Determination of nanoparticle size distribution together with density or molecular weight by 2D analytical ultracentrifugation

Abstract

Nanoparticles are finding many research and industrial applications, yet their characterization remains a challenge. Their cores are often polydisperse and coated by a stabilizing shell that varies in size and composition. No single technique can characterize both the size distribution and the nature of the shell. Advances in analytical ultracentrifugation allow for the extraction of the sedimentation (s) and diffusion coefficients (D). Here we report an approach to transform the s and D distributions of nanoparticles in solution into precise molecular weight (M), density (ρ(P)) and particle diameter (d(p)) distributions. M for mixtures of discrete nanocrystals is found within 4% of the known quantities. The accuracy and the density information we achieve on nanoparticles are unparalleled. A single experimental run is sufficient for full nanoparticle characterization, without the need for standards or other auxiliary measurements. We believe that our method is of general applicability and we discuss its limitations.

Figure 1. Typical characterization schemes for core–shell nanoparticles.

The core density (ρ_c) is normally taken as the bulk density or quantified by x-ray diffraction assuming a conformation to a particular model. TEM, scanning transmission electron microscopy, and x-ray diffraction are the most commonly used methods to investigate core radius (r_c) and composition; yet, these techniques provide little information on the organic ligand shell (due to the low contrast of organic material). Furthermore, core size distributions extracted from TEM images are generally skewed by the choice of the selected area of the sample, small sampling size (a few thousand particles at most) and the undercounting of the smallest particles (due to their low TEM contrast). To measure total particle diameter (d_P), dynamic light scattering (DLS) is not particularly sensitive for small particles and atomic force microscopy (AFM) or scanning tunnelling microscopy (STM) are slow and share the same sampling selection limitations of TEM. Both size exclusion chromatography and gel electrophoresis require a standard. For small particles (<40 kDa), mass spectroscopy (MS), in particular electrospray ionization MS (ESI-MS), is the preferred method to measure particle molecular weight (M); but, problems in stability and complexity limit this technique. To characterize the organic ligand shell density (ρ_L), thermogravimetric analysis can be utilized, but it is accurate only for a monodisperse species. Nuclear magnetic resonance (NMR) can also provide information on the composition and density of the ligand shell, but counterions present a major problem, and again, the technique is limited only to large sizes. No single technique can simultaneously measure all six parameters with a single experiment.

Figure 2. 2D AUC distribution for Au₁₄₄(SR)₆₀ nanoclusters.

The sedimentation and diffusion coefficient distributions for the Au₁₄₄(SR)₆₀ magic-sized nanocluster in toluene (T=20 °C).

Figure 3. 2D AUC distributions for both nanoclusters and PDT-capped nanoparticles.

The three 'magic-sized' clusters were mixed in toluene (T=20 °C) and sedimented simultaneously, to illustrate the accuracy and ease of measuring sedimentation and diffusion coefficients for a distribution of species. (a) The integrated 1D sedimentation coefficient distribution over the respective values of diffusion coefficients. (b) 2D sedimentation and diffusion coefficient distributions for three thiolated gold nanoclusters. (c) The integrated one-dimensional distribution of sedimentation coefficients taken over all diffusion coefficients and the multi-peak Gaussian fit illustrating the resolution of two PDT-NP peaks. (d) The sedimentation and diffusion coefficient distributions for PDT-NPs.

Figure 4. 2D AUC distribution of polydisperse gold nanoparticles.

(a) The integrated 1D distribution of sedimentation coefficients taken over all diffusion coefficients and the overlaid particle size distribution by TEM, to illustrate the increase in resolution by AUC. (b) The sedimentation and diffusion coefficient distributions for the polydisperse NP sample.