Robust and accurate measurements of gold nanoparticle concentrations using UV-visible spectrophotometry

This paper provides an empirical formula to calculate the extinction efficiencies of gold nanoparticles over the size range 1-1000 nm in fluids with refractive indexes which extend from n = 1 to n = 1.62. The formula contains a shape factor to account for nonspherical particles and aggregates. The empirical curves are fitted to values calculated from accurate Mie and T-Matrix theory and confirm previous descriptions which are restricted to nearly spherical particles in water of diameter between 5 and 100 nm. This paper demonstrates that these previous descriptions will be in error for fluids other than water and for nonspherical particles greater than 100 nm in size. An empirical description is provided which matches calculated values to within a few percent across most of the range. The description also matches experimental data to within the standard relative error, currently 5% at best, using other methods which directly measure the particle concentration. These extinction efficiencies can be used to validate the concentration of gold nanoparticles in a wide range of situations to support the drive for reproducibility in nanoparticle research.