Fractal analysis of inter-particle interaction forces in gold nanoparticles aggregates

Self-assembly of gold nanoparticles (AuNPs) can be used for several applications including sensors, lab on chips, and surface enhanced Raman scattering sensitive substrates. The architecture of the AuNPs aggregates is driven by the nanoparticle size, surface charge, and dielectric constant, and by the surface functionality of the substrate, which determine the mutual interaction forces among the AuNPs. These forces were indirectly investigated by means of fractal analysis of the resulting patterns of aggregates. We drop-cast AuNPs dispersions with five different values of concentration onto glass substrates, which resulted in self-assembled thin films with different aggregation density. We imaged the AuNPs aggregates with scanning electron microscope and studied their topological properties. We observed an increase in the fractal dimension of the aggregates with the AuNPs concentration, reaching a fractal dimension value of 1.56 +/- 0.01 for the low-density samples and 1.88 +/- 0.01 for the high-density samples. Concurrently, the photoluminescence peak showed only a weak red-shift with increasing concentration, while the X-ray photoelectron spectroscopy showed higher binding energy than in the bulk gold, due to the different structural arrangement of the AuNPs. Thus, a correlation was established between the fractal dimension and the inter-particle interaction forces that control the aggregation.