Evaluation of nanoparticle-ligand distributions to determine nanoparticle concentration

The concentration of nanoparticles in solution is an important, yet challenging, parameter to quantify. In this work, a facile strategy for the determination of nanoparticle concentration is presented. The method relies on the quantitative analysis of the inherent distribution of nanoparticle-ligand conjugates that are generated when nanoparticles are functionalized with ligands. Validation of the method was accomplished by applying it to gold nanoparticles and semiconductor nanoparticles (CdSe/ZnS; core/shell). Poly(ethylene glycol) based ligands, with functional groups that quantitatively react with the nanoparticles, were incubated with the nanoparticles at varying equivalences. Agarose gel electrophoresis was subsequently used to separate and quantify the nanoparticle-ligand conjugates of varying valences. The distribution in the nanoparticle-ligand conjugates agreed well with that predicted by the Poisson model. A protocol was then developed, where a series of only eight different ligand amounts could provide an estimate of the nanoparticle concentration that spans 3 orders of magnitude (1 μM to 1 mM). For the gold nanoparticles and semiconductor nanoparticles, the measured concentrations were found to deviate by only 7% and 2%, respectively, from those determined by UV-vis spectroscopy. The precision of the assay was evaluated, resulting in a coefficient of variation of 5-7%. Finally, the protocol was used to determine the extinction coefficient of alloyed semiconductor nanoparticles (CdSxSe1-x/ZnS), for which a reliable estimate is currently unavailable, of three different emission wavelengths (525, 575, and 630 nm). The extinction coefficient of the nanoparticles of all emission wavelengths was similar and was found to be 2.1 × 10(5) M(-1)cm(-1).