Size histograms of gold nanoparticles measured by gravitational sedimentation

Sedimentation curves of gold nanoparticles in water were obtained by measuring the optical density of a suspension over time. The results are not subject to sampling errors, and refer to the particles in situ. Curves obtained simultaneously at several wave lengths were analyzed together to derive the size histogram of the sedimenting particles. The bins in the histogram were 5 nm wide and centered at diameters 60, 65, …, 110 nm. To get the histogram, we weighted previously calculated solutions to the Mason-Weaver sedimentation-diffusion equation for various particle diameters with absorption/scattering coefficients and size (diameter) abundances {c(j)}, and found the {c(j)} which gave the best fit to all the theoretical sedimentation curves. The effects of changing the number of bins and the wave lengths used were studied. Going to smaller bins would mean determining more parameters and require more wave lengths. The histograms derived from sedimentation agreed quite well in general with the histogram derived from TEM. Differences found for the smallest particle diameters are partly due to statistical fluctuations (TEM found only 1-2 particles out of 103 with these diameters). More important is that the TEM histogram indicates 12% of the particles have diameters of 75±2.5 nm, and the sedimentation histogram shows none. We show that this reflects the difference between the particles in situ, which possess a low-density shell about 1 nm thick, and the bare particles on the TEM stage. Correcting for this makes agreement between the two histograms excellent. Comparing sedimentation-derived with TEM-derived histograms thus shows differences between the particles in situ and on the TEM stage.