Intelligent Fitting Identification of the Best Equation for the Determination of Gold Nanoparticle Size from the Optical Absorption Spectrum

The increasing demand for gold nanoparticle (Au NP) exploitation and the surge of scalable and continuous production methods demand real-time and low-cost tools for the assessment of Au NP size. Here, the correlation between the optical absorbance of Au NP colloids and the NP average size is studied with a data-driven intelligent approach. This analysis led to the identification of the best analytical formulas for estimation of the mean particle size from the absorbance values at selected wavelengths in the region of gold interband transitions. Despite the complex data set being constituted of real Au NP samples with a variety of surface ligands and dispersity, a mean absolute error <11% is achieved in the prediction of the average size of spherical nonaggregated Au NPs in water ranging from 4.4 to 103 nm, improving the 17% of previously reported empirical formulas. Our analysis also provided the simplest known method for the empirical calibration of the parameter for the correction of the gold dielectric function due to intrinsic size effects. The limitations of the analytical model are discussed, and a program for immediate size evaluation from the absorption spectrum is made available with this study, enabling streamlined real-time quantification of Au NP size.