Precision size and refractive index analysis of weakly scattering nanoparticles in polydispersions

Abstract

Characterization of the size and material properties of particles in liquid suspensions is in very high demand, for example, in the analysis of colloidal samples or of bodily fluids such as urine or blood plasma. However, existing methods are limited in their ability to decipher the constituents of realistic samples. Here we introduce iNTA as a new method that combines interferometric detection of scattering with nanoparticle tracking analysis to reach unprecedented sensitivity and precision in determining the size and refractive index distributions of nanoparticles in suspensions. After benchmarking iNTA with samples of colloidal gold, we present its remarkable ability to resolve the constituents of various multicomponent and polydisperse samples of known origin. Furthermore, we showcase the method by elucidating the refractive index and size distributions of extracellular vesicles from Leishmania parasites and human urine. The current performance of iNTA already enables advances in several important applications, but we also discuss possible improvements.

Fig. 1. iSCAT setup and trajectory extraction.

a, Wide-field iSCAT setup for tracking freely diffusing particles. Linearly polarized light from a laser traverses a neutral density filter (ND) used to adjust the incident power, passes a PBS) followed by a λ/4 plate that renders its polarization circular. A wide-field lens (WFL, f = 400 mm) focuses the light at the back focal plane of the objective. An imaging lens (IL, f = 500 mm) projects the reflected (solid green area) and scattered (dashed line) light on a CMOS camera chip. b, Three examples of iPSF (left) and the corresponding RVT images (right). Scale bar, 1 μm. c, A 7 × 7 μm² frame showing an RVT image of three 15 nm GNPs with an overlaid trajectory of one GNP recorded over 220 ms.

Fig. 2. Monodisperse particle samples.

a, MSD versus delay time for GNP samples of different sizes. Thin lines show the MSD extracted from each individual trajectory. Thick lines show the weighted average (by trajectory length). Diffusion constants extracted from the fits are listed in the legend. b, Diffusion constants extracted from the data in a versus the nominal GNP diameter provided by the manufacturer. Dashed gray line indicates the SE relation for T = 21 °C. Solid line is a fit to the SE relation yielding an offset in particle radius by the hydration layer thickness of l_H = 1.8 ± 0.3 nm. Inset: diffusion constants for 30 nm GNPs at different temperatures. The solid line shows the prediction of equation (1) for l_H = 1.8 nm. The shaded area indicates the 95% confidence interval for l_H of ± 0.3 nm. Dashed line shows the outcome of SE for $\overline{d}$_nom. c, Histograms of particle diameters extracted from the SE relation. Individual measurements were weighed by their trajectory lengths (Supplementary Section 3.2). The data for 10 nm, 15 nm, 20 nm and 30 nm GNPs were recorded at 40 mW illumination power; the rest were recorded at 2 mW. Inset: symbols show l_H and its error bars as defined in Table 1. Dashed line indicates the value of l_H obtained from the global fit in b. d, Comparison between different measurement techniques. The output of DLS measurements represents the number-weighted distribution.

Fig. 3. Polydisperse particle samples.

a–c DLS (a), NTA (b) and iNTA (c) measurements of a mixture of 15 nm, 20 nm and 30 nm GNPs. d–g, iNTA measurements of various mixtures as labeled in each graph. The horizontal and vertical axes denote the measured diameter and the third root of the iSCAT contrast, respectively. The transparency of each datapoint indicates the length of its trajectory. In each panel, a 2D GMM is used to identify different populations highlighted in color. The gray curves establish the relationship between $\sqrt[3]{C}$ and d_mes according to the respective refractive indices and the shaded regions indicate the uncertainties in the refractive index data found in the literature: silica refractive index between 1.43 and 1.48, polystyrene refractive index between 1.58 and 1.68. Crosses in c–g signify the medians of each data cloud.

Fig. 4. Extracellular vesicles.

a, iNTA scatter plots of synthetically produced liposomes. Color bar denotes point density. The gray dashed contours correspond to different refractive indices of the inner part of the liposomes, starting at 1.334 (water) and increasing in steps of 0.02 from 1.34 for n_sh = 1.48 and t_sh = 5.7 nm. Inset: cartoon of a vesicle. b, Isosurfaces of constant particle size and iSCAT contrast for the points marked in a over a range of values for n_in, n_sh and t_sh. c, iNTA scatter plots of EVs from Leishmania parasites. The green line indicates the best fit value for n_in, while the solid (dashed) olive lines indicate the 25th and 75th (10th and 90th) percentiles of the extracted n_in. d, Same as b but for the points marked in c. e, iNTA scatter plots of EVs from urine of a healthy human donor. The red line indicates the best fit value for n_in, and the solid (dashed) maroon lines indicate the 25th and 75th (10th and 90th) percentiles of the extracted n_in. f, Same as b but for the points marked in e. Each plot shows the outcome of one iNTA measurement performed on one sample. The results from more samples are shown in Supplementary Fig. 18.