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Single-particle tracking spectroscopy: (a) Illustration of angle-dependent plasmon scattering from a nearly spherical metallic nanoparticle when illuminated by a white light source. [(b)–(d)] Experimental design concept for detecting spectral anisotropy by time-dependent spectroscopy on a freely diffusing gold nanoparticle. As the nanoparticle rotates stochastically in water, its angle-dependent scattering spectrum is sampled statistically by the spectrometer. (e) A schematic of the single-particle tracking spectrometer. A portion of the collected scattering light is directed into a spectrometer. The spectrometer can be configured to measure either the spectral contrast or the polarization contrast as shown in panels (f) and (g), respectively. (f) After a polarizer, the spectral contrast is measured by a dichromatic beam splitter that sorts the light into the red (R) and the blue (B) channels, and detected by corresponding avalanche photodiodes (APDs). (g) To measure the polarization contrast, a polarization beam splitter categorizes the light into the mutually orthogonal vertical and horizontal components, and detected by corresponding APDs.
Scattering spectrum of a gold nanoparticles in water. A typical scattering spectrum from a gold nanoparticle freely moving in water illuminated by a tungsten lamp (integration ). As a reference, the ensemble-averaged absorption spectrum from the same sample is also shown (red dashed line). The inset shows transmitted electron microscope images of representative gold nanoparticles. The scale bar in the inset is .
Spectra anisotropy and color bunching: (a) Coordinate system of a spheroidal nanoparticle freely rotating in water with respect to the laboratory frame . The thick arrow is a vector depicting the orientation of the spectrally anisotropic nanoparticle. Using The Rayleigh–Gans electrostatic approximation for spheroids (Refs. 33 and 34), the nanoparticle is assumed to scatter red light more efficiently when the nanoparticle is at an orientation with the arrow aligned with the axis (Ref. 29). (b) A 3D representation of detected color contrast [see main text Eq. (1) for definition] for the model in (a) at different orientations defined by the azimuth and zenith , where realistic experimental parameters are used. As the spectrally anisotropic nanoparticle undergoes rotational random walk, its orientation, represented by the white spots in the unit sphere, will also change to result in corresponding changes in the detected color contrast. Note that it is the relative changes in color contrast that gives evidence for spectrally anisotropic scattering, not the absolute value. (c) A cartoon illustrating how the scattering spectrum (recorded as color contrast) changes as the spectrally anisotropic nanoparticle dynamically reorients itself over time. (d) A typical color contrast time trace, , from a gold nanoparticle freely moves in water. To avoid congestion in visualization, the trajectory (originally recorded with time resolution) is binned at , and only one out of every five data points are shown. [(e)–(h)] Scattered plots of against at various time delays to visualize color correlation in the trajectory shown in (a). A spectrally anisotropic nanoparticle scattering with color at time is likely to scatter the same color at time when is small compared to its reorientation timescale. This is indicated by the diagonally elongated pattern at short-time delays (red dashed line; eye guide). The correlation is quantified by the correlation coefficient . The probability of observing color bunching diminishes and eventually disappears at longer time delays to result in an uncorrelated scatter pattern in the plot with the correlation coefficient approaching 0.
Spectral contrast autocorrelation: Autocorrelation of spectral contrast as a function of time . The green trace is from an gold nanoparticle in 80% glycerol/water mixture and is overlaid with a fit to a single exponential decay of time constant (black curve). The pink trace is from a silicate microsphere suspended in water, and the dark brown curve from an immobilized gold nanoparticle. The trajectories used to calculate the correlation functions are 13, 1.28, and for the pink, green, and brown curves, respectively.
Test of the DSE relation: (a) Correlation between color contrast fluctuation-correlation time and hydrodynamic radius of gold nanoparticles in water on a log-log plot. The four samples studied in this experiment were gold nanoparticles suspended in water with nominal sizes (green), (red), (blue), and (black). The hydrodynamic radius of individual nanoparticles was measured from translational Brownian motion. The dashed black line is the DSE rotational diffusion model with at . The light turquoise-shaded area bounded between two red dashed lines corresponds to 15% deviation from the DSE line. Inset: Typical color contrast fluctuation-correlation decay curves for 80, 100, and nanoparticles. The black dashed lines are fits to single exponential with fitted time constants , , and for the 80, 100, and nanoparticles, respectively. (b) Correlation between polarization contrast fluctuation-correlation time and hydrodynamic radius of gold nanoparticles in water on a log-log plot with the same color coding as in (a). Inset: A representative 3D trajectory of a nanoparticle ( long). The position trajectory was recorded at . To avoid congestion in visualization, here the nanoparticle’s 3D position is plotted every .
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