A schematic drawing of the experimental setup is shown in Figure 1. The white light from a halogen lamp (LM) is directed to an electro-optical filter (EOF) that filters the light into its constituent wavelengths. The filtered spectral wavelengths coming from the tunable optical filter are then coupled to the epi-illuminator (IL) of the microscope and focused on the sample surface (SM) through a beam-splitter (BS) and a dark-field objective (OB). A CMOS camera placed at the image plane of the experimental setup collects the scattered light for each illumination wavelength. The optical microscope is equipped with a diascopic illuminator, thus in case of using transparent substrates such as in this work, it is able to perform imaging and micro spectrophotometry of the same sample region (more technical details are available in Methods).
As a proof of concept, we assess the validity of the method by performing experiments on spherical gold nanoparticles (Nanopartz, Inc.) with seven different nominal sizes, dispersed at different concentration in milliQ® water. Before the experiments each nanoparticle lot was resuspended at a concentration of 200 µg/µl, wich is high enough for ensuring a good nanoparticle monodispersion but also suitable for achieving enough statistics with a single image capture (more informations are available in Methods).
Nanoparticles were drop-casted on a glass slide, dried, and imbued in a drop of glycerol (Figure 2a); the use of glycerol allows reducing the refractive index mismatch27 between the underneath glass substrate and the surrounding medium. In this way, nanoparticles are surrounded in a homogeneous medium, so splitting of substrate-mediated plasmonic modes is avoided,26,28 and the optical response is well predicted by standard Mie theory.25,29
Before performing nanoparticle spectrophotometry, nanoparticles are imaged with the diascopic illuminator; a cropped dark-field image of 100 nm GNPs is shown in Figure 2b; by using a proprietary algorithm based on the analysis of brightness and color of each individual optical spot present on the surface, it is possible to identify monomers from the rest of particles. One single image provides enough data to perform this analysis, allowing for fast measurement process (for more technical details, see the Supplementary Information).
Spectral measurements are then performed by measuring the scattering signal of the entire field of view at different spectral wavelengths. In a standard measurement, the complete 3D dataset is composed of 101 spectral images (from 450 nm to 650 nm with spectral steps every 2 nm) acquired in about 2 minutes. In order to eliminate any variations coming from pixel-to-pixel sensitivity of the detector and from distortions in the optical detection and illumination path, each dark-field image is flat-field corrected pixel-by-pixel according to the procedure described in the Supplementary Information.
A stack of dark-field images of a single monomer taken at different spectral wavelengths is shown in Figure 2C. Scattering spectra of each monomer are calculated by integrating the wavelength-dependent scattering in a circular region around each monomer bound to the surface (Supplementary Information). The scattering spectrum of a single100 nm GNP shown in Figure 2D is in good agreement with Mie scattering theory: a clear plasmon resonance peak around 575 nm is observed.
It is important to remark that all the detailed spectral features here illustrated for a single nanoparticle are also readily available for all other GNPs present within the field of view of the optical instrument. As in the current optical setup the entire field of view is about 0.55 mm2, resulting in an average nanoparticle density higher than 0.05 µm2, the DF-SPS is able to perform a spectral analysis of at least 5,000 particles in a single shot. Scattering spectra collected from more than 15,000 monomers are shown in Figure 3a; the red curve represents the average of the scattering spectra coming from the entire monomer population, showing an average resonance peak around 580 nm. The amplitude and the spectral variability observed in Figure 3A are produced by the variability in size of the GNPs. It is remarkable that, although the GNPs present a very tight size distribution (CV < 5%), the amplitude variability is significantly higher (CV around 30%), in good agreement with Mie scattering theory.
The spectrum of each single monomer has been fitted with a Lorentzian peak, allowing to determine the wavelength of the plasmon resonance peak with an uncertainty below 1 nm (more details about data analysis can be found in the Supplementary Information). The histogram of the plasmon resonance peaks of 15,000 monomers is shown in Figure 3B. For GNPs, the relationship between the nanoparticle size and the wavelength of the plasmon resonance peak can be well approximated with a simple logarithmic function:
where λ0 , C1 and C2 are constants whose values depends on the optical properties of the nanoparticle material; in case of gold λ0 =530 nm , C1 =6.53 nm and C2 =0.0216 nm -1 (more technical details about the derivation of Equation 1 can be found in the Supplementary Information).
By making use of Equation 1, the top axis of Figure 3B has been converted to nanoparticle diameter; this conversion is extremely useful because it provides a quick and direct estimation of the nanoparticle size based on its plasmon resonance peak. The histogram data of Figure 3B has been fitted with a Gaussian function, 30 yielding an average size of 101.6 nm ± 2.8 nm and a CV around 6%; the values found here are in very good agreement with the technical specifications given by the manufacturer (nominal size and CV of 100 nm and 4%, respectively).
Following the same procedure described previously for 100 nm nanoparticles, other nanoparticle lots with different nominal size have been measured; in total, seven different lots with diameters ranging from 50 nm to 125 nm have been studied. TEM images shown in Figure 4a confirm that, except for the 70 nm GNP lot that has a more pronounced elliptical shape, all others characterized lots present a high spherical shape. (more technical details about TEM measurmeents and characterization can be found in the Supplementary Information). All histogram distributions of the plasmon resonance peak for each nanoparticle lot are summarized in Figure 4b; the histogram’s top axis of Figure 4B has been converted to nanoparticle diameter by using Equation (1). For each lot, at least 5,000 GNPs monomers have been characterized. The histogram corresponding to each lot has been fitted with a Gaussian distribution. Although the estimated diameters and their CV tightly match the nominal values given by the manufacturer, a significant deviation from a Gaussian distribution is observed in the case of 70 nm; while the rest of the lots have an R-squared value of ~0.99, for 70 nm this parameter is ~0.95 (the closer the fit is to the data points, the closer R-squared will be to 1). As mentioned above, the lower roundness of this nanoparticle lot could explain the increased deviation.
In order to check the accuracy of the DF-SPS technique in the diameter estimation, a direct comparison with TEM is needed. The graph in Figure 5 shows the correlation between the real diameter measured with TEM and the diameter estimated with DF-SPS; the error bars in X and Y are the uncertainties coming from TEM and DF-SPS, respectively. The correlation graph presents excellent agreement between TEM and DF-SPS, with a mean discrepancy around 3% (additional compared data between TEM and DF-SPS can be found in the Supplementaty Information S8). Taking into account all seven characterized lots, the resulting Pearson’s correlation coefficient between the sizes estimated with both techniques is 0.9904, indicating a dependence very close to a perfect linear relationship. Although the feasibility of the method has been here proved by using spherical nanoparticles, the true strengthness of the method is that it can be easily generalized also to nanoparticles with more complex geometries such as nanorods, nanocubes, nanoplates or core-shell geometries.31
Remaining now to the specific case of spherical nanoparticles, we will analyze in the following how the size accuracy tends to be lower for particles smaller than 40-50 nm. This aspect becomes clear once Equation (1) is analyzed and plotted (see Figure 6a). For nanoparticles smaller than 40 nm, the wavelength of the plasmon resonance peak remains almost constant, thus producing a significant uncertainty in the diameter estimation.
The percentage uncertainty of the DF-SPS can be obtained using the following equation:
where is the first derivative of Equation (1), d is the nanoparticle diameter and is the wavelength uncertainty that in the current experimental setup is around 1 nm.
The percentage uncertainty curve (Figure 6b) presents a significant diameter-dependence; For instance, nanoparticles of 100 nm feature an uncertainty below 2%. As the particle size decreases, the uncertainty progressively increases: an uncertainty below 5% can be reached for particles of 70 nm, whereas nanoparticles of 50 nm present a percentage uncertainty of around 10%.