Quantitative determination of ligand densities on nanomaterials by X-ray photoelectron spectroscopy.

X-ray photoelectron spectroscopy (XPS) is a nearly universal method for quantitative characterization of both organic and inorganic layers on surfaces. When applied to nanoparticles, the analysis is complicated by the strong curvature of the surface and by the fact that the electron attenuation length can be comparable to the diameter of the nanoparticles, making it necessary to explicitly include the shape of the nanoparticle to achieve quantitative analysis. We describe a combined experimental and computational analysis of XPS data for molecular ligands on gold nanoparticles. The analysis includes scattering in both Au core and organic shells and is valid even for nanoparticles having diameters comparable to the electron attenuation length (EAL). To test this model, we show experimentally how varying particle diameter from 1.3 to 6.3 nm leads to a change in the measured AC/AAu peak area ratio, changing by a factor of 15. By analyzing the data in a simple computational model, we demonstrate that ligand densities can be obtained, and, moreover, that the actual ligand densities for these nanoparticles are a constant value of 3.9 ± 0.2 molecules nm(-2). This model can be easily extended to a wide range of core-shell nanoparticles, providing a simple pathway to extend XPS quantitative analysis to a broader range of nanomaterials.