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

In order to understand more deeply the surface enhanced Raman scattering (S ERS) effect, this article develops a model, based upon the simulation of th e UV-visible extinction spectra which allows the determination of the morph ology of metallic particles in silver and gold colloids either unaggregated or in any aggregation state. The main assumptions of this model are (i) li ght scattering by independent particles or clusters (objects) which enables us to express the total extinction cross section as a suitably weighted su m 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 approxim ation (DDA) for objects of any shape and size; (iii) the weight of each ind ividual cross section is determined using a minimization process (simplex m ethod) which looks for the best possible agreement between the experimental and calculated spectrum; (iv) lastly a simple calculation, based on the as sumption 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 l eading 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 experime ntal and calculated intensities which might result from the tendency of DDA to underestimate the individual cross sections and/or from a lack of valid ity of the compact approximation. The clusters histogram deduced from the s imulation process reveals small spheres (unaggregated particles) and elonga ted objects small compared to the visible light wavelength. This latter res ult is different from that obtained by TEM data in which the likely occurre nce of a further aggregation leads to the observation of large aggregates. (C) 1999 American Institute of Physics. [S0021-9606(99)71027-5].