We use optical darkfield micro-spectroscopy to characterize the plasmon resonance of individual silver nanoparticles in the presence of a substrate. The optical system permits multiple individual nanoparticles to be identified visually for simultaneous spectroscopic study. For silver particles bound to a silanated glass substrate, we observe changes in the plasmon resonance due to induced variations in the local refractive index. The shifts in the plasmon resonance are investigated using a simple analytical theory in which the contributions from the substrate and environment are weighted with distance from the nanoparticle. The theory is compared with experimental results to determine a weighting factor which facilitates modeling of environmental refractive index changes using standard Mie code. Use of the optical system for characterizing nanoparticles attached to substrates for biosensing applications is discussed.
© 2005 Optical Society of America
There has been much recent interest in the development of biosensors which exploit surface plasmon resonances (SPRs) in noble metal nanoparticles (NPs) for the sensitive detection of changes in the NPs’ local environments. Specifically, changes in local refractive index cause a shift in the particles’ resonant wavelength and peak intensity. Precise measurements of these changes form the basis of NP sensors. In one implementation, biological receptors are attached to the NP, with binding of an analyte of interest causing a change in the local refractive index and, in turn, the optical properties of the NP1–4. The change in optical properties may then be correlated to the concentration of the analyte in solution. We have previously demonstrated real-time quantification of a model analyte by measuring exctinction due to the SPR of a monolayer of gold NPs that are chemisorbed on a functionalized glass slide1. An alternative implementation which measures the scattering of individual NPs, presents the possibility of low cost, disposable chip-based sensors, as well as the ability to create massively multiplexed assays using off-the-shelf, low cost components.
The rational design of NP-based sensors to optimize their sensitivity, detection limit, resolution, and dynamic range for a specific application requires the systematic development of quantitative relationships between the composition, structure, and shape of metal NPs and their optical properties. However, at the present time, only limited experimental information on these relationships is available. The problem is compounded by the fact that theoretical approaches to simulate the optical response of metal NPs attached to substrates are either inadequate or computationally very intensive. Hence, the design of NP-based sensors is still largely empirical.
In this paper, we have taken the first step toward addressing these limitations by designing an optical setup and a complementary analysis procedure that will enable high-throughput quantitation and modeling of the optical properties of metal nanospheres. The optical setup is specifically designed to allow the rapid and simultaneous determination of the SPR scattering spectra of several individual NPs attached to an optically transparent substrate. The analysis procedure allows changes in the plasmon resonance due to induced variations in the local refractive to be modeled quickly, using readily available Mie code, by including the contributions from the substrate and environment in an averaged refractive index. We believe that the integrated experimental system and modeling procedure will allow rapid, high-throughput studies of the geometry-dependent optical properties of noble metal NPs, with implication for the rational design and optimization of nanoparticle SPR sensors.
2. System design
The foundation of our system (Fig. 1) is a Zeiss Axiovert 200 inverted microscope with an oil immersion ultra-darkfield condenser (numerical aperture=1.2-1.4) and a 100× oil immersion Plan-neofluar® (Zeiss) objective (adjustable numerical aperture, from 0.7 to 1.3). Illumination is provided by an integrated 100W halogen source. A two-way TV adapter with selectable output is connected to the microscope’s camera port. This allows the sample image to be directed to either a color digital camera or a line-imaging spectrometer. The imaging camera is a Photometrics CoolSnap cf cooled color CCD with dimensions of 1392×1040 and (4.65 µm)2 pixels. This camera records the microscope’s field of view for co-registration with the spectrometer. The spectrometer is an Acton Research SpectraPro 2150i with a dual turret holding gratings of 1200 lines/mm for 0.1 nm spectral resolution and 300 lines/mm for 1 nm resolution. For the broad spectra presented here, the 300 lines/mm grating was used. A programmable shutter is mounted internal to an entrance slit, the width of which is manually adjustable from 10 µm to 3 mm. In the experiments below, the slit width was set at 20 µm to ensure that only one diffraction- limited spot was imaged within the slit width. At the detection plane of the spectrometer is a Roper Scientific Spec-10 cooled CCD with overall dimensions of 1340×400 pixels and pixel dimensions of (20 µm)2. The spectrometer allows simultaneous measurement of 400 independent spectra in the visible wavelength range from one line through the microscope’s field of view.
3. Experiments and results
We have used this system to measure the scattering from silver nanospheres on a glass coverslip (Fig. 2). A visual image (Fig. 2(a)) is used to select NPs of interest for spectral analysis. Four hundred spectra are obtained simultaneously from a line through this region of interest (Fig. 2(b)). Individual spectra are then selected for detailed analysis (Fig. 2(c)). Although the data in Fig. 2 were acquired using a polydisperse NP sample, the measurements in the experiments below were performed using samples created from a commercially available (British Biocell International) suspension of silver nanospheres (nominal diameter of 80 +/- 7 nm). Samples were prepared by diluting the provided particle suspension in deionized water at a ratio of 10:1 water:NP suspension. A drop of the diluted suspension was then placed on one side of a silanated (APTES, Aldrich) coverslip for 1.5 minutes to produce a sparse field of bound particles. At the end of the incubation period, the suspension was withdrawn, and fresh deionized water was applied and withdrawn four times to rinse the region.
For all experiments, the NP sample was fixed to a custom-designed carrier, which was placed on the microscope stage. The NP side of the sample was immersed in a medium of desired refractive index (water, nwater=1.33; glycerol, nglycerol=1.47; or index-matching oil, noil=nglass=1.52). A second, untreated coverslip was then placed on top of the sample. The condenser and objective were coupled to the sample using immersion oil (Zeiss Immersol), completing the high index light path required for the high NA objective and condenser.
The spectrometer wavelength scale was calibrated with an external source (Ocean Optics HG1), and the co-registration between the camera and the spectrometer was determined by imaging the output of a fiber-coupled diode laser (Thorlabs S1FC635). For acquisition of sample spectra, the objective iris was set to a NA of 0.7 and the exposure time was 30 seconds. Source correction for each sample spectrum was performed by subtracting an appropriate dark spectrum and dividing by a source spectrum, from which a dark spectrum had also been subtracted. The spectral lines corresponding to scattering by a particular particle were averaged to yield each particle’s individual spectrum. All spectra were fit to a fourth-order polynomial to determine peak wavelength.
Theoretical predictions of the SPR peak were made using Mie calculations, performed on MiePlot5. In the calculations, wavelength-invariant refractive indices (see above) were used for the surrounding media, and Johnson and Christy’s6 complex refractive indices of bulk silver were used for the NPs. Although Mie’s solution to Maxwell’s equations has been a powerful tool in studying nanoparticle scattering, a significant limitation is that is does not permit calculations of scattering from spheres on substrates. A number of researchers have undertaken to develop alternate solutions which avoid this limitation7–12, but none is as readily accessible as the widely-used Mie solution. A different approach to including the substrate effects is to determine an effective refractive index (Eq. 1) accounting for the medium and substrate, then use standard Mie calculations. This is accomplished by determining an appropriate weighting factor α for the medium and substrate indices.
Others have suggested and used such an approach for evaluating experimental data13–15, but these investigators have not reported use of a weighting factor to accurately predict shifts in SPR due to refractive index changes.
Here, we propose an analytical approach for determining an appropriate weighting factor based on including the form of the nanosphere environmental sensitivity. Previous studies have characterized this sensitivity by using an exponential dependence on the radial distance from the NP, characterized by a 1/e sensing distance equal to the particle radius16–19. The radially dependent sensitivity suggests two possible approaches to analytically determine the weighting factor α. One approach is to model the sensing volume as a shell of uniform sensitivity that extends a distance of one particle radius from the particle surface. This yields a weighting factor of α=0.82. A second, more physically relevant approach is to use an exponentially dependent sensitivity and integrate from the particle surface to infinity. This approach yields a weighting factor of α=0.70. These weighting factors are used to determine an effective medium refractive index to model the NP scattering using Mie code. A derivation of both approaches is available (see note below on supporting information).
Figure 3 shows data from nanospheres in oil that is index-matched to the substrate. Measurements of the spectra of three typical particles, denoted A, B, and C, yield SPR peak wavelengths at 480, 490, and 525 nm, respectively. These peaks are in agreement with Mie calculations for silver spheres of 75, 80, and 96 nm diameter, respectively, in a homogeneous medium (n=1.52), as shown in Table 1. As these sizes are consistent with the manufacturer’s specifications, these results show that the size of the NP can be determined using Mie calculations in a homogeneous environment.
Figure 4 shows the SPR peak wavelengths seen for a nanosphere, denoted particle D, when immersed in oil (n=1.52) and in water (n=1.33). This particle shows a shift in the SPR peak wavelength from 530 nm in the index-matching oil to 499 nm in water. Comparing this first peak to Mie calculations allows us to determine the diameter of the particle to be 98 nm. By using this diameter to calculate the SPR peak expected for a NP in water, we see that the data are fit by using an effective refractive index of 1.41. This corresponds to a weighting factor of α=0.58. The peaks obtained when using the other weighting factors, proposed above, are presented in Table 2. We comment on the applicability of these other factors below.
To assess the validity of using the empirical weighting factor found above to predict shifts in SPR peak wavelength upon a local refractive index change, the expected peak shifts were modeled for particles transferred from water to glycerol. Figure 5 shows data for two similar particles, denoted E and F, which exhibit SPR peak wavelengths at 458 and 455 nm in water, and at 476 and 475 nm in glycerol, respectively. The similarity of these scattering peaks indicates that these particles are almost identical in size. The empirical weighting factor of α=0.58 again provides the best fit, with a 76 nm diameter particle yielding a peak at 456 nm in water and at 475 nm in glycerol. Table 3 shows these results, as well as the peaks predicted with the other weighting factors.
The spectra of particles A, B, and C show agreement between the nominal size of the nanospheres and the Mie-determined sizes, indicating that Mie theory can be used to determine the size of a particle in an index-matched medium. Although Mie calculations predict dipole and multipole peaks, as shown clearly by the second peak in the Mie spectrum for particle C, the multipole peak (at the lower wavelength) is in a region of the spectrum with low signal-to-noise for our measurements of particles A and B. The peak is apparent in our experimental results for particle C, although its intensity, in comparison with the Mie prediction, is reduced. Another interesting discrepancy between our data and Mie theory is the observed peak narrowing for larger particles in the experiments. This phenomenon was previously observed for larger NPs by Sönnichsen et al. and attributed to lifetime broadening due to various decay processes20. Although the width of the peak was not investigated in the present study, further studies are needed to assess the impact of this effect on the sensing behavior of NPs.
Upon examining scattering spectra of nanospheres in media with a refractive index different from the substrate (particle D), the effect of the substrate is evident. Although Mie theory cannot directly account for a substrate, we find we obtain an accurate SPR peak wavelength using our weighted refractive index and a weighting factor of α=0.58. The theoretically-determined factors of α=0.82 and α=0.70 provide better fits than simply assuming a uniform environment with a refractive index of the immersion medium, but the fits are not as accurate as the empirical factor. Since the theoretically-determined factors are based on a particular sensing distance, modifying the sensing distance is one way to adapt this theory to fit the experiment. For example, a 1/e sensing distance of three times the particle radius produces a weighting factor of α=0.58, in agreement with the empirical result. Given the complex behavior of nanoparticle resonances and their dependence on the surrounding environment, it is not surprising that the empirical factor is not predicted by either theoretical model.
The utility of the empirical weighting factor was further validated by modeling SPR peaks for nanospheres in a water-to-glycerol medium exchange. As shown in Table 3, the factor of α=0.58 provides an excellent match to the experimental results in both water and glycerol for particles of 76 nm diameter. In this case, no measurement in a uniform-index environment was needed to determine the diameter. Instead, the diameter and weighting factor were determined using two independent measurements, the spectra of the substrate-bound NP in water and that of the particle in glycerol. While both diameter and weighting factor influence the peak wavelength observed for a particle in a given refractive index medium, only one combination of the two accurately reproduces the peak wavelengths seen in both spectra. Since the particle sizes are not known independently, it is assumed that the same weighting factor can be applied to model the scattering of particles in both water and glycerol. This assumption is justified by the consistency observed when using the weighting factor to model the spectra seen for the water-to-oil and water-to-glycerol exchanges.
The agreement in weighting factor across different medium exchange experiments validates our modeling approach for our specific experimental configuration and the NP size, shape, and composition in these experiments. Although the theoretical approach used to derive the weighting factors suggests that it does not depend on the size or composition of the NP, we expect that other geometries and materials may have their own unique weighting factors. We believe that experiments in progress, which aim to establish the relationship between the weighting factor needed to model a NP’s scattering characteristics and its size, shape, and composition, will have a great impact on our understanding of the sensing capabilities of NPs.
In summary, we have developed a method for detecting, analyzing, and predicting the change in the SPR of silver nanospheres attached to a substrate in response to environmental refractive index changes. The method uses a darkfield micro-spectroscopy system to interrogate the NPs, which not only enables visualization of the NP sample but allows several individual NPs to be selected for immediate simultaneous spectral analysis. Analysis of the spectral data predicts the shifts in the SPR peaks of NPs using Mie theory, despite the presence of a substrate, by incorporating an average refractive index based on an empirical weighting factor. To demonstrate the utility of the method, we have observed and predicted the changes in the scattering spectra of individual silver nanospheres bound to a silanated glass coverslip in response to local refractive index changes. In conclusion, we believe that the parallel acquisition abilities of the instrument described here and the capability of the analytical approach to rapidly model the spectra of individual particles in the presence of a substrate will serve as the foundation for high-throughput NP characterization studies that are essential for the rational development of chip-based nanoparticle SPR sensors.
We have taken two approaches to deriving weighting factors based on the radially-dependent environmental sensitivity of nanospheres. The first is to model the sensing volume as a shell of uniform sensitivity that extends a distance of one particle radius from the particle surface. This integration is performed by dividing the sensing volume at the substrate surface and integrating discs with radii that vary as a function of distance from the substrate (dimension z in a cylindrical coordinate system). For the volume above the substrate, the volume of the particle is subtracted. In this way, an integrated sensing volume is calculated for the region above and below the substrate. Each region is normalized by the sum of the two to deterimine the weighting factors for the immersion medium surrounding the particle, and that for the substrate below it. This approach yields a weighting factor of α=0.82 for the immersion medium, as shown in Fig. 6.
The second approach is to integrate the exponentially decreasing sensitivity from the particle surface to infinity. This was accomplished by integrating along z and ρ in a cylindrical coordinate system. This calculation yields a weighting factor of α=0.70 when the 1/e distance is assumed to be equal to the particle radius, as shown in Fig. 7.
The authors thank Stella Marinakos for her suggestions on sample preparation and the Centers for Disease Control for financial support through grant NCID R01 CI-00097-01 to Ashutosh Chilkoti.
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