Determination of the concentration and the average number of gold atoms in a gold nanoparticle by osmotic pressure

For an ideal solution, an analytical expression for the macromolecule concentration, electrolyte concentration, and solution osmotic pressure is obtained on the basis of the van't Hoff equation and the Donnan equilibrium. The expression was further applied to a colloid solution of about 3 nm glutathione-stabilized gold nanoparticles. The concentration of the colloid solution and the average net ion charge number for each gold nanoparticle were determined with the measured osmotic pressure data. Meanwhile, the gold contents of the solutions were analyzed by means of atomic absorption spectrophotometry, and the results were combined with the determined concentration of gold nanoparticle colloids to determine that the average number of gold atoms per 3 nm gold nanoparticle is 479, which is 1/1.7 times the number of atoms in bulk metallic gold of the same size. The same proportion also occurred in the 2 nm 4-mercaptobenzoic acid monolayer-protected gold nanoparticles prepared by Ackerson et al., who utilized the quantitative high-angle annular dark-field scanning transmission electron microscope to determine the average number of gold atoms per nanoparticle (Ackerson, C. J.; Jadzinsky, P. D.; Sexton J. Z.; Bushnell, D. A.; Kornberg, R. D. Synthesis and Bioconjugation of 2 and 3 nm-Diameter Gold Nanoparticles. Bioconjugate Chem. 2010, 21, 214-218).