Discrete dipole approximation for ultraviolet–visible extinction spectra simulation of silver and gold colloids

Abstract

In order to understand more deeply the surface enhanced Raman scattering (SERS) effect, this article develops a model, based upon the simulation of the UV–visible extinction spectra which allows the determination of the morphology of metallic particles in silver and gold colloids either unaggregated or in any aggregation state. The main assumptions of this model are (i) light scattering by independent particles or clusters (objects) which enables us to express the total extinction cross section as a suitably weighted sum of cross sections of individual objects (targets); (ii) these targets are supposed to be compact and their individual cross sections are determined either from the Mie theory for spheres or from the discrete dipole approximation (DDA) for objects of any shape and size; (iii) the weight of each individual cross section is determined using a minimization process (simplex method) which looks for the best possible agreement between the experimental and calculated spectrum; (iv) lastly a simple calculation, based on the assumption of compact objects, provides the absorbance (optical density). In the case of unaggregated silver and gold colloids, this model gives a very good agreement between experimental and simulated extinction spectra thus leading to a particle size histogram which is consistent to that determined from transmission electronic microscopy (TEM) measurements. For aggregated colloids, an excellent agreement is still obtained between experimental and simulated band profiles; a slight discrepancy is observed between experimental and calculated intensities which might result from the tendency of DDA to underestimate the individual cross sections and/or from a lack of validity of the compact approximation. The clusters histogram deduced from the simulation process reveals small spheres (unaggregated particles) and elongated objects small compared to the visible light wavelength. This latter result is different from that obtained by TEM data in which the likely occurrence of a further aggregation leads to the observation of large aggregates.