Abstract
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.
Highlights
Gold nanoparticles are used in such a wide range of biotechnological and other applications that it is not feasible to list them all in a brief introduction, many reviews exist which provide a better overview.1–6 Their chemical and optical properties are not necessarily unique, but these are combined with a generally low reactivity, inertness to oxidation, insolubility, ease of surface modification, and wide availability
A detailed investigation of the uncertainties of differential centrifugal sedimentation (DCS), with a detector operating at a wavelength of 405 nm and a fluid with a refractive index greater than that of water led to a deeper insight into the use of UV-visible spectrophotometry for gold nanoparticle concentration
The analyses presented by Haiss et al.16 and Khlebtsov14 form the foundation for this work and we extend the validity of their gold nanoparticle concentration measurements to cover particles larger than 100 nm in size, where particle shape becomes important, and to fluids with different refractive indexes
Summary
Gold nanoparticles are used in such a wide range of biotechnological and other applications that it is not feasible to list them all in a brief introduction, many reviews exist which provide a better overview. Their chemical and optical properties are not necessarily unique, but these are combined with a generally low reactivity, inertness to oxidation, insolubility, ease of surface modification, and wide availability. Even for linear chains and random clusters of particles, this region is relatively invariant.12,19 This makes it useful for concentration measurements, as previously described.. A detailed investigation of the uncertainties of DCS, with a detector operating at a wavelength of 405 nm and a fluid with a refractive index greater than that of water led to a deeper insight into the use of UV-visible spectrophotometry for gold nanoparticle concentration. The analyses presented by Haiss et al. and Khlebtsov form the foundation for this work and we extend the validity of their gold nanoparticle concentration measurements to cover particles larger than 100 nm in size, where particle shape becomes important, and to fluids with different refractive indexes
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