Nature of the Anomalous Size Dependence of Resonance Red Shifts in Ultrafine Plasmonic Nanoparticles

Plasmonic red shifts of nanoparticles are commonly used in imaging technologies to probe the character of local environments, and the understanding of their dependence on size, shape, and surrounding media has therefore become an important target for research. The red shift of plasmon resonances changes character at about 8-10 nm of size for spherical gold nanoparticles─above this value, the red shift progresses linearly with particle size, while below this size, the red shift changes nonlinearly and more strongly with size. Using an atomistic discrete interaction model, we have studied the special properties of the nanoparticle surface layers and discovered its importance for ultrafine plasmonic nanoparticles and their red shifts. We find that the physical origin for the specific properties inherent to the surface layer of atoms near the nanoparticle boundary is related to the anisotropy of the local environment of atoms in this layer by other atoms. The anisotropy changes the conditions for light-induced nonlocal interactions of neighboring atoms with each other and with the incident radiation compared to the atoms located in the particle core with isotropic nearest surroundings by other atoms. The local anisotropy of the nanoparticle crystal lattice is a geometric factor that increases toward its boundary and that is the most fundamental factor underlying the physical differences between the nanoparticle surface layer and the core material. It is shown that the inflexion point at 8-10 nm is due to a change in the dominant physical origin of the red shift─from chaotization of atomically light-induced dipoles within the surface layer in the case of ultrafine nanoparticles to retardation effects for large nanoparticles in which the relative volume of the surface layer decreases rapidly to a negligible value with increasing nanoparticle size. The patterns revealed are the basis for predicting the manifestation of surface layer effects in ultrafine plasmonic nanoparticles of different shapes and composed of different plasmonic materials.