Article pubs.acs.org/JPCC
Predicting the Localized Surface Plasmon Resonances of Spherical Nanoparticles on a Substrate: Electrostatic Eigenmode Method Alison Chou,*,† Kristy C. Vernon,‡ Lennart Piro,‡,§ Babak Radi,† Esa A. Jaatinen,‡ and Timothy J. Davis∥ †
Chemistry Discipline and ‡Applied Optics and Nanotechnology, Queensland University of Technology, Brisbane 4001, Queensland, Australia § Karlsruhe Institute of Technology, Karlsruhe, Germany ∥ CSIRO Materials Science and Engineering, Clayton 3169, Victoria, Australia ABSTRACT: We present experimental results that demonstrate that the wavelength of the fundamental localized surface plasmon resonance for spherical gold nanoparticles on glass can be predicted using a simple one-line analytical formula derived from the electrostatic eigenmode method. This allows the role of the substrate in lifting mode degeneracies to be determined and the role of local environment refractive indices in the plasmon resonance to be investigated. The effect of adding silica to the casting solution in minimizing nanopaticle agglomeration is also discussed.
1. INTRODUCTION Surface plasmon polaritons are surface-charge waves supported at a metal−dielectric interface, such as the interface between a metal film and air or the surface of a metal nanoparticle and the surrounding dielectric environment.1 On the surfaces of metal nanoparticles, the surface charges can form standing waves at particular frequencies; these are called localized surface plasmon resonances (LSPRs). They are coherent oscillations of the conduction electrons of the metal nanostructure that can be excited by an incident light beam. The wavelength λmax of the LSPR peak depends on the size, type, and shape of the nanoparticle as well as the dielectric properties of the local environment including the substrate, solvent, and adsorbates.2,3 Metal nanoparticles are used extensively in spectroscopic, biomedical, and photonic applications. Such nanoparticles can be used as sensors based on the coupling of the incident light to the LSPR, with sensitivities related to the wavelength change of the LSPR with molecular binding.4−8 In many applications, the nanoparticles must be placed on a support substrate, which leads to a shift in the LSPR wavelength3,9−11 and, in some cases, a change in the degeneracy of the LSPR modes.12,13 The wavelength shift in the LSPR can be predicted from first principles for spherical and ellipsoidal particles using the method of images.9−12 Vernon et al.9 have also demonstrated that the LSPR wavelength can be estimated for an arbitrarily shaped nanoparticle on a substrate by using a combination of the method of images and the electrostatic eigenmode method.14 As demonstrated in ref 11, not only can the method be used to estimate the changes in LSPR wavelengths that arise from particle−substrate interactions, but it can also be used to infer the mechanisms and strength of the particle−substrate © 2012 American Chemical Society
interaction. An important development of this work is a simple analytical formula that gives the LSPR wavelength of the particle on a substrate if the wavelength of the LSPR of the same particle is known when in a homogeneous medium.9 Such a formula is quick to use as long as the coupling strength and plasmon resonance in the absence of a substrate are known.9 The validity of this formula for nanorods was demonstrated by comparing the predictions to measured scattering spectra of gold nanorods on indium tin oxide (ITO).9 However, the fundamental LSPR of nanorods is nondegenerate. This is in stark contrast to highly symmetrical nanoparticles such as spheres, nanoshells, and nanocubes.11,12 In recent years, there has been much work on the properties of symmetric nanoparticles on substrate resulting from the lifting of the degeneracy in the presence of a substrate. This lifting of the degeneracy modifies the coupling of the LSPR to the far field, and additional scattering and absorption peaks may form.11,12 In this article, we will verify that the approach devised by Vernon et al.9 is valid for predicting the LSPR of 25 nm spherical gold nanoparticles (AuNP's) deposited on a glass substrate (AuNP/glass) in various solvents. We show that the method can be used to investigate the lifting of degeneracy in a homogeneous medium to the resonance of the particle on the substrate. A full-field numerical solution using COMSOL Multiphysics 4.2a was also conducted for technique comparison. The measured dependence of the LSPR wavelength on Received: July 30, 2012 Revised: September 23, 2012 Published: October 1, 2012 26517
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M-5, average particle length of 0.2−0.3 μm) was kept constant at 1 mg/mL of water (0.1 wt %), and the AuNP concentration was varied by diluting the original concentration. The original AuNP concentration was 1.6 × 1013 nanoparticles/mL. The dilution series was three-fourths, one-half, one-fourth, and oneeighth the original AuNP concentration. Samples were prepared in demineralized water and subjected to 40 kHz sonication for 10 min prior to use. 2.2. Electron Microscopy. Transmission electron microscope (TEM) images of AuNP's were collected using a JEOL JEM2100 LaB6 STEM. The morphology of the AuNP films was investigated using a field-emission scanning electron microscope (JEOL JSM-7001F) operated at 10 kV. Imaging of the AuNP film on the glass slide was initially attempted. However, the images were distorted by the surface potential caused by charging. The charging effect could be reduced by coating with evaporated gold films, but this was not considered because the gold coating might interfere with the morphology of the AuNP's. Thus, AuNP's were dropped onto stainless steel slides for SEM imaging purposes. 2.3. Extinction Measurements. The extinction spectra of spherical gold nanoparticles on glass were obtained with a Cary 100 spectrophotometer using a CW broadband light source. To measure the extinction of glass-bound spherical gold nanoparticles in different refractive index environment, four liquids of index 1.3 to 1.5 were selected. The liquids were water, acetonitrile, isopropanol, and benzene. The liquid to be tested was dropped onto a AuNP/glass slide and placed inside a clean, dry transparent sleeve constructed from coverslips (20 mm × 20 mm, 0.085 mm thick) with a snug fit to prevent the solvent from evaporating during the measurement. Measurements in air were also carried out.
the refractive index shows good agreement with the theoretical prediction. Commonly used drop casting of colloids onto a substrate was used to prepare the AuNP/glass samples. However, drying in air by evaporation can cause particles in close proximity to each another to agglomerate because of diffusion-limited agglomeration.15 The agglomeration state of AuNP's has an effect on their optical properties. As the nanoparticles are brought close together, they have a strong dipole−dipole interaction shifting the LSPR band to higher wavelength.16,17 Such an interparticleinteraction-induced wavelength shift should be minimized as much as feasible. In this work, particle separation was controlled by dispersing gold nanoparticles in a 0.1 wt % silica suspension in deionized water. We postulate that the abundant hydroxyl groups (silanol) on the surface of silica can hydrogen bond with the citrate-capped gold nanoparticles, thus minimizing the nanoparticle agglomeration as water evaporates. By ensuring a sufficient separation distance between the nanoparticles, interparticle coupling is minimized. To establish whether our approach to minimizing aggregation using silica is effective, AuNP films prepared with and without silica were compared. Silica (0.1 wt %) was added to a series of casting solutions containing different AuNP concentrations (2 × 1012, 4 × 1012, 8 × 1012, 12 × 1012, and 16 × 1012 particles/mL) and compared to those cast without silica to examine the degree of particle agglomeration when dried on glass at room temperature. Different AuNP concentrations were investigated because the extent of particle agglomeration can also be influenced merely by adjusting the AuNP concentration; as the particle−particle distance increases with dilution, the attraction between particles is weakened, resulting in less agglomeration. Agglomeration was analyzed by comparing the LSPR wavelength of the glass-bound AuNP's prepared from different AuNP concentrations with (AuNPsilica/ glass) and without silica (AuNP's/glass) on the basis of the red shifting of the plasmon resonance as the cluster size is increased. From this experiment, an appropriate ratio of AuNP to silica was determined and used for the measurement of LSPR of spherical nanoparticles on glass for various refractive index liquids. Although it is possible to encapsulate AuNP's with silica to ensure a much greater range of interparticle spacing,18 our aim is to measure the LSPR of glass-bound AuNP's in direct contact with different optical environment surroundings.
3. RESULTS AND DISCUSSION Figure 1a shows a TEM image of the spherical AuNP's used in this work. The average diameter of the AuNP's is ∼25 nm. The LSPR λmax of the AuNP's suspended in water with and without 0.1 wt % silica is 523 nm and did not vary significantly with AuNP concentration (Figure 1b). When suspended in water, surface contact between AuNP's is prevented by the negative surface charge repulsion from the citrate ions on the surfaces of AuNP's. For agglomeration to occur, the repulsive electrostatic force must be overcome. However, no significant correlation between the LSPR λmax and the AuNP concentration was observed, suggesting that the critical concentration for AuNP's to agglomerate in water is probably outside the concentration range studied. A 0.1 wt % silica suspension in water showed negligible extinction between 900 and 350 nm. A photograph of the AuNP films prepared from different AuNP concentrations is shown in Figure 2a. The top row shows the films cast without silica, and the bottom row contains 0.1 wt % silica in the casting solution. The AuNP concentration effect on the LSPR λmax is more pronounced when the nanoparticles are dried on glass. According to the full-field numerical simulation with COMSOL Multiphysics, the predicted LSPR λmax is 512 nm for a single gold nanoparticle on glass. In comparison, the experimental λmax of the AuNP/ glass (undiluted) is red shifted 30 nm from the theoretical prediction (542 nm). The wavelength shift becomes less as the AuNP concentration decreases; 539 nm for films cast from onefourth of the original AuNP concentration, indicating that dilution can reduce the interparticle-induced LSPR λmax shift (Figure 2b). A similar correlation trend between the AuNP
2. EXPERIMENTAL SECTION 2.1. Preparation of Spherical Gold Nanoparticles. The spherical AuNP's used in this work were synthesized using the citrate reduction method.19 Sodium citrate (20 mL of a 4% solution) was added to 100 mL of 4 mM HAuCl4 at 90 °C. The mixture was kept at 90 °C with stirring for 20 min and cooled to room temperature before use. The size of the gold nanoparticle can be controlled by varying the citrate/gold precursor concentration ratio.20 Gold nanoparticle concentrations were calculated using an extinction value of 8.78 × 108 M−1 cm−1 from Liu.21 The AuNP's were deposited onto clean glass slides by delivering 400 μL of casting solution to a clean, dry microscope glass slide and allowed to dry at room temperature. The refractive index of the microscope glass slide used was 1.5 between 400 and 600 nm as measured by an ellipsometer (J. A. Woolam Co.). Casting solutions of different AuNP to silica ratios were prepared by adjusting the AuNP concentration. The concentration of fumed silica (CAB-O-SIL 26518
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Figure 3. Fraction of original AuNP concentration with and without 0.1 wt % silica plotted against LSPR λmax. The error bars show a standard deviation over six measurements at different positions near the center of the film, and the lines are regression lines. The AuNP concentrations were 2 × 1012, 4 × 1012, 8 × 1012, 1.2 × 1013, and 1.6 × 1013 particles/mL. Figure 1. (a) TEM image showing the spherical gold nanoparticles used in this work. (b) Overlay extinction spectra of the spherical AuNP's and AuNP's plus 0.1 wt % fumed silica suspended in water. Extinction increases with increasing AuNP concentration as shown by the vertical arrow. The red trace corresponds to the original AuNP concentration. The dotted line shows the LSPR λmax at 523 nm.
which the AuNP concentration−aggregation correlation becomes strong and uninfluenced by the 0.1 wt % silica. A probable explanation is surface saturation of silica with excess AuNP's agglomerating into clusters. The difference between the λmax wavelengths of AuNP/glass and AuNPsilica/glass is attributed to the extent of particle agglomeration, which is reduced in the presence of silica as shown in the SEM images in Figure 4a,b. The SEM image of the AuNP-only film shows clusters of AuNP's with the sizes of the clusters between 50 and 200 nm. The agglomeration of a colloidal suspension during drying has been investigated before.22,23 Agglomeration occurs during droplet drying because as the water evaporates the amount of water mass
Figure 2. (a) Photograph of the AuNP films on glass. Extinction spectra of AuNP/glass films prepared from different gold concentrations (b) without and (c) with 0.1 wt % silica. The yellow trace corresponds to 0.1 wt % silica dried on glass with no AuNP's. Spectra plotted at increasing AuNP concentration from bottom to top. The dashed line shows the LSPR λmax at 512 nm predicted by the COMSOL simulation.
concentration and the LSPR λmax was observed with AuNPsilica/ glass but with a smaller wavelength shift overall (Figure 2c). The LSPR λmax values for AuNPsilica/glass cast from the undiluted AuNP were 532 and 523 nm for the one-fourth dilution. This is closer to COMSOL’s prediction at 512 nm. However, the effectiveness of silica is still limited to the AuNP concentration. As shown in Figure 3, silica is effective at onesixth and one-fourth the original AuNP concentration, above
Figure 4. SEM images of the AuNP film on a stainless steel slide. (a) AuNP-only solution (one-fourth dilution). (b) AuNP (one-fourth dilution) and 0.1 wt % fumed silica. The white dots are AuNP's. (c) Schematic representation of the intermolecular hydrogen bonding between citrate ions on AuNP's and the silanol groups on the surface of fused silica. (d) Histogram showing the separation between gold nanoparticles on glass in the presence of silica. N = 96. The average distance measured is 123 nm. 26519
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Figure 5. (a) Extinction spectra of spherical gold nanoparticles on glass measured in media with different refractive indices. (b) Experimental resonance data compared to calculations based on eq 1 and on full-field numerical simulations using COMSOL. For eq 1, two different γ values with one degenerate mode were used to represent two fundamental plasmon modes of a sphere with respect to incoming unpolarized light: S and P polarizations. The permittivity of gold was taken from Johnson and Christy.26 Error bars of the measured values denote five independent measurements. The inset shows a schematic illustration of the dipolar modes of spherical gold nanoparticles on a glass substrate. The 3-folddegenerate dipolar mode splits into a mode oriented perpendicular to the substrate (S mode) and two degenerate dipolar modes (P modes) oriented parallel to the substrate. Blue represents regions of negative charge, and green represents regions of positive charge. (c) Left-hand side (LHS) of eq 1. The straight line is a linear fit to the real part of gold permittivity for wavelengths from 520 nm onward. The five data points are the locations of the peak LSPR for air and the four solvents used as predicted by eq 1.
⎛ ε ⎞⎛ 1 + Re(ε(ωs)) = Re(ε(ωR ))⎜ b ⎟⎜ ⎝ εR ⎠⎜⎝ 1 +
decreases while the AuNP mass remains constant and the droplet diameter continuously shrinks. Consequently, the evaporation losses of the water account for the motion of the AuNP's. If a wet particle collides with another particle and is bound by a liquid bridge, then the capillary force of the liquid bridge will pull the particles toward each other, leading to agglomeration.24 However, the AuNP film containing 0.1 wt % silica appears to be more dispersed and less agglomerated. We attribute the difference to the possible hydrogen bonding between the carboxyliate from the citrate and the surface silanol groups from silica (Figure 4c). We examined the separation of the nanoparticles on glass in the presence of silica from the SEM image shown in Figure 4b. The average separation distance was 123 nm from 96 measurements of distances between two randomly selected particles. The smallest separation between two particles was 20 nm (Figure 4d). When AuNP's are dried on glass, the LSPR λmax can be affected by the substrate and the refractive index of the medium. It can also be affected by the AuNP agglomeration, which is influenced by the AuNP concentration as shown. This result shows the effect of silica in reducing particle agglomeration because the refractive indexes of the medium (air) and the substrate (glass) were the same in both cases. Samples for measurement in different refractive index media were prepared with the one-fourth dilution (4 × 1016 AuNP's) in 0.1 wt % fumed silica. Figure 5a shows the results of the measurements of the LSPR extinction band for the 25 nm spherical gold nanoparticle deposited on glass and placed in solvents with different refractive indexes. As the refractive index of the solvent increases, λmax of the fundamental LSPR increases as expected. The simple analytical formula derived from the electrostatic eigenmode method was then used to predict λmax and was compared to the experimental results (Figure 5b). The following simple analytical equation was used
ηT 1+γ ηT 1−γ
⎞ ⎟ ⎟ ⎠
(1)
where ωs is the frequency of the LSPR for the gold nanoparticle on the substrate, ωR is the frequency of the LSPR for the gold nanoparticle in a homogeneous medium, εb is the permittivity of the solvent, εR is the permittivity of the homogeneous medium, T is the coupling strength of the particle to the substrate when the fundamental LSPR is excited, γ is the eigenmode of the particle when the fundamental plasmon mode is excited, and η is ⎛ ε − εs ⎞ η=⎜ b ⎟ ⎝ εb + εs ⎠
(2)
The T and γ values for the sphere depend on which of the fundamental LSPRs is excited. In a homogeneous medium, the fundamental LSPR of the sphere is 3-fold degenerate. However, when the sphere is placed on a dielectric substrate such as a glass plane, the degeneracy is lifted.25 The 3-fold-degenerate dipolar mode splits into a mode oriented perpendicular to the substrate (S mode) that red shifts compared to the two degenerate dipolar modes (P modes) oriented parallel to the substrate. The T values for the two eigenmodes are −0.24 and −0.48 with the associated γ value of 3.0. A schematic of the surface charge distribution of the S and P modes is shown in the inset of Figure 5b. The homogeneous medium used in eq 1 is the gold nanoparticles in water, which had a measured LSPR extinction wavelength of 523 nm (Figure 1e). Figure 5b shows a comparison among the full-field COMSOL numerical simulations, the analytical formula (eq 1), and the experimental data. The theoretical predictions from eq 1 were less than 3% different from the experimentally measured values, thus demonstrating the validity of eq 1 for predicting the shifted LSPR of metal nanoparticles on a substrate, even in the presence of lifting the mode degeneracy.9 The clear match between the COMSOL data and the experiment indicates that the particles are well dispersed so 26520
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that no interparticle interactions are occurring (COMSOL data was given for a single gold nanoparticle of diameter 25 nm). The largest difference between theory and experiment occurs for gold nanoparticles on glass in air. Using eq 1, we predicted the wavelength of LSPR in air to be between 501 and 504 nm depending on whether the S or P modes are considered. COMSOL simulations yield an LSPR wavelength of 512 nm, which is closer to the experimental value. We propose that the departure from the value predicated by eq 1 for the case of air is due to the nonlinear dependence of the gold dielectric permittivity wavelength, which is caused by the electronic interband transitions in gold below 500 nm. Figure 3c is a plot of the real part of the permittivity of gold versus the wavelength. It can be seen that the permittivity is essentially a function of wavelength for wavelengths greater than 520 nm. When the nanoparticle is placed in an environment where the refractive index is 1.2 or greater as in the case of water, acetonitrile, isopropanol, and benzene, λmax of the fundamental LSPR predicted by eq 1 falls in the region where the permittivity is linearly dependent on the wavelength. In air, the value is on the cusp of the region where the permittivity deviates from linear behavior. This implies that eq 1 works well in the regime where the permittivity of gold depends linearly on the wavelength, but below 500 nm, eq 1 starts to break down in the region where the gold electronic interband transitions from the 5d band to empty states above the Fermi level in the 6sp conduction band become more dominant.27 This region is associated with enhanced absorption and an imaginary component of the metal permittivity that begins to dominate the real component. This imaginary term is not accounted for in the electrostatic model, which therefore underestimates LSPR λmax. The electromagnetic eigenmode method is a theoretical description that takes into account the electromagnetic field generated by collective oscillations of the quasi-free electrons in metals. In the electrostatic eigenmode method, the LSPRs of a metallic nanoparticle are represented by surface charge oscillations on the particle coupled with their electric fields.14 In this article, we use the electrostatic eigenmode method to calculate the changes in LSPR wavelengths that arise from particle−solvent interactions for particles of spherical shape. Though other theories such as Mie theory could have been used, eq 1 is a simple alternative method that is quick to use if T, γ, and ωR are known for the particle of interest. Mode splitting due to the substrate can be taken into account using this technique.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Author Contributions
This article was written through them contributions of all authors. All authors have given approval to the final version of the article. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS K.C.V. acknowledges the Australian Research Council for their support through Discovery Project DP110101454 and Boolean Plasmonics and QUT for their support through the High Performance Computing Centre and ECARD grant scheme. L.P. thanks DAAD for their support through the DAAD internship program. A.C. thanks Dr. Jamie Riches for assistance with TEM imaging and Dr. Hui Diao for SEM imaging.
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4. CONCLUSIONS We have shown an alternative method for predicting the LSPR of spherical gold nanoparticles in solvents of different refractive indexes ranging from 1 to 1.5. The simple analytical formula developed by Vernon et al.9 predicts the wavelength of the LSPRs of these systems that matches the experimental value with differences of less than 3% for a refractive index between 1 and 1.5. Using this technique, we can taken into account the lifting of the degeneracy due to the substrate, though the effect on the LSPR extinction wavelength was minimal in this case. The influence of the interparticle separation on the position of the LSPR was demonstrated, and it was shown that by including silica in the casting solution the interparticle interaction can be reduced by hydrogen bonding between citrate ions on AuNP's and the silanol groups on the surface of fused silica. 26521
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(26) Johnson, P. B.; Christy, R. W. Phys. Rev. B 1972, 6, 4370−4379. (27) Pinchuk, A.; von Plessen, G.; Kreibig, U. J. Phys. D 2004, 37, 3133−3139.
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