining experimental observations and a powerful design tool that can be used to create new systems with specific properties. In the simplest case, coupling occurs between two spherical metallic nanoparticles of the same size and material, which are located close enough to interact also known as a dimer. The dipolar plasmons of the individual nanoparticles hybridize to form bonding and antibonding modes of lower and higher energies, respectively.2 In the vast majority of experimental work where this hybridization model is invoked and used to explain observable quantities of metallic nanoparticle dimers, the constituents are arranged directly on a supporting substrate and their properties are usually probed only at normal incidence. This configuration is favored since the controlled extension of dimers into the third dimension remains challenging and seems to be accessible only with top-down techniques such as electron beam lithography.3 However, metallic discs that are separated by a dielectric spacer4 rather than spherical nanoparticles are usually considered. The thickness of this spacer cannot be made sufficiently thin as it would not lead to a homogeneous film. This restriction in the degree of freedom to arrange particles limits the insights into the system. In particular, for homodimers made of identical spheres only one bonding and one antibonding mode, which exhibit a resulting dipole moment, could be excited for normal incidence. The remaining two are governed by resulting quadrupole moments and appear as dark modes. Although Alivisatos et al. showed that it is possible to excite all of the bonding and r 2011 American Chemical Society
antibonding modes through the preparation of compositionally asymmetric dimers, more experimental insights into the specific coupling of plasmonic entities upon arranging them in the longitudinal direction are required.5 The plasmon hybridization model itself is not only restricted to a consideration of spheres but has also been used to explain the coupling observed in assemblies containing particles of more complex geometries such as nanorods6 and concentric nanorings.1 The system under question in this study focuses on the coupling between two large-scale (cm2) gold nanoparticle (GNP) arrays immobilized on a substrate. The particles are sufficiently diluted within the arrays such that lateral coupling can be neglected. However, when the layer separation is within the constraints of the coupling limit of the particles7 their plasmon resonances interact in an assembly that can be approximated to being that of a single dimer.8 A clear signature of this coupling is a splitting into a bonding and an antibonding mode and a shift in the resonance wavelength of the LSPR sustained by the coupled GNP layers when compared to the individual. The extent of any change observed in the spectral profile upon the introduction of a second GNP array is dependent on the size of the nanoparticles,9 their separation,10 and the polarization of the incoming radiation with respect to the orientation of the main axis of the dimer.8 The necessary control of spacing is achieved in our contribution through the build-up of individual polyelectrolyte (PE) layers inbetween the GNP arrays in an extensively studied process known as layer-by-layer assembly.11 Here, the separation distance between the layered arrays of GNPs depends solely on the number of polymer layers used and the minimum separation is imposed Received: February 3, 2011 Revised: April 4, 2011 Published: April 20, 2011 8955
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The Journal of Physical Chemistry C by the thickness of an individual PE layer. The electrostatic attraction between the oppositely charged polymers and the introduction of negatively charged GNPs gives rise to a highly flexible system with a large degree of control over a wide variety of parameters, almost to within nanometer precision. Other than for reasons of practicality, no limitations exist in the fabrication of these structures in that as many polymer and GNP layers can be deposited as is deemed fit for the purposes required, allowing the further tuning of the optical properties. These assemblies can be realized by allowing the layers to self-assemble in a true bottomup approach12 or through the utilization of other techniques such as spin-coating.13 Whereas no long-range order between GNPs is observed, several advantages exist over certain studies of ordered binary nanoparticle superlattices.14,15 The simplicity and robustness of the system gives a large degree of flexibility, which would otherwise be difficult to achieve, allowing the inclusion of almost any charged species. Additionally, the large scale of the deposition process, whereby films covering several square centimeters can be routinely fabricated, offers the very real possibility of developing applications for such structures by incorporating them into optical components. With largely enhanced electromagnetic fields existing in the space between dimers of GNPs, it can be envisaged that such assemblies have applications in the field of surface-enhanced Raman spectroscopy (SERS).16,17 It has also been shown that such assemblies of GNPs can be used in the control of the propagation of light and in the preparation of nanolenses.18 Additionally, when the bottom-up nature of the fabrication process and small dimensions involved are considered it can be seen that such systems also offer possibilities in the field of optical metamaterials where the down-scaling of structures and the extension toward truly 3D metamaterials are some of the principal challenges faced by the community.1921 In our work, we present complementary results taken from experimental work and simulation relating to the interaction between two large-scale arrays of GNPs. The effect of particle size is shown along with GNP array separation at a variety of defined distances.
’ EXPERIMENTAL METHODS All chemicals were purchased from Sigma-Aldrich. All solutions were prepared using Milli-Q water (18.2 MΩ-cm). GNPs were prepared according to the well-known Turkevich method.22 Briefly, 600 mL of a 0.25 mM solution of HAuCl4 under constant magnetic stirring was heated to 100 °C in an oil bath. The gold was then reduced through the addition of 15 mL of a 0.03 M sodium citrate solution. A series of color changes were observed before a deep-red solution was produced and after 15 min the reaction vessel was removed from the oil bath and allowed to cool to room temperature. Silicon and glass substrates, used for electron microscopy and spectral measurements respectively, were prepared according to the same method. They were first rinsed with water and ethanol before being dried under a stream of nitrogen. The surfaces were then cleaned and hydroxylated through immersion in a piranha solution (3:1 mixture of concentrated sulfuric acid to 30% hydrogen peroxide) for 30 min. Piranha solution is strongly acidic and highly oxidizing and should be handled with caution. The substrates were next rinsed with copious amounts of water and again dried under a stream of nitrogen. Subsequently, the
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Figure 1. SEM micrograph showing GNPs of radius 10 nm deposited on a functionalized silicon substrate.
surface chemistry was altered through the functionalization with an organosilane.23 Here, the substrates were immersed in a 5% (v/v) solution of N-[3-(Trimethoxysilyl)propyl]ethylenediamine in ethanol for 30 min before being rinsed with water, dried, and set in an oven at 120 °C for a further 30 min. The positive charge of the terminal amine group on the functionalized substrate allows the deposition of both GNPs and a negatively charged PE through purely electrostatic interactions. Similarly, positive PE layers can be deposited on either GNPs or negative PE layers. Single layers of GNPs were deposited by immersing them in a solution of GNPs for a period of four hours. PE layers were deposited from 5 mg/mL solutions of poly(allylamine hydrochloride) and poly(sodium 4-styrenesulfonate) in a 0.1 M solution of sodium chloride in water. PE layers were deposited for 1 min before being rinsed with water and dried under a stream of nitrogen. The electrostatic nature of the fabrication process allows for the cyclic build-up of multiple GNP and PE layers. The Turkevich method results in nearly spherical GNPs. Therefore, the measured spectra can be simulated by relying upon analytical solutions of Maxwell’s equations for a single sphere, better known as Mie theory. The framework of Mie theory is extendable to layers of periodically arranged spheres,24 known as the Korringa Kohn Rostoker (KKR) method, or to an arbitrary arrangement of spherical particles.25,26 Applying both mentioned extensions of Mie theory in this contribution allows for the simulation of the measured spectra. In the simulations, the material parameters of gold were taken from literature.27 A sizedependent correction was taken into account to reflect that the material properties of such small particles will deviate from those of the bulk.28 In the simulations, all structures were illuminated by a linearly polarized plane wave.
’ RESULTS AND DISCUSSION The deposition of GNPs of radius 10 nm directly on a functionalized silicon substrate resulted in a complete single layer as can be seen in the SEM micrograph as shown in Figure 1. The GNPs are well dispersed and approximately equally spaced. However, they do not show a discernible organization or order. They have a density in the order of 850 particles/μm2, equating to a total surface coverage of 27%. Figure 2 shows the measured extinction cross section from such an array and results 8956
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Figure 2. Experimental extinction cross section of a single layer of GNPs immobilized on a glass substrate (green trace, right-hand axis) and corresponding simulated extinction cross sections for a single gold sphere (red trace, left-hand axis) and gold spheres arranged onto a square lattice (blue trace, left-hand axis) covering 27% of the surface.
Figure 3. LSPR wavelength of a single array of GNPs (radius 10 nm) on a glass substrate as a function of the number of covering PE layers deposited. Both experimental (red squares) and simulated (blue diamonds) data are shown.
from simulations, where two configurations were considered. As can be seen, the simulated extinction cross section of a layer of GNPs arranged onto a square lattice with an identical surface coverage to that observed experimentally coincides with the extinction spectra from an isolated sphere. The extinction of the single GNP was simulated by integrating the electromagnetic fields (as obtained from Mie theory for a single sphere) over the surface of a sphere surrounding the GNP. To access the extinction of the square lattice of GNPs, we simulate the transmittance t through an infinite extended slab of GNPs on a square lattice under normal plane wave incidence with the KKR method. Then the extinction is defined as 1-t. Because both simulated extinctions almost coincide, the optical response of the fabricated GNP array should be largely dominated by that of the single GNP, which is linked to the excitation of a localized surface plasmon polariton. Although the strict periodic arrangement in the simulations deviates from the observed amorphous order in the experiments, it is feasible to describe the optical response of the fabricated structure with such an assumption because coupling in the transverse direction can be safely neglected at the particle separations observed. Moreover, the critical distances both between GNPs within layers and between layers are much smaller than the wavelength of light, which could otherwise led to additional interesting phenomena.29,30 The validity of the assumed model is supported by the close correlation between the
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Figure 4. Magnitude of the electric field (in terms of the incident field) with direction k and polarization E for a GNP with 10 nm radius at the LSPR resonance wavelength in the central cross section of the GNP.
experimental and simulated traces shown in Figure 2. The only noticeable discrepancy is a weak broadening and damping of all spectrally resolved quantities for an amorphous structure. This is caused by the distribution of the separation between nearest neighbor GNPs that induce a minor shift of the LSPR to both longer and shorter wavelengths as well as being due to radiative coupling of particles in the lattice.31 Additionally, the preparation method produces particles that are extremely monodisperse although slight variations in particle size do exist also contributing to broadening of spectra. The LSPR is highly sensitive to changes in the surrounding medium, with an overall increase in dielectric constant resulting in the peak position shifting to higher wavelengths.32 No splitting of the resonance will occur. As such, the deposition of PEs on an array of citrate capped GNPs, which were previously exposed to air causes a red-shift of the LSPR wavelength, as can be seen in Figure 3. The differential shift decreases upon successive depositions, which can be explained by the exponential decay of the evanescent fields of the LSPR localized at the surface of the GNP. Outwith the exponential penetration depth the localized field no longer probes the surrounding medium and the spectral position of the resonance tends to saturate. Figure 3 shows the excellent agreement between the simulation of depositing PE layers on a periodic arrangement of the GNPs with a surface coverage of 27%, represented by diamonds, and the corresponding experimental measurements, represented by squares. Numerous factors, such as polymer molecular weight, deposition time, and ionic strength of solution, influence the polymer layer thickness and to match the experimental results the thickness of 1 PE layer has to be chosen as 0.9 nm and the corresponding refractive index set to 1.5. These values, selected to represent the structure, allow for a good fit between experimental and simulated data and are on a comparable scale to literature values given for similar systems.33,34 Furthermore, this agreement could only be achieved when the PEs were allowed to penetrate to a certain extent into the gaps of the GNP layer. Such penetration sensitively affects the surface plasmon band because the field distribution of the LSPR localizes in close vicinity to the GNPs. The maximum field enhancement occurs parallel to both the polarization of the electric field and to the GNP layer as can be seen in Figure 4. If the PEs were stacked perfectly on top of the GNP layer, the maximum field enhancement would occur in the region of air and no remarkable red shift could be measured because a large portion of the field does not experience the modified dielectric surrounding. Following an odd number of PEs, a second GNP array can be deposited. Figure 5 is an SEM micrograph showing two layers of 8957
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Figure 7. Red-shift upon addition of a second layer of GNPs (radius 10 nm) as a function of layer separation. Both experimental (squares) and simulated (blue solid line) data are shown. Figure 5. SEM micrograph showing two separate GNP (radius 10 nm) arrays separated by 31 polyeletrolyte layers.
Figure 6. Schematic showing hybridization of plasmons. Red crosses indicate dark modes that only offer a weak excitation for the present configuration.
GNPs separated by 31 PE layers. The initial GNP array can be seen below as gray shadows, whereas the second array is clearly seen above. The second deposition of GNPs occurs preferentially, although not exclusively, in the gaps between the GNPs of the first array and has the same particle density as described above for the first GNP array. The addition of a second array of GNPs results in a splitting of the single resonance into two, where the dominant one is strongly red-shifted. Because the optical response within a single GNP layer was dominated by the LSPR of a single sphere, this red-shifted resonance should be governed by the mutual coupling of spheres from distinct GNP layers. As outlined in the Introduction, the coupling of two spheres can be described with the principles of plasmon hybridization theory shown schematically in Figure 6. Both the bonding and the antibonding situations are shown with the resonance of the single particles being treated as a pure dipole oscillation. The interaction of two equal spheres results in four hybridized plasmonic modes in
the coupling regime. Because of symmetry considerations, only two of these modes display a net dipole moment and will show a strong scattering of light into the far-field at relevant frequencies and angles of incidence. Conversely, both the antibonding mode for incident light parallel to the main axis of the dimer (σ*) and the bonding mode for incident light perpendicular to the main axis of the dimer (π) have no net dipole moment and are known as dark modes (noted in Figure 6 with red crosses) that can only be observed by breaking the symmetry of the system and for large spheres with extremely small interparticle distances. These dark modes contribute predominately to the absorption of the system because the resulting quadrupole moments offer only a weak coupling to the far field. The deposition of a second GNP layer, as shown in Figure 5, also excites the dark eigenmodes because the symmetry is broken along the propagation direction. As the arrangement in both GNP layers offers a completely amorphous order compared to the polarization of the incident light, all eigenmodes, the two bonding and the two antibonding, are potentially excited in the experiments. However, as is seen in Figure 6, the dominating mode that shifts to longer wavelengths is the bonding mode with a resulting net dipole moment. Therefore, the authors wish to stress that the excitation of this eigenmode, indicated as σ in Figure 6, dominates the extinction in the experiments. The magnitude of the spectral shift of the dominant resonance is strongly dependent upon the separation of the two layers as can be seen in Figure 7. The red-shift decreases with increasing layer separation until the particles are moved outwith their coupling limit. An excellent agreement between experimental (squares) and simulated (solid line) results is observed. The shift in resonance due to coupling was extracted by subtracting the LSPR wavelength of the second GNP array after the deposition of a finite number of PE layers from that of the first GNP array after the deposition of the same number of PE layers. This was in order to accommodate for the additional red-shift observed, seen in Figure 3, when the PE layers cover the initial GNP array. In the simulation of the experimental results of two GNP layers, we investigated dimer structures that consist of two GNPs. As shown before, the optical response of a single GNP layer is dominated by the single particle resonance and not by the interaction between neighboring particles. On the one hand, the average center to center distance between two neighboring particles inside a single layer is about 34 nm for GNPs with a radius of 10 nm, which simply follows from the surface coverage of 27%. On the other hand, the distance between two consecutive 8958
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Figure 8. Geometrical configuration of the dimer structure showing the direction of the impinging wavevector (k), one polarization of the electric field (E) (the other considered polarization is parallel to the y axis) and both the lateral (dx) and vertical (dz) separation of the GNPs.
Figure 10. Experimental extinction cross section of one GNP (radius 20 nm) array (left-hand axis, black trace) and several GNP bilayer arrays separated by 11, 21, 41 PE layers (right-hand axis; blue, red, and green traces, respectively).
Figure 9. Red-shift upon addition of a second layer of GNPs (radius 20 nm) as a function of layer separation. Both experimental (squares) and simulated (blue solid line) data are shown.
GNP layers can be very small due to the thickness of a single PE layer, which for the purposes of this study was chosen to be 0.9 nm. The refractive index of the PE layers was set at 1.5. With the geometrical parameters in mind, it is clear that the optical response of the structure consisting of two stacked GNP layers and only a few PEs in-between should be dominated by the interaction between particles in different layers. As a consequence, all observations can be explained by considering the coupling of just two GNPs, one from the bottom layer and one from the top layer. Figure 8 shows the arrangement of the dimer that was considered in the simulations. The lateral separating distance, dx, was derived from the average GNP separation and the observation that most of the spheres from the second GNP layers occur in the gaps of the first GNP layer. The vertical separating distance, dz, describes the thickness of the added PEs in-between the GNP layers. Both polarizations of the incident field (perpendicular and parallel to the dimer orientation) were superposed to take into account the isotropic orientation around the surface normal, which suggests no polarization preference at normal incidence. The surrounding medium was chosen as an ordinary dielectric with a permittivity corresponding to that of the PEs. The same procedure to extract the shift in the resonance wavelength as described above was applied to diminish the deviations that occur because of the more complex dielectric surroundings in the experiments, that is the presence of a substrate and the presence of air above the second GNP array. Overall, in the experiments and in the simulation, a remarkable shift of up to 110 nm is observed for only one separating PE layer, corresponding to a distance between the GNP arrays of 0.9 nm. The excellent agreement between simulation and experiments opens up the possibility of designing, with a great degree of freedom, dimer particles with a fixed separation and tailored optical properties.
Figure 11. Evolution of longitudinal plasmon peak at shorter GNP (radius 10 nm) layer separations. Shown are the optical responses of a single array of GNPs measured on a glass substrate (lower solid line, lefthand axis) and both the experimental (left-hand axis, upper solid line) and simulated (right-hand axis, dashed line) spectra of a double array of GNPs with one separating PE layer.
The interaction between particles is even stronger and extends further for larger particles coupling limits being essentially a function of particle size. Therefore, a more pronounced red-shift is observed for comparable separations when larger particles are used, as shown in Figure 9. Again, an excellent agreement between experimental (squares) and simulated (solid line) results exists. Additionally, it can be seen that larger separations are required to shift the layers of particles outwith the coupling limits. This further increase of PE layers results in a reduction of the interaction of the GNPs and the optical response should again be dominated by that of a single particle with no observable red-shift. The spectral evolution corresponding to the data given in Figure 9 are shown in Figure 10. Here, the spectra of two GNP (20 nm radius) arrays separated by 11, 21, and 41 PE layers (lefthand axis; blue, red, and green traces, respectively) are compared with that of a single GNP array (left-hand axis, black trace). It can clearly be seen to what extent it is possible to tune the spectral response of such systems simply by varying the number of separating layers. Note that the spectral shift in Figure 9 has been corrected for the additional shifts observed upon the deposition of PE layers, as described in Figure 3. In addition to the increasing red-shift detected at smaller array separations, another measure of the extent of interaction between the two GNP layers is the degree of peak broadening observed. As can be seen in Figure 10, the full width at half maximum (fwhm) of the 8959
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The Journal of Physical Chemistry C spectra of two coupled GNP arrays increases as the particle separation decreases, giving further proof that the coupling strength between GNP arrays is greater when they approach. When GNP array separation is extremely small, for example by depositing only a single PE layer between two arrays, a rather amorphous structure containing a variety of dimer orientations relative to the incident wave vector results. In such a configuration, all of the bonding and antibonding eigenmodes can be excited as has been previously discussed in this contribution and demonstrated.35 Again, only the eigemodes with a resulting dipole moment dominate the extinction spectra. As a consequence, both of them should be simultaneously excited and the LSPR should split into two individual and resolvable resonances. This was both observed experimentally and predicted by simulation as can be seen in Figure 11. The simulated trace is shown (dashed line, right-hand axis) in addition to both the measured optical response from a single layer of GNPs (lower solid line, left-hand axis) and the splitting is observed when a second layer of GNPs is deposited with only one PE separating layer between (upper solid line, left-hand axis). In Figure 11, both eigenmodes with a resulting dipole moment, π* and σ (Figure 6), can be observed with the π* (σ) coupled plasmon being observed at shorter (longer) wavelengths.
’ CONCLUSIONS In conclusion, a means to fabricate a sequence of layered arrays of gold nanoparticles with tunable interlayer separations as well as a detailed study of their optical properties has been presented. Good agreement was found between experimental and simulated data. It was shown that the deposition of PE layers on a single GNP layer could be modeled accurately and followed trends expected from rigorous simulations of Maxwell’s equations. A decrease in coupling strength as a function of separating distance between two layered arrays of GNPs was observed and simulated as well as the effect that particle size has on this system. It was shown that with larger particles a stronger coupling occurs for comparable layer spacing. Additionally, at short separations plasmon hybridization was seen to occur with the splitting of the dipolar excitation observed in single GNPs into two separate resonances the longitudinal σ and transversal π* modes. ’ AUTHOR INFORMATION Corresponding Author
*Tel: þ41 22 379 65 52, E-mail:
[email protected]. Present Addresses §
Departement de Chimie Physique, Universite de Geneve, Quai Ernest-Ansermet 30 1211 Geneve 4, Switzerland.
’ ACKNOWLEDGMENT Financial support from the European Union FP7 project NANOGOLD and the German Federal Ministry of Education and Research (PhoNa) is acknowledged.
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