Light Absorption by the Clusters of Colloidal Gold and Silver Particles Formed During Slow and Fast Aggregation

Spectra of absorption (400–800 nm) by the aggregates of colloidal gold (5, 15, and 30 nm in diameter) and silver (20 nm in diameter) particles were studied experimentally and theoretically. It was revealed that, during fast aggregation corresponding to the diffusion-limited cluster aggregation (DLCA), the pattern of spectra is dependent on the size of primary particles. Spectra with the additional absorption maximum in the red region are observed for 15 and 30 nm gold and 20 nm silver particles, while the absorption spectrum for 5 nm particles is characterized by only one maximum shifted to the red region. The slow aggregation resulted in a decrease in plasmon absorption peak with no marked shift to the red region and to the broadening of long-wave absorption wing. From data on electron microscopy, typical branched DLCA-clusters were formed during fast aggregation, whereas small compact aggregates and a noticeable number of single particles were observed in a system during slow aggregation. The computer model of the diffusion-limited cluster-cluster aggregation was used to explain these results. Optical properties of aggregates were calculated using coupled dipole method (CDM or DDA) and the exact method of a multipole expansion. Corrections for the size effect were introduced into the bulk optical constants of metals for nanosized particles. It was shown that a modified version of DDA (Markel et al.,Phys. Rev. B, 1996, vol. 53, no. 5, p. 2425) allows us to explain the pattern of experimental spectra of DLCA-aggregates and their dependence on a monomer size. The exact method was applied to calculate the extinction cross sections of metallic aggregates demonstrating strong electrodynamic interaction between particles. The number of higher multipoles that are required to adequately describe this interaction is much larger than the number of terms of an ordinary Mie series and is the main obstacle to the exact calculation of the spectra of metallic aggregates with a large number of particles.