Effect of size distribution, skewness and roughness on the optical properties of colloidal plasmonic nanoparticles

It is a generally accepted idea that the particle size distribution strongly affects the optical spectra of colloidal plasmonic nanoparticles. It is often quoted as one of the main reasons while explaining the mismatch between the theoretical and experimental optical spectra of such nanoparticles. In this work, these aspects are critically analyzed by means of a bottom up statistical approach that considers variables such as mean, standard deviation and skewness of the nanoparticle size distribution independently from one another. By assuming normal and log-normal distributions of the particle size, the effect of the statistical parameters on the Mie analytical optical spectra of colloidal nanoparticles was studied. The effect of morphology was also studied numerically in order to understand to what extent it can play a role. It is our finding that the particle polydispersity, skewness and surface morphology in fact only weakly impact the optical spectra. While, the selection of suitable optical constants with regard to the crystallinity of the nanoparticles is a far more influential factor for correctly predicting both the plasmon band position and the plasmon bandwidth in theoretical simulations of the optical spectra. It is shown that the mean particle size can be correctly estimated directly from the plasmon band position, as it is the mean that determines the resonance wavelength. The standard deviation can on the other hand be estimated from the intensity distribution data obtained from dynamic light scattering experiments. The results reported herein clear the ambiguity around particle size distribution and optical response of colloidal plasmonic nanoparticles.