Determination of the aspect ratio statistical distribution of gold nanorods in solution from a theoretical fit of the observed inhomogeneously broadened longitudinal plasmon resonance absorption spectrum

The determination of the statistical distribution of aspect ratios of a nanorod solution is desirable for experimentally synthesized solutions. The traditional method of using transmission electron microscopy (TEM) images for size determination gives statistically incorrect values due to distortions introduced by TEM sample preparation and by difficulties in counting a sufficiently large number of rods. In the present work, we propose a method to obtain the aspect ratio distribution using the observed longitudinal surface plasmon resonance absorption spectrum of gold nanorods in solution. The observed inhomogeneously broadened spectrum is fitted with a collection of homogeneously broadened spectra of nanorods each with a specific aspect ratio and population contribution using Gans extension [Ann. Phys. 47, 270 (1915)] of Mie theory. The fit generates an aspect ratio distribution for the rods in solution from which the median value and the statistical distribution are determined. This method is statistical...